From b584e2f51f84949813b8c52c6e8367482bb2e2c5 Mon Sep 17 00:00:00 2001 From: morsch Date: Fri, 30 Jul 2010 10:39:47 +0000 Subject: [PATCH] - Update to pythia8140 - Make independent of TPythia8 for grid tests. --- PYTHIA8/AliDecayerPythia8.cxx | 669 +- PYTHIA8/AliDecayerPythia8.h | 24 +- PYTHIA8/AliPythia8.cxx | 10 +- PYTHIA8/AliPythia8.h | 4 +- PYTHIA8/AliPythia8LinkDef.h | 1 + PYTHIA8/AliTPythia8.cxx | 300 + PYTHIA8/AliTPythia8.h | 101 + PYTHIA8/libAliPythia8.pkg | 4 +- PYTHIA8/libpythia8.pkg | 93 +- PYTHIA8/pythia8.C | 1 - PYTHIA8/pythia8140/include/Analysis.h | 353 + PYTHIA8/pythia8140/include/Basics.h | 404 + PYTHIA8/pythia8140/include/BeamParticle.h | 305 + PYTHIA8/pythia8140/include/BeamRemnants.h | 96 + PYTHIA8/pythia8140/include/BeamShape.h | 64 + PYTHIA8/pythia8140/include/BoseEinstein.h | 92 + PYTHIA8/pythia8140/include/Event.h | 566 ++ .../pythia8140/include/FragmentationFlavZpT.h | 179 + .../pythia8140/include/FragmentationSystems.h | 190 + PYTHIA8/pythia8140/include/HadronLevel.h | 116 + PYTHIA8/pythia8140/include/HepMCInterface.h | 105 + PYTHIA8/pythia8140/include/Info.h | 284 + PYTHIA8/pythia8140/include/LHAFortran.h | 119 + PYTHIA8/pythia8140/include/LHAPDFInterface.h | 83 + PYTHIA8/pythia8140/include/LesHouches.h | 347 + .../include/MiniStringFragmentation.h | 86 + .../pythia8140/include/MultipleInteractions.h | 259 + PYTHIA8/pythia8140/include/ParticleData.h | 594 ++ PYTHIA8/pythia8140/include/ParticleDecays.h | 146 + .../pythia8140/include/PartonDistributions.h | 455 + PYTHIA8/pythia8140/include/PartonLevel.h | 163 + PYTHIA8/pythia8140/include/PartonSystems.h | 95 + PYTHIA8/pythia8140/include/PhaseSpace.h | 514 ++ PYTHIA8/pythia8140/include/ProcessContainer.h | 180 + PYTHIA8/pythia8140/include/ProcessLevel.h | 152 + PYTHIA8/pythia8140/include/Pythia.h | 303 + PYTHIA8/pythia8140/include/PythiaComplex.h | 21 + PYTHIA8/pythia8140/include/PythiaStdlib.h | 88 + PYTHIA8/pythia8140/include/ResonanceDecays.h | 80 + PYTHIA8/pythia8140/include/ResonanceWidths.h | 670 ++ PYTHIA8/pythia8140/include/Settings.h | 234 + .../pythia8140/include/SigmaCompositeness.h | 270 + PYTHIA8/pythia8140/include/SigmaEW.h | 1057 +++ PYTHIA8/pythia8140/include/SigmaExtraDim.h | 729 ++ PYTHIA8/pythia8140/include/SigmaGeneric.h | 148 + PYTHIA8/pythia8140/include/SigmaHiggs.h | 812 ++ .../pythia8140/include/SigmaLeftRightSym.h | 275 + PYTHIA8/pythia8140/include/SigmaLeptoquark.h | 176 + .../pythia8140/include/SigmaNewGaugeBosons.h | 185 + PYTHIA8/pythia8140/include/SigmaOnia.h | 294 + PYTHIA8/pythia8140/include/SigmaProcess.h | 585 ++ PYTHIA8/pythia8140/include/SigmaQCD.h | 848 ++ PYTHIA8/pythia8140/include/SigmaSUSY.h | 598 ++ PYTHIA8/pythia8140/include/SigmaTotal.h | 99 + PYTHIA8/pythia8140/include/SpaceShower.h | 223 + PYTHIA8/pythia8140/include/StandardModel.h | 176 + .../pythia8140/include/StringFragmentation.h | 174 + PYTHIA8/pythia8140/include/SusyCouplings.h | 139 + PYTHIA8/pythia8140/include/SusyLesHouches.h | 603 ++ PYTHIA8/pythia8140/include/TimeShower.h | 252 + PYTHIA8/pythia8140/include/UserHooks.h | 216 + PYTHIA8/pythia8140/src/Analysis.cxx | 892 ++ PYTHIA8/pythia8140/src/Basics.cxx | 1214 +++ PYTHIA8/pythia8140/src/BeamParticle.cxx | 916 ++ PYTHIA8/pythia8140/src/BeamRemnants.cxx | 1135 +++ PYTHIA8/pythia8140/src/BeamShape.cxx | 151 + PYTHIA8/pythia8140/src/BoseEinstein.cxx | 281 + PYTHIA8/pythia8140/src/Event.cxx | 706 ++ .../pythia8140/src/FragmentationFlavZpT.cxx | 759 ++ .../pythia8140/src/FragmentationSystems.cxx | 491 + PYTHIA8/pythia8140/src/HadronLevel.cxx | 919 ++ PYTHIA8/pythia8140/src/Info.cxx | 187 + PYTHIA8/pythia8140/src/LesHouches.cxx | 529 ++ .../src/MiniStringFragmentation.cxx | 320 + .../pythia8140/src/MultipleInteractions.cxx | 2095 +++++ PYTHIA8/pythia8140/src/ParticleData.cxx | 2055 +++++ PYTHIA8/pythia8140/src/ParticleDecays.cxx | 1248 +++ .../pythia8140/src/PartonDistributions.cxx | 2153 +++++ PYTHIA8/pythia8140/src/PartonLevel.cxx | 1055 +++ PYTHIA8/pythia8140/src/PartonSystems.cxx | 118 + PYTHIA8/pythia8140/src/PhaseSpace.cxx | 3295 +++++++ PYTHIA8/pythia8140/src/ProcessContainer.cxx | 2298 +++++ PYTHIA8/pythia8140/src/ProcessLevel.cxx | 1373 +++ PYTHIA8/pythia8140/src/Pythia.cxx | 1912 ++++ PYTHIA8/pythia8140/src/PythiaStdlib.cxx | 41 + PYTHIA8/pythia8140/src/ResonanceDecays.cxx | 805 ++ PYTHIA8/pythia8140/src/ResonanceWidths.cxx | 2129 +++++ PYTHIA8/pythia8140/src/Settings.cxx | 677 ++ PYTHIA8/pythia8140/src/SigmaCompositeness.cxx | 616 ++ PYTHIA8/pythia8140/src/SigmaEW.cxx | 2851 ++++++ PYTHIA8/pythia8140/src/SigmaExtraDim.cxx | 2490 +++++ PYTHIA8/pythia8140/src/SigmaGeneric.cxx | 333 + PYTHIA8/pythia8140/src/SigmaHiggs.cxx | 2531 ++++++ PYTHIA8/pythia8140/src/SigmaLeftRightSym.cxx | 808 ++ PYTHIA8/pythia8140/src/SigmaLeptoquark.cxx | 310 + .../pythia8140/src/SigmaNewGaugeBosons.cxx | 757 ++ PYTHIA8/pythia8140/src/SigmaOnia.cxx | 626 ++ PYTHIA8/pythia8140/src/SigmaProcess.cxx | 1111 +++ PYTHIA8/pythia8140/src/SigmaQCD.cxx | 1533 ++++ PYTHIA8/pythia8140/src/SigmaSUSY.cxx | 1939 ++++ PYTHIA8/pythia8140/src/SigmaTotal.cxx | 332 + PYTHIA8/pythia8140/src/SpaceShower.cxx | 1787 ++++ PYTHIA8/pythia8140/src/StandardModel.cxx | 490 + .../pythia8140/src/StringFragmentation.cxx | 1220 +++ PYTHIA8/pythia8140/src/SusyCouplings.cxx | 765 ++ PYTHIA8/pythia8140/src/SusyLesHouches.cxx | 1253 +++ PYTHIA8/pythia8140/src/TimeShower.cxx | 3390 +++++++ PYTHIA8/pythia8140/src/UserHooks.cxx | 203 + .../pythia8140/xmldoc/ASecondHardProcess.xml | 398 + .../xmldoc/AccessPYTHIA6Processes.xml | 110 + PYTHIA8/pythia8140/xmldoc/AdvancedUsage.xml | 209 + PYTHIA8/pythia8140/xmldoc/BeamParameters.xml | 270 + PYTHIA8/pythia8140/xmldoc/BeamRemnants.xml | 303 + PYTHIA8/pythia8140/xmldoc/BeamShape.xml | 79 + PYTHIA8/pythia8140/xmldoc/Bibliography.xml | 275 + .../pythia8140/xmldoc/BoseEinsteinEffects.xml | 116 + .../xmldoc/CompositenessProcesses.xml | 207 + .../pythia8140/xmldoc/CouplingsAndScales.xml | 287 + PYTHIA8/pythia8140/xmldoc/Diffraction.xml | 234 + .../xmldoc/ElectroweakProcesses.xml | 267 + PYTHIA8/pythia8140/xmldoc/ErrorChecks.xml | 71 + PYTHIA8/pythia8140/xmldoc/EventAnalysis.xml | 512 ++ .../pythia8140/xmldoc/EventInformation.xml | 465 + PYTHIA8/pythia8140/xmldoc/EventRecord.xml | 500 ++ PYTHIA8/pythia8140/xmldoc/EventStatistics.xml | 118 + PYTHIA8/pythia8140/xmldoc/ExternalDecays.xml | 72 + .../xmldoc/ExtraDimensionalProcesses.xml | 445 + .../pythia8140/xmldoc/FlavourSelection.xml | 356 + PYTHIA8/pythia8140/xmldoc/FourVectors.xml | 418 + .../xmldoc/FourthGenerationProcesses.xml | 175 + PYTHIA8/pythia8140/xmldoc/Fragmentation.xml | 310 + PYTHIA8/pythia8140/xmldoc/Frontpage.xml | 142 + PYTHIA8/pythia8140/xmldoc/Glossary.xml | 92 + .../xmldoc/HadronLevelStandalone.xml | 165 + PYTHIA8/pythia8140/xmldoc/HepMCInterface.xml | 176 + .../xmldoc/HiddenValleyProcesses.xml | 318 + PYTHIA8/pythia8140/xmldoc/HiggsProcesses.xml | 910 ++ PYTHIA8/pythia8140/xmldoc/Histograms.xml | 304 + .../pythia8140/xmldoc/ImplementNewShowers.xml | 471 + PYTHIA8/pythia8140/xmldoc/Index.xml | 121 + PYTHIA8/pythia8140/xmldoc/JetFinders.xml | 27 + .../xmldoc/LeftRightSymmetryProcesses.xml | 183 + .../pythia8140/xmldoc/LeptoquarkProcesses.xml | 84 + .../pythia8140/xmldoc/LesHouchesAccord.xml | 593 ++ .../pythia8140/xmldoc/MainProgramSettings.xml | 200 + PYTHIA8/pythia8140/xmldoc/MasterSwitches.xml | 172 + .../xmldoc/MultipleInteractions.xml | 507 ++ .../xmldoc/NewGaugeBosonProcesses.xml | 344 + PYTHIA8/pythia8140/xmldoc/OniaProcesses.xml | 301 + PYTHIA8/pythia8140/xmldoc/PDFSelection.xml | 405 + .../xmldoc/PYTHIA6TranslationTable.xml | 100 + PYTHIA8/pythia8140/xmldoc/ParticleData.xml | 7998 +++++++++++++++++ .../pythia8140/xmldoc/ParticleDataScheme.xml | 1498 +++ PYTHIA8/pythia8140/xmldoc/ParticleDecays.xml | 255 + .../pythia8140/xmldoc/ParticleProperties.xml | 688 ++ .../pythia8140/xmldoc/PartonDistributions.xml | 132 + PYTHIA8/pythia8140/xmldoc/PhaseSpaceCuts.xml | 257 + .../pythia8140/xmldoc/ProcessSelection.xml | 140 + PYTHIA8/pythia8140/xmldoc/ProgramClasses.xml | 220 + PYTHIA8/pythia8140/xmldoc/ProgramFiles.xml | 348 + PYTHIA8/pythia8140/xmldoc/ProgramFlow.xml | 1073 +++ PYTHIA8/pythia8140/xmldoc/ProgramMethods.xml | 17 + PYTHIA8/pythia8140/xmldoc/QCDProcesses.xml | 261 + PYTHIA8/pythia8140/xmldoc/ROOTusage.xml | 162 + .../pythia8140/xmldoc/RandomNumberSeed.xml | 32 + PYTHIA8/pythia8140/xmldoc/RandomNumbers.xml | 140 + PYTHIA8/pythia8140/xmldoc/ResonanceDecays.xml | 317 + .../xmldoc/SUSYLesHouchesAccord.xml | 106 + PYTHIA8/pythia8140/xmldoc/SUSYProcesses.xml | 241 + .../pythia8140/xmldoc/SampleMainPrograms.xml | 181 + PYTHIA8/pythia8140/xmldoc/SaveSettings.xml | 150 + .../xmldoc/SemiInternalProcesses.xml | 477 + .../xmldoc/SemiInternalResonances.xml | 209 + PYTHIA8/pythia8140/xmldoc/SettingsScheme.xml | 420 + .../pythia8140/xmldoc/SpacelikeShowers.xml | 340 + .../xmldoc/StandardModelParameters.xml | 285 + 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PYTHIA8/pythia8140/xmldoc/pomH1FitA.data | 1219 +++ PYTHIA8/pythia8140/xmldoc/pomH1FitB.data | 1219 +++ PYTHIA8/pythia8140/xmldoc/pomH1FitBlo.data | 1219 +++ PYTHIA8/pythia8140/xmldoc/pomH1JetsCharm.data | 1528 ++++ PYTHIA8/pythia8140/xmldoc/pomH1JetsGluon.data | 1528 ++++ .../pythia8140/xmldoc/pomH1JetsSinglet.data | 1528 ++++ 200 files changed, 152261 insertions(+), 373 deletions(-) create mode 100644 PYTHIA8/AliTPythia8.cxx create mode 100644 PYTHIA8/AliTPythia8.h create mode 100644 PYTHIA8/pythia8140/include/Analysis.h create mode 100644 PYTHIA8/pythia8140/include/Basics.h create mode 100644 PYTHIA8/pythia8140/include/BeamParticle.h create mode 100644 PYTHIA8/pythia8140/include/BeamRemnants.h create mode 100644 PYTHIA8/pythia8140/include/BeamShape.h create mode 100644 PYTHIA8/pythia8140/include/BoseEinstein.h create mode 100644 PYTHIA8/pythia8140/include/Event.h create mode 100644 PYTHIA8/pythia8140/include/FragmentationFlavZpT.h create mode 100644 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PYTHIA8/pythia8140/xmldoc/mstw2008lo.00.dat create mode 100644 PYTHIA8/pythia8140/xmldoc/mstw2008nlo.00.dat create mode 100644 PYTHIA8/pythia8140/xmldoc/pomH1FitA.data create mode 100644 PYTHIA8/pythia8140/xmldoc/pomH1FitB.data create mode 100644 PYTHIA8/pythia8140/xmldoc/pomH1FitBlo.data create mode 100644 PYTHIA8/pythia8140/xmldoc/pomH1JetsCharm.data create mode 100644 PYTHIA8/pythia8140/xmldoc/pomH1JetsGluon.data create mode 100644 PYTHIA8/pythia8140/xmldoc/pomH1JetsSinglet.data diff --git a/PYTHIA8/AliDecayerPythia8.cxx b/PYTHIA8/AliDecayerPythia8.cxx index 2f9a4376dee..86599d8c8a6 100644 --- a/PYTHIA8/AliDecayerPythia8.cxx +++ b/PYTHIA8/AliDecayerPythia8.cxx @@ -19,7 +19,8 @@ // Author: andreas.morsch@cern.ch #include #include -#include +#include +#include "AliTPythia8.h" #include "AliDecayerPythia8.h" #include "ParticleData.h" @@ -28,13 +29,37 @@ ClassImp(AliDecayerPythia8) Bool_t AliDecayerPythia8::fgInit = kFALSE; AliDecayerPythia8::AliDecayerPythia8(): - TPythia8Decayer(), - fDecay(kAll), - fHeavyFlavour(kTRUE) + TVirtualMCDecayer(), + fPythia8(new AliTPythia8()), + fDebug(0), + fDecay(kAll), + fHeavyFlavour(kTRUE) { // Constructor + fPythia8->Pythia8()->readString("SoftQCD:elastic = on"); + fPythia8->Pythia8()->init(); } +//___________________________________________________________________________ +void AliDecayerPythia8::Decay(Int_t pdg, TLorentzVector* p) +{ + // Decay a single particle + ClearEvent(); + AppendParticle(pdg, p); + Int_t idPart = fPythia8->Pythia8()->event[0].id(); + fPythia8->Pythia8()->particleData.mayDecay(idPart,kTRUE); + fPythia8->Pythia8()->moreDecays(); + if (fDebug > 0) fPythia8->EventListing(); +} + +//___________________________________________________________________________ +Int_t AliDecayerPythia8::ImportParticles(TClonesArray *particles) +{ + //import the decay products into particles array + return (fPythia8->ImportParticles(particles, "All")); +} + + void AliDecayerPythia8::Init() { // Initialisation @@ -51,9 +76,9 @@ void AliDecayerPythia8::Init() // fPythia->ResetDecayTable(); for (j=0; j < 14; j++) { if (fDecay == kNoDecayHeavy) { - TPythia8::Instance()->ReadString(Form("%d:onMode = off", heavy[j])); + AliTPythia8::Instance()->ReadString(Form("%d:onMode = off", heavy[j])); } else { - TPythia8::Instance()->ReadString(Form("%d:onMode = on", heavy[j])); + AliTPythia8::Instance()->ReadString(Form("%d:onMode = on", heavy[j])); } } @@ -61,18 +86,18 @@ void AliDecayerPythia8::Init() //...Switch off decay of pi0, K0S, Lambda, Sigma+-, Xi0-, Omega-. if (fDecay != kNeutralPion) { - TPythia8::Instance()->ReadString("111:onMode = off"); + AliTPythia8::Instance()->ReadString("111:onMode = off"); } else { - TPythia8::Instance()->ReadString("111:onMode = on"); + AliTPythia8::Instance()->ReadString("111:onMode = on"); } - TPythia8::Instance()->ReadString("310:onMode = off"); - TPythia8::Instance()->ReadString("3112:onMode = off"); - TPythia8::Instance()->ReadString("3212:onMode = off"); - TPythia8::Instance()->ReadString("3222:onMode = off"); - TPythia8::Instance()->ReadString("3312:onMode = off"); - TPythia8::Instance()->ReadString("3322:onMode = off"); - TPythia8::Instance()->ReadString("3334:onMode = off"); + AliTPythia8::Instance()->ReadString("310:onMode = off"); + AliTPythia8::Instance()->ReadString("3112:onMode = off"); + AliTPythia8::Instance()->ReadString("3212:onMode = off"); + AliTPythia8::Instance()->ReadString("3222:onMode = off"); + AliTPythia8::Instance()->ReadString("3312:onMode = off"); + AliTPythia8::Instance()->ReadString("3322:onMode = off"); + AliTPythia8::Instance()->ReadString("3334:onMode = off"); // .. Force decay channels ForceDecay(); } @@ -85,7 +110,7 @@ void AliDecayerPythia8::ForceDecay() if (!fHeavyFlavour) SwitchOffHeavyFlavour(); // Decay_t decay = fDecay; - TPythia8::Instance()->ReadString("HadronLevel:Decay = on"); + AliTPythia8::Instance()->ReadString("HadronLevel:Decay = on"); if (decay == kNoDecayHeavy) return; @@ -95,423 +120,423 @@ void AliDecayerPythia8::ForceDecay() { case kHardMuons: // B0 -> mu X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 13 443 100443"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 13 443 100443"); // B+/- -> mu X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 13 443 100443"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 13 443 100443"); // Bs -> mu X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 13 443 100443"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 13 443 100443"); // Lambda_b -> mu X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 13 443 100443"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 13 443 100443"); // Sigma_b- -> mu X - TPythia8::Instance()->ReadString("5132:onMode = off"); - TPythia8::Instance()->ReadString("5132:onIfAny = 13 443 100443"); + AliTPythia8::Instance()->ReadString("5132:onMode = off"); + AliTPythia8::Instance()->ReadString("5132:onIfAny = 13 443 100443"); // Sigma_b0 -> mu X - TPythia8::Instance()->ReadString("5232:onMode = off"); - TPythia8::Instance()->ReadString("5232:onIfAny = 13 443 100443"); + AliTPythia8::Instance()->ReadString("5232:onMode = off"); + AliTPythia8::Instance()->ReadString("5232:onIfAny = 13 443 100443"); // Omega_b -> mu X - TPythia8::Instance()->ReadString("5332:onMode = off"); - TPythia8::Instance()->ReadString("5332:onIfAny = 13 443 100443"); + AliTPythia8::Instance()->ReadString("5332:onMode = off"); + AliTPythia8::Instance()->ReadString("5332:onIfAny = 13 443 100443"); // Psi' -> mu+ mu- - TPythia8::Instance()->ReadString("100443:onMode = off"); - TPythia8::Instance()->ReadString("100443:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("100443:onMode = off"); + AliTPythia8::Instance()->ReadString("100443:onIfAny = 443"); // Psi -> mu+ mu- - TPythia8::Instance()->ReadString("443:onMode = off"); - TPythia8::Instance()->ReadString("443:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("443:onMode = off"); + AliTPythia8::Instance()->ReadString("443:onIfAll = 13 13"); // D+/- -> mu X - TPythia8::Instance()->ReadString("411:onMode = off"); - TPythia8::Instance()->ReadString("411:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("411:onMode = off"); + AliTPythia8::Instance()->ReadString("411:onIfAll = 13"); // D0 -> mu X - TPythia8::Instance()->ReadString("421:onMode = off"); - TPythia8::Instance()->ReadString("421:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("421:onMode = off"); + AliTPythia8::Instance()->ReadString("421:onIfAll = 13"); // D_s -> mu X - TPythia8::Instance()->ReadString("431:onMode = off"); - TPythia8::Instance()->ReadString("431:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("431:onMode = off"); + AliTPythia8::Instance()->ReadString("431:onIfAll = 13"); // Lambda_c -> mu X - TPythia8::Instance()->ReadString("4122:onMode = off"); - TPythia8::Instance()->ReadString("4122:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4122:onMode = off"); + AliTPythia8::Instance()->ReadString("4122:onIfAll = 13"); // Sigma_c -> mu X - TPythia8::Instance()->ReadString("4132:onMode = off"); - TPythia8::Instance()->ReadString("4132:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4132:onMode = off"); + AliTPythia8::Instance()->ReadString("4132:onIfAll = 13"); // Sigma_c+ -> mu X - TPythia8::Instance()->ReadString("4232:onMode = off"); - TPythia8::Instance()->ReadString("4232:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4232:onMode = off"); + AliTPythia8::Instance()->ReadString("4232:onIfAll = 13"); // Omega_c -> mu X - TPythia8::Instance()->ReadString("4332:onMode = off"); - TPythia8::Instance()->ReadString("4332:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4332:onMode = off"); + AliTPythia8::Instance()->ReadString("4332:onIfAll = 13"); break; case kChiToJpsiGammaToMuonMuon: // Chi_1c -> J/Psi Gamma - TPythia8::Instance()->ReadString("20443:onMode = off"); - TPythia8::Instance()->ReadString("20443:onIfAll = 443 22"); + AliTPythia8::Instance()->ReadString("20443:onMode = off"); + AliTPythia8::Instance()->ReadString("20443:onIfAll = 443 22"); // Chi_2c -> J/Psi Gamma - TPythia8::Instance()->ReadString("445:onMode = off"); - TPythia8::Instance()->ReadString("445:onIfAll = 443 22"); + AliTPythia8::Instance()->ReadString("445:onMode = off"); + AliTPythia8::Instance()->ReadString("445:onIfAll = 443 22"); // J/Psi -> mu+ mu- - TPythia8::Instance()->ReadString("443:onMode = off"); - TPythia8::Instance()->ReadString("443:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("443:onMode = off"); + AliTPythia8::Instance()->ReadString("443:onIfAll = 13 13"); break; case kChiToJpsiGammaToElectronElectron: // Chi_1c -> J/Psi Gamma - TPythia8::Instance()->ReadString("20443:onMode = off"); - TPythia8::Instance()->ReadString("20443:onIfAll = 443 22"); + AliTPythia8::Instance()->ReadString("20443:onMode = off"); + AliTPythia8::Instance()->ReadString("20443:onIfAll = 443 22"); // Chi_2c -> J/Psi Gamma - TPythia8::Instance()->ReadString("445:onMode = off"); - TPythia8::Instance()->ReadString("445:onIfAll = 443 22"); + AliTPythia8::Instance()->ReadString("445:onMode = off"); + AliTPythia8::Instance()->ReadString("445:onIfAll = 443 22"); // J/Psi -> e+ e- - TPythia8::Instance()->ReadString("443:onMode = off"); - TPythia8::Instance()->ReadString("443:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("443:onMode = off"); + AliTPythia8::Instance()->ReadString("443:onIfAll = 11 11"); break; case kBSemiMuonic: // B0 -> mu X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 13"); // B+/- -> mu X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 13"); // B_s -> mu X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 13"); // Lambda_b -> mu X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 13"); // Sigma_b -> mu X - TPythia8::Instance()->ReadString("5132:onMode = off"); - TPythia8::Instance()->ReadString("5132:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5132:onMode = off"); + AliTPythia8::Instance()->ReadString("5132:onIfAny = 13"); // Sigma_b0 -> mu X - TPythia8::Instance()->ReadString("5232:onMode = off"); - TPythia8::Instance()->ReadString("5232:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5232:onMode = off"); + AliTPythia8::Instance()->ReadString("5232:onIfAny = 13"); // Omega_b -> mu X - TPythia8::Instance()->ReadString("5332:onMode = off"); - TPythia8::Instance()->ReadString("5332:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5332:onMode = off"); + AliTPythia8::Instance()->ReadString("5332:onIfAny = 13"); break; case kSemiMuonic: // D+- -> mu X - TPythia8::Instance()->ReadString("411:onMode = off"); - TPythia8::Instance()->ReadString("411:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("411:onMode = off"); + AliTPythia8::Instance()->ReadString("411:onIfAll = 13"); // D0 -> mu X - TPythia8::Instance()->ReadString("421:onMode = off"); - TPythia8::Instance()->ReadString("421:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("421:onMode = off"); + AliTPythia8::Instance()->ReadString("421:onIfAll = 13"); // D_s -> mu X - TPythia8::Instance()->ReadString("431:onMode = off"); - TPythia8::Instance()->ReadString("431:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("431:onMode = off"); + AliTPythia8::Instance()->ReadString("431:onIfAll = 13"); // Lambda_c -> mu X - TPythia8::Instance()->ReadString("4122:onMode = off"); - TPythia8::Instance()->ReadString("4122:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4122:onMode = off"); + AliTPythia8::Instance()->ReadString("4122:onIfAll = 13"); // Sigma_c -> mu X - TPythia8::Instance()->ReadString("4132:onMode = off"); - TPythia8::Instance()->ReadString("4132:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4132:onMode = off"); + AliTPythia8::Instance()->ReadString("4132:onIfAll = 13"); // Sigma -> mu X - TPythia8::Instance()->ReadString("4232:onMode = off"); - TPythia8::Instance()->ReadString("4232:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4232:onMode = off"); + AliTPythia8::Instance()->ReadString("4232:onIfAll = 13"); // Omega_c -> mu X - TPythia8::Instance()->ReadString("4332:onMode = off"); - TPythia8::Instance()->ReadString("4332:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4332:onMode = off"); + AliTPythia8::Instance()->ReadString("4332:onIfAll = 13"); // B0 -> mu X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 13"); // B+/- -> mu X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 13"); // B_s -> mu X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 13"); // Lambda_c -> mu X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 13"); // Sigma_c -> mu X - TPythia8::Instance()->ReadString("5132:onMode = off"); - TPythia8::Instance()->ReadString("5132:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5132:onMode = off"); + AliTPythia8::Instance()->ReadString("5132:onIfAny = 13"); // Sigma_c -> mu X - TPythia8::Instance()->ReadString("5232:onMode = off"); - TPythia8::Instance()->ReadString("5232:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5232:onMode = off"); + AliTPythia8::Instance()->ReadString("5232:onIfAny = 13"); // Omega_c -> mu X - TPythia8::Instance()->ReadString("5332:onMode = off"); - TPythia8::Instance()->ReadString("5332:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("5332:onMode = off"); + AliTPythia8::Instance()->ReadString("5332:onIfAny = 13"); break; case kDiMuon: // Rho -> mu+ mu- - TPythia8::Instance()->ReadString("113:onMode = off"); - TPythia8::Instance()->ReadString("113:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("113:onMode = off"); + AliTPythia8::Instance()->ReadString("113:onIfAll = 13 13"); // Eta-> mu+ mu- - TPythia8::Instance()->ReadString("221:onMode = off"); - TPythia8::Instance()->ReadString("221:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("221:onMode = off"); + AliTPythia8::Instance()->ReadString("221:onIfAll = 13 13"); // omega-> mu+ mu- - TPythia8::Instance()->ReadString("223:onMode = off"); - TPythia8::Instance()->ReadString("223:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("223:onMode = off"); + AliTPythia8::Instance()->ReadString("223:onIfAll = 13 13"); // phi-> mu+ mu- - TPythia8::Instance()->ReadString("333:onMode = off"); - TPythia8::Instance()->ReadString("333:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("333:onMode = off"); + AliTPythia8::Instance()->ReadString("333:onIfAll = 13 13"); // J/Psi-> mu+ mu- - TPythia8::Instance()->ReadString("443:onMode = off"); - TPythia8::Instance()->ReadString("443:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("443:onMode = off"); + AliTPythia8::Instance()->ReadString("443:onIfAll = 13 13"); // Psi'-> mu+ mu- - TPythia8::Instance()->ReadString("100443:onMode = off"); - TPythia8::Instance()->ReadString("100443:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("100443:onMode = off"); + AliTPythia8::Instance()->ReadString("100443:onIfAll = 13 13"); // Ups-> mu+ mu- - TPythia8::Instance()->ReadString("553:onMode = off"); - TPythia8::Instance()->ReadString("553:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("553:onMode = off"); + AliTPythia8::Instance()->ReadString("553:onIfAll = 13 13"); // Ups'-> mu+ mu- - TPythia8::Instance()->ReadString("100553:onMode = off"); - TPythia8::Instance()->ReadString("100553:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("100553:onMode = off"); + AliTPythia8::Instance()->ReadString("100553:onIfAll = 13 13"); // Ups''-> mu+ mu- - TPythia8::Instance()->ReadString("200553:onMode = off"); - TPythia8::Instance()->ReadString("200553:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("200553:onMode = off"); + AliTPythia8::Instance()->ReadString("200553:onIfAll = 13 13"); break; case kBSemiElectronic: // B0 - > e+ e- - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 11"); // B+- -> e+ e- - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 11"); // B_s -> e+ e- - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 11"); // Lambda_b -> e+ e- - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 11"); // Sigma_b -> e+ e- - TPythia8::Instance()->ReadString("5132:onMode = off"); - TPythia8::Instance()->ReadString("5132:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5132:onMode = off"); + AliTPythia8::Instance()->ReadString("5132:onIfAny = 11"); // Sigma_b -> e+ e- - TPythia8::Instance()->ReadString("5232:onMode = off"); - TPythia8::Instance()->ReadString("5232:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5232:onMode = off"); + AliTPythia8::Instance()->ReadString("5232:onIfAny = 11"); // Omega_b ->e+ e- - TPythia8::Instance()->ReadString("5332:onMode = off"); - TPythia8::Instance()->ReadString("5332:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5332:onMode = off"); + AliTPythia8::Instance()->ReadString("5332:onIfAny = 11"); break; case kSemiElectronic: // D+/- -> e X - TPythia8::Instance()->ReadString("411:onMode = off"); - TPythia8::Instance()->ReadString("411:onIfAll = 11"); + AliTPythia8::Instance()->ReadString("411:onMode = off"); + AliTPythia8::Instance()->ReadString("411:onIfAll = 11"); // D0 -> e X - TPythia8::Instance()->ReadString("421:onMode = off"); - TPythia8::Instance()->ReadString("421:onIfAll = 11"); + AliTPythia8::Instance()->ReadString("421:onMode = off"); + AliTPythia8::Instance()->ReadString("421:onIfAll = 11"); // D_s ->e X - TPythia8::Instance()->ReadString("431:onMode = off"); - TPythia8::Instance()->ReadString("431:onIfAll = 11"); + AliTPythia8::Instance()->ReadString("431:onMode = off"); + AliTPythia8::Instance()->ReadString("431:onIfAll = 11"); // Lambda_c -> e X - TPythia8::Instance()->ReadString("4122:onMode = off"); - TPythia8::Instance()->ReadString("4122:onIfAll = 11"); + AliTPythia8::Instance()->ReadString("4122:onMode = off"); + AliTPythia8::Instance()->ReadString("4122:onIfAll = 11"); // Sigma_c -> e X - TPythia8::Instance()->ReadString("4132:onMode = off"); - TPythia8::Instance()->ReadString("4132:onIfAll = 11"); + AliTPythia8::Instance()->ReadString("4132:onMode = off"); + AliTPythia8::Instance()->ReadString("4132:onIfAll = 11"); // Sigma_c -> e X - TPythia8::Instance()->ReadString("4232:onMode = off"); - TPythia8::Instance()->ReadString("4232:onIfAll = 11"); + AliTPythia8::Instance()->ReadString("4232:onMode = off"); + AliTPythia8::Instance()->ReadString("4232:onIfAll = 11"); // Omega_c -> e X - TPythia8::Instance()->ReadString("4332:onMode = off"); - TPythia8::Instance()->ReadString("4332:onIfAll = 11"); + AliTPythia8::Instance()->ReadString("4332:onMode = off"); + AliTPythia8::Instance()->ReadString("4332:onIfAll = 11"); // B0 -> e X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 11"); // B+/- -> e X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 11"); // B_s -> e X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 11"); // Lambda_b -> e X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 11"); // Sigma_b -> e X - TPythia8::Instance()->ReadString("5132:onMode = off"); - TPythia8::Instance()->ReadString("5132:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5132:onMode = off"); + AliTPythia8::Instance()->ReadString("5132:onIfAny = 11"); // Sigma_b -> e X - TPythia8::Instance()->ReadString("5232:onMode = off"); - TPythia8::Instance()->ReadString("5232:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5232:onMode = off"); + AliTPythia8::Instance()->ReadString("5232:onIfAny = 11"); // Omega_b -> e X - TPythia8::Instance()->ReadString("5332:onMode = off"); - TPythia8::Instance()->ReadString("5332:onIfAny = 11"); + AliTPythia8::Instance()->ReadString("5332:onMode = off"); + AliTPythia8::Instance()->ReadString("5332:onIfAny = 11"); break; case kDiElectron: // Rho -> e+e- - TPythia8::Instance()->ReadString("113:onMode = off"); - TPythia8::Instance()->ReadString("113:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("113:onMode = off"); + AliTPythia8::Instance()->ReadString("113:onIfAll = 11 11"); // Eta -> e+e- - TPythia8::Instance()->ReadString("221:onMode = off"); - TPythia8::Instance()->ReadString("221:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("221:onMode = off"); + AliTPythia8::Instance()->ReadString("221:onIfAll = 11 11"); // omega -> e+e- - TPythia8::Instance()->ReadString("223:onMode = off"); - TPythia8::Instance()->ReadString("223:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("223:onMode = off"); + AliTPythia8::Instance()->ReadString("223:onIfAll = 11 11"); // phi -> e+e- - TPythia8::Instance()->ReadString("333:onMode = off"); - TPythia8::Instance()->ReadString("333:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("333:onMode = off"); + AliTPythia8::Instance()->ReadString("333:onIfAll = 11 11"); // J/Psi -> e+e- - TPythia8::Instance()->ReadString("443:onMode = off"); - TPythia8::Instance()->ReadString("443:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("443:onMode = off"); + AliTPythia8::Instance()->ReadString("443:onIfAll = 11 11"); // Psi' -> e+e- - TPythia8::Instance()->ReadString("100443:onMode = off"); - TPythia8::Instance()->ReadString("100443:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("100443:onMode = off"); + AliTPythia8::Instance()->ReadString("100443:onIfAll = 11 11"); // Ups -> e+e- - TPythia8::Instance()->ReadString("553:onMode = off"); - TPythia8::Instance()->ReadString("553:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("553:onMode = off"); + AliTPythia8::Instance()->ReadString("553:onIfAll = 11 11"); // Ups' -> e+e- - TPythia8::Instance()->ReadString("100553:onMode = off"); - TPythia8::Instance()->ReadString("100553:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("100553:onMode = off"); + AliTPythia8::Instance()->ReadString("100553:onIfAll = 11 11"); // Ups'' -> e+e- - TPythia8::Instance()->ReadString("200553:onMode = off"); - TPythia8::Instance()->ReadString("200553:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("200553:onMode = off"); + AliTPythia8::Instance()->ReadString("200553:onIfAll = 11 11"); break; case kBJpsiDiMuon: // B0 -> J/Psi (Psi') X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 443 100443"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 443 100443"); // B+/- -> J/Psi (Psi') X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 443 100443"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 443 100443"); // B_s -> J/Psi (Psi') X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 443 100443"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 443 100443"); // Lambda_b -> J/Psi (Psi') X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 443 100443"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 443 100443"); // // J/Psi -> mu+ mu- - TPythia8::Instance()->ReadString("443:onMode = off"); - TPythia8::Instance()->ReadString("443:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("443:onMode = off"); + AliTPythia8::Instance()->ReadString("443:onIfAll = 13 13"); // Psi' -> mu+ mu- - TPythia8::Instance()->ReadString("100443:onMode = off"); - TPythia8::Instance()->ReadString("100443:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("100443:onMode = off"); + AliTPythia8::Instance()->ReadString("100443:onIfAll = 13 13"); break; case kBPsiPrimeDiMuon: // B0 -> Psi' X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 100443"); // B+/- -> Psi' X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 100443"); // B_s -> Psi' X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 100443"); // Lambda_b -> Psi' X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 100443"); // // Psi' -> mu+ mu- - TPythia8::Instance()->ReadString("100443:onMode = off"); - TPythia8::Instance()->ReadString("100443:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("100443:onMode = off"); + AliTPythia8::Instance()->ReadString("100443:onIfAll = 13 13"); break; case kBJpsiDiElectron: // B0 -> Psi X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 443"); // B+/- -> Psi X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 443"); // B_s -> Psi X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 443"); // Lambda_b -> Psi X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 443"); // // Psi -> mu+ mu- - TPythia8::Instance()->ReadString("443:onMode = off"); - TPythia8::Instance()->ReadString("443:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("443:onMode = off"); + AliTPythia8::Instance()->ReadString("443:onIfAll = 11 11"); break; case kBJpsi: // B0 -> Psi X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 443"); // B+/- -> Psi X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 443"); // B_s -> Psi X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 443"); // Lambda_b -> Psi X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 443"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 443"); break; case kBPsiPrimeDiElectron: // B0 -> Psi' X - TPythia8::Instance()->ReadString("511:onMode = off"); - TPythia8::Instance()->ReadString("511:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("511:onMode = off"); + AliTPythia8::Instance()->ReadString("511:onIfAny = 100443"); // B+/- -> Psi' X - TPythia8::Instance()->ReadString("521:onMode = off"); - TPythia8::Instance()->ReadString("521:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("521:onMode = off"); + AliTPythia8::Instance()->ReadString("521:onIfAny = 100443"); // B_s -> Psi' X - TPythia8::Instance()->ReadString("531:onMode = off"); - TPythia8::Instance()->ReadString("531:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("531:onMode = off"); + AliTPythia8::Instance()->ReadString("531:onIfAny = 100443"); // Lambda_b -> Psi' X - TPythia8::Instance()->ReadString("5122:onMode = off"); - TPythia8::Instance()->ReadString("5122:onIfAny = 100443"); + AliTPythia8::Instance()->ReadString("5122:onMode = off"); + AliTPythia8::Instance()->ReadString("5122:onIfAny = 100443"); // // Psi' -> mu+ mu- - TPythia8::Instance()->ReadString("100443:onMode = off"); - TPythia8::Instance()->ReadString("100443:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("100443:onMode = off"); + AliTPythia8::Instance()->ReadString("100443:onIfAll = 11 11"); break; case kPiToMu: // pi -> mu nu - TPythia8::Instance()->ReadString("211:onMode = off"); - TPythia8::Instance()->ReadString("211:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("211:onMode = off"); + AliTPythia8::Instance()->ReadString("211:onIfAny = 13"); break; case kKaToMu: // K -> mu nu - TPythia8::Instance()->ReadString("321:onMode = off"); - TPythia8::Instance()->ReadString("321:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("321:onMode = off"); + AliTPythia8::Instance()->ReadString("321:onIfAny = 13"); break; case kAllMuonic: // pi/K -> mu - TPythia8::Instance()->ReadString("211:onMode = off"); - TPythia8::Instance()->ReadString("211:onIfAny = 13"); - TPythia8::Instance()->ReadString("321:onMode = off"); - TPythia8::Instance()->ReadString("321:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("211:onMode = off"); + AliTPythia8::Instance()->ReadString("211:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("321:onMode = off"); + AliTPythia8::Instance()->ReadString("321:onIfAny = 13"); break; case kWToMuon: // W -> mu X - TPythia8::Instance()->ReadString("24:onMode = off"); - TPythia8::Instance()->ReadString("24:onIfAny = 13"); + AliTPythia8::Instance()->ReadString("24:onMode = off"); + AliTPythia8::Instance()->ReadString("24:onIfAny = 13"); break; case kWToCharm: // W -> c X - TPythia8::Instance()->ReadString("24:onMode = off"); - TPythia8::Instance()->ReadString("24:onIfAny = 4"); + AliTPythia8::Instance()->ReadString("24:onMode = off"); + AliTPythia8::Instance()->ReadString("24:onIfAny = 4"); break; case kWToCharmToMuon: // W -> c X - TPythia8::Instance()->ReadString("24:onMode = off"); - TPythia8::Instance()->ReadString("24:onIfAny = 4"); + AliTPythia8::Instance()->ReadString("24:onMode = off"); + AliTPythia8::Instance()->ReadString("24:onIfAny = 4"); // D+- -> mu X - TPythia8::Instance()->ReadString("411:onMode = off"); - TPythia8::Instance()->ReadString("411:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("411:onMode = off"); + AliTPythia8::Instance()->ReadString("411:onIfAll = 13"); // D0 -> mu X - TPythia8::Instance()->ReadString("421:onMode = off"); - TPythia8::Instance()->ReadString("421:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("421:onMode = off"); + AliTPythia8::Instance()->ReadString("421:onIfAll = 13"); // D_s -> mu X - TPythia8::Instance()->ReadString("431:onMode = off"); - TPythia8::Instance()->ReadString("431:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("431:onMode = off"); + AliTPythia8::Instance()->ReadString("431:onIfAll = 13"); // Lambda_c -> mu X - TPythia8::Instance()->ReadString("4122:onMode = off"); - TPythia8::Instance()->ReadString("4122:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4122:onMode = off"); + AliTPythia8::Instance()->ReadString("4122:onIfAll = 13"); // Sigma_c -> mu X - TPythia8::Instance()->ReadString("4132:onMode = off"); - TPythia8::Instance()->ReadString("4132:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4132:onMode = off"); + AliTPythia8::Instance()->ReadString("4132:onIfAll = 13"); // Sigma_c -> mu X - TPythia8::Instance()->ReadString("4232:onMode = off"); - TPythia8::Instance()->ReadString("4232:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4232:onMode = off"); + AliTPythia8::Instance()->ReadString("4232:onIfAll = 13"); // Omega_c -> mu X - TPythia8::Instance()->ReadString("4332:onMode = off"); - TPythia8::Instance()->ReadString("4332:onIfAll = 13"); + AliTPythia8::Instance()->ReadString("4332:onMode = off"); + AliTPythia8::Instance()->ReadString("4332:onIfAll = 13"); break; case kZDiMuon: // Z -> mu+ mu- - TPythia8::Instance()->ReadString("23:onMode = off"); - TPythia8::Instance()->ReadString("23:onIfAll = 13 13"); + AliTPythia8::Instance()->ReadString("23:onMode = off"); + AliTPythia8::Instance()->ReadString("23:onIfAll = 13 13"); break; case kZDiElectron: // Z -> e+ e- - TPythia8::Instance()->ReadString("23:onMode = off"); - TPythia8::Instance()->ReadString("23:onIfAll = 11 11"); + AliTPythia8::Instance()->ReadString("23:onMode = off"); + AliTPythia8::Instance()->ReadString("23:onIfAll = 11 11"); break; case kHadronicD: ForceHadronicD(1); @@ -521,21 +546,21 @@ void AliDecayerPythia8::ForceDecay() break; case kPhiKK: // Phi-> K+ K- - TPythia8::Instance()->ReadString("333:onMode = off"); - TPythia8::Instance()->ReadString("333:onIfAll = 321 321"); + AliTPythia8::Instance()->ReadString("333:onMode = off"); + AliTPythia8::Instance()->ReadString("333:onIfAll = 321 321"); break; case kOmega: // Omega -> Lambda K - TPythia8::Instance()->ReadString("3334:onMode = off"); - TPythia8::Instance()->ReadString("3334:onIfAll = 3122 321 "); + AliTPythia8::Instance()->ReadString("3334:onMode = off"); + AliTPythia8::Instance()->ReadString("3334:onIfAll = 3122 321 "); case kLambda: // Lambda -> p pi- - TPythia8::Instance()->ReadString("3122:onMode = off"); - TPythia8::Instance()->ReadString("3122:onIfAll = 2212 211 "); + AliTPythia8::Instance()->ReadString("3122:onMode = off"); + AliTPythia8::Instance()->ReadString("3122:onIfAll = 2212 211 "); case kAll: break; case kNoDecay: - TPythia8::Instance()->ReadString("HadronLevel:Decay = off"); + AliTPythia8::Instance()->ReadString("HadronLevel:Decay = off"); break; case kNoDecayHeavy: case kNoDecayBeauty: @@ -549,18 +574,16 @@ Float_t AliDecayerPythia8::GetPartialBranchingRatio(Int_t ipart) { // Get the partial branching ration for the forced decay channels - Pythia8::Pythia* thePythia = TPythia8::Instance()->Pythia8(); - Pythia8::ParticleDataTable table = thePythia->particleData; - Pythia8::ParticleDataEntry* pd = table.particleDataPtr(ipart); - Pythia8::DecayTable decays = pd->decay; - - - Int_t nc = decays.size(); + Pythia8::Pythia* thePythia = AliTPythia8::Instance()->Pythia8(); + Pythia8::ParticleData & table = thePythia->particleData; + Pythia8::ParticleDataEntry* pd = table.particleDataEntryPtr(ipart); + + Int_t nc = pd->sizeChannels(); Float_t br = 0.; // // Loop over decay channels for (Int_t ic = 0; ic < nc; ic++) { - Pythia8::DecayChannel& decCh = decays[ic]; + Pythia8::DecayChannel& decCh = pd->channel(ic); for (Int_t i = 0; i < decCh.multiplicity(); i++) { br += decCh.bRatio(); } @@ -572,10 +595,10 @@ Float_t AliDecayerPythia8::GetPartialBranchingRatio(Int_t ipart) Float_t AliDecayerPythia8::GetLifetime(Int_t kf) { // Return lifetime of particle - Pythia8::Pythia* thePythia = TPythia8::Instance()->Pythia8(); - Pythia8::ParticleDataTable table = thePythia->particleData; + Pythia8::Pythia* thePythia = AliTPythia8::Instance()->Pythia8(); + Pythia8::ParticleData& table = thePythia->particleData; Float_t tau = table.tau0(kf); - return ( tau); + return (tau); } void AliDecayerPythia8::SwitchOffHeavyFlavour() @@ -583,11 +606,11 @@ void AliDecayerPythia8::SwitchOffHeavyFlavour() // Switch off heavy flavour production // // Maximum number of quark flavours used in pdf - TPythia8::Instance()->ReadString("PDFinProcess:nQuarkIn = 3"); + AliTPythia8::Instance()->ReadString("PDFinProcess:nQuarkIn = 3"); // Maximum number of flavors that can be used in showers - TPythia8::Instance()->ReadString("SpaceShower:nQuarkIn = 3"); - TPythia8::Instance()->ReadString("TimeShower:nGammaToQuark = 3"); - TPythia8::Instance()->ReadString("TimeShower:nGluonToQuark = 3"); + AliTPythia8::Instance()->ReadString("SpaceShower:nQuarkIn = 3"); + AliTPythia8::Instance()->ReadString("TimeShower:nGammaToQuark = 3"); + AliTPythia8::Instance()->ReadString("TimeShower:nGluonToQuark = 3"); } @@ -597,59 +620,81 @@ void AliDecayerPythia8::ForceHadronicD(Int_t optUse4Bodies) // Force golden D decay modes // // K* -> K pi - TPythia8::Instance()->ReadString("313:onMode = off"); - TPythia8::Instance()->ReadString("313:onIfAll = 321 211"); + AliTPythia8::Instance()->ReadString("313:onMode = off"); + AliTPythia8::Instance()->ReadString("313:onIfAll = 321 211"); // for Ds -> Phi pi+ - TPythia8::Instance()->ReadString("333:onMode = off"); - TPythia8::Instance()->ReadString("333:onIfAll = 321 321"); + AliTPythia8::Instance()->ReadString("333:onMode = off"); + AliTPythia8::Instance()->ReadString("333:onIfAll = 321 321"); // for D0 -> rho0 pi+ k- - TPythia8::Instance()->ReadString("113:onMode = off"); - TPythia8::Instance()->ReadString("113:onIfAll = 211 211"); + AliTPythia8::Instance()->ReadString("113:onMode = off"); + AliTPythia8::Instance()->ReadString("113:onIfAll = 211 211"); // for Lambda_c -> Delta++ K- - TPythia8::Instance()->ReadString("2224:onMode = off"); - TPythia8::Instance()->ReadString("2224:onIfAll = 2212 211"); + AliTPythia8::Instance()->ReadString("2224:onMode = off"); + AliTPythia8::Instance()->ReadString("2224:onIfAll = 2212 211"); // for Lambda_c -> Lambda(1520) K- - TPythia8::Instance()->ReadString("3124:onMode = off"); - TPythia8::Instance()->ReadString("3124:onIfAll = 2212 321"); + AliTPythia8::Instance()->ReadString("3124:onMode = off"); + AliTPythia8::Instance()->ReadString("3124:onIfAll = 2212 321"); - TPythia8::Instance()->ReadString("411:onMode = off"); - TPythia8::Instance()->ReadString("421:onMode = off"); - TPythia8::Instance()->ReadString("431:onMode = off"); - TPythia8::Instance()->ReadString("4112:onMode = off"); - TPythia8::Instance()->ReadString("4122:onMode = off"); + AliTPythia8::Instance()->ReadString("411:onMode = off"); + AliTPythia8::Instance()->ReadString("421:onMode = off"); + AliTPythia8::Instance()->ReadString("431:onMode = off"); + AliTPythia8::Instance()->ReadString("4112:onMode = off"); + AliTPythia8::Instance()->ReadString("4122:onMode = off"); // D+/- -> K pi pi - TPythia8::Instance()->ReadString("411:onIfMatch = 321 211 211"); + AliTPythia8::Instance()->ReadString("411:onIfMatch = 321 211 211"); // D+/- -> K* pi - TPythia8::Instance()->ReadString("411:onIfMatch = 313 211"); + AliTPythia8::Instance()->ReadString("411:onIfMatch = 313 211"); // D0 -> K pi - TPythia8::Instance()->ReadString("421:onIfMatch = 321 211"); + AliTPythia8::Instance()->ReadString("421:onIfMatch = 321 211"); if (optUse4Bodies) { // D0 -> K pi pi pi - TPythia8::Instance()->ReadString("421:onIfMatch = 321 211 211 211"); + AliTPythia8::Instance()->ReadString("421:onIfMatch = 321 211 211 211"); // D0 -> K pi rho - TPythia8::Instance()->ReadString("421:onIfMatch = 321 211 113"); + AliTPythia8::Instance()->ReadString("421:onIfMatch = 321 211 113"); // D0 -> K*0 pi pi - TPythia8::Instance()->ReadString("421:onIfMatch = 313 211 211"); + AliTPythia8::Instance()->ReadString("421:onIfMatch = 313 211 211"); } // D_s -> K K* - TPythia8::Instance()->ReadString("431:onIfMatch = 321 313"); + AliTPythia8::Instance()->ReadString("431:onIfMatch = 321 313"); // D_s -> Phi pi - TPythia8::Instance()->ReadString("431:onIfMatch = 333 211"); + AliTPythia8::Instance()->ReadString("431:onIfMatch = 333 211"); // Lambda_c -> p K* - TPythia8::Instance()->ReadString("4122:onIfMatch = 2212 313"); + AliTPythia8::Instance()->ReadString("4122:onIfMatch = 2212 313"); // Lambda_c -> Delta K - TPythia8::Instance()->ReadString("4122:onIfMatch = 2224 321"); + AliTPythia8::Instance()->ReadString("4122:onIfMatch = 2224 321"); // Lambda_c -> Lambda(1520) pi - TPythia8::Instance()->ReadString("4122:onIfMatch = 3124 211"); + AliTPythia8::Instance()->ReadString("4122:onIfMatch = 3124 211"); // Lambda_c -> p K pi - TPythia8::Instance()->ReadString("4122:onIfMatch = 2212 321 211"); + AliTPythia8::Instance()->ReadString("4122:onIfMatch = 2212 321 211"); // Lambda_c -> Lambda pi - TPythia8::Instance()->ReadString("4122:onIfMatch = 3122 211"); + AliTPythia8::Instance()->ReadString("4122:onIfMatch = 3122 211"); } +//___________________________________________________________________________ +void AliDecayerPythia8::ReadDecayTable() +{ + //to read a decay table (not yet implemented) +} + + +//___________________________________________________________________________ +void AliDecayerPythia8::AppendParticle(Int_t pdg, TLorentzVector* p) +{ + // Append a particle to the stack + fPythia8->Pythia8()->event.append(pdg, 11, 0, 0, p->Px(), p->Py(), p->Pz(), p->E(), p->M()); +} + + +//___________________________________________________________________________ +void AliDecayerPythia8::ClearEvent() +{ + // Clear the event stack + fPythia8->Pythia8()->event.clear(); +} + diff --git a/PYTHIA8/AliDecayerPythia8.h b/PYTHIA8/AliDecayerPythia8.h index 8582024a290..40e58abd9ad 100644 --- a/PYTHIA8/AliDecayerPythia8.h +++ b/PYTHIA8/AliDecayerPythia8.h @@ -8,28 +8,40 @@ // Implementation of TVirtualMCDecayer using Pythia8 // Author: andreas.morsch@cern.ch -#include #include +#include #include "AliDecayer.h" -class AliDecayerPythia8 : public TPythia8Decayer { +class AliDecayerPythia8 : public TVirtualMCDecayer { public: AliDecayerPythia8(); virtual ~AliDecayerPythia8(){;} virtual void Init(); + virtual void Decay(Int_t pdg, TLorentzVector* p); + virtual Int_t ImportParticles(TClonesArray *particles); virtual void SetForceDecay(Decay_t decay) {fDecay=decay;} virtual void SetForceDecay(Int_t decay) {SetForceDecay((Decay_t) decay);} virtual void ForceDecay(); virtual Float_t GetPartialBranchingRatio(Int_t ipart); virtual void HeavyFlavourOff() {fHeavyFlavour = kFALSE;} virtual Float_t GetLifetime(Int_t kf); + virtual void ReadDecayTable(); + + virtual void SetDebugLevel(Int_t debug) {fDebug = debug;} + + protected: + void AppendParticle(Int_t pdg, TLorentzVector* p); + void ClearEvent(); private: void SwitchOffHeavyFlavour(); void ForceHadronicD(Int_t optUser4Bodies = 1); - protected: - Decay_t fDecay; // Forced decay mode - Bool_t fHeavyFlavour; //! Flag for heavy flavors - static Bool_t fgInit; //! initialization flag + + AliTPythia8* fPythia8; // Pointer to pythia8 + Int_t fDebug; // Debug level + + Decay_t fDecay; // Forced decay mode + Bool_t fHeavyFlavour; //! Flag for heavy flavors + static Bool_t fgInit; //! initialization flag ClassDef(AliDecayerPythia8, 1) // Particle Decayer using Pythia8 }; #endif diff --git a/PYTHIA8/AliPythia8.cxx b/PYTHIA8/AliPythia8.cxx index 7071693baae..a57bd8caecc 100644 --- a/PYTHIA8/AliPythia8.cxx +++ b/PYTHIA8/AliPythia8.cxx @@ -53,7 +53,7 @@ ClassImp(AliPythia8) AliPythia8* AliPythia8::fgAliPythia8=NULL; AliPythia8::AliPythia8(): - TPythia8(), + AliTPythia8(), AliPythiaBase(), fProcess(kPyMb), fEcms(0.), @@ -74,7 +74,7 @@ AliPythia8::AliPythia8(): } AliPythia8::AliPythia8(const AliPythia8& pythia): - TPythia8(), + AliTPythia8(), AliPythiaBase(), fProcess(kPyMb), fEcms(0.), @@ -594,7 +594,7 @@ void AliPythia8::GetJet(Int_t i, Float_t& px, Float_t& py, Float_t& pz, Float_t& void AliPythia8::GenerateEvent() { // Generate one event - TPythia8::GenerateEvent(); + AliTPythia8::GenerateEvent(); } void AliPythia8::GenerateMIEvent() @@ -606,13 +606,13 @@ void AliPythia8::GenerateMIEvent() void AliPythia8::PrintStatistics() { // End of run statistics - TPythia8::PrintStatistics(); + AliTPythia8::PrintStatistics(); } void AliPythia8::EventListing() { // End of run statistics - TPythia8::EventListing(); + AliTPythia8::EventListing(); } Int_t AliPythia8::ProcessCode() diff --git a/PYTHIA8/AliPythia8.h b/PYTHIA8/AliPythia8.h index bd3ed6fb823..2f5f3480d5e 100644 --- a/PYTHIA8/AliPythia8.h +++ b/PYTHIA8/AliPythia8.h @@ -5,12 +5,12 @@ /* $Id: AliPythia.h,v 1.22 2007/10/09 08:43:24 morsch Exp $ */ -#include #include "Analysis.h" #include "AliPythiaBase.h" +#include "AliTPythia8.h" class AliStack; -class AliPythia8 : public TPythia8, public AliPythiaBase +class AliPythia8 :public AliTPythia8, public AliPythiaBase { public: diff --git a/PYTHIA8/AliPythia8LinkDef.h b/PYTHIA8/AliPythia8LinkDef.h index 089c96a7491..5dca74a94ec 100644 --- a/PYTHIA8/AliPythia8LinkDef.h +++ b/PYTHIA8/AliPythia8LinkDef.h @@ -2,6 +2,7 @@ #pragma link off all globals; #pragma link off all classes; #pragma link off all functions; +#pragma link C++ class AliTPythia8+; #pragma link C++ class AliPythia8+; #pragma link C++ class AliDecayerPythia8+; #endif diff --git a/PYTHIA8/AliTPythia8.cxx b/PYTHIA8/AliTPythia8.cxx new file mode 100644 index 00000000000..0de8209dea9 --- /dev/null +++ b/PYTHIA8/AliTPythia8.cxx @@ -0,0 +1,300 @@ +/************************************************************************** + * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * + * * + * Author: The ALICE Off-line Project. * + * Contributors are mentioned in the code where appropriate. * + * * + * Permission to use, copy, modify and distribute this software and its * + * documentation strictly for non-commercial purposes is hereby granted * + * without fee, provided that the above copyright notice appears in all * + * copies and that both the copyright notice and this permission notice * + * appear in the supporting documentation. The authors make no claims * + * about the suitability of this software for any purpose. It is * + * provided "as is" without express or implied warranty. * + **************************************************************************/ + +// Author: Andreas Morsch 27/10/2007 +//////////////////////////////////////////////////////////////////////////////// +// // +// TPythia8 // +// // +// TPythia is an interface class to C++ version of Pythia 8.1 // +// event generators, written by T.Sjostrand. // +// // +// The user is assumed to be familiar with the Pythia package. // +// This class includes only a basic interface to Pythia8. Because Pythia8 is // +// also written in C++, its functions/classes can be called directly from a // +// compiled C++ script. // +// To call Pythia functions not available in this interface a dictionary must // +// be generated. // +// see $ROOTSYS/tutorials/pythia/pythia8.C for an example of use from CINT. // +// // +//////////////////////////////////////////////////////////////////////////////// +/* +*------------------------------------------------------------------------------------* + | | + | *------------------------------------------------------------------------------* | + | | | | + | | | | + | | PPP Y Y TTTTT H H III A Welcome to the Lund Monte Carlo! | | + | | P P Y Y T H H I A A This is PYTHIA version 8.100 | | + | | PPP Y T HHHHH I AAAAA Last date of change: 20 Oct 2007 | | + | | P Y T H H I A A | | + | | P Y T H H III A A Now is 27 Oct 2007 at 18:26:53 | | + | | | | + | | Main author: Torbjorn Sjostrand; CERN/PH, CH-1211 Geneva, Switzerland, | | + | | and Department of Theoretical Physics, Lund University, Lund, Sweden; | | + | | phone: + 41 - 22 - 767 82 27; e-mail: torbjorn@thep.lu.se | | + | | Author: Stephen Mrenna; Computing Division, Simulations Group, | | + | | Fermi National Accelerator Laboratory, MS 234, Batavia, IL 60510, USA; | | + | | phone: + 1 - 630 - 840 - 2556; e-mail: mrenna@fnal.gov | | + | | Author: Peter Skands; CERN/PH, CH-1211 Geneva, Switzerland, | | + | | and Theoretical Physics Department, | | + | | Fermi National Accelerator Laboratory, MS 106, Batavia, IL 60510, USA; | | + | | phone: + 41 - 22 - 767 24 59; e-mail: skands@fnal.gov | | + | | | | + | | The main program reference is the 'Brief Introduction to PYTHIA 8.1', | | + | | T. Sjostrand, S. Mrenna and P. Skands, arXiv:0710.3820 | | + | | | | + | | The main physics reference is the 'PYTHIA 6.4 Physics and Manual', | | + | | T. Sjostrand, S. Mrenna and P. Skands, JHEP05 (2006) 026 [hep-ph/0603175]. | | + | | | | + | | An archive of program versions and documentation is found on the web: | | + | | http://www.thep.lu.se/~torbjorn/Pythia.html | | + | | | | + | | This program is released under the GNU General Public Licence version 2. | | + | | Please respect the MCnet Guidelines for Event Generator Authors and Users. | | + | | | | + | | Disclaimer: this program comes without any guarantees. | | + | | Beware of errors and use common sense when interpreting results. | | + | | | | + | | Copyright (C) 2007 Torbjorn Sjostrand | | + | | | | + | | | | + | *------------------------------------------------------------------------------* | + | | + *------------------------------------------------------------------------------------* +*/ + +#include "AliTPythia8.h" + +#include "TClonesArray.h" +#include "TParticle.h" +#include "TDatabasePDG.h" +#include "TLorentzVector.h" + +ClassImp(AliTPythia8) + +AliTPythia8* AliTPythia8::fgInstance = 0; + +//___________________________________________________________________________ +AliTPythia8::AliTPythia8(): + TGenerator("AliTPythia8", "AliTPythia8"), + fPythia(0), + fNumberOfParticles(0) +{ + // Constructor + if (fgInstance) + Fatal("AliTPythia8", "There's already an instance of AliTPythia8"); + + delete fParticles; // was allocated as TObjArray in TGenerator + + fParticles = new TClonesArray("TParticle",50); + fPythia = new Pythia8::Pythia(); +} + +//___________________________________________________________________________ +AliTPythia8::AliTPythia8(const char *xmlDir): + TGenerator("AliTPythia8", "AliTPythia8"), + fPythia(0), + fNumberOfParticles(0) +{ + // Constructor with an xmlDir (eg "../xmldoc" + if (fgInstance) + Fatal("AliTPythia8", "There's already an instance of AliTPythia8"); + + delete fParticles; // was allocated as TObjArray in TGenerator + + fParticles = new TClonesArray("TParticle",50); + fPythia = new Pythia8::Pythia(xmlDir); +} + +//___________________________________________________________________________ +AliTPythia8::~AliTPythia8() +{ + // Destructor + if (fParticles) { + fParticles->Delete(); + delete fParticles; + fParticles = 0; + } + delete fPythia; +} + +//___________________________________________________________________________ +AliTPythia8* AliTPythia8::Instance() +{ + // Return an instance of AliTPythia8 + return fgInstance ? fgInstance : (fgInstance = new AliTPythia8()) ; +} + +//___________________________________________________________________________ +Bool_t AliTPythia8::Initialize(Int_t idAin, Int_t idBin, Double_t ecms) +{ + // Initialization + AddParticlesToPdgDataBase(); + return fPythia->init(idAin, idBin, ecms); +} + +//___________________________________________________________________________ +void AliTPythia8::GenerateEvent() +{ + // Generate the next event + fPythia->next(); + fNumberOfParticles = fPythia->event.size() - 1; + ImportParticles(); +} + +//___________________________________________________________________________ +Int_t AliTPythia8::ImportParticles(TClonesArray *particles, Option_t *option) +{ + // Import particles from Pythia stack + if (particles == 0) return 0; + TClonesArray &clonesParticles = *particles; + clonesParticles.Clear(); + Int_t nparts=0; + Int_t i; + fNumberOfParticles = fPythia->event.size() - 1; + + if (!strcmp(option,"") || !strcmp(option,"Final")) { + for (i = 0; i <= fNumberOfParticles; i++) { + if (fPythia->event[i].id() == 90) continue; + if (fPythia->event[i].isFinal()) { + new(clonesParticles[nparts]) TParticle( + fPythia->event[i].id(), + fPythia->event[i].isFinal(), + fPythia->event[i].mother1() - 1, + fPythia->event[i].mother2() - 1, + fPythia->event[i].daughter1() - 1, + fPythia->event[i].daughter2() - 1, + fPythia->event[i].px(), // [GeV/c] + fPythia->event[i].py(), // [GeV/c] + fPythia->event[i].pz(), // [GeV/c] + fPythia->event[i].e(), // [GeV] + fPythia->event[i].xProd(), // [mm] + fPythia->event[i].yProd(), // [mm] + fPythia->event[i].zProd(), // [mm] + fPythia->event[i].tProd()); // [mm/c] + nparts++; + } // final state partice + } // particle loop + } else if (!strcmp(option,"All")) { + for (i = 0; i <= fNumberOfParticles; i++) { + if (fPythia->event[i].id() == 90) continue; + new(clonesParticles[nparts]) TParticle( + fPythia->event[i].id(), + fPythia->event[i].isFinal(), + fPythia->event[i].mother1() - 1, + fPythia->event[i].mother2() - 1, + fPythia->event[i].daughter1() - 1, + fPythia->event[i].daughter2() - 1, + fPythia->event[i].px(), // [GeV/c] + fPythia->event[i].py(), // [GeV/c] + fPythia->event[i].pz(), // [GeV/c] + fPythia->event[i].e(), // [GeV] + fPythia->event[i].xProd(), // [mm] + fPythia->event[i].yProd(), // [mm] + fPythia->event[i].zProd(), // [mm] + fPythia->event[i].tProd()); // [mm/c] + nparts++; + } // particle loop + } + return nparts; +} + +//___________________________________________________________________________ +TObjArray* AliTPythia8::ImportParticles(Option_t* /* option */) +{ + // Import particles from Pythia stack + fParticles->Clear(); + Int_t numpart = fPythia->event.size() - 1; + TClonesArray &a = *((TClonesArray*)fParticles); + for (Int_t i = 1; i <= numpart; i++) { + new(a[i]) TParticle( + fPythia->event[i].id(), + fPythia->event[i].isFinal(), + fPythia->event[i].mother1() - 1, + fPythia->event[i].mother2() - 1, + fPythia->event[i].daughter1() - 1, + fPythia->event[i].daughter2() - 1, + fPythia->event[i].px(), // [GeV/c] + fPythia->event[i].py(), // [GeV/c] + fPythia->event[i].pz(), // [GeV/c] + fPythia->event[i].e(), // [GeV] + fPythia->event[i].xProd(), // [mm] + fPythia->event[i].yProd(), // [mm] + fPythia->event[i].zProd(), // [mm] + fPythia->event[i].tProd()); // [mm/c] + } + return fParticles; +} + +//___________________________________________________________________________ +Int_t AliTPythia8::GetN() const +{ + // Initialization + return (fPythia->event.size() - 1); +} + +//___________________________________________________________________________ +void AliTPythia8::ReadString(const char* string) const +{ + // Configuration + fPythia->readString(string); +} + +//___________________________________________________________________________ +void AliTPythia8::ReadConfigFile(const char* string) const +{ + // Configuration + fPythia->readFile(string); +} + +//___________________________________________________________________________ +void AliTPythia8::PrintStatistics() const +{ + // Print end of run statistics + fPythia->statistics(); +} + +//___________________________________________________________________________ +void AliTPythia8::EventListing() const +{ + // Event listing + fPythia->event.list(); +} + +//___________________________________________________________________________ +void AliTPythia8::AddParticlesToPdgDataBase() +{ + // Add some pythia specific particle code to the data base + + TDatabasePDG *pdgDB = TDatabasePDG::Instance(); + pdgDB->AddParticle("string","string", 0, kTRUE, + 0, 0, "QCD string", 90); + pdgDB->AddParticle("rho_diff0", "rho_diff0", 0, kTRUE, + 0, 0, "QCD diffr. state", 9900110); + pdgDB->AddParticle("pi_diffr+", "pi_diffr+", 0, kTRUE, + 0, 1, "QCD diffr. state", 9900210); + pdgDB->AddParticle("omega_di", "omega_di", 0, kTRUE, + 0, 0, "QCD diffr. state", 9900220); + pdgDB->AddParticle("phi_diff","phi_diff", 0, kTRUE, + 0, 0, "QCD diffr. state", 9900330); + pdgDB->AddParticle("J/psi_di", "J/psi_di", 0, kTRUE, + 0, 0, "QCD diffr. state", 9900440); + pdgDB->AddParticle("n_diffr0","n_diffr0",0,kTRUE, + 0, 0, "QCD diffr. state", 9902110); + pdgDB->AddParticle("p_diffr+","p_diffr+", 0, kTRUE, + 0, 1, "QCD diffr. state", 9902210); +} + diff --git a/PYTHIA8/AliTPythia8.h b/PYTHIA8/AliTPythia8.h new file mode 100644 index 00000000000..09f003973b5 --- /dev/null +++ b/PYTHIA8/AliTPythia8.h @@ -0,0 +1,101 @@ +#ifndef ALITPYTHIA8_H +#define ALITPYTHIA8_H +/* Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * + * See cxx source for full Copyright notice */ + +/* $Id$ */ + + +//////////////////////////////////////////////////////////////////////////////// +// // +// TPythia8 // +// // +// TPythia is an interface class to C++ version of Pythia 8.1 // +// event generators, written by T.Sjostrand. // +//////////////////////////////////////////////////////////////////////////////// +/* +*------------------------------------------------------------------------------------* + | | + | *------------------------------------------------------------------------------* | + | | | | + | | | | + | | PPP Y Y TTTTT H H III A Welcome to the Lund Monte Carlo! | | + | | P P Y Y T H H I A A This is PYTHIA version 8.100 | | + | | PPP Y T HHHHH I AAAAA Last date of change: 20 Oct 2007 | | + | | P Y T H H I A A | | + | | P Y T H H III A A Now is 27 Oct 2007 at 18:26:53 | | + | | | | + | | Main author: Torbjorn Sjostrand; CERN/PH, CH-1211 Geneva, Switzerland, | | + | | and Department of Theoretical Physics, Lund University, Lund, Sweden; | | + | | phone: + 41 - 22 - 767 82 27; e-mail: torbjorn@thep.lu.se | | + | | Author: Stephen Mrenna; Computing Division, Simulations Group, | | + | | Fermi National Accelerator Laboratory, MS 234, Batavia, IL 60510, USA; | | + | | phone: + 1 - 630 - 840 - 2556; e-mail: mrenna@fnal.gov | | + | | Author: Peter Skands; CERN/PH, CH-1211 Geneva, Switzerland, | | + | | and Theoretical Physics Department, | | + | | Fermi National Accelerator Laboratory, MS 106, Batavia, IL 60510, USA; | | + | | phone: + 41 - 22 - 767 24 59; e-mail: skands@fnal.gov | | + | | | | + | | The main program reference is the 'Brief Introduction to PYTHIA 8.1', | | + | | T. Sjostrand, S. Mrenna and P. Skands, arXiv:0710.3820 | | + | | | | + | | The main physics reference is the 'PYTHIA 6.4 Physics and Manual', | | + | | T. Sjostrand, S. Mrenna and P. Skands, JHEP05 (2006) 026 [hep-ph/0603175]. | | + | | | | + | | An archive of program versions and documentation is found on the web: | | + | | http://www.thep.lu.se/~torbjorn/Pythia.html | | + | | | | + | | This program is released under the GNU General Public Licence version 2. | | + | | Please respect the MCnet Guidelines for Event Generator Authors and Users. | | + | | | | + | | Disclaimer: this program comes without any guarantees. | | + | | Beware of errors and use common sense when interpreting results. | | + | | | | + | | Copyright (C) 2007 Torbjorn Sjostrand | | + | | | | + | | | | + | *------------------------------------------------------------------------------* | + | | + *------------------------------------------------------------------------------------* +*/ + +#include "TGenerator.h" +#include "Pythia.h" + + +class TClonesArray; +class TObjArray; + +class AliTPythia8 : public TGenerator +{ +public: + AliTPythia8(); + AliTPythia8(const char *xmlDir); + virtual ~AliTPythia8(); + static AliTPythia8 *Instance(); + Pythia8::Pythia *Pythia8() {return fPythia;} + + // Interface + virtual void GenerateEvent(); + virtual Int_t ImportParticles(TClonesArray *particles, Option_t *option=""); + virtual TObjArray *ImportParticles(Option_t *option=""); + + // Others + void ReadString(const char* string) const; + void ReadConfigFile(const char* string) const; + Bool_t Initialize(Int_t idAin, Int_t idBin, Double_t ecms); + void PrintStatistics() const; + void EventListing() const; + Int_t GetN() const; + +protected: + static AliTPythia8 *fgInstance; //! singleton instance + Pythia8::Pythia *fPythia; //! The pythia8 instance + Int_t fNumberOfParticles; //! Number of particles +private: + void AddParticlesToPdgDataBase(); + ClassDef(AliTPythia8, 1) // Interface class of Pythia8 +}; + +#endif + diff --git a/PYTHIA8/libAliPythia8.pkg b/PYTHIA8/libAliPythia8.pkg index ab6c42b54b7..642eb4bf7b6 100644 --- a/PYTHIA8/libAliPythia8.pkg +++ b/PYTHIA8/libAliPythia8.pkg @@ -1,4 +1,4 @@ -SRCS= AliPythia8.cxx AliDecayerPythia8.cxx +SRCS= AliTPythia8.cxx AliPythia8.cxx AliDecayerPythia8.cxx HDRS:= $(SRCS:.cxx=.h) DHDR:= AliPythia8LinkDef.h -EINCLUDE:= $(PYTHIA8)/include PYTHIA6 +EINCLUDE:= PYTHIA8/pythia8140/include PYTHIA6 diff --git a/PYTHIA8/libpythia8.pkg b/PYTHIA8/libpythia8.pkg index aba88f2b332..7deb9339565 100644 --- a/PYTHIA8/libpythia8.pkg +++ b/PYTHIA8/libpythia8.pkg @@ -1,51 +1,54 @@ #-*- Mode: Makefile -*- - SRCS:= \ -pythia8130/src/Analysis.cxx \ -pythia8130/src/Basics.cxx \ -pythia8130/src/BeamParticle.cxx \ -pythia8130/src/BeamRemnants.cxx \ -pythia8130/src/BeamShape.cxx \ -pythia8130/src/BoseEinstein.cxx \ -pythia8130/src/Event.cxx \ -pythia8130/src/FragmentationFlavZpT.cxx \ -pythia8130/src/FragmentationSystems.cxx \ -pythia8130/src/HadronLevel.cxx \ -pythia8130/src/Info.cxx \ -pythia8130/src/LesHouches.cxx \ -pythia8130/src/MiniStringFragmentation.cxx \ -pythia8130/src/MultipleInteractions.cxx \ -pythia8130/src/ParticleData.cxx \ -pythia8130/src/ParticleDecays.cxx \ -pythia8130/src/PartonDistributions.cxx \ -pythia8130/src/PartonLevel.cxx \ -pythia8130/src/PhaseSpace.cxx \ -pythia8130/src/ProcessContainer.cxx \ -pythia8130/src/ProcessLevel.cxx \ -pythia8130/src/Pythia.cxx \ -pythia8130/src/ResonanceDecays.cxx \ -pythia8130/src/ResonanceWidths.cxx \ -pythia8130/src/Settings.cxx \ -pythia8130/src/SigmaCompositeness.cxx \ -pythia8130/src/SigmaEW.cxx \ -pythia8130/src/SigmaExtraDim.cxx \ -pythia8130/src/SigmaHiggs.cxx \ -pythia8130/src/SigmaLeftRightSym.cxx \ -pythia8130/src/SigmaLeptoquark.cxx \ -pythia8130/src/SigmaNewGaugeBosons.cxx \ -pythia8130/src/SigmaOnia.cxx \ -pythia8130/src/SigmaProcess.cxx \ -pythia8130/src/SigmaQCD.cxx \ -pythia8130/src/SigmaSUSY.cxx \ -pythia8130/src/SigmaTotal.cxx \ -pythia8130/src/SpaceShower.cxx \ -pythia8130/src/StandardModel.cxx \ -pythia8130/src/StringFragmentation.cxx \ -pythia8130/src/SusyLesHouches.cxx \ -pythia8130/src/TimeShower.cxx \ -pythia8130/src/UserHooks.cxx +pythia8140/src/Analysis.cxx \ +pythia8140/src/Basics.cxx \ +pythia8140/src/BeamParticle.cxx \ +pythia8140/src/BeamRemnants.cxx \ +pythia8140/src/BeamShape.cxx \ +pythia8140/src/BoseEinstein.cxx \ +pythia8140/src/Event.cxx \ +pythia8140/src/FragmentationFlavZpT.cxx \ +pythia8140/src/FragmentationSystems.cxx \ +pythia8140/src/HadronLevel.cxx \ +pythia8140/src/Info.cxx \ +pythia8140/src/LesHouches.cxx \ +pythia8140/src/MiniStringFragmentation.cxx \ +pythia8140/src/MultipleInteractions.cxx \ +pythia8140/src/ParticleData.cxx \ +pythia8140/src/ParticleDecays.cxx \ +pythia8140/src/PartonDistributions.cxx \ +pythia8140/src/PartonLevel.cxx \ +pythia8140/src/PartonSystems.cxx \ +pythia8140/src/PhaseSpace.cxx \ +pythia8140/src/ProcessContainer.cxx \ +pythia8140/src/ProcessLevel.cxx \ +pythia8140/src/Pythia.cxx \ +pythia8140/src/PythiaStdlib.cxx \ +pythia8140/src/ResonanceDecays.cxx \ +pythia8140/src/ResonanceWidths.cxx \ +pythia8140/src/Settings.cxx \ +pythia8140/src/SigmaCompositeness.cxx \ +pythia8140/src/SigmaEW.cxx \ +pythia8140/src/SigmaExtraDim.cxx \ +pythia8140/src/SigmaGeneric.cxx \ +pythia8140/src/SigmaHiggs.cxx \ +pythia8140/src/SigmaLeftRightSym.cxx \ +pythia8140/src/SigmaLeptoquark.cxx \ +pythia8140/src/SigmaNewGaugeBosons.cxx \ +pythia8140/src/SigmaOnia.cxx \ +pythia8140/src/SigmaProcess.cxx \ +pythia8140/src/SigmaQCD.cxx \ +pythia8140/src/SigmaSUSY.cxx \ +pythia8140/src/SigmaTotal.cxx \ +pythia8140/src/SpaceShower.cxx \ +pythia8140/src/StandardModel.cxx \ +pythia8140/src/StringFragmentation.cxx \ +pythia8140/src/SusyCouplings.cxx \ +pythia8140/src/SusyLesHouches.cxx \ +pythia8140/src/TimeShower.cxx \ +pythia8140/src/UserHooks.cxx -EINCLUDE:= PYTHIA8/pythia8130/include +EINCLUDE:= PYTHIA8/pythia8140/include ifeq (macosxicc,$(ALICE_TARGET)) PACKFFLAGS := $(filter-out -O%,$(FFLAGS)) endif diff --git a/PYTHIA8/pythia8.C b/PYTHIA8/pythia8.C index 267d5b73b09..3cf67997596 100644 --- a/PYTHIA8/pythia8.C +++ b/PYTHIA8/pythia8.C @@ -8,7 +8,6 @@ void pythia8(Int_t nev = 1, char* filename = "galice.root") gSystem->Load("libpythia6.so"); gSystem->Load("libAliPythia6.so"); gSystem->Load("libpythia8.so"); - gSystem->Load("libEGPythia8.so"); gSystem->Load("libAliPythia8.so"); AliRunLoader* rl = AliRunLoader::Open("galice.root","FASTRUN","recreate"); diff --git a/PYTHIA8/pythia8140/include/Analysis.h b/PYTHIA8/pythia8140/include/Analysis.h new file mode 100644 index 00000000000..b1d4c9b5f87 --- /dev/null +++ b/PYTHIA8/pythia8140/include/Analysis.h @@ -0,0 +1,353 @@ +// Analysis.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for the Sphericity, Thrust, ClusterJet and CellJet classes. +// Sphericity: sphericity analysis of the event. +// Thrust: thrust analysis of the event. +// ClusterJet: clustering jet finder. +// CellJet: calorimetric cone jet finder. + +#ifndef Pythia8_Analysis_H +#define Pythia8_Analysis_H + +#include "Basics.h" +#include "Event.h" +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// Sphericity class. +// This class performs (optionally modified) sphericity analysis on an event. + +class Sphericity { + +public: + + // Constructor. + Sphericity(double powerIn = 2., int selectIn = 2) : power(powerIn), + select(selectIn), nFew(0), nBack(0) {powerInt = 0; + if (abs(power - 1.) < 0.01) powerInt = 1; + if (abs(power - 2.) < 0.01) powerInt = 2; + powerMod = 0.5 * power - 1.;} + + // Analyze event. + bool analyze(const Event& event, ostream& os = cout); + + // Return info on results of analysis. + double sphericity() const {return 1.5 * (eVal2 + eVal3);} + double aplanarity() const {return 1.5 * eVal3;} + double eigenValue(int i) const {return (i < 2) ? eVal1 : + ( (i < 3) ? eVal2 : eVal3 ) ;} + Vec4 eventAxis(int i) const {return (i < 2) ? eVec1 : + ( (i < 3) ? eVec2 : eVec3 ) ;} + + // Provide a listing of the info. + void list(ostream& os = cout) const; + + // Tell how many events could not be analyzed. + int nError() const {return nFew + nBack;} + +private: + + // Constants: could only be changed in the code itself. + static const int NSTUDYMIN, TIMESTOPRINT; + static const double P2MIN, EIGENVALUEMIN; + + // Properties of analysis. + double power; + int select, powerInt; + double powerMod; + + // Outcome of analysis. + double eVal1, eVal2, eVal3; + Vec4 eVec1, eVec2, eVec3; + + // Error statistics; + int nFew, nBack; + +}; + +//========================================================================== + +// Thrust class. +// This class performs thrust analysis on an event. + +class Thrust { + +public: + + // Constructor. + Thrust(int selectIn = 2) : select(selectIn), nFew(0) {} + + // Analyze event. + bool analyze(const Event& event, ostream& os = cout); + + // Return info on results of analysis. + double thrust() const {return eVal1;} + double tMajor() const {return eVal2;} + double tMinor() const {return eVal3;} + double oblateness() const {return eVal2 - eVal3;} + Vec4 eventAxis(int i) const {return (i < 2) ? eVec1 : + ( (i < 3) ? eVec2 : eVec3 ) ;} + + // Provide a listing of the info. + void list(ostream& os = cout) const; + + // Tell how many events could not be analyzed. + int nError() const {return nFew;} + +private: + + // Constants: could only be changed in the code itself. + static const int NSTUDYMIN, TIMESTOPRINT; + static const double MAJORMIN; + + // Properties of analysis. + int select; + + // Outcome of analysis. + double eVal1, eVal2, eVal3; + Vec4 eVec1, eVec2, eVec3; + + // Error statistics; + int nFew; + +}; + +//========================================================================== + +// SingleClusterJet class. +// Simple helper class to ClusterJet for a jet and its contents. + +class SingleClusterJet { + +public: + + // Constructors. + SingleClusterJet(Vec4 pJetIn = 0., int motherIn = 0) : + pJet(pJetIn), mother(motherIn), daughter(0), multiplicity(1), + isAssigned(false) {pAbs = max( PABSMIN, pJet.pAbs());} + SingleClusterJet& operator=(const SingleClusterJet& j) { if (this != &j) + { pJet = j.pJet; mother = j.mother; daughter = j.daughter; + multiplicity = j.multiplicity; pAbs = j.pAbs; + isAssigned = j.isAssigned;} return *this; } + + // Properties of jet. + // Note: mother, daughter and isAssigned only used for original + // particles, multiplicity and pTemp only for reconstructed jets. + Vec4 pJet; + int mother, daughter, multiplicity; + bool isAssigned; + double pAbs; + Vec4 pTemp; + + // Distance measures (Lund, JADE, Durham) with friend. + friend double dist2Fun(int measure, const SingleClusterJet& j1, + const SingleClusterJet& j2); + +private: + + // Constants: could only be changed in the code itself. + static const double PABSMIN; + +} ; + +//========================================================================== + +// ClusterJet class. +// This class performs a jet clustering according to different +// distance measures: Lund, JADE or Durham. + +class ClusterJet { + +public: + + // Constructor. + ClusterJet(string measureIn = "Lund", int selectIn = 2, int massSetIn = 2, + bool preclusterIn = false, bool reassignIn = false) : measure(1), + select(selectIn), massSet(massSetIn), doPrecluster(preclusterIn), + doReassign(reassignIn), nFew(0) { + char firstChar = toupper(measureIn[0]); + if (firstChar == 'J') measure = 2; + if (firstChar == 'D') measure = 3; + } + + // Analyze event. + bool analyze(const Event& event, double yScaleIn, double pTscaleIn, + int nJetMinIn = 1, int nJetMaxIn = 0, ostream& os = cout); + + // Return info on jets produced. + int size() const {return jets.size();} + Vec4 p(int i) const {return jets[i].pJet;} + + // Return belonging of particle to one of the jets (-1 if none). + int jetAssignment(int i) const { + for (int iP = 0; iP < int(particles.size()); ++iP) + if (particles[iP].mother == i) return particles[iP].daughter; + return -1;} + + // Provide a listing of the info. + void list(ostream& os = cout) const; + + // Return info on clustering values. + int distanceSize() const {return distances.size();} + double distance(int i) const { + return (i < distanceSize()) ? distances[i] : 0.; } + + // Tell how many events could not be analyzed. + int nError() const {return nFew;} + +private: + + // Constants: could only be changed in the code itself. + static const int TIMESTOPRINT; + static const double PIMASS, PABSMIN, PRECLUSTERFRAC, PRECLUSTERSTEP; + + // Properties of analysis. + int measure, select, massSet; + bool doPrecluster, doReassign; + double yScale, pTscale; + int nJetMin, nJetMax; + + // Temporary results. + double piMass, dist2Join, dist2BigMin, distPre, dist2Pre; + vector particles; + int nParticles; + + // Error statistics; + int nFew; + + // Member functions for some operations (for clarity). + void precluster(); + void reassign(); + + // Outcome of analysis: ET-ordered list of jets. + vector jets; + + // Outcome of analysis: the distance values where the jets were merged. + deque distances; + +}; + +//========================================================================== + +// SingleCell class. +// Simple helper class to CellJet for a cell and its contents. + +class SingleCell { + +public: + + // Constructor. + SingleCell(int iCellIn = 0, double etaCellIn = 0., double phiCellIn = 0., + double eTcellIn = 0., int multiplicityIn = 0) : iCell(iCellIn), + etaCell(etaCellIn), phiCell(phiCellIn), eTcell(eTcellIn), + multiplicity(multiplicityIn), canBeSeed(true), isUsed(false), + isAssigned(false) {} + + // Properties of cell. + int iCell; + double etaCell, phiCell, eTcell; + int multiplicity; + bool canBeSeed, isUsed, isAssigned; + +} ; + +//========================================================================== + +// SingleCellJet class. +// Simple helper class to CellJet for a jet and its contents. + +class SingleCellJet { + +public: + + // Constructor. + SingleCellJet(double eTjetIn = 0., double etaCenterIn = 0., + double phiCenterIn = 0., double etaWeightedIn = 0., + double phiWeightedIn = 0., int multiplicityIn = 0, + Vec4 pMassiveIn = 0.) : eTjet(eTjetIn), etaCenter(etaCenterIn), + phiCenter(phiCenterIn), etaWeighted(etaWeightedIn), + phiWeighted(phiWeightedIn), multiplicity(multiplicityIn), + pMassive(pMassiveIn) {} + + // Properties of jet. + double eTjet, etaCenter, phiCenter, etaWeighted, phiWeighted; + int multiplicity; + Vec4 pMassive; + +} ; + +//========================================================================== + +// CellJet class. +// This class performs a cone jet search in (eta, phi, E_T) space. + +class CellJet { + +public: + + // Constructor. + CellJet(double etaMaxIn = 5., int nEtaIn = 50, int nPhiIn = 32, + int selectIn = 2, int smearIn = 0, double resolutionIn = 0.5, + double upperCutIn = 2., double thresholdIn = 0., Rndm* rndmPtrIn = 0) + : etaMax(etaMaxIn), nEta(nEtaIn), nPhi(nPhiIn), select(selectIn), + smear(smearIn), resolution(resolutionIn), upperCut(upperCutIn), + threshold(thresholdIn), nFew(0), rndmPtr(rndmPtrIn) { } + + // Analyze event. + bool analyze(const Event& event, double eTjetMinIn = 20., + double coneRadiusIn = 0.7, double eTseedIn = 1.5, ostream& os = cout); + + // Return info on results of analysis. + int size() const {return jets.size();} + double eT(int i) const {return jets[i].eTjet;} + double etaCenter(int i) const {return jets[i].etaCenter;} + double phiCenter(int i) const {return jets[i].phiCenter;} + double etaWeighted(int i) const {return jets[i].etaWeighted;} + double phiWeighted(int i) const {return jets[i].phiWeighted;} + int multiplicity(int i) const {return jets[i].multiplicity;} + Vec4 pMassless(int i) const {return jets[i].eTjet * Vec4( + cos(jets[i].phiWeighted), sin(jets[i].phiWeighted), + sinh(jets[i].etaWeighted), cosh(jets[i].etaWeighted) );} + Vec4 pMassive(int i) const {return jets[i].pMassive;} + double m(int i) const {return jets[i].pMassive.mCalc();} + + // Provide a listing of the info. + void list(ostream& os = cout) const; + + // Tell how many events could not be analyzed: so far never. + int nError() const {return nFew;} + +private: + + // Constants: could only be changed in the code itself. + static const int TIMESTOPRINT; + + // Properties of analysis. + double etaMax; + int nEta, nPhi, select, smear; + double resolution, upperCut, threshold; + double eTjetMin, coneRadius, eTseed; + + // Error statistics; + int nFew; + + // Outcome of analysis: ET-ordered list of jets. + vector jets; + + // Pointer to the random number generator (needed for energy smearing). + Rndm* rndmPtr; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // end Pythia8_Analysis_H + diff --git a/PYTHIA8/pythia8140/include/Basics.h b/PYTHIA8/pythia8140/include/Basics.h new file mode 100644 index 00000000000..c35338c0d19 --- /dev/null +++ b/PYTHIA8/pythia8140/include/Basics.h @@ -0,0 +1,404 @@ +// Basics.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for basic, often-used helper classes. +// RndmEngine: base class for external random number generators. +// Rndm: random number generator. +// Vec4: simple four-vectors. +// RotBstMatrix: matrices encoding rotations and boosts of Vec4 objects. +// Hist: simple one-dimensional histograms. + +#ifndef Pythia8_Basics_H +#define Pythia8_Basics_H + +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// RndmEngine is the base class for external random number generators. +// There is only one pure virtual method, that should do the generation. + +class RndmEngine { + +public: + + // A pure virtual method, wherein the derived class method + // generates a random number uniformly distributed between 1 and 1. + virtual double flat() = 0; + +protected: + + // Destructor. + virtual ~RndmEngine() {} + +}; + +//========================================================================== + +// Rndm class. +// This class handles random number generation according to the +// Marsaglia-Zaman-Tsang algorithm. + +class Rndm { + +public: + + // Constructors. + Rndm() : initRndm(false), seedSave(0), sequence(0), + useExternalRndm(false), rndmEngPtr(0) { } + Rndm(int seedIn) : initRndm(false), seedSave(0), sequence(0), + useExternalRndm(false), rndmEngPtr(0) { init(seedIn);} + + // Possibility to pass in pointer for external random number generation. + bool rndmEnginePtr( RndmEngine* rndmEngPtrIn); + + // Initialize, normally at construction or in first call. + void init(int seedIn = 0) ; + + // Generate next random number uniformly between 0 and 1. + double flat() ; + + // Generate random numbers according to exp(-x). + double exp() { return -log(flat()) ;} + + // Generate random numbers according to x * exp(-x). + double xexp() { return -log(flat() * flat()) ;} + + // Generate random numbers according to exp(-x^2/2). + double gauss() {return sqrt(-2. * log(flat())) * cos(M_PI * flat());} + + // Generate two random numbers according to exp(-x^2/2-y^2/2). + pair gauss2() {double r = sqrt(-2. * log(flat())); + double phi = 2. * M_PI * flat(); + return pair(r * sin(phi), r * cos(phi));} + + // Pick one option among vector of (positive) probabilities. + int pick(const vector& prob) ; + + // Save or read current state to or from a binary file. + bool dumpState(string fileName); + bool readState(string fileName); + +private: + + // Default random number sequence. + static const int DEFAULTSEED; + + // State of the random number generator. + bool initRndm; + int i97, j97, defaultSeed, seedSave; + long sequence; + double u[97], c, cd, cm; + + // Pointer for external random number generation. + bool useExternalRndm; + RndmEngine* rndmEngPtr; + +}; + +//========================================================================== + +// Forward reference to RotBstMatrix class. +class RotBstMatrix; + +//========================================================================== + +// Vec4 class. +// This class implements four-vectors, in energy-momentum space. +// (But can equally well be used to hold space-time four-vectors.) + +class Vec4 { + +public: + + // Constructors. + Vec4(double xIn = 0., double yIn = 0., double zIn = 0., double tIn = 0.) + : xx(xIn), yy(yIn), zz(zIn), tt(tIn) { } + Vec4(const Vec4& v) : xx(v.xx), yy(v.yy), zz(v.zz), tt(v.tt) { } + Vec4& operator=(const Vec4& v) { if (this != &v) { xx = v.xx; yy = v.yy; + zz = v.zz; tt = v.tt; } return *this; } + Vec4& operator=(double value) { xx = value; yy = value; zz = value; + tt = value; return *this; } + + // Member functions for input. + void reset() {xx = 0.; yy = 0.; zz = 0.; tt = 0.;} + void p(double xIn, double yIn, double zIn, double tIn) + {xx = xIn; yy = yIn; zz = zIn; tt = tIn;} + void p(Vec4 pIn) {xx = pIn.xx; yy = pIn.yy; zz = pIn.zz; tt = pIn.tt;} + void px(double xIn) {xx = xIn;} + void py(double yIn) {yy = yIn;} + void pz(double zIn) {zz = zIn;} + void e(double tIn) {tt = tIn;} + + // Member functions for output. + double px() const {return xx;} + double py() const {return yy;} + double pz() const {return zz;} + double e() const {return tt;} + double mCalc() const {double temp = tt*tt - xx*xx - yy*yy - zz*zz; + return (temp >= 0.) ? sqrt(temp) : -sqrt(-temp);} + double m2Calc() const {return tt*tt - xx*xx - yy*yy - zz*zz;} + double pT() const {return sqrt(xx*xx + yy*yy);} + double pT2() const {return xx*xx + yy*yy;} + double pAbs() const {return sqrt(xx*xx + yy*yy + zz*zz);} + double pAbs2() const {return xx*xx + yy*yy + zz*zz;} + double eT() const {double temp = xx*xx + yy*yy; + return tt * sqrt( temp / (temp + zz*zz) );} + double eT2() const {double temp = xx*xx + yy*yy; + return tt*tt * temp / (temp + zz*zz);} + double theta() const {return atan2(sqrt(xx*xx + yy*yy), zz);} + double phi() const {return atan2(yy,xx);} + double thetaXZ() const {return atan2(xx,zz);} + double pPos() const {return tt + zz;} + double pNeg() const {return tt - zz;} + + // Member functions that perform operations. + void rescale3(double fac) {xx *= fac; yy *= fac; zz *= fac;} + void rescale4(double fac) {xx *= fac; yy *= fac; zz *= fac; tt *= fac;} + void flip3() {xx = -xx; yy = -yy; zz = -zz;} + void flip4() {xx = -xx; yy = -yy; zz = -zz; tt = -tt;} + void rot(double thetaIn, double phiIn); + void rotaxis(double phiIn, double nx, double ny, double nz); + void rotaxis(double phiIn, const Vec4& n); + void bst(double betaX, double betaY, double betaZ); + void bst(double betaX, double betaY, double betaZ, double gamma); + void bst(const Vec4& pIn); + void bst(const Vec4& pIn, double mIn); + void bstback(const Vec4& pIn); + void bstback(const Vec4& pIn, double mIn); + void rotbst(const RotBstMatrix& M); + + // Operator overloading with member functions + Vec4 operator-() {Vec4 tmp; tmp.xx = -xx; tmp.yy = -yy; tmp.zz = -zz; + tmp.tt = -tt; return tmp;} + Vec4& operator+=(const Vec4& v) {xx += v.xx; yy += v.yy; zz += v.zz; + tt += v.tt; return *this;} + Vec4& operator-=(const Vec4& v) {xx -= v.xx; yy -= v.yy; zz -= v.zz; + tt -= v.tt; return *this;} + Vec4& operator*=(double f) {xx *= f; yy *= f; zz *= f; + tt *= f; return *this;} + Vec4& operator/=(double f) {xx /= f; yy /= f; zz /= f; + tt /= f; return *this;} + + // Operator overloading with friends + friend Vec4 operator+(const Vec4& v1, const Vec4& v2); + friend Vec4 operator-(const Vec4& v1, const Vec4& v2); + friend Vec4 operator*(double f, const Vec4& v1); + friend Vec4 operator*(const Vec4& v1, double f); + friend Vec4 operator/(const Vec4& v1, double f); + friend double operator*(const Vec4& v1, const Vec4& v2); + + // Invariant mass of a pair and its square. + friend double m(const Vec4& v1, const Vec4& v2); + friend double m2(const Vec4& v1, const Vec4& v2); + + // Scalar and cross product of 3-vector parts. + friend double dot3(const Vec4& v1, const Vec4& v2); + friend Vec4 cross3(const Vec4& v1, const Vec4& v2); + + // theta is polar angle between v1 and v2. + friend double theta(const Vec4& v1, const Vec4& v2); + friend double costheta(const Vec4& v1, const Vec4& v2); + + // phi is azimuthal angle between v1 and v2 around z axis. + friend double phi(const Vec4& v1, const Vec4& v2); + friend double cosphi(const Vec4& v1, const Vec4& v2); + + // phi is azimuthal angle between v1 and v2 around n axis. + friend double phi(const Vec4& v1, const Vec4& v2, const Vec4& n); + friend double cosphi(const Vec4& v1, const Vec4& v2, const Vec4& n); + + // Print a four-vector + friend ostream& operator<<(ostream&, const Vec4& v) ; + +private: + + // Constants: could only be changed in the code itself. + static const double TINY; + + // The four-vector data members. + double xx, yy, zz, tt; + +}; + +// Implementation of operator overloading with friends. + +inline Vec4 operator+(const Vec4& v1, const Vec4& v2) + {Vec4 v = v1 ; return v += v2;} + +inline Vec4 operator-(const Vec4& v1, const Vec4& v2) + {Vec4 v = v1 ; return v -= v2;} + +inline Vec4 operator*(double f, const Vec4& v1) + {Vec4 v = v1; return v *= f;} + +inline Vec4 operator*(const Vec4& v1, double f) + {Vec4 v = v1; return v *= f;} + +inline Vec4 operator/(const Vec4& v1, double f) + {Vec4 v = v1; return v /= f;} + +inline double operator*(const Vec4& v1, const Vec4& v2) + {return v1.tt*v2.tt - v1.xx*v2.xx - v1.yy*v2.yy - v1.zz*v2.zz;} + +//========================================================================== + +// RotBstMatrix class. +// This class implements 4 * 4 matrices that encode an arbitrary combination +// of rotations and boosts, that can be applied to Vec4 four-vectors. + +class RotBstMatrix { + +public: + + // Constructors. + RotBstMatrix() {for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) + { M[i][j] = (i==j) ? 1. : 0.; } } } + RotBstMatrix(const RotBstMatrix& Min) { + for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) { + M[i][j] = Min.M[i][j]; } } } + RotBstMatrix& operator=(const RotBstMatrix& Min) {if (this != &Min) { + for (int i = 0; i < 4; ++i) { for (int j = 0; j < 4; ++j) { + M[i][j] = Min.M[i][j]; } } } return *this; } + + // Member functions. + void rot(double = 0., double = 0.); + void rot(const Vec4& p); + void bst(double = 0., double = 0., double = 0.); + void bst(const Vec4&); + void bstback(const Vec4&); + void bst(const Vec4&, const Vec4&); + void toCMframe(const Vec4&, const Vec4&); + void fromCMframe(const Vec4&, const Vec4&); + void rotbst(const RotBstMatrix&); + void invert(); + void reset(); + + // Crude estimate deviation from unit matrix. + double deviation() const; + + // Print a transformation matrix. + friend ostream& operator<<(ostream&, const RotBstMatrix&) ; + + // Private members to be accessible from Vec4. + friend class Vec4; + +private: + + // Constants: could only be changed in the code itself. + static const double TINY; + + // The rotation-and-boost matrix data members. + double M[4][4]; + +}; + +//========================================================================== + +// Hist class. +// This class handles a single histogram at a time. + +class Hist{ + +public: + + // Constructors, including copy constructors. + Hist() {;} + Hist(string titleIn, int nBinIn = 100, double xMinIn = 0., + double xMaxIn = 1.) { + book(titleIn, nBinIn, xMinIn, xMaxIn);} + Hist(const Hist& h) + : title(h.title), nBin(h.nBin), nFill(h.nFill), xMin(h.xMin), + xMax(h.xMax), dx(h.dx), under(h.under), inside(h.inside), + over(h.over), res(h.res) { } + Hist(string titleIn, const Hist& h) + : title(titleIn), nBin(h.nBin), nFill(h.nFill), xMin(h.xMin), + xMax(h.xMax), dx(h.dx), under(h.under), inside(h.inside), + over(h.over), res(h.res) { } + Hist& operator=(const Hist& h) { if(this != &h) { + nBin = h.nBin; nFill = h.nFill; xMin = h.xMin; xMax = h.xMax; + dx = h.dx; under = h.under; inside = h.inside; over = h.over; + res = h.res; } return *this; } + + // Book a histogram. + void book(string titleIn = " ", int nBinIn = 100, double xMinIn = 0., + double xMaxIn = 1.) ; + + // Set title of a histogram. + void name(string titleIn = " ") {title = titleIn; } + + // Reset bin contents. + void null() ; + + // Fill bin with weight. + void fill(double x, double w = 1.) ; + + // Print a histogram with overloaded << operator. + friend ostream& operator<<(ostream& os, const Hist& h) ; + + // Print histogram contents as a table (e.g. for Gnuplot). + void table(ostream& os = cout) const ; + void table(string fileName) const { + ofstream streamName(fileName.c_str()); table(streamName); } + + + // Return content of specific bin: -1 gives underflow and nBin overflow. + double getBinContent(int iBin) ; + + // Return number of entries + int getEntries() {return nFill; } + + // Check whether another histogram has same size and limits. + bool sameSize(const Hist& h) const ; + + // Take logarithm (base 10 or e) of bin contents. + void takeLog(bool tenLog = true) ; + + // Operator overloading with member functions + Hist& operator+=(const Hist& h) ; + Hist& operator-=(const Hist& h) ; + Hist& operator*=(const Hist& h) ; + Hist& operator/=(const Hist& h) ; + Hist& operator+=(double f) ; + Hist& operator-=(double f) ; + Hist& operator*=(double f) ; + Hist& operator/=(double f) ; + + // Operator overloading with friends + friend Hist operator+(double f, const Hist& h1); + friend Hist operator+(const Hist& h1, double f); + friend Hist operator+(const Hist& h1, const Hist& h2); + friend Hist operator-(double f, const Hist& h1); + friend Hist operator-(const Hist& h1, double f); + friend Hist operator-(const Hist& h1, const Hist& h2); + friend Hist operator*(double f, const Hist& h1); + friend Hist operator*(const Hist& h1, double f); + friend Hist operator*(const Hist& h1, const Hist& h2); + friend Hist operator/(double f, const Hist& h1); + friend Hist operator/(const Hist& h1, double f); + friend Hist operator/(const Hist& h1, const Hist& h2); + +private: + + // Constants: could only be changed in the code itself. + static const int NBINMAX, NCOLMAX, NLINES; + static const double TOLERANCE, TINY, SMALLFRAC, DYAC[]; + static const char NUMBER[]; + + // Properties and contents of a histogram. + string title; + int nBin, nFill; + double xMin, xMax, dx, under, inside, over; + vector res; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // end Pythia8_Basics_H diff --git a/PYTHIA8/pythia8140/include/BeamParticle.h b/PYTHIA8/pythia8140/include/BeamParticle.h new file mode 100644 index 00000000000..947e7c9600a --- /dev/null +++ b/PYTHIA8/pythia8140/include/BeamParticle.h @@ -0,0 +1,305 @@ +// BeamParticle.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for information on incoming beams. +// ResolvedParton: an initiator or remnant in beam. +// BeamParticle: contains partons, parton densities, etc. + +#ifndef Pythia8_BeamParticle_H +#define Pythia8_BeamParticle_H + +#include "Basics.h" +#include "Event.h" +#include "FragmentationFlavZpT.h" +#include "Info.h" +#include "ParticleData.h" +#include "PartonDistributions.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// This class holds info on a parton resolved inside the incoming beam, +// i.e. either an initiator (part of a hard or a multiple interaction) +// or a remnant (part of the beam remnant treatment). + +// The companion code is -1 from onset and for g, is -2 for an unmatched +// sea quark, is >= 0 for a matched sea quark, with the number giving the +// companion position, and is -3 for a valence quark. + +// Rescattering partons properly do not belong here, but bookkeeping is +// simpler with them, so they are stored with companion code -10. + +class ResolvedParton { + +public: + + // Constructor. + ResolvedParton( int iPosIn = 0, int idIn = 0, double xIn = 0., + int companionIn = -1) : iPosRes(iPosIn), idRes(idIn), xRes(xIn), + companionRes(companionIn), xqCompRes(0.), mRes(0.), factorRes(1.), + colRes(0), acolRes(0) { } + + // Set info on initiator or remnant parton. + void iPos( int iPosIn) {iPosRes = iPosIn;} + void id( int idIn) {idRes = idIn;} + void x( double xIn) {xRes = xIn;} + void update( int iPosIn, int idIn, double xIn) {iPosRes = iPosIn; + idRes = idIn; xRes = xIn;} + void companion( int companionIn) {companionRes = companionIn;} + void xqCompanion( double xqCompIn) {xqCompRes = xqCompIn;} + void p(Vec4 pIn) {pRes = pIn;} + void px(double pxIn) {pRes.px(pxIn);} + void py(double pyIn) {pRes.py(pyIn);} + void pz(double pzIn) {pRes.pz(pzIn);} + void e(double eIn) {pRes.e(eIn);} + void m(double mIn) {mRes = mIn;} + void col(int colIn) {colRes = colIn;} + void acol(int acolIn) {acolRes = acolIn;} + void cols(int colIn = 0,int acolIn = 0) + {colRes = colIn; acolRes = acolIn;} + void scalePT( double factorIn) {pRes.px(factorIn * pRes.px()); + pRes.py(factorIn * pRes.py()); factorRes *= factorIn;} + void scaleX( double factorIn) {xRes *= factorIn;} + + // Get info on initiator or remnant parton. + int iPos() const {return iPosRes;} + int id() const {return idRes;} + double x() const {return xRes;} + int companion() const {return companionRes;} + bool isValence() const {return (companionRes == -3);} + bool isUnmatched() const {return (companionRes == -2);} + bool isCompanion() const {return (companionRes >= 0);} + bool isFromBeam() const {return (companionRes > -10);} + double xqCompanion() const {return xqCompRes;} + Vec4 p() const {return pRes;} + double px() const {return pRes.px();} + double py() const {return pRes.py();} + double pz() const {return pRes.pz();} + double e() const {return pRes.e();} + double m() const {return mRes;} + double pT() const {return pRes.pT();} + double mT2() const {return (mRes >= 0.) + ? mRes*mRes + pRes.pT2() : - mRes*mRes + pRes.pT2();} + double pPos() const {return pRes.e() + pRes.pz();} + double pNeg() const {return pRes.e() - pRes.pz();} + int col() const {return colRes;} + int acol() const {return acolRes;} + double pTfactor() const {return factorRes;} + +private: + + // Properties of a resolved parton. + int iPosRes, idRes; + double xRes; + // Companion code and distribution value, if any. + int companionRes; + double xqCompRes; + // Four-momentum and mass; for remnant kinematics construction. + Vec4 pRes; + double mRes, factorRes; + // Colour codes. + int colRes, acolRes; + +}; + +//========================================================================== + +// This class holds info on a beam particle in the evolution of +// initial-state radiation and multiple interactions. + +class BeamParticle { + +public: + + // Constructor. + BeamParticle() : nInit(0) {Q2ValFracSav = -1.;} + + // Initialize data on a beam particle and save pointers. + void init( int idIn, double pzIn, double eIn, double mIn, + Info* infoPtrIn, Settings& settings, ParticleData* particleDataPtrIn, + Rndm* rndmPtrIn, PDF* pdfInPtr, PDF* pdfHardInPtr, bool isUnresolvedIn, + StringFlav* flavSelPtrIn); + + // For mesons like pi0 valence content varies from event to event. + void newValenceContent(); + + // Set new pZ and E, but keep the rest the same. + void newPzE( double pzIn, double eIn) {pBeam = Vec4( 0., 0., pzIn, eIn);} + + // Member functions for output. + int id() const {return idBeam;} + Vec4 p() const {return pBeam;} + double px() const {return pBeam.px();} + double py() const {return pBeam.py();} + double pz() const {return pBeam.pz();} + double e() const {return pBeam.e();} + double m() const {return mBeam;} + bool isLepton() const {return isLeptonBeam;} + bool isUnresolved() const {return isUnresolvedBeam;} + // As hadrons here we only count those we know how to handle remnants for. + bool isHadron() const {return isHadronBeam;} + bool isMeson() const {return isMesonBeam;} + bool isBaryon() const {return isBaryonBeam;} + + // Maximum x remaining after previous MI and ISR, plus safety margin. + double xMax(int iSkip = -1); + + // Special hard-process parton distributions (can agree with standard ones). + double xfHard(int idIn, double x, double Q2) + {return pdfHardBeamPtr->xf(idIn, x, Q2);} + + // Standard parton distributions. + double xf(int idIn, double x, double Q2) + {return pdfBeamPtr->xf(idIn, x, Q2);} + + // Ditto, split into valence and sea parts (where gluon counts as sea). + double xfVal(int idIn, double x, double Q2) + {return pdfBeamPtr->xfVal(idIn, x, Q2);} + double xfSea(int idIn, double x, double Q2) + {return pdfBeamPtr->xfSea(idIn, x, Q2);} + + // Rescaled parton distributions, as needed for MI and ISR. + // For ISR also allow split valence/sea, and only return relevant part. + double xfMI(int idIn, double x, double Q2) + {return xfModified(-1, idIn, x, Q2);} + double xfISR(int indexMI, int idIn, double x, double Q2) + {return xfModified( indexMI, idIn, x, Q2);} + + // Decide whether chosen quark is valence, sea or companion. + int pickValSeaComp(); + + // Initialize kind of incoming beam particle. + void initBeamKind(); + + // Overload index operator to access a resolved parton from the list. + ResolvedParton& operator[](int i) {return resolved[i];} + + // Total number of partons extracted from beam, and initiators only. + int size() const {return resolved.size();} + int sizeInit() const {return nInit;} + + // Clear list of resolved partons. + void clear() {resolved.resize(0); nInit = 0;} + + // Add a resolved parton to list. + int append( int iPos, int idIn, double x, int companion = -1) + {resolved.push_back( ResolvedParton( iPos, idIn, x, companion) ); + return resolved.size() - 1;} + + // Print extracted parton list; for debug mainly. + void list(ostream& os = cout) const; + + // How many different flavours, and how many quarks of given flavour. + int nValenceKinds() const {return nValKinds;} + int nValence(int idIn) const {for (int i = 0; i < nValKinds; ++i) + if (idIn == idVal[i]) return nVal[i]; return 0;} + + // Test whether a lepton is to be considered as unresolved. + bool isUnresolvedLepton(); + + // Add extra remnant flavours to make valence and sea come out right. + bool remnantFlavours(Event& event); + + // Correlate all initiators and remnants to make a colour singlet. + bool remnantColours(Event& event, vector& colFrom, + vector& colTo); + + // Pick unrescaled x of remnant parton (valence or sea). + double xRemnant(int i); + + // Tell whether a junction has been resolved, and its junction colours. + bool hasJunction() const {return hasJunctionBeam;} + int junctionCol(int i) const {return junCol[i];} + void junctionCol(int i, int col) {junCol[i] = col;} + + // For a diffractive system, decide whether to kick out gluon or quark. + bool pickGluon(double mDiff); + + // Pick a valence quark at random, and provide the remaining flavour. + int pickValence(); + int pickRemnant() const {return idVal2;} + + // Share lightcone momentum between two remnants in a diffractive system. + // At the same time generate a relative pT for the two. + double zShare( double mDiff, double m1, double m2); + double pxShare() const {return pxRel;} + double pyShare() const {return pyRel;} + +private: + + // Constants: could only be changed in the code itself. + static const double XMINUNRESOLVED; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to PDF sets. + PDF* pdfBeamPtr; + PDF* pdfHardBeamPtr; + + // Pointer to class for flavour generation. + StringFlav* flavSelPtr; + + // Initialization data, normally only set once. + bool allowJunction; + int maxValQuark, companionPower; + double valencePowerMeson, valencePowerUinP, valencePowerDinP, + valenceDiqEnhance, pickQuarkNorm, pickQuarkPower, + diffPrimKTwidth, diffLargeMassSuppress; + + // Basic properties of a beam particle. + int idBeam, idBeamAbs; + Vec4 pBeam; + double mBeam; + // Beam kind. Valence flavour content for hadrons. + bool isLeptonBeam, isUnresolvedBeam, isHadronBeam, isMesonBeam, + isBaryonBeam; + int nValKinds, idVal[3], nVal[3]; + + // Current parton density, by valence, sea and companion. + int idSave, iSkipSave, nValLeft[3]; + double xqgTot, xqVal, xqgSea, xqCompSum; + + // The list of resolved partons. + vector resolved; + + // Status after all initiators have been accounted for. Junction content. + int nInit; + bool hasJunctionBeam; + int junCol[3]; + + // Routine to calculate pdf's given previous interactions. + double xfModified( int iSkip, int idIn, double x, double Q2); + + // Fraction of hadron momentum sitting in a valence quark distribution. + double xValFrac(int j, double Q2); + double Q2ValFracSav, uValInt, dValInt; + + // Fraction of hadron momentum sitting in a companion quark distribution. + double xCompFrac(double xs); + + // Value of companion quark PDF, also given the sea quark x. + double xCompDist(double xc, double xs); + + // Valence quark subdivision for diffractive systems. + int idVal1, idVal2, idVal3; + double zRel, pxRel, pyRel; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_BeamParticle_H diff --git a/PYTHIA8/pythia8140/include/BeamRemnants.h b/PYTHIA8/pythia8140/include/BeamRemnants.h new file mode 100644 index 00000000000..af7be2fd48f --- /dev/null +++ b/PYTHIA8/pythia8140/include/BeamRemnants.h @@ -0,0 +1,96 @@ +// BeamRemnants.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for beam-remnants handling. +// BeamRemnants: matches the remnants between the two beams. + +#ifndef Pythia8_BeamRemnants_H +#define Pythia8_BeamRemnants_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Event.h" +#include "FragmentationFlavZpT.h" +#include "Info.h" +#include "ParticleData.h" +#include "PartonDistributions.h" +#include "PartonSystems.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// This class matches the kinematics of the hard-scattering subsystems +// (with primordial kT added) to that of the two beam remnants. + +class BeamRemnants { + +public: + + // Constructor. + BeamRemnants() { } + + // Initialization. + bool init( Info* infoPtrIn, Settings& settings, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + PartonSystems* partonSystemsPtrIn); + + // New beams possible for handling of hard diffraction. + void reassignBeamPtrs( BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn) + {beamAPtr = beamAPtrIn; beamBPtr = beamBPtrIn;} + + // Select the flavours/kinematics/colours of the two beam remnants. + bool add( Event& event); + +private: + + // Constants: could only be changed in the code itself. + static const bool ALLOWCOLOURTWICE, CORRECTMISMATCH; + static const int NTRYCOLMATCH, NTRYKINMATCH; + + // Initialization data, read from Settings. + bool doPrimordialKT, allowRescatter, doRescatterRestoreY, doReconnect; + double primordialKTsoft, primordialKThard, primordialKTremnant, + halfScaleForKT, halfMassForKT, reconnectRange, + pT0Ref, ecmRef, ecmPow; + + // Information set for events. + int nSys, oldSize; + double eCM, sCM, pT0, pT20Rec; + + // Colour collapses (when one colour is mapped onto another). + vector colFrom, colTo; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to the two incoming beams. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + + // Pointer to information on subcollision parton locations. + PartonSystems* partonSystemsPtr; + + // Do the kinematics of the collision subsystems and two beam remnants. + bool setKinematics( Event& event); + + // Allow colour reconnections. + bool reconnectColours( Event& event); + + // Check that colours are consistent. + bool checkColours( Event& event); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_BeamRemnants_H diff --git a/PYTHIA8/pythia8140/include/BeamShape.h b/PYTHIA8/pythia8140/include/BeamShape.h new file mode 100644 index 00000000000..d89e861ff8c --- /dev/null +++ b/PYTHIA8/pythia8140/include/BeamShape.h @@ -0,0 +1,64 @@ +// BeamShape.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header for classes to set beam momentum and interaction vertex spread. + +#ifndef Pythia8_BeamShape_H +#define Pythia8_BeamShape_H + +#include "Basics.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// Base class to set beam momentum and interaction spot spread. + +class BeamShape { + +public: + + // Constructor. + BeamShape() {} + + // Destructor. + virtual ~BeamShape() {} + + // Initialize beam parameters. + virtual void init( Settings& settings, Rndm* rndmPtrIn); + + // Set the two beam momentum deviations and the beam vertex. + virtual void pick(); + + // Methods to read out the choice made with the above method. + Vec4 deltaPA() const {return Vec4( deltaPxA, deltaPyA, deltaPzA, 0);} + Vec4 deltaPB() const {return Vec4( deltaPxB, deltaPyB, deltaPzB, 0);} + Vec4 vertex() const {return Vec4( vertexX, vertexY, vertexZ, vertexT);} + +protected: + + // Values to be set. + double deltaPxA, deltaPyA, deltaPzA, deltaPxB, deltaPyB, deltaPzB, + vertexX, vertexY, vertexZ, vertexT; + + // Parameters of Gaussian parametrizations. + bool allowMomentumSpread, allowVertexSpread; + double sigmaPxA, sigmaPyA, sigmaPzA, maxDevA, sigmaPxB, sigmaPyB, + sigmaPzB, maxDevB, sigmaVertexX, sigmaVertexY, sigmaVertexZ, + maxDevVertex, sigmaTime, maxDevTime, offsetX, offsetY, + offsetZ, offsetT; + + // Pointer to the random number generator. + Rndm* rndmPtr; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_BeamShape_H diff --git a/PYTHIA8/pythia8140/include/BoseEinstein.h b/PYTHIA8/pythia8140/include/BoseEinstein.h new file mode 100644 index 00000000000..48f0f439789 --- /dev/null +++ b/PYTHIA8/pythia8140/include/BoseEinstein.h @@ -0,0 +1,92 @@ +// Bose-Einstein.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the classes to handle Bose-Einstein effects. +// BoseEinsteinHadron: simple working container for particle momenta. +// BoseEinstein: main class to perform the task. + +#ifndef Pythia8_BoseEinstein_H +#define Pythia8_BoseEinstein_H + +#include "Basics.h" +#include "Event.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// The BoseEinsteinHadron class is a simple container for studied hadrons. + +class BoseEinsteinHadron { + +public: + + // Constructors. + BoseEinsteinHadron() : id(0), iPos(0), p(0.), pShift(0.), pComp(0.), + m2(0.) {} + BoseEinsteinHadron(int idIn, int iPosIn, Vec4 pIn, double mIn) : + id(idIn), iPos(iPosIn), p(pIn), pShift(0.), pComp(0.) {m2 = mIn*mIn;} + + // Information on hadron - all public. + int id, iPos; + Vec4 p, pShift, pComp; + double m2; + +}; + +//========================================================================== + +// The BoseEinstein class shifts the momenta of identical particles relative +// to each other, to simulate Bose-Einstein effects to some approximation. + +class BoseEinstein { + +public: + + // Constructor. + BoseEinstein() {} + + // Find settings. Precalculate table used to find momentum shifts. + bool init(Info* infoPtrIn, Settings& settings, ParticleData& particleData); + + // Perform Bose-Einstein corrections on an event. + bool shiftEvent( Event& event); + +private: + + // Constants: could only be changed in the code itself. + static const int IDHADRON[9], ITABLE[9], NCOMPSTEP; + static const double STEPSIZE, Q2MIN, COMPRELERR, COMPFACMAX; + + // Initialization data, read from Settings. + bool doPion, doKaon, doEta; + double lambda, QRef; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Table of momentum shifts for different hadron species. + int nStep[4], nStep3[4], nStored[10]; + double QRef2, QRef3, R2Ref, R2Ref2, R2Ref3, mHadron[9], + mPair[4], m2Pair[4], deltaQ[4], deltaQ3[4], maxQ[4], maxQ3[4]; + double shift[4][200], shift3[4][200]; + + // Vector of hadrons to study. + vector hadronBE; + + // Calculate shift and (unnormalized) compensation for pair. + void shiftPair(int i1, int i2, int iHad); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_BoseEinstein_H + diff --git a/PYTHIA8/pythia8140/include/Event.h b/PYTHIA8/pythia8140/include/Event.h new file mode 100644 index 00000000000..697917bb394 --- /dev/null +++ b/PYTHIA8/pythia8140/include/Event.h @@ -0,0 +1,566 @@ +// Event.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for the Particle and Event classes. +// Particle: information on an instance of a particle. +// Junction: information on a junction between three colours. +// Event: list of particles in the current event. + +#ifndef Pythia8_Event_H +#define Pythia8_Event_H + +#include "Basics.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// Forward references to ParticleDataEntry and ResonanceWidths classes. +class ParticleDataEntry; +class ResonanceWidths; + +//========================================================================== + +// Particle class. +// This class holds info on a particle in general. + +class Particle { + +public: + + // Constructors. + Particle() : idSave(0), statusSave(0), mother1Save(0), mother2Save(0), + daughter1Save(0), daughter2Save(0), colSave(0), acolSave(0), + pSave(Vec4(0.,0.,0.,0.)), mSave(0.), scaleSave(0.), + hasVertexSave(false), vProdSave(Vec4(0.,0.,0.,0.)), tauSave(0.), + pdePtr(0), pdtPtr(0) { } + Particle(int idIn, int statusIn = 0, int mother1In = 0, + int mother2In = 0, int daughter1In = 0, int daughter2In = 0, + int colIn = 0, int acolIn = 0, double pxIn = 0., double pyIn = 0., + double pzIn = 0., double eIn = 0., double mIn = 0., double scaleIn = 0.) + : idSave(idIn), statusSave(statusIn), mother1Save(mother1In), + mother2Save(mother2In), daughter1Save(daughter1In), + daughter2Save(daughter2In), colSave(colIn), acolSave(acolIn), + pSave(Vec4(pxIn, pyIn, pzIn, eIn)), mSave(mIn), scaleSave(scaleIn), + hasVertexSave(false), vProdSave(Vec4(0.,0.,0.,0.)), tauSave(0.), + pdePtr(0), pdtPtr(0) { } + Particle(int idIn, int statusIn, int mother1In, int mother2In, + int daughter1In, int daughter2In, int colIn, int acolIn, + Vec4 pIn, double mIn = 0., double scaleIn = 0.) + : idSave(idIn), statusSave(statusIn), mother1Save(mother1In), + mother2Save(mother2In), daughter1Save(daughter1In), + daughter2Save(daughter2In), colSave(colIn), acolSave(acolIn), + pSave(pIn), mSave(mIn), scaleSave(scaleIn), hasVertexSave(false), + vProdSave(Vec4(0.,0.,0.,0.)), tauSave(0.), pdePtr(0), pdtPtr(0) { } + Particle(const Particle& pt) : idSave(pt.idSave), + statusSave(pt.statusSave), mother1Save(pt.mother1Save), + mother2Save(pt.mother2Save), daughter1Save(pt.daughter1Save), + daughter2Save(pt.daughter2Save), colSave(pt.colSave), + acolSave(pt.acolSave), pSave(pt.pSave), mSave(pt.mSave), + scaleSave(pt.scaleSave), hasVertexSave(pt.hasVertexSave), + vProdSave(pt.vProdSave), tauSave(pt.tauSave), + pdePtr(pt.pdePtr), pdtPtr(pt.pdtPtr) { } + Particle& operator=(const Particle& pt) {if (this != &pt) { + idSave = pt.idSave; statusSave = pt.statusSave; + mother1Save = pt.mother1Save; mother2Save = pt.mother2Save; + daughter1Save = pt.daughter1Save; daughter2Save = pt.daughter2Save; + colSave = pt.colSave; acolSave = pt.acolSave; pSave = pt.pSave; + mSave = pt.mSave; scaleSave = pt.scaleSave; + hasVertexSave = pt.hasVertexSave; vProdSave = pt.vProdSave; + tauSave = pt.tauSave; pdePtr = pt.pdePtr; pdtPtr = pt.pdtPtr; } + return *this; } + + // Member functions to set the ParticleData and ParticleDataEntry pointers. + void setPDTPtr(ParticleData* pdtPtrIn) { pdtPtr = pdtPtrIn; setPDEPtr();} + void setPDEPtr() {pdePtr = (pdtPtr > 0) + ? pdtPtr->particleDataEntryPtr( idSave) : 0;} + + // Member functions for input. + void id(int idIn) {idSave = idIn; setPDEPtr();} + void status(int statusIn) {statusSave = statusIn;} + void statusPos() {statusSave = abs(statusSave);} + void statusNeg() {statusSave = -abs(statusSave);} + void statusCode(int statusIn) {statusSave = + (statusSave > 0) ? abs(statusIn) : -abs(statusIn);} + void mother1(int mother1In) {mother1Save = mother1In;} + void mother2(int mother2In) {mother2Save = mother2In;} + void mothers(int mother1In = 0, int mother2In = 0) + {mother1Save = mother1In; mother2Save = mother2In;} + void daughter1(int daughter1In) {daughter1Save = daughter1In;} + void daughter2(int daughter2In) {daughter2Save = daughter2In;} + void daughters(int daughter1In = 0, int daughter2In = 0) + {daughter1Save = daughter1In; daughter2Save = daughter2In;} + void col(int colIn) {colSave = colIn;} + void acol(int acolIn) {acolSave = acolIn;} + void cols(int colIn = 0,int acolIn = 0) {colSave = colIn; + acolSave = acolIn;} + void p(Vec4 pIn) {pSave = pIn;} + void p(double pxIn, double pyIn, double pzIn, double eIn) + {pSave.p(pxIn, pyIn, pzIn, eIn);} + void px(double pxIn) {pSave.px(pxIn);} + void py(double pyIn) {pSave.py(pyIn);} + void pz(double pzIn) {pSave.pz(pzIn);} + void e(double eIn) {pSave.e(eIn);} + void m(double mIn) {mSave = mIn;} + void scale(double scaleIn) {scaleSave = scaleIn;} + void vProd(Vec4 vProdIn) {vProdSave = vProdIn; hasVertexSave = true;} + void vProd(double xProdIn, double yProdIn, double zProdIn, double tProdIn) + {vProdSave.p(xProdIn, yProdIn, zProdIn, tProdIn); hasVertexSave = true;} + void xProd(double xProdIn) {vProdSave.px(xProdIn); hasVertexSave = true;} + void yProd(double yProdIn) {vProdSave.py(yProdIn); hasVertexSave = true;} + void zProd(double zProdIn) {vProdSave.pz(zProdIn); hasVertexSave = true;} + void tProd(double tProdIn) {vProdSave.e(tProdIn); hasVertexSave = true;} + void tau(double tauIn) {tauSave = tauIn;} + + // Member functions for output. + int id() const {return idSave;} + int status() const {return statusSave;} + int mother1() const {return mother1Save;} + int mother2() const {return mother2Save;} + int daughter1() const {return daughter1Save;} + int daughter2() const {return daughter2Save;} + int col() const {return colSave;} + int acol() const {return acolSave;} + Vec4 p() const {return pSave;} + double px() const {return pSave.px();} + double py() const {return pSave.py();} + double pz() const {return pSave.pz();} + double e() const {return pSave.e();} + double m() const {return mSave;} + double scale() const {return scaleSave;} + bool hasVertex() const {return hasVertexSave;} + Vec4 vProd() const {return vProdSave;} + double xProd() const {return vProdSave.px();} + double yProd() const {return vProdSave.py();} + double zProd() const {return vProdSave.pz();} + double tProd() const {return vProdSave.e();} + double tau() const {return tauSave;} + + // Member functions for output; derived int and bool quantities. + int idAbs() const {return abs(idSave);} + int statusAbs() const {return abs(statusSave);} + bool isFinal() const {return (statusSave > 0);} + bool isRescatteredIncoming() const {return + (statusSave == -34 || statusSave == -45 || + statusSave == -46 || statusSave == -54);} + + // Member functions for output; derived double quantities. + double m2() const {return (mSave >= 0.) ? mSave*mSave + : -mSave*mSave;} + double mCalc() const {return pSave.mCalc();} + double m2Calc() const {return pSave.m2Calc();} + double eCalc() const {return sqrt(abs(m2() + pSave.pAbs2()));} + double pT() const {return pSave.pT();} + double pT2() const {return pSave.pT2();} + double mT() const {double temp = m2() + pSave.pT2(); + return (temp >= 0.) ? sqrt(temp) : -sqrt(-temp);} + double mT2() const {return m2() + pSave.pT2();} + double pAbs() const {return pSave.pAbs();} + double pAbs2() const {return pSave.pAbs2();} + double eT() const {return pSave.eT();} + double eT2() const {return pSave.eT2();} + double theta() const {return pSave.theta();} + double phi() const {return pSave.phi();} + double thetaXZ() const {return pSave.thetaXZ();} + double pPos() const {return pSave.pPos();} + double pNeg() const {return pSave.pNeg();} + double y() const; + double eta() const; + Vec4 vDec() const {return (tauSave > 0. && mSave > 0.) + ? vProdSave + tauSave * pSave / mSave : vProdSave;} + double xDec() const {return (tauSave > 0. && mSave > 0.) + ? vProdSave.px() + tauSave * pSave.px() / mSave : vProdSave.px();} + double yDec() const {return (tauSave > 0. && mSave > 0.) + ? vProdSave.py() + tauSave * pSave.py() / mSave : vProdSave.py();} + double zDec() const {return (tauSave > 0. && mSave > 0.) + ? vProdSave.pz() + tauSave * pSave.pz() / mSave : vProdSave.pz();} + double tDec() const {return (tauSave > 0. && mSave > 0.) + ? vProdSave.e() + tauSave * pSave.e() / mSave : vProdSave.e();} + + // Further output, based on a pointer to a ParticleDataEntry object. + string name() const { + return (pdePtr > 0) ? pdePtr->name(idSave) : " ";} + string nameWithStatus(int maxLen = 20) const; + int spinType() const { + return (pdePtr > 0) ? pdePtr->spinType() : 0;} + int chargeType() const { + return (pdePtr > 0) ? pdePtr->chargeType(idSave) : 0;} + double charge() const { + return (pdePtr > 0) ? pdePtr->charge(idSave) : 0;} + bool isCharged() const { + return (pdePtr > 0) ? (pdePtr->chargeType(idSave) != 0) : false;} + bool isNeutral() const { + return (pdePtr > 0) ? (pdePtr->chargeType(idSave) == 0) : false;} + int colType() const { + return (pdePtr > 0) ? pdePtr->colType(idSave) : 0;} + double m0() const { + return (pdePtr > 0) ? pdePtr->m0() : 0.;} + double mWidth() const { + return (pdePtr > 0) ? pdePtr->mWidth() : 0.;} + double mMin() const { + return (pdePtr > 0) ? pdePtr->mMin() : 0.;} + double mMax() const { + return (pdePtr > 0) ? pdePtr->mMax() : 0.;} + double mass() const { + return (pdePtr > 0) ? pdePtr->mass() : 0.;} + double constituentMass() const { + return (pdePtr > 0) ? pdePtr->constituentMass() : 0.;} + double tau0() const { + return (pdePtr > 0) ? pdePtr->tau0() : 0.;} + bool mayDecay() const { + return (pdePtr > 0) ? pdePtr->mayDecay() : false;} + bool canDecay() const { + return (pdePtr > 0) ? pdePtr->canDecay() : false;} + bool doExternalDecay() const { + return (pdePtr > 0) ? pdePtr->doExternalDecay() : false;} + bool isResonance() const { + return (pdePtr > 0) ? pdePtr->isResonance() : false;} + bool isVisible() const { + return (pdePtr > 0) ? pdePtr->isVisible() : false;} + bool isLepton() const { + return (pdePtr > 0) ? pdePtr->isLepton() : false;} + bool isQuark() const { + return (pdePtr > 0) ? pdePtr->isQuark() : false;} + bool isGluon() const { + return (pdePtr > 0) ? pdePtr->isGluon() : false;} + bool isHadron() const { + return (pdePtr > 0) ? pdePtr->isHadron() : false;} + ParticleDataEntry& particleDataEntry() const {return *pdePtr;} + + // Member functions that perform operations. + void rescale3(double fac) {pSave.rescale3(fac);} + void rescale4(double fac) {pSave.rescale4(fac);} + void rescale5(double fac) {pSave.rescale4(fac); mSave *= fac;} + void rot(double thetaIn, double phiIn) {pSave.rot(thetaIn, phiIn); + if (hasVertexSave) vProdSave.rot(thetaIn, phiIn);} + void bst(double betaX, double betaY, double betaZ) { + pSave.bst(betaX, betaY, betaZ); + if (hasVertexSave) vProdSave.bst(betaX, betaY, betaZ);} + void bst(double betaX, double betaY, double betaZ, double gamma) { + pSave.bst(betaX, betaY, betaZ, gamma); + if (hasVertexSave) vProdSave.bst(betaX, betaY, betaZ, gamma);} + void bst(const Vec4& pBst) {pSave.bst(pBst); + if (hasVertexSave) vProdSave.bst(pBst);} + void bst(const Vec4& pBst, double mBst) {pSave.bst(pBst, mBst); + if (hasVertexSave) vProdSave.bst(pBst, mBst);} + void bstback(const Vec4& pBst) {pSave.bstback(pBst); + if (hasVertexSave) vProdSave.bstback(pBst);} + void bstback(const Vec4& pBst, double mBst) {pSave.bstback(pBst, mBst); + if (hasVertexSave) vProdSave.bstback(pBst, mBst);} + void rotbst(const RotBstMatrix& M) {pSave.rotbst(M); + if (hasVertexSave) vProdSave.rotbst(M);} + void offsetHistory( int minMother, int addMother, int minDaughter, + int addDaughter); + void offsetCol( int addCol); + +private: + + // Constants: could only be changed in the code itself. + static const double TINY; + + // Properties of the current particle. + int idSave, statusSave, mother1Save, mother2Save, daughter1Save, + daughter2Save, colSave, acolSave; + Vec4 pSave; + double mSave, scaleSave; + bool hasVertexSave; + Vec4 vProdSave; + double tauSave; + + // Pointer to properties of the particle species. + // Should no be saved in a persistent copy of the event record. + // The //! below is ROOT notation that this member should not be saved. + // Event::restorePtrs() can be called to restore the missing information. + ParticleDataEntry* pdePtr; //! + + // Pointer to the whole particle data table. Used to update the above pointer + // when id(...) changes identity. As above it should not be saved. + ParticleData* pdtPtr; //! + +}; + +// Invariant mass of a pair and its square. +// (Not part of class proper, but tightly linked.) +double m(const Particle&, const Particle&); +double m2(const Particle&, const Particle&); + +//========================================================================== + +// The junction class stores what kind of junction it is, the colour indices +// of the legs at the junction and as far out as legs have been traced, +// and the status codes assigned for fragmentation of each leg. + +class Junction { + +public: + + // Constructors. + Junction() : remainsSave(true), kindSave(0) { + for (int j = 0; j < 3; ++j) { + colSave[j] = 0; endColSave[j] = 0; statusSave[j] = 0; } } + Junction( int kindIn, int col0In, int col1In, int col2In) + : remainsSave(true), kindSave(kindIn) {colSave[0] = col0In; + colSave[1] = col1In; colSave[2] = col2In; + for (int j = 0; j < 3; ++j) { + endColSave[j] = colSave[j]; statusSave[j] = 0; } } + Junction(const Junction& ju) : remainsSave(ju.remainsSave), + kindSave(ju.kindSave) { for (int j = 0; j < 3; ++j) { + colSave[j] = ju.colSave[j]; endColSave[j] = ju.endColSave[j]; + statusSave[j] = ju.statusSave[j]; } } + Junction& operator=(const Junction& ju) {if (this != &ju) { + remainsSave = ju.remainsSave; kindSave = ju.kindSave; + for (int j = 0; j < 3; ++j) { colSave[j] = ju.colSave[j]; + endColSave[j] = ju.endColSave[j]; statusSave[j] = ju.statusSave[j]; } } + return *this; } + + // Set values. + void remains(bool remainsIn) {remainsSave = remainsIn;} + void col(int j, int colIn) {colSave[j] = colIn; endColSave[j] = colIn;} + void cols(int j, int colIn, int endColIn) {colSave[j] = colIn; + endColSave[j] = endColIn;} + void endCol(int j, int endColIn) {endColSave[j] = endColIn;} + void status(int j, int statusIn) {statusSave[j] = statusIn;} + + // Read out value. + bool remains() const {return remainsSave;} + int kind() const {return kindSave;} + int col(int j) const {return colSave[j];} + int endCol(int j) const {return endColSave[j];} + int status(int j) const {return statusSave[j];} + +private: + + // Kind, positions of the three ends and their status codes. + bool remainsSave; + int kindSave, colSave[3], endColSave[3], statusSave[3]; + +}; + +//========================================================================== + +// The Event class holds all info on the generated event. + +class Event { + +public: + + // Constructors. + Event(int capacity = 100) {entry.reserve(capacity); startColTag = 100; + headerList = "----------------------------------------"; + particleDataPtr = 0;} + Event& operator=(const Event& oldEvent); + + // Initialize header for event listing, particle data table, and colour. + void init( string headerIn = "", ParticleData* particleDataPtrIn = 0, + int startColTagIn = 100) { + headerList.replace(0, headerIn.length() + 2, headerIn + " "); + particleDataPtr = particleDataPtrIn; startColTag = startColTagIn;} + + // Clear event record. + void clear() {entry.resize(0); maxColTag = startColTag; scaleSave = 0.; + scaleSecondSave = 0.; clearJunctions();} + + // Clear event record, and set first particle empty. + void reset() {clear(); append(90, -11, 0, 0, 0., 0., 0., 0., 0.);} + + // Overload index operator to access element of event record. + Particle& operator[](int i) {return entry[i];} + const Particle& operator[](int i) const {return entry[i];} + + // Event record size. + int size() const {return entry.size();} + + // Put a new particle at the end of the event record; return index. + int append(Particle entryIn) { + entry.push_back(entryIn); setPDTPtr(); + if (entryIn.col() > maxColTag) maxColTag = entryIn.col(); + if (entryIn.acol() > maxColTag) maxColTag = entryIn.acol(); + return entry.size() - 1; + } + int append(int id, int status, int mother1, int mother2, int daughter1, + int daughter2, int col, int acol, double px, double py, double pz, + double e, double m = 0., double scaleIn = 0.) {entry.push_back( + Particle(id, status, mother1, mother2, daughter1, daughter2, col, acol, + px, py, pz, e, m, scaleIn) ); setPDTPtr(); + if (col > maxColTag) maxColTag = col; + if (acol > maxColTag) maxColTag = acol; + return entry.size() - 1; + } + int append(int id, int status, int mother1, int mother2, int daughter1, + int daughter2, int col, int acol, Vec4 p, double m = 0., + double scaleIn = 0.) {entry.push_back( Particle(id, status, mother1, + mother2, daughter1, daughter2, col, acol, p, m, scaleIn) ); setPDTPtr(); + if (col > maxColTag) maxColTag = col; + if (acol > maxColTag) maxColTag = acol; + return entry.size() - 1; + } + + // Brief versions of append: no mothers and no daughters. + int append(int id, int status, int col, int acol, double px, double py, + double pz, double e, double m = 0.) {entry.push_back( Particle(id, + status, 0, 0, 0, 0, col, acol, px, py, pz, e, m, 0.) ); setPDTPtr(); + if (col > maxColTag) maxColTag = col; + if (acol > maxColTag) maxColTag = acol; + return entry.size() - 1; + } + int append(int id, int status, int col, int acol, Vec4 p, double m = 0.) + {entry.push_back( Particle(id, status, 0, 0, 0, 0, col, acol, p, m, 0.) ); + setPDTPtr(); + if (col > maxColTag) maxColTag = col; + if (acol > maxColTag) maxColTag = acol; + return entry.size() - 1; + } + + // Set pointer to ParticleData for a particle, by default latest one. + void setPDTPtr(int iSet = -1) {if (iSet < 0) iSet = entry.size() - 1; + entry[iSet].setPDTPtr( particleDataPtr);} + + // Add a copy of an existing particle at the end of the event record. + int copy(int iCopy, int newStatus = 0); + + // Implement reference "back" to access last element. + Particle& back() {return entry.back();} + + // List the particles in an event. + void list() const; + void list(ostream& os) const; + void list(bool showScaleAndVertex, bool showMothersAndDaughters = false) + const; + void list(bool showScaleAndVertex, bool showMothersAndDaughters, + ostream& os) const; + + // Remove last n entries. + void popBack(int nRemove = 1) { if (nRemove ==1) entry.pop_back(); + else {int newSize = max( 0, size() - nRemove); + entry.resize(newSize);} } + + // Restore all ParticleDataEntry* pointers in the Particle vector. + // Useful when a persistent copy of the event record is read back in. + void restorePtrs() { for (int i = 0; i < size(); ++i) setPDTPtr(i); } + + // Save or restore the size of the event record (throwing at the end). + void saveSize() {savedSize = entry.size();} + void restoreSize() {entry.resize(savedSize);} + + // Initialize and access colour tag information. + void initColTag(int colTag = 0) {maxColTag = max( colTag,startColTag);} + int lastColTag() const {return maxColTag;} + int nextColTag() {return ++maxColTag;} + + // Access scale for which event as a whole is defined. + void scale( double scaleIn) {scaleSave = scaleIn;} + double scale() const {return scaleSave;} + + // Need a second scale if two hard interactions in event. + void scaleSecond( double scaleSecondIn) {scaleSecondSave = scaleSecondIn;} + double scaleSecond() const {return scaleSecondSave;} + + // Find complete list of daughters and mothers. + vector motherList(int i) const; + vector daughterList(int i) const; + + // Convert to HepMC status code conventions. + int statusHepMC(int i) const; + + // Trace the first and last copy of one and the same particle. + int iTopCopy(int i) const; + int iBotCopy(int i) const; + + // Trace the first and last copy of a particle, using flavour match. + int iTopCopyId(int i) const; + int iBotCopyId(int i) const; + + // Find list of sisters, also tracking up and down identical copies. + vector sisterList(int i) const; + vector sisterListTopBot(int i, bool widenSearch = true) const; + + // Check whether two particles have a direct mother-daughter relation. + bool isAncestor(int i, int iAncestor) const; + + // Member functions for rotations and boosts of an event. + void rot(double theta, double phi) + {for (int i = 0; i < size(); ++i) entry[i].rot(theta, phi);} + void bst(double betaX, double betaY, double betaZ) + {for (int i = 0; i < size(); ++i) entry[i].bst(betaX, betaY, betaZ);} + void bst(double betaX, double betaY, double betaZ, double gamma) + {for (int i = 0; i < size(); ++i) entry[i].bst(betaX, betaY, betaZ, + gamma);} + void bst(const Vec4& vec) + {for (int i = 0; i < size(); ++i) entry[i].bst(vec);} + void rotbst(const RotBstMatrix& M) + {for (int i = 0; i < size(); ++i) entry[i].rotbst(M);} + + // Clear the list of junctions. + void clearJunctions() {junction.resize(0);} + + // Add a junction to the list, study it or extra input. + void appendJunction( int kind, int col0, int col1, int col2) + { junction.push_back( Junction( kind, col0, col1, col2) );} + void appendJunction(Junction junctionIn) {junction.push_back(junctionIn);} + int sizeJunction() const {return junction.size();} + bool remainsJunction(int i) const {return junction[i].remains();} + void remainsJunction(int i, bool remainsIn) {junction[i].remains(remainsIn);} + int kindJunction(int i) const {return junction[i].kind();} + int colJunction( int i, int j) const {return junction[i].col(j);} + void colJunction( int i, int j, int colIn) {junction[i].col(j, colIn);} + int endColJunction( int i, int j) const {return junction[i].endCol(j);} + void endColJunction( int i, int j, int endColIn) + {junction[i].endCol(j, endColIn);} + int statusJunction( int i, int j) const {return junction[i].status(j);} + void statusJunction( int i, int j, int statusIn) + {junction[i].status(j, statusIn);} + Junction& getJunction(int i) {return junction[i];} + const Junction& getJunction(int i) const {return junction[i];} + void eraseJunction(int i); + + // Save or restore the size of the junction list (throwing at the end). + void saveJunctionSize() {savedJunctionSize = junction.size();} + void restoreJunctionSize() {junction.resize(savedJunctionSize);} + + // List any junctions in the event; for debug mainly. + void listJunctions(ostream& os = cout) const; + + // Operator overloading allows to append one event to an existing one. + // Warning: particles should be OK, but some other information unreliable. + Event& operator+=(const Event& addEvent); + +private: + + // Constants: could only be changed in the code itself. + static const int IPERLINE; + + // Initialization data, normally only set once. + int startColTag; + + // The event: a vector containing all particles (entries). + vector entry; + + // The list of junctions. + vector junction; + + // The maximum colour tag of the event so far. + int maxColTag; + + // Saved entry and junction list sizes, for simple restoration. + int savedSize, savedJunctionSize; + + // The scale of the event; linear quantity in GeV. + double scaleSave, scaleSecondSave; + + // Header specification in event listing (at most 40 characters wide). + string headerList; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // end Pythia8_Event_H diff --git a/PYTHIA8/pythia8140/include/FragmentationFlavZpT.h b/PYTHIA8/pythia8140/include/FragmentationFlavZpT.h new file mode 100644 index 00000000000..4af59d9261c --- /dev/null +++ b/PYTHIA8/pythia8140/include/FragmentationFlavZpT.h @@ -0,0 +1,179 @@ +// FragmentationFlavZpT.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains helper classes for fragmentation. +// StringFlav is used to select quark and hadron flavours. +// StringPT is used to select transverse momenta. +// StringZ is used to sample the fragmentation function f(z). + +#ifndef Pythia8_FragmentationFlavZpT_H +#define Pythia8_FragmentationFlavZpT_H + +#include "Basics.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + + +//========================================================================== + +// The FlavContainer class is a simple container for flavour, +// including the extra properties needed for popcorn baryon handling. +// id = current flavour. +// rank = current rank; 0 for endpoint flavour and then increase by 1. +// nPop = number of popcorn mesons yet to be produced (1 or 0). +// idPop = (absolute sign of) popcorn quark, shared between B and Bbar. +// idVtx = (absolute sign of) vertex (= non-shared) quark in diquark. + +class FlavContainer { + +public: + + // Constructor. + FlavContainer(int idIn = 0, int rankIn = 0, int nPopIn = 0, + int idPopIn = 0, int idVtxIn = 0) : id(idIn), rank(rankIn), + nPop(nPopIn), idPop(idPopIn), idVtx(idVtxIn) {} + + // Overloaded equal operator. + FlavContainer& operator=(const FlavContainer& flav) { if (this != &flav) { + id = flav.id; rank = flav.rank; nPop = flav.nPop; idPop = flav.idPop; + idVtx = flav.idVtx; } return *this; } + + // Invert flavour. + FlavContainer& anti() {id = -id; return *this;} + + // Read in a container into another, without/with id sign flip. + FlavContainer& copy(const FlavContainer& flav) { if (this != &flav) { + id = flav.id; rank = flav.rank; nPop = flav.nPop; idPop = flav.idPop; + idVtx = flav.idVtx; } return *this; } + FlavContainer& anti(const FlavContainer& flav) { if (this != &flav) { + id = -flav.id; rank = flav.rank; nPop = flav.nPop; idPop = flav.idPop; + idVtx = flav.idVtx; } return *this; } + + // Stored properties. + int id, rank, nPop, idPop, idVtx; + +}; + +//========================================================================== + +// The StringFlav class is used to select quark and hadron flavours. + +class StringFlav { + +public: + + // Constructor. + StringFlav() {} + + // Initialize data members. + void init(Settings& settings, Rndm* rndmPtrIn); + + // Pick a light d, u or s quark according to fixed ratios. + int pickLightQ() { double rndmFlav = probQandS * rndmPtr->flat(); + if (rndmFlav < 1.) return 1; if (rndmFlav < 2.) return 2; return 3; } + + // Pick a new flavour (including diquarks) given an incoming one. + FlavContainer pick(FlavContainer& flavOld); + + // Combine two flavours (including diquarks) to produce a hadron. + int combine(FlavContainer& flav1, FlavContainer& flav2); + + // Assign popcorn quark inside an original (= rank 0) diquark. + void assignPopQ(FlavContainer& flav); + + // Combine two quarks to produce a diquark. + int makeDiquark(int id1, int id2, int idHad = 0); + +private: + + // Constants: could only be changed in the code itself. + static const int mesonMultipletCode[6]; + static const double baryonCGOct[6], baryonCGDec[6]; + + // Initialization data, to be read from Settings. + bool suppressLeadingB; + double probQQtoQ, probStoUD, probSQtoQQ, probQQ1toQQ0, probQandQQ, + probQandS, probQandSinQQ, probQQ1corr, probQQ1corrInv, probQQ1norm, + mesonRate[4][6], mesonRateSum[4], mesonMix1[2][6], mesonMix2[2][6], + etaSup, etaPrimeSup, decupletSup, baryonCGSum[6], baryonCGMax[6], + popcornRate, popcornSpair, popcornSmeson, scbBM[3], popFrac, + popS[3], dWT[3][7], lightLeadingBSup, heavyLeadingBSup; + + // Pointer to the random number generator. + Rndm* rndmPtr; + +}; + +//========================================================================== + +// The StringZ class is used to sample the fragmentation function f(z). + +class StringZ { + +public: + + // Constructor. + StringZ() {} + + // Initialize data members. + void init(Settings& settings, ParticleData& particleData, Rndm* rndmPtrIn); + + // Fragmentation function: top-level to determine parameters. + double zFrag( int idOld, int idNew = 0, double mT2 = 1.); + +private: + + // Constants: could only be changed in the code itself. + static const double CFROMUNITY, AFROMZERO, AFROMC, EXPMAX; + + // Initialization data, to be read from Settings. + bool usePetersonC, usePetersonB, usePetersonH; + double mc2, mb2, aLund, bLund, aExtraDiquark, rFactC, rFactB, rFactH, + epsilonC, epsilonB, epsilonH; + + // Fragmentation function: select z according to provided parameters. + double zLund( double a, double b, double c = 1.); + double zPeterson( double epsilon); + + // Pointer to the random number generator. + Rndm* rndmPtr; + +}; + +//========================================================================== + +// The StringPT class is used to select select transverse momenta. + +class StringPT { + +public: + + // Constructor. + StringPT() {} + + // Initialize data members. + void init(Settings& settings, Rndm* rndmPtrIn); + + // Return px and py as a pair in the same call. + pair pxy(); + +private: + + // Initialization data, to be read from Settings. + double sigmaQ, enhancedFraction, enhancedWidth; + + // Pointer to the random number generator. + Rndm* rndmPtr; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_FragmentationFlavZpT_H diff --git a/PYTHIA8/pythia8140/include/FragmentationSystems.h b/PYTHIA8/pythia8140/include/FragmentationSystems.h new file mode 100644 index 00000000000..b4a3073091a --- /dev/null +++ b/PYTHIA8/pythia8140/include/FragmentationSystems.h @@ -0,0 +1,190 @@ +// FragmentationSystems.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains auxiliary classes in the fragmentation process. +// ColSinglet contains info on an individual singlet. +// ColConfig describes the colour configuration of the whole event. +// StringRegion keeps track on string momenta and directions. +// StringSystem contains all the StringRegions of the colour singlet. + +#ifndef Pythia8_FragmentationSystems_H +#define Pythia8_FragmentationSystems_H + +#include "Basics.h" +#include "Event.h" +#include "FragmentationFlavZpT.h" +#include "Info.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// The ColSinglet class contains info on an individual singlet. +// Only to be used inside ColConfig, so no private members. + +class ColSinglet { + +public: + + // Constructors. + ColSinglet() : pSum(0., 0., 0., 0.), mass(0.), massExcess(0.), + hasJunction(false), isClosed(false), isCollected(false) {} + ColSinglet(vector& iPartonIn, Vec4 pSumIn, double massIn, + double massExcessIn, bool hasJunctionIn = false, + bool isClosedIn = false, bool isCollectedIn = false) + : iParton(iPartonIn), pSum(pSumIn), mass(massIn), + massExcess(massExcessIn), hasJunction(hasJunctionIn), + isClosed(isClosedIn), isCollected(isCollectedIn) {} + + // Size of iParton array. + int size() const { return iParton.size();} + + // Stored quantities. + vector iParton; + Vec4 pSum; + double mass, massExcess; + bool hasJunction, isClosed, isCollected; + +}; + +//========================================================================== + +// The ColConfig class describes the colour configuration of the whole event. + +class ColConfig { + +public: + + // Constructor. + ColConfig() {singlets.resize(0);} + + // Initialize and save pointers. + void init(Info* infoPtrIn, Settings& settings, StringFlav* flavSelPtrIn); + + // Number of colour singlets. + int size() const {return singlets.size();} + + // Overload index operator to access separate colour singlets. + ColSinglet& operator[](int iSub) {return singlets[iSub];} + + // Clear contents. + void clear() {singlets.resize(0);} + + // Insert a new colour singlet system in ascending mass order. + // Calculate its properties. Join nearby partons. + bool insert( vector& iPartonIn, Event& event); + + // Collect all partons of singlet to be consecutively ordered. + void collect(int iSub, Event& event); + + // List all currently identified singlets. + void list(ostream& os = cout) const; + +private: + + // Constants: could only be changed in the code itself. + static const double CONSTITUENTMASS; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to class for flavour generation. + StringFlav* flavSelPtr; + + // Initialization data, to be read from Settings. + double mJoin, mJoinJunction, mStringMin; + + // List of all separate colour singlets. + vector singlets; + + // Join two legs of junction to a diquark for small invariant masses. + bool joinJunction( vector& iPartonIn, Event& event, + double massExcessIn); + +}; + +//========================================================================== + +// The StringRegion class contains the information related to +// one string section in the evolution of a multiparton system. +// Only to be used inside StringFragmentation and MiniStringFragmentation, +// so no private members. + +class StringRegion { + +public: + + // Constructor. + StringRegion() : isSetUp(false), isEmpty(true) {} + + // Constants: could only be changed in the code itself. + static const double MJOIN, TINY; + + // Data members. + bool isSetUp, isEmpty; + Vec4 pPos, pNeg, eX, eY; + double w2, xPosProj, xNegProj, pxProj, pyProj; + + // Set up four-vectors for longitudinal and transverse directions. + void setUp(Vec4 p1, Vec4 p2, bool isMassless = false); + + // Construct a four-momentum from (x+, x-, px, py). + Vec4 pHad( double xPosIn, double xNegIn, double pxIn, double pyIn) + { return xPosIn * pPos + xNegIn * pNeg + pxIn * eX + pyIn * eY; } + + // Project a four-momentum onto (x+, x-, px, py). Read out projection. + void project(Vec4 pIn); + void project( double pxIn, double pyIn, double pzIn, double eIn) + { project( Vec4( pxIn, pyIn, pzIn, eIn) ); } + double xPos() const {return xPosProj;} + double xNeg() const {return xNegProj;} + double px() const {return pxProj;} + double py() const {return pyProj;} + +}; + +//========================================================================== + +// The StringSystem class contains the complete set of all string regions. +// Only to be used inside StringFragmentation, so no private members. + +class StringSystem { + +public: + + // Constructor. + StringSystem() {} + + // Set up system from parton list. + void setUp(vector& iSys, Event& event); + + // Calculate string region from (iPos, iNeg) pair. + int iReg( int iPos, int iNeg) const + {return (iPos * (indxReg - iPos)) / 2 + iNeg;} + + // Reference to string region specified by (iPos, iNeg) pair. + StringRegion& region(int iPos, int iNeg) {return system[iReg(iPos, iNeg)];} + + // Reference to low string region specified either by iPos or iNeg. + StringRegion& regionLowPos(int iPos) {return system[iReg(iPos, iMax - iPos)];} + StringRegion& regionLowNeg(int iNeg) {return system[iReg(iMax - iNeg, iNeg)];} + + // Main content: a vector with all the string regions of the system. + vector system; + + // Other data members. + int sizePartons, sizeStrings, sizeRegions, indxReg, iMax; + double mJoin, m2Join; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_FragmentationSystems_H diff --git a/PYTHIA8/pythia8140/include/HadronLevel.h b/PYTHIA8/pythia8140/include/HadronLevel.h new file mode 100644 index 00000000000..bbbed48fc30 --- /dev/null +++ b/PYTHIA8/pythia8140/include/HadronLevel.h @@ -0,0 +1,116 @@ +// HadronLevel.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the main class for hadron-level generation. +// HadronLevel: handles administration of fragmentation and decay. + +#ifndef Pythia8_HadronLevel_H +#define Pythia8_HadronLevel_H + +#include "Basics.h" +#include "BoseEinstein.h" +#include "Event.h" +#include "FragmentationFlavZpT.h" +#include "FragmentationSystems.h" +#include "Info.h" +#include "MiniStringFragmentation.h" +#include "ParticleData.h" +#include "ParticleDecays.h" +#include "PythiaStdlib.h" +#include "Settings.h" +#include "StringFragmentation.h" +#include "TimeShower.h" + +namespace Pythia8 { + +//========================================================================== + +// The HadronLevel class contains the top-level routines to generate +// the transition from the partonic to the hadronic stage of an event. + +class HadronLevel { + +public: + + // Constructor. + HadronLevel() {} + + // Initialize HadronLevel classes as required. + bool init(Info* infoPtrIn, Settings& settings, ParticleData& particleData, + Rndm* rndmPtrIn, TimeShower* timesDecPtr, DecayHandler* decayHandlePtr, + vector handledParticles); + + // Get pointer to StringFlav instance (needed by BeamParticle). + StringFlav* getStringFlavPtr() {return &flavSel;} + + // Generate the next event. + bool next(Event& event); + + // Special routine to allow more decays if on/off switches changed. + bool moreDecays(Event& event); + +private: + + // Constants: could only be changed in the code itself. + static const int NTRYJNREST; + static const double JJSTRINGM2MAX, JJSTRINGM2FRAC, CONVJNREST, MTHAD; + + // Initialization data, read from Settings. + bool doHadronize, doDecay, doBoseEinstein; + double mStringMin, eNormJunction, widthSepBE; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Configuration of colour-singlet systems. + ColConfig colConfig; + + // Colour information. + vector iColEnd, iAcolEnd, iColAndAcol, iParton, iPartonJun, + iPartonAntiJun, iJunLegA, iJunLegB, iJunLegC, + iAntiLegA, iAntiLegB, iAntiLegC, iGluLeg; + vector m2Pair; + + // The generator class for normal string fragmentation. + StringFragmentation stringFrag; + + // The generator class for special low-mass string fragmentation. + MiniStringFragmentation ministringFrag; + + // The generator class for normal decays. + ParticleDecays decays; + + // The generator class for Bose-Einstein effects. + BoseEinstein boseEinstein; + + // Classes for flavour, pT and z generation. + StringFlav flavSel; + StringPT pTSel; + StringZ zSel; + + // Special case: colour-octet onium decays, to be done initially. + bool decayOctetOnia(Event& event); + + // Trace colour flow in the event to form colour singlet subsystems. + bool findSinglets(Event& event); + + // Trace a colour line, from a colour, from an anticolour, or in loop. + bool traceFromCol(int indxCol, Event& event, int iJun = -1, int iCol = -1); + bool traceFromAcol(int indxCol, Event& event, int iJun = -1, int iCol = -1); + bool traceInLoop(int indxCol, int indxAcol, Event& event); + + // Split junction-antijunction system into two, or simplify other way. + bool splitJunctionPair(Event& event); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_HadronLevel_H diff --git a/PYTHIA8/pythia8140/include/HepMCInterface.h b/PYTHIA8/pythia8140/include/HepMCInterface.h new file mode 100644 index 00000000000..6367484efd4 --- /dev/null +++ b/PYTHIA8/pythia8140/include/HepMCInterface.h @@ -0,0 +1,105 @@ +// HepMCInterface.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Mikhail Kirsanov, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for I_Pythia8 class, +// which converts a PYTHIA event record to the standard HepMC format. + +#ifndef Pythia8_HepMCInterface_H +#define Pythia8_HepMCInterface_H + +#include +#include +#include "HepMC/IO_BaseClass.h" +#include "Pythia.h" + +namespace HepMC { + + class GenEvent; + class GenVertex; + class GenParticle; + class ParticleDataTable; + +//========================================================================== + + class I_Pythia8 : public IO_BaseClass { + public: + I_Pythia8(); + virtual ~I_Pythia8(); + bool fill_next_event( Pythia8::Event& pyev, GenEvent* evt, + int ievnum = -1 ); + bool fill_next_event( Pythia8::Pythia& pythia, GenEvent* evt, + int ievnum = -1, + bool convertGluonTo0 = false ); + void put_pdf_info( GenEvent* evt, Pythia8::Pythia& pythia, + bool convertGluonTo0 = false ); + + // See comments below for these switches. + bool trust_both_mothers_and_daughters() const; + bool trust_mothers_before_daughters() const; + bool print_inconsistency_errors() const; + void set_trust_mothers_before_daughters( bool b = 1 ); + void set_trust_both_mothers_and_daughters( bool b = 0 ); + void set_print_inconsistency_errors( bool b = 1 ); + void set_crash_on_problem( bool b = 1 ); + void set_convert_to_mev( bool b = 1 ); + void set_nofreepartonwarnings( bool b = 0 ); + + private: // following are not (yet?) implemented for this class + virtual bool fill_next_event( GenEvent* ) { return 0; } + virtual void write_event( const GenEvent* ) {;} + virtual void write_particle_data_table( const ParticleDataTable* ){} + virtual bool fill_particle_data_table( ParticleDataTable* ) + { return 0; } + + private: // use of copy constructor is not allowed + I_Pythia8( const I_Pythia8& ) : IO_BaseClass() {} + + private: // data members + + bool m_trust_mothers_before_daughters; + bool m_trust_both_mothers_and_daughters; + bool m_print_inconsistency_errors; + int m_internal_event_number; + bool m_crash_on_problem; + bool m_convert_to_mev; + float m_mom_scale_factor; + bool m_freepartonwarnings; + + }; + + // INLINES access methods. + + inline bool I_Pythia8::trust_both_mothers_and_daughters() const + { return m_trust_both_mothers_and_daughters; } + + inline bool I_Pythia8::trust_mothers_before_daughters() const + { return m_trust_mothers_before_daughters; } + + inline bool I_Pythia8::print_inconsistency_errors() const + { return m_print_inconsistency_errors; } + + inline void I_Pythia8::set_trust_both_mothers_and_daughters( bool b ) + { m_trust_both_mothers_and_daughters = b; } + + inline void I_Pythia8::set_trust_mothers_before_daughters( bool b ) + { m_trust_mothers_before_daughters = b; } + + inline void I_Pythia8::set_print_inconsistency_errors( bool b ) + { m_print_inconsistency_errors = b; } + + inline void I_Pythia8::set_crash_on_problem( bool b ) + { m_crash_on_problem = b; } + + inline void I_Pythia8::set_convert_to_mev( bool b ) + { m_convert_to_mev = b; m_mom_scale_factor = 1000.; } + + inline void I_Pythia8::set_nofreepartonwarnings( bool b ) + { m_freepartonwarnings = b; } + +//========================================================================== + +} // end namespace HepMC + +#endif // end Pythia8_HepMCInterface_H diff --git a/PYTHIA8/pythia8140/include/Info.h b/PYTHIA8/pythia8140/include/Info.h new file mode 100644 index 00000000000..d61b5c612cd --- /dev/null +++ b/PYTHIA8/pythia8140/include/Info.h @@ -0,0 +1,284 @@ +// Info.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains a class that keep track of generic event info. +// Info: contains information on the generation process and errors. + +#ifndef Pythia8_Info_H +#define Pythia8_Info_H + +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// The Info class contains a mixed bag of information on the event +// generation activity, especially on the current subprocess properties, +// and on the number of errors encountered. This is used by the +// generation machinery, but can also be read by the user. +// Note: some methods that maybe should not be accessible to the user +// are still public, to work also for user-written FSR/ISR classes. + +class Info { + +public: + + // Constructor. + Info() {lowPTmin = false; for (int i = 0; i < 40; ++i) counters[i] = 0;} + + // Listing of most available information on current event. + void list(ostream& os = cout) const; + + // Beam particles (in rest frame). CM energy of event. + int idA() const {return idASave;} + int idB() const {return idBSave;} + double pzA() const {return pzASave;} + double pzB() const {return pzBSave;} + double eA() const {return eASave;} + double eB() const {return eBSave;} + double mA() const {return mASave;} + double mB() const {return mBSave;} + double eCM() const {return eCMSave;} + double s() const {return sSave;} + + // Warnings from initialization. + bool tooLowPTmin() const {return lowPTmin;} + + // Process name and code, and the number of final-state particles. + string name() const {return nameSave;} + int code() const {return codeSave;} + int nFinal() const {return nFinalSave;} + + // Are beam particles resolved, with pdf's? Are they diffractive? + bool isResolved() const {return isRes;} + bool isDiffractiveA() const {return isDiffA;} + bool isDiffractiveB() const {return isDiffB;} + bool isMinBias() const {return isMB;} + + // Information for Les Houches Accord and reading files. + bool isLHA() const {return isLH;} + bool atEndOfFile() const {return atEOF;} + + // For minbias and Les Houches Accord identify hardest subprocess. + bool hasSub() const {return hasSubSave;} + string nameSub() const {return nameSubSave;} + int codeSub() const {return codeSubSave;} + int nFinalSub() const {return nFinalSubSave;} + + // Incoming parton flavours and x values. + int id1() const {return id1Save;} + int id2() const {return id2Save;} + double x1() const {return x1Save;} + double x2() const {return x2Save;} + double y() const {return 0.5 * log( x1Save / x2Save );} + double tau() const {return x1Save * x2Save;} + + // Incoming parton densities, hard process couplings, Q2 scales. + double pdf1() const {return pdf1Save;} + double pdf2() const {return pdf2Save;} + double QFac() const {return sqrtpos(Q2FacSave);} + double Q2Fac() const {return Q2FacSave;} + bool isValence1() const {return isVal1;} + bool isValence2() const {return isVal2;} + double alphaS() const {return alphaSSave;} + double alphaEM() const {return alphaEMSave;} + double QRen() const {return sqrtpos(Q2RenSave);} + double Q2Ren() const {return Q2RenSave;} + + // Mandelstam variables (notation as if subcollision). + double mHat() const {return sqrt(sH);} + double sHat() const {return sH;} + double tHat() const {return tH;} + double uHat() const {return uH;} + double pTHat() const {return pTH;} + double pT2Hat() const {return pTH*pTH;} + double m3Hat() const {return m3H;} + double m4Hat() const {return m4H;} + double thetaHat() const {return thetaH;} + double phiHat() const {return phiH;} + + // Weight of current event; normally 1, but used for Les Houches events. + double weight() const {return weightSave;} + + // Number of times other steps have been carried out. + int nISR() const {return nISRSave;} + int nFSRinProc() const {return nFSRinProcSave;} + int nFSRinRes() const {return nFSRinResSave;} + + // Maximum pT scales for MI, ISR and FSR (in hard process). + double pTmaxMI() const {return pTmaxMISave;} + double pTmaxISR() const {return pTmaxISRSave;} + double pTmaxFSR() const {return pTmaxFSRSave;} + + // Current evolution scale (for UserHooks). + double pTnow() const {return pTnowSave;} + + // Impact parameter picture. + double bMI() const {return (bIsSet) ? bMISave : 1.;} + double enhanceMI() const {return (bIsSet) ? enhanceMISave : 1.;} + + // Number of multiple interactions, with code and pT for them. + int nMI() const {return nMISave;} + int codeMI(int i) const {return codeMISave[i];} + double pTMI(int i) const {return pTMISave[i];} + int iAMI(int i) const {return iAMISave[i];} + int iBMI(int i) const {return iBMISave[i];} + + // Cross section estimate. + long nTried() const {return nTry;} + long nSelected() const {return nSel;} + long nAccepted() const {return nAcc;} + double sigmaGen() const {return sigGen;} + double sigmaErr() const {return sigErr;} + + // Counters for number of loops in various places. + int getCounter( int i) const {return counters[i];} + + // Set or increase the value stored in a counter. + void setCounter( int i, int value = 0) {counters[i] = value;} + void addCounter( int i, int value = 1) {counters[i] += value;} + + // Reset to empty map of error messages. + void errorReset() {messages.clear();} + + // Print a message the first few times. Insert in database. + void errorMsg(string messageIn, string extraIn = " ", + bool showAlways = false, ostream& os = cout); + + // Provide total number of errors/aborts/warnings experienced to date. + int errorTotalNumber(); + + // Print statistics on errors/aborts/warnings. + void errorStatistics(ostream& os = cout); + + // Set initialization warning flag when too low pTmin in ISR/FSR/MI. + void setTooLowPTmin(bool lowPTminIn) {lowPTmin = lowPTminIn;} + +private: + + // Number of times the same error message is repeated, unless overridden. + static const int TIMESTOPRINT; + + // Store common beam quantities. + int idASave, idBSave; + double pzASave, eASave,mASave, pzBSave, eBSave, mBSave, eCMSave, sSave; + + // Store initialization information. + bool lowPTmin; + + // Store common integrated cross section quantities. + long nTry, nSel, nAcc; + double sigGen, sigErr; + + // Store current-event quantities. + bool isRes, isDiffA, isDiffB, isMB, isLH, hasSubSave, bIsSet, evolIsSet, + atEOF, isVal1, isVal2; + int codeSave, codeSubSave, nFinalSave, nFinalSubSave, nTotal, + id1Save, id2Save, nMISave, nISRSave, nFSRinProcSave, nFSRinResSave; + double x1Save, x2Save, pdf1Save, pdf2Save, Q2FacSave, alphaEMSave, + alphaSSave, Q2RenSave, sH, tH, uH, pTH, m3H, m4H, thetaH, phiH, + weightSave, bMISave, enhanceMISave, pTmaxMISave, pTmaxISRSave, + pTmaxFSRSave, pTnowSave; + string nameSave, nameSubSave; + vector codeMISave, iAMISave, iBMISave; + vector pTMISave; + + // Vector of various loop counters. + int counters[50]; + + // Map for all error messages. + map messages; + + // Friend classes allowed to set info. + friend class Pythia; + friend class ProcessLevel; + friend class ProcessContainer; + friend class PartonLevel; + friend class MultipleInteractions; + + // Set info on the two incoming beams: only from Pythia class. + void setBeamA( int idAin, double pzAin, double eAin, double mAin) { + idASave = idAin; pzASave = pzAin; eASave = eAin; mASave = mAin;} + void setBeamB( int idBin, double pzBin, double eBin, double mBin) { + idBSave = idBin; pzBSave = pzBin; eBSave = eBin; mBSave = mBin;} + void setECM( double eCMin) {eCMSave = eCMin; sSave = eCMSave * eCMSave;} + + // Reset info for current event: only from Pythia class. + void clear() { isRes = isDiffA = isDiffB = isMB = isLH = atEOF = bIsSet + = isVal1 =isVal2 = false; codeSave = nFinalSave = nTotal = id1Save + = id2Save = nMISave = nISRSave = nFSRinProcSave = nFSRinResSave = 0; + x1Save = x2Save = pdf1Save = pdf2Save = Q2FacSave = alphaEMSave + = alphaSSave = Q2RenSave = sH = tH = uH = pTH = m3H = m4H = thetaH + = phiH = 0.; nameSave = " "; weightSave = bMISave = enhanceMISave = 1.; + codeMISave.resize(0); pTMISave.resize(0); iAMISave.resize(0); + iBMISave.resize(0); } + + // Set info on the (sub)process: from ProcessLevel, ProcessContainer or + // MultipleInteractions classes. + void setType( string nameIn, int codeIn, int nFinalIn, + bool isMinBiasIn = false, bool isResolvedIn = true, + bool isDiffractiveAin = false, bool isDiffractiveBin = false, + bool isLHAin = false) {nameSave = nameIn; codeSave = codeIn; + nFinalSave = nFinalIn; isMB = isMinBiasIn; isRes = isResolvedIn; + isDiffA = isDiffractiveAin; isDiffB = isDiffractiveBin; isLH = isLHAin; + nTotal = 2 + nFinalSave; bIsSet = false; hasSubSave = false; + nameSubSave = " "; codeSubSave = 0; nFinalSubSave = 0; evolIsSet = false;} + void setSubType( string nameSubIn, int codeSubIn, int nFinalSubIn) { + hasSubSave = true; nameSubSave = nameSubIn; codeSubSave = codeSubIn; + nFinalSubSave = nFinalSubIn;} + void setPDFalpha( int id1In, int id2In, double pdf1In, double pdf2In, + double Q2FacIn, double alphaEMIn, double alphaSIn, double Q2RenIn) + {id1Save = id1In; id2Save = id2In; pdf1Save = pdf1In; pdf2Save = pdf2In; + Q2FacSave = Q2FacIn; alphaEMSave = alphaEMIn; alphaSSave = alphaSIn; + Q2RenSave = Q2RenIn;} + void setKin( double x1In, double x2In, double sHatIn, double tHatIn, + double uHatIn, double pTHatIn, double m3HatIn, double m4HatIn, + double thetaHatIn, double phiHatIn) {x1Save = x1In; x2Save = x2In; + sH = sHatIn; tH = tHatIn; uH = uHatIn; pTH = pTHatIn; m3H = m3HatIn; + m4H = m4HatIn; thetaH = thetaHatIn; phiH = phiHatIn;} + void setTypeMI( int codeMIIn, double pTMIIn, int iAMIIn = 0, int iBMIIn = 0) { + codeMISave.push_back(codeMIIn); pTMISave.push_back(pTMIIn); + iAMISave.push_back(iAMIIn); iBMISave.push_back(iBMIIn);} + + // Set info on cross section: from ProcessLevel. + void setSigma( long nTryIn, long nSelIn, long nAccIn, double sigGenIn, + double sigErrIn) { nTry = nTryIn; nSel = nSelIn; nAcc = nAccIn; + sigGen = sigGenIn; sigErr = sigErrIn;} + + // Set info on valence character of hard collision partons: from PartonLevel. + void setValence( bool isVal1In, bool isVal2In) {isVal1 = isVal1In; + isVal2 = isVal2In;} + + // Set info on impact parameter: from PartonLevel. + void setImpact( double bMIIn, double enhanceMIIn) {bMISave = bMIIn; + enhanceMISave = enhanceMIIn, bIsSet = true;} + + // Set info on pTmax scales and number of evolution steps: from PartonLevel. + void setPartEvolved( int nMIIn, int nISRIn) { + nMISave = nMIIn; nISRSave = nISRIn;} + void setEvolution( double pTmaxMIIn, double pTmaxISRIn, double pTmaxFSRIn, + int nMIIn, int nISRIn, int nFSRinProcIn, int nFSRinResIn) { + pTmaxMISave = pTmaxMIIn; pTmaxISRSave = pTmaxISRIn; + pTmaxFSRSave = pTmaxFSRIn; nMISave = nMIIn; nISRSave = nISRIn; + nFSRinProcSave = nFSRinProcIn; nFSRinResSave = nFSRinResIn; + evolIsSet = true;} + + // Set current pT evolution scale for MI/ISR/FSR; from PartonLevel. + void setPTnow( double pTnowIn) {pTnowSave = pTnowIn;} + + // Set info whether reading of Les Houches Accord file at end. + void setEndOfFile( bool atEOFin) {atEOF = atEOFin;} + + // Set event weight; currently only for Les Houches description. + void setWeight( double weightIn) {weightSave = weightIn;} + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_Info_H diff --git a/PYTHIA8/pythia8140/include/LHAFortran.h b/PYTHIA8/pythia8140/include/LHAFortran.h new file mode 100644 index 00000000000..05ee997bc39 --- /dev/null +++ b/PYTHIA8/pythia8140/include/LHAFortran.h @@ -0,0 +1,119 @@ +// LHAFortran.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for Fortran Les Houches Accord user process information. +// LHAupFortran: derived class with the HEPRUP and HEPEUP Fortran info. +// You are expected to supply the fillHepRup and fillHepEup methods. + +#ifndef Pythia8_LHAFortran_H +#define Pythia8_LHAFortran_H + +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// Give access to the HEPRUP and HEPEUP Fortran commonblocks. + +#ifdef _WIN32 + #define heprup_ HEPRUP + #define hepeup_ HEPEUP +#endif + +extern "C" { + + extern struct { + int idbmup[2]; + double ebmup[2]; + int pdfgup[2], pdfsup[2], idwtup, nprup; + double xsecup[100], xerrup[100], xmaxup[100]; + int lprup[100]; + } heprup_; + + extern struct { + int nup, idprup; + double xwgtup, scalup, aqedup, aqcdup; + int idup[500], istup[500], mothup[500][2], icolup[500][2]; + double pup[500][5], vtimup[500],spinup[500]; + } hepeup_; + +} + +//========================================================================== + +// A derived class with initialization information from the HEPRUP +// Fortran commonblock and event information from the HEPEUP one. + +class LHAupFortran : public LHAup { + +public: + + // Constructor. + LHAupFortran() {} + + // Routine for doing the job of setting initialization info. + bool setInit() { + // Call the routine that does the job. + if (!fillHepRup()) return false; + // Store beam and strategy info. + setBeamA(heprup_.idbmup[0], heprup_.ebmup[0], heprup_.pdfgup[0], + heprup_.pdfsup[0]); + setBeamB(heprup_.idbmup[1], heprup_.ebmup[1], heprup_.pdfgup[1], + heprup_.pdfsup[1]); + setStrategy(heprup_.idwtup); + // Store process info. Protect against vanishing cross section. + for (int ip = 0; ip < heprup_.nprup; ++ip) { + double xsec = max( 1e-10, heprup_.xsecup[ip]); + addProcess( heprup_.lprup[ip], xsec, heprup_.xerrup[ip], + heprup_.xmaxup[ip] ); + } + // Store the beam energies to calculate x values later. + eBeamA = heprup_.ebmup[0]; + eBeamB = heprup_.ebmup[1]; + // Done. + return true; + } + + // Routine for doing the job of setting info on next event. + bool setEvent(int idProcIn = 0) { + // In some strategies the type of the next event has been set. + hepeup_.idprup = idProcIn; + // Call the routine that does the job. + if (!fillHepEup()) return false; + // Store process info. + setProcess(hepeup_.idprup, hepeup_.xwgtup, hepeup_.scalup, + hepeup_.aqedup, hepeup_.aqcdup); + // Store particle info. + for (int ip = 0; ip < hepeup_.nup; ++ip) addParticle(hepeup_.idup[ip], + hepeup_.istup[ip], hepeup_.mothup[ip][0], hepeup_.mothup[ip][1], + hepeup_.icolup[ip][0], hepeup_.icolup[ip][1], hepeup_.pup[ip][0], + hepeup_.pup[ip][1], hepeup_.pup[ip][2], hepeup_.pup[ip][3], + hepeup_.pup[ip][4], hepeup_.vtimup[ip], hepeup_.spinup[ip]) ; + // Store x values (here E = pup[ip][3]), but note incomplete info. + setPdf( hepeup_.idup[0], hepeup_.idup[1], hepeup_.pup[0][3]/eBeamA, + hepeup_.pup[1][3]/eBeamB, 0., 0., 0., false); + // Done. + return true; + } + +private: + + // Save beam energies to calculate x values. + double eBeamA, eBeamB; + + // User-written routine that does the intialization and fills heprup. + bool fillHepRup(); + + // User-written routine that does the event generation and fills hepeup. + bool fillHepEup(); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_LHAFortran_H diff --git a/PYTHIA8/pythia8140/include/LHAPDFInterface.h b/PYTHIA8/pythia8140/include/LHAPDFInterface.h new file mode 100644 index 00000000000..761468b4943 --- /dev/null +++ b/PYTHIA8/pythia8140/include/LHAPDFInterface.h @@ -0,0 +1,83 @@ +// LHAPDFInterface.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for the LHAPDF f77 external linkage to C++. +// All required code is contained here, i.e. there is no matching .cc file. + +#ifndef Pythia8_LHAPDFInterface_H +#define Pythia8_LHAPDFInterface_H + +namespace Pythia8 { + +//========================================================================== + +// Declare the LHAPDF f77 subroutines that are needed. + +extern "C" { + + extern void initpdfsetm_(int&, const char*, int); + + extern void initpdfsetbynamem_(int&, const char*, int); + + extern void initpdfm_(int&, int&); + + extern void evolvepdfm_(int&, double&, double&, double*); + + extern void evolvepdfphotonm_(int&, double&, double&, double*, double&); + + extern void setlhaparm_(const char*, int); + +} + +//========================================================================== + +// Interfaces to the above routines, to make the C++ calls similar to f77. + +class LHAPDFInterface { + +public: + + // Initialize set with full pathname, allowing multiple sets. + static void initPDFsetM( int& nSet, string name) { + const char* cName = name.c_str(); int lenName = name.length(); + initpdfsetm_( nSet, cName, lenName); + } + + // Initialize set with simple name, allowing multiple sets. + static void initPDFsetByNameM( int& nSet, string name) { + const char* cName = name.c_str(); int lenName = name.length(); + initpdfsetbynamem_( nSet, cName, lenName); + } + + // Initialize member of set. + static void initPDFM(int& nSet, int member) { + initpdfm_(nSet, member); + } + + // Evaluate x f_i(x, Q). + static void evolvePDFM( int& nSet, double x, double Q, double* xfArray) { + evolvepdfm_( nSet, x, Q, xfArray); + } + + // Evaluate x f_i(x, Q) including photon + static void evolvePDFPHOTONM( int& nSet, double x, double Q, + double* xfArray, double& xPhoton) { + evolvepdfphotonm_( nSet, x, Q, xfArray, xPhoton); + } + + // Extrapolate PDF set beyond boundaries, or freeze them there. + static void setPDFparm(string name) { + const char* cName = name.c_str(); int lenName = name.length(); + setlhaparm_( cName, lenName); + } + + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_LHAPDFInterface_H diff --git a/PYTHIA8/pythia8140/include/LesHouches.h b/PYTHIA8/pythia8140/include/LesHouches.h new file mode 100644 index 00000000000..800f44859de --- /dev/null +++ b/PYTHIA8/pythia8140/include/LesHouches.h @@ -0,0 +1,347 @@ +// LesHouches.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for Les Houches Accord user process information. +// LHAProcess: stores a single process; used by the other classes. +// LHAParticle: stores a single particle; used by the other classes. +// LHAup: base class for initialization and event information. +// LHAupLHEF: derived class for reading from an Les Houches Event File. +// Code for interfacing with Fortran commonblocks is found in LHAFortran.h. + +#ifndef Pythia8_LesHouches_H +#define Pythia8_LesHouches_H + +#include "Event.h" +#include "Info.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// A class for the processes stored in LHAup. + +class LHAProcess { + +public: + + // Constructors. + LHAProcess() : idProc(0), xSecProc(0.), xErrProc(0.), xMaxProc(0.) { } + LHAProcess(int idProcIn, double xSecIn, double xErrIn, double xMaxIn) : + idProc(idProcIn), xSecProc(xSecIn), xErrProc(xErrIn), + xMaxProc(xMaxIn) { } + + // Process properties. + int idProc; + double xSecProc, xErrProc, xMaxProc; + +} ; + +//========================================================================== + +// A class for the particles stored in LHAup. + +class LHAParticle { + +public: + + // Constructors. + LHAParticle() : idPart(0), statusPart(0), mother1Part(0), + mother2Part(0), col1Part(0), col2Part(0), pxPart(0.), pyPart(0.), + pzPart(0.), ePart(0.), mPart(0.), tauPart(0.), spinPart(9.) { } + LHAParticle(int idIn, int statusIn, int mother1In, int mother2In, + int col1In, int col2In, double pxIn, double pyIn, double pzIn, + double eIn, double mIn, double tauIn, double spinIn) : + idPart(idIn), statusPart(statusIn), mother1Part(mother1In), + mother2Part(mother2In), col1Part(col1In), col2Part(col2In), + pxPart(pxIn), pyPart(pyIn), pzPart(pzIn), ePart(eIn), mPart(mIn), + tauPart(tauIn), spinPart(spinIn) { } + + // Particle properties. + int idPart, statusPart, mother1Part, mother2Part, col1Part, col2Part; + double pxPart, pyPart, pzPart, ePart, mPart, tauPart, spinPart; + +} ; + +//========================================================================== + +// LHAup is base class for initialization and event information +// from an external parton-level generator. + +class LHAup { + +public: + + // Destructor. + virtual ~LHAup() {} + + // Set info pointer. + void setPtr(Info* infoPtrIn) {infoPtr = infoPtrIn;} + + // Method to be used for LHAupLHEF derived class. + virtual bool fileFound() {return true;} + + // A pure virtual method setInit, wherein all initialization information + // is supposed to be set in the derived class. Can do this by reading a + // file or some other way, as desired. Returns false if it did not work. + virtual bool setInit() = 0; + + // Give back info on beams. + int idBeamA() const {return idBeamASave;} + int idBeamB() const {return idBeamBSave;} + double eBeamA() const {return eBeamASave;} + double eBeamB() const {return eBeamBSave;} + int pdfGroupBeamA() const {return pdfGroupBeamASave;} + int pdfGroupBeamB() const {return pdfGroupBeamBSave;} + int pdfSetBeamA() const {return pdfSetBeamASave;} + int pdfSetBeamB() const {return pdfSetBeamBSave;} + + // Give back weight strategy. + int strategy() const {return strategySave;} + + // Give back info on processes. + int sizeProc() const {return processes.size();} + int idProcess(int proc) const {return processes[proc].idProc;} + double xSec(int proc) const {return processes[proc].xSecProc;} + double xErr(int proc) const {return processes[proc].xErrProc;} + double xMax(int proc) const {return processes[proc].xMaxProc;} + + // Print the initialization info; useful to check that setting it worked. + void listInit(ostream& os = cout); + + // A pure virtual method setEvent, wherein information on the next event + // is supposed to be set in the derived class. + // Strategies +-1 and +-2: idProcIn is the process type, selected by PYTHIA. + // Strategies +-3 and +-4: idProcIn is dummy; process choice is made locally. + // The method can find the next event by a runtime interface to another + // program, or by reading a file, as desired. + // The method should return false if it did not work. + virtual bool setEvent(int idProcIn = 0) = 0; + + // Give back process number, weight, scale, alpha_em, alpha_s. + int idProcess() const {return idProc;} + double weight() const {return weightProc;} + double scale() const {return scaleProc;} + double alphaQED() const {return alphaQEDProc;} + double alphaQCD() const {return alphaQCDProc;} + + // Give back info on separate particle. + int sizePart() const {return particles.size();} + int id(int part) const {return particles[part].idPart;} + int status(int part) const {return particles[part].statusPart;} + int mother1(int part) const {return particles[part].mother1Part;} + int mother2(int part) const {return particles[part].mother2Part;} + int col1(int part) const {return particles[part].col1Part;} + int col2(int part) const {return particles[part].col2Part;} + double px(int part) const {return particles[part].pxPart;} + double py(int part) const {return particles[part].pyPart;} + double pz(int part) const {return particles[part].pzPart;} + double e(int part) const {return particles[part].ePart;} + double m(int part) const {return particles[part].mPart;} + double tau(int part) const {return particles[part].tauPart;} + double spin(int part) const {return particles[part].spinPart;} + + // Optional: give back info on parton density values of event. + bool pdfIsSet() const {return pdfIsSetSave;} + int id1() const {return id1Save;} + int id2() const {return id2Save;} + double x1() const {return x1Save;} + double x2() const {return x2Save;} + double scalePDF() const {return scalePDFSave;} + double xpdf1() const {return xpdf1Save;} + double xpdf2() const {return xpdf2Save;} + + // Print the info; useful to check that reading an event worked. + void listEvent(ostream& os = cout); + + // Skip ahead a number of events, which are not considered further. + // Mainly intended for debug when using the LHAupLHEF class. + virtual bool skipEvent(int nSkip) { + for (int iSkip = 0; iSkip < nSkip; ++iSkip) + if (!setEvent()) return false; return true;} + + // Four routines to write a Les Houches Event file in steps. + bool openLHEF(string fileNameIn); + bool initLHEF(); + bool eventLHEF(); + bool closeLHEF(bool updateInit = false); + +protected: + + // Constructor. Sets default to be that events come with unit weight. + LHAup(int strategyIn = 3) : strategySave(strategyIn) + { processes.reserve(10); particles.reserve(20); } + + // Allow conversion from mb to pb. + static const double CONVERTMB2PB; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Input beam info. + void setBeamA(int idIn, double eIn, int pdfGroupIn = 0, int pdfSetIn = 0) + { idBeamASave = idIn; eBeamASave = eIn; pdfGroupBeamASave = pdfGroupIn; + pdfSetBeamASave = pdfSetIn;} + void setBeamB(int idIn, double eIn, int pdfGroupIn = 0, int pdfSetIn = 0) + { idBeamBSave = idIn; eBeamBSave = eIn; pdfGroupBeamBSave = pdfGroupIn; + pdfSetBeamBSave = pdfSetIn;} + + // Input process weight strategy. + void setStrategy(int strategyIn) {strategySave = strategyIn;} + + // Input process info. + void addProcess(int idProcIn, double xSecIn = 1., double xErrIn = 0., + double xMaxIn = 1.) { processes.push_back( LHAProcess( idProcIn, + xSecIn, xErrIn, xMaxIn)); } + + // Possibility to update some cross section info at end of run. + void setXSec(int iP, double xSecIn) {processes[iP].xSecProc = xSecIn;} + void setXErr(int iP, double xErrIn) {processes[iP].xErrProc = xErrIn;} + void setXMax(int iP, double xMaxIn) {processes[iP].xMaxProc = xMaxIn;} + + // Input info on the selected process. + void setProcess(int idProcIn = 0, double weightIn = 1., double + scaleIn = 0., double alphaQEDIn = 0.0073, double alphaQCDIn = 0.12) { + idProc = idProcIn; weightProc = weightIn; scaleProc = scaleIn; + alphaQEDProc = alphaQEDIn; alphaQCDProc = alphaQCDIn; + // Clear particle list. Add empty zeroth particle for correct indices. + particles.clear(); addParticle(0); pdfIsSetSave = false;} + + // Input particle info, one particle at the time. + void addParticle(LHAParticle particleIn) { + particles.push_back(particleIn);} + void addParticle(int idIn, int statusIn = 0, int mother1In = 0, + int mother2In = 0, int col1In = 0, int col2In = 0, double pxIn = 0., + double pyIn = 0., double pzIn = 0., double eIn = 0., double mIn = 0., + double tauIn = 0., double spinIn = 9.) { + particles.push_back( LHAParticle( idIn, statusIn, mother1In, mother2In, + col1In, col2In, pxIn, pyIn, pzIn, eIn, mIn, tauIn, spinIn)); } + + // Optionally input info on parton density values of event. + void setPdf(int id1In, int id2In, double x1In, double x2In, + double scalePDFIn, double xpdf1In, double xpdf2In, bool pdfIsSetIn) + { id1Save = id1In; id2Save = id2In; x1Save = x1In; x2Save = x2In; + scalePDFSave = scalePDFIn; xpdf1Save = xpdf1In; xpdf2Save = xpdf2In; + pdfIsSetSave = pdfIsSetIn;} + + // Three routines for LHEF files, but put here for flexibility. + bool setInitLHEF(ifstream& is); + bool setNewEventLHEF(ifstream& is); + bool setOldEventLHEF(); + + // Event properties from LHEF files, for repeated use. + int nupSave, idprupSave; + double xwgtupSave, scalupSave, aqedupSave, aqcdupSave; + vector particlesSave; + bool getPDFSave; + int id1InSave, id2InSave; + double x1InSave, x2InSave, scalePDFInSave, xpdf1InSave, xpdf2InSave; + +private: + + // Event weighting and mixing strategy. + int strategySave; + + // Beam particle properties. + int idBeamASave, idBeamBSave; + double eBeamASave, eBeamBSave; + int pdfGroupBeamASave, pdfGroupBeamBSave, pdfSetBeamASave, pdfSetBeamBSave; + + // The process list, stored as a vector of processes. + vector processes; + + // Store info on the selected process. + int idProc; + double weightProc, scaleProc, alphaQEDProc, alphaQCDProc; + + // The particle list, stored as a vector of particles. + vector particles; + + // Optional info on parton density values of event. + bool pdfIsSetSave; + int id1Save, id2Save; + double x1Save, x2Save, scalePDFSave, xpdf1Save, xpdf2Save; + + // File to which to write Les Houches Event File information. + string fileName; + fstream osLHEF; + char dateNow[12]; + char timeNow[9]; + +}; + +//========================================================================== + +// A derived class with information read from a Les Houches Event File. + +class LHAupLHEF : public LHAup { + +public: + + // Constructor. + LHAupLHEF(const char* fileIn) : is(fileIn) {} + + // Destructor. + ~LHAupLHEF() {} + + // Confirm that file was found and opened as expected. + bool fileFound() {return is.good();} + + // Routine for doing the job of reading and setting initialization info. + bool setInit() {return setInitLHEF(is);} + + // Routine for doing the job of reading and setting info on next event. + bool setEvent(int = 0) {if (!setNewEventLHEF(is)) return false; + return setOldEventLHEF();} + + // Skip ahead a number of events, which are not considered further. + bool skipEvent(int nSkip) {for (int iSkip = 0; iSkip < nSkip; ++iSkip) + if (!setNewEventLHEF(is)) return false; return true;} + +private: + + // File from which to read. + ifstream is; + +}; + +//========================================================================== + +// A derived class with information read from PYTHIA 8 itself, for output. + +class LHAupFromPYTHIA8 : public LHAup { + +public: + + // Constructor. + LHAupFromPYTHIA8(Event* processPtrIn, Info* infoPtrIn) { + processPtr = processPtrIn; infoPtr = infoPtrIn;} + + // Destructor. + ~LHAupFromPYTHIA8() {} + + // Routine for doing the job of reading and setting initialization info. + bool setInit(); + + // Routine for doing the job of reading and setting info on next event. + bool setEvent(int = 0); + + // Update cross-section information at the end of the run. + bool updateSigma(); + +private: + + // Pointers to process event record and further information. + Event* processPtr; + Info* infoPtr; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_LesHouches_H diff --git a/PYTHIA8/pythia8140/include/MiniStringFragmentation.h b/PYTHIA8/pythia8140/include/MiniStringFragmentation.h new file mode 100644 index 00000000000..92db7471fc2 --- /dev/null +++ b/PYTHIA8/pythia8140/include/MiniStringFragmentation.h @@ -0,0 +1,86 @@ +// MiniStringFragmentation.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the class for "cluster" fragmentation. +// MiniStringFragmentation: handle the fragmentation of low-mass systems. + +#ifndef Pythia8_MiniStringFragmentation_H +#define Pythia8_MiniStringFragmentation_H + +#include "Basics.h" +#include "Event.h" +#include "FragmentationFlavZpT.h" +#include "FragmentationSystems.h" +#include "Info.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// The MiniStringFragmentation class contains the routines to fragment +// occasional low-mass colour singlet partonic systems, where the string +// approach is not directly applicable (for technical reasons). + +class MiniStringFragmentation { + +public: + + // Constructor. + MiniStringFragmentation() {} + + // Initialize and save pointers. + void init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + StringFlav* flavSelPtrIn); + + // Do the fragmentation: driver routine. + bool fragment( int iSub, ColConfig& colConfig, Event& event, + bool isDiff = false); + +private: + + // Constants: could only be changed in the code itself. + static const int NTRYDIFFRACTIVE, NTRYLASTRESORT, NTRYFLAV; + static const double SIGMAMIN; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointer to class for flavour generation. + StringFlav* flavSelPtr; + + // Initialization data, read from Settings. + int nTryMass; + double sigma, sigma2Had, bLund; + + // Data members. + bool isClosed; + double mSum, m2Sum; + Vec4 pSum; + vector iParton; + FlavContainer flav1, flav2; + + // Attempt to produce two particles from a cluster. + bool ministring2two( int nTry, Event& event); + + // Attempt to produce one particle from a cluster. + bool ministring2one( int iSub, ColConfig& colConfig, Event& event); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_MiniStringFragmentation_H diff --git a/PYTHIA8/pythia8140/include/MultipleInteractions.h b/PYTHIA8/pythia8140/include/MultipleInteractions.h new file mode 100644 index 00000000000..5f3a0626c47 --- /dev/null +++ b/PYTHIA8/pythia8140/include/MultipleInteractions.h @@ -0,0 +1,259 @@ +// MultipleInteractions.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the main classes for multiple interactions physics. +// SigmaMultiple stores allowed processes by in-flavour combination. +// MultipleInteractions: generates multiple parton-parton interactions. + +#ifndef Pythia8_MultipleInteractions_H +#define Pythia8_MultipleInteractions_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Event.h" +#include "Info.h" +#include "PartonSystems.h" +#include "PythiaStdlib.h" +#include "Settings.h" +#include "SigmaTotal.h" +#include "SigmaProcess.h" +#include "StandardModel.h" + +namespace Pythia8 { + +//========================================================================== + +// SigmaMultiple is a helper class to MultipleInteractions. +// It packs pointers to the allowed processes for different +// flavour combinations and levels of ambition. + +class SigmaMultiple { + +public: + + // Constructor. + SigmaMultiple() {} + + // Destructor. + ~SigmaMultiple() { + for (int i = 0; i < int(sigmaT.size()); ++i) delete sigmaT[i]; + for (int i = 0; i < int(sigmaU.size()); ++i) delete sigmaU[i];} + + // Initialize list of processes. + bool init(int inState, int processLevel, Info* infoPtr, + Settings* settingsPtr, ParticleData* particleDataPtr, Rndm* rndmPtrIn, + BeamParticle* beamAPtr, BeamParticle* beamBPtr, CoupSM* coupSMPtr); + + // Calculate cross section summed over possibilities. + double sigma( int id1, int id2, double x1, double x2, double sHat, + double tHat, double uHat, double alpS, double alpEM, + bool restore = false, bool pickOtherIn = false); + + // Return whether the other, rare processes were selected. + bool pickedOther() {return pickOther;} + + // Return one subprocess, picked according to relative cross sections. + SigmaProcess* sigmaSel(); + bool swapTU() {return pickedU;} + + // Return code or name of a specified process, for statistics table. + int nProc() const {return nChan;} + int codeProc(int iProc) const {return sigmaT[iProc]->code();} + string nameProc(int iProc) const {return sigmaT[iProc]->name();} + +private: + + // Constants: could only be changed in the code itself. + static const double MASSMARGIN, OTHERFRAC; + + // Number of processes. Some use massive matrix elements. + int nChan; + vector needMasses; + vector m3Fix, m4Fix, sHatMin; + + // Vector of process list, one for t-channel and one for u-channel. + vector sigmaT, sigmaU; + + // Values of cross sections in process list above. + vector sigmaTval, sigmaUval; + double sigmaTsum, sigmaUsum; + bool pickOther, pickedU; + + // Pointer to the random number generator. + Rndm* rndmPtr; + +}; + +//========================================================================== + +// The MultipleInteractions class contains the main methods for the +// generation of multiple parton-parton interactions in hadronic collisions. + +class MultipleInteractions { + +public: + + // Constructor. + MultipleInteractions() {} + + // Initialize the generation process for given beams. + bool init( bool doMIinit, int diffractiveModeIn, Info* infoPtrIn, + Settings& settings, ParticleData* particleDataPtr, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, CoupSM* coupSMPtrIn, + PartonSystems* partonSystemsPtrIn, SigmaTotal* sigmaTotPtrIn, + ostream& os = cout); + + // Reset impact parameter choice and update the CM energy. + void reset(); + + // Select first = hardest pT in minbias process. + void pTfirst(); + + // Set up kinematics for first = hardest pT in minbias process. + void setupFirstSys( Event& process); + + // Find whether to limit maximum scale of emissions. + bool limitPTmax( Event& event); + + // Prepare system for evolution. + void prepare(double pTscale = 1000.) { + if (!bSetInFirst) overlapNext(pTscale);} + + // Select next pT in downwards evolution. + double pTnext( double pTbegAll, double pTendAll, Event& event); + + // Set up kinematics of acceptable interaction. + void scatter( Event& event); + + // Get some information on current interaction. + double Q2Ren() const {return pT2Ren;} + double alphaSH() const {return alpS;} + double alphaEMH() const {return alpEM;} + double x1H() const {return x1;} + double x2H() const {return x2;} + double Q2Fac() const {return pT2Fac;} + double pdf1() const {return xPDF1now;} + double pdf2() const {return xPDF2now;} + double bMI() const {return (bIsSet) ? bNow / bAvg : 0.;} + double enhanceMI() const {return (bIsSet) ? enhanceB / zeroIntCorr : 1.;} + + // Update and print statistics on number of processes. + void accumulate() { int iBeg = (infoPtr->isMinBias()) ? 0 : 1; + for (int i = iBeg; i < infoPtr->nMI(); ++i) ++nGen[ infoPtr->codeMI(i) ];} + void statistics(bool resetStat = false, ostream& os = cout); + +private: + + // Constants: could only be changed in the code itself. + static const bool SHIFTFACSCALE, PREPICKRESCATTER; + static const double SIGMAFUDGE, RPT20, PT0STEP, SIGMASTEP, PT0MIN, + EXPPOWMIN, PROBATLOWB, BSTEP, BMAX, EXPMAX, + KCONVERGE, CONVERT2MB, ROOTMIN, ECMDEV; + + // Initialization data, read from Settings. + bool allowRescatter, allowDoubleRes; + int pTmaxMatch, alphaSorder, alphaEMorder, bProfile, processLevel, + rescatterMode, nQuarkIn, nSample, enhanceScreening; + double alphaSvalue, Kfactor, pT0Ref, ecmRef, ecmPow, pTmin, coreRadius, + coreFraction, expPow, ySepResc, deltaYResc, sigmaPomP, + mMaxPertDiff, mMinPertDiff; + + // Other initialization data. + bool hasBaryonBeams, hasLowPow; + int diffractiveMode; + double eCM, sCM, pT0, pT20, pT2min, pTmax, pT2max, pT20R, pT20minR, + pT20maxR, pT20min0maxR, pT2maxmin, sigmaND, pT4dSigmaMax, + pT4dProbMax, dSigmaApprox, sigmaInt, sudExpPT[101], + zeroIntCorr, normOverlap, nAvg, kNow, normPi, bAvg, bDiv, + probLowB, radius2B, radius2C, fracA, fracB, fracC, fracAhigh, + fracBhigh, fracChigh, fracABChigh, expRev, cDiv, cMax; + + // Properties specific to current system. + bool bIsSet, bSetInFirst, isAtLowB, pickOtherSel; + int id1, id2, i1Sel, i2Sel, id1Sel, id2Sel; + double bNow, enhanceB, pT2, pT2shift, pT2Ren, pT2Fac, x1, x2, xT, xT2, + tau, y, sHat, tHat, uHat, alpS, alpEM, xPDF1now, xPDF2now, + dSigmaSum, x1Sel, x2Sel, sHatSel, tHatSel, uHatSel; + + // Stored values for mass interpolation for diffractive systems. + int nStep, iStepFrom, iStepTo; + double eCMsave, eStepSize, eStepSave, eStepFrom, eStepTo, pT0Save[5], + pT4dSigmaMaxSave[5], pT4dProbMaxSave[5], sigmaIntSave[5], + sudExpPTSave[5][101], zeroIntCorrSave[5], normOverlapSave[5], + kNowSave[5], bAvgSave[5], bDivSave[5], probLowBSave[5], + fracAhighSave[5], fracBhighSave[5], fracChighSave[5], + fracABChighSave[5], cDivSave[5], cMaxSave[5]; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to the two incoming beams. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + + // Pointers to Standard Model couplings. + CoupSM* coupSMPtr; + + // Pointer to information on subcollision parton locations. + PartonSystems* partonSystemsPtr; + + // Pointer to total cross section parametrization. + SigmaTotal* sigmaTotPtr; + + // Collections of parton-level 2 -> 2 cross sections. Selected one. + SigmaMultiple sigma2gg, sigma2qg, sigma2qqbarSame, sigma2qq; + SigmaMultiple* sigma2Sel; + SigmaProcess* dSigmaDtSel; + + // Statistics on generated 2 -> 2 processes. + map nGen; + + // alphaStrong and alphaEM calculations. + AlphaStrong alphaS; + AlphaEM alphaEM; + + // Scattered partons. + vector scatteredA, scatteredB; + + // Determine constant in d(Prob)/d(pT2) < const / (pT2 + r * pT20)^2. + void upperEnvelope(); + + // Integrate the parton-parton interaction cross section. + void jetCrossSection(); + + // Evaluate "Sudakov form factor" for not having a harder interaction. + double sudakov(double pT2sud, double enhance = 1.); + + // Do a quick evolution towards the next smaller pT. + double fastPT2( double pT2beg); + + // Calculate the actual cross section, either for the first interaction + // (including at initialization) or for any subsequent in the sequence. + double sigmaPT2scatter(bool isFirst = false); + + // Find the partons that may rescatter. + void findScatteredPartons( Event& event); + + // Calculate the actual cross section for a rescattering. + double sigmaPT2rescatter( Event& event); + + // Calculate factor relating matter overlap and interaction rate. + void overlapInit(); + + // Pick impact parameter and interaction rate enhancement, + // either before the first interaction (for minbias) or after it. + void overlapFirst(); + void overlapNext(double pTscale); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_MultipleInteractions_H diff --git a/PYTHIA8/pythia8140/include/ParticleData.h b/PYTHIA8/pythia8140/include/ParticleData.h new file mode 100644 index 00000000000..25ed8888e6e --- /dev/null +++ b/PYTHIA8/pythia8140/include/ParticleData.h @@ -0,0 +1,594 @@ +// ParticleData.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for the classes containing particle data. +// DecayChannel contains info on a single decay channel. +// ParticleDataEntry contains info on a single particle species. +// ParticleData collects info on all particles as a map. + +#ifndef Pythia8_ParticleData_H +#define Pythia8_ParticleData_H + +#include "Basics.h" +#include "Info.h" +#include "PythiaStdlib.h" +#include "ResonanceWidths.h" +#include "Settings.h" +#include "StandardModel.h" + +namespace Pythia8 { + +//========================================================================== + +// Forward reference to some classes. +class ParticleData; +class ResonanceWidths; +class CoupSM; + +//========================================================================== + +// This class holds info on a single decay channel. + +class DecayChannel { + +public: + // Constructor. + DecayChannel(int onModeIn = 0, double bRatioIn = 0., int meModeIn = 0, + int prod0 = 0, int prod1 = 0, int prod2 = 0, int prod3 = 0, + int prod4 = 0, int prod5 = 0, int prod6 = 0, int prod7 = 0) + : onModeSave(onModeIn), bRatioSave(bRatioIn), currentBRSave(0.), + onShellWidthSave(0.), openSecPos(1.), openSecNeg(1.), + meModeSave(meModeIn), nProd(0), hasChangedSave(true) { + prod[0] = prod0; prod[1] = prod1; prod[2] = prod2; prod[3] = prod3; + prod[4] = prod4; prod[5] = prod5; prod[6] = prod6; prod[7] = prod7; + for (int j = 0; j < 8; ++j) if (prod[j] != 0 && j == nProd) ++nProd; } + + // Member functions for input. + void onMode(int onModeIn) {onModeSave = onModeIn; hasChangedSave = true;} + void bRatio(double bRatioIn, bool countAsChanged = true) { + bRatioSave = bRatioIn; if (countAsChanged) hasChangedSave = true;} + void rescaleBR(double fac) {bRatioSave *= fac; hasChangedSave = true;} + void meMode(int meModeIn) {meModeSave = meModeIn; hasChangedSave = true;} + void multiplicity(int multIn) {nProd = multIn; hasChangedSave = true;} + void product(int i, int prodIn) {prod[i] = prodIn; nProd = 0; + for (int j = 0; j < 8; ++j) if (prod[j] != 0 && j == nProd) ++nProd; + hasChangedSave = true;} + void setHasChanged(bool hasChangedIn) {hasChangedSave = hasChangedIn;} + + // Member functions for output. + int onMode() const {return onModeSave;} + double bRatio() const {return bRatioSave;} + int meMode() const {return meModeSave;} + int multiplicity() const {return nProd;} + int product(int i) const {return (i >= 0 && i < nProd) ? prod[i] : 0;} + bool hasChanged() const { return hasChangedSave;} + + // Check for presence of particles anywhere in decay list. + bool contains(int id1) const; + bool contains(int id1, int id2) const; + bool contains(int id1, int id2, int id3) const; + + // Input/output for current selection of decay modes. + // Takes into account on/off switches and dynamic width for resonances. + void currentBR(double currentBRIn) {currentBRSave = currentBRIn;} + double currentBR() const {return currentBRSave;} + + // Input/output for nominal partial width; used by resonances. + void onShellWidth(double onShellWidthIn) { + onShellWidthSave = onShellWidthIn;} + double onShellWidth() const {return onShellWidthSave;} + void onShellWidthFactor(double factor) {onShellWidthSave *= factor;} + + // Input/output for fraction of secondary open widths; used by resonances. + void openSec(int idSgn, double openSecIn) { + if (idSgn > 0) openSecPos = openSecIn; else openSecNeg = openSecIn;} + double openSec(int idSgn) const { + return (idSgn > 0) ? openSecPos : openSecNeg;} + +private: + + // Decay channel info. + int onModeSave; + double bRatioSave, currentBRSave, onShellWidthSave, openSecPos, + openSecNeg; + int meModeSave, nProd, prod[8]; + bool hasChangedSave; + +}; + +//========================================================================== + +// This class holds info on a single particle species. + +class ParticleDataEntry { + +public: + + // Constructors: for antiparticle exists or not. + ParticleDataEntry(int idIn = 0, string nameIn = " ", + int spinTypeIn = 0, int chargeTypeIn = 0, int colTypeIn = 0, + double m0In = 0., double mWidthIn = 0., double mMinIn = 0., + double mMaxIn = 0., double tau0In = 0.) : idSave(abs(idIn)), + nameSave(nameIn), antiNameSave("void"), spinTypeSave(spinTypeIn), + chargeTypeSave(chargeTypeIn), colTypeSave(colTypeIn), m0Save(m0In), + mWidthSave (mWidthIn), mMinSave(mMinIn), mMaxSave(mMaxIn), + tau0Save(tau0In), hasAntiSave(false), hasChangedSave(true), + resonancePtr(0) {setDefaults();} + ParticleDataEntry(int idIn, string nameIn, string antiNameIn, + int spinTypeIn = 0, int chargeTypeIn = 0, int colTypeIn = 0, + double m0In = 0., double mWidthIn = 0., double mMinIn = 0., + double mMaxIn = 0., double tau0In = 0.) : idSave(abs(idIn)), + nameSave(nameIn), antiNameSave(antiNameIn), spinTypeSave(spinTypeIn), + chargeTypeSave(chargeTypeIn), colTypeSave(colTypeIn), m0Save(m0In), + mWidthSave (mWidthIn), mMinSave(mMinIn), mMaxSave(mMaxIn), + tau0Save(tau0In), hasAntiSave(true), hasChangedSave(true), + resonancePtr(0) {setDefaults(); + if (toLower(antiNameIn) == "void") hasAntiSave = false;} + + // Destructor: delete any ResonanceWidths object. + ~ParticleDataEntry(); + + // Initialization of some particle flags. + void setDefaults(); + + // Store pointer to whole particle data table/database. + void initPtr( ParticleData* particleDataPtrIn) { + particleDataPtr = particleDataPtrIn;} + + // Reset all the properties of an existing particle. + void setAll(string nameIn, string antiNameIn, int spinTypeIn = 0, + int chargeTypeIn = 0, int colTypeIn = 0, double m0In = 0., + double mWidthIn = 0., double mMinIn = 0., double mMaxIn = 0., + double tau0In = 0.) + {nameSave = nameIn; antiNameSave = antiNameIn; hasAntiSave = true; + if (toLower(antiNameIn) == "void") hasAntiSave = false; + spinTypeSave = spinTypeIn; chargeTypeSave = chargeTypeIn; + colTypeSave = colTypeIn; m0Save = m0In; mWidthSave = mWidthIn; + mMinSave = mMinIn; mMaxSave = mMaxIn; tau0Save = tau0In; + setDefaults(); hasChangedSave = true;} + + // Change current values one at a time (or set if not set before). + // (Must use set here since else name+signature clash with get methods.) + void setName(string nameIn) {nameSave = nameIn; hasChangedSave = true;} + void setAntiName(string antiNameIn) {antiNameSave = antiNameIn; + hasChangedSave = true;} + void setNames(string nameIn, string antiNameIn) {nameSave = nameIn; + antiNameSave = antiNameIn; hasAntiSave = true; if (toLower(antiNameIn) + == "void") hasAntiSave = false; hasChangedSave = true;} + void setSpinType(int spinTypeIn) {spinTypeSave = spinTypeIn; + hasChangedSave = true;} + void setChargeType(int chargeTypeIn) {chargeTypeSave = chargeTypeIn; + hasChangedSave = true;} + void setColType(int colTypeIn) {colTypeSave = colTypeIn; + hasChangedSave = true;} + void setM0(double m0In) {m0Save = m0In; setConstituentMass(); + hasChangedSave = true;} + void setMWidth(double mWidthIn, bool countAsChanged = true) { + mWidthSave = mWidthIn; if (countAsChanged) hasChangedSave = true;} + void setMMin(double mMinIn) {mMinSave = mMinIn; hasChangedSave = true;} + void setMMax(double mMaxIn) {mMaxSave = mMaxIn; hasChangedSave = true;} + void setTau0(double tau0In) {tau0Save = tau0In; hasChangedSave = true;} + void setIsResonance(bool isResonanceIn) {isResonanceSave = isResonanceIn; + hasChangedSave = true;} + void setMayDecay(bool mayDecayIn, bool countAsChanged = true) { + mayDecaySave = mayDecayIn; if (countAsChanged) hasChangedSave = true;} + void setDoExternalDecay(bool doExternalDecayIn) + {doExternalDecaySave = doExternalDecayIn; hasChangedSave = true;} + void setIsVisible(bool isVisibleIn) {isVisibleSave = isVisibleIn; + hasChangedSave = true;} + void setDoForceWidth(bool doForceWidthIn) {doForceWidthSave = doForceWidthIn; + hasChangedSave = true;} + void setHasChanged(bool hasChangedIn) {hasChangedSave = hasChangedIn; + for (int i = 0; i < int(channels.size()); ++i) + channels[i].setHasChanged(hasChangedIn);} + + // Give back current values. + int id() const { return idSave; } + bool hasAnti() const { return hasAntiSave; } + string name(int idIn = 1) const { + return (idIn > 0) ? nameSave : antiNameSave; } + int spinType() const {return spinTypeSave; } + int chargeType(int idIn = 1) const { + return (idIn > 0) ? chargeTypeSave : -chargeTypeSave; } + double charge(int idIn = 1) const { + return (idIn > 0) ? chargeTypeSave / 3. : -chargeTypeSave / 3.; } + int colType(int idIn = 1) const { + if (colTypeSave == 2) return colTypeSave; + return (idIn > 0) ? colTypeSave : -colTypeSave; } + double m0() const { return m0Save; } + double mWidth() const { return mWidthSave; } + double mMin() const { return mMinSave; } + double mMax() const { return mMaxSave; } + double m0Min() const { + return (modeBWnow == 0) ? m0Save : mMinSave; } + double m0Max() const { + return (modeBWnow == 0) ? m0Save : mMaxSave; } + double tau0() const { return tau0Save; } + bool isResonance() const { return isResonanceSave; } + bool mayDecay() const { return mayDecaySave; } + bool doExternalDecay() const { return doExternalDecaySave; } + bool isVisible() const { return isVisibleSave; } + bool doForceWidth() const { return doForceWidthSave; } + bool hasChanged() const { if (hasChangedSave) return true; + for (int i = 0; i < int(channels.size()); ++i) + if (channels[i].hasChanged()) return true; return false;} + + // Set and give back several mass-related quantities. + void initBWmass(); + double constituentMass() const { return constituentMassSave; } + double mass(); + double mRun(double mH); + + // Give back other quantities. + bool useBreitWigner() const { return (modeBWnow > 0); } + bool canDecay() const { return (channels.size() > 0);} + bool isLepton() const { return (idSave > 10 && idSave < 19);} + bool isQuark() const { return (idSave != 0 && idSave < 9);} + bool isGluon() const { return (idSave == 21);} + bool isDiquark() const { return (idSave > 1000 && idSave < 10000 + && (idSave/10)%10 == 0);} + bool isHadron() const; + bool isMeson() const; + bool isBaryon() const; + + // Intermediate octet ccbar or bbar states in colour-octet model. + bool isOctetHadron() const {return (idSave == 9900441 + || idSave == 9900443 || idSave == 9900551 || idSave == 9900553 + || idSave == 9910441 || idSave == 9910551); } + int heaviestQuark(int idIn = 1) const; + int baryonNumberType(int idIn = 1) const; + + // Reset to empty decay table. + void clearChannels() {channels.resize(0);} + + // Add a decay channel to the decay table. + void addChannel(int onMode = 0, double bRatio = 0., int meMode = 0, + int prod0 = 0, int prod1 = 0, int prod2 = 0, int prod3 = 0, + int prod4 = 0, int prod5 = 0, int prod6 = 0, int prod7 = 0) { + channels.push_back( DecayChannel( onMode, bRatio, meMode, prod0, + prod1, prod2, prod3, prod4, prod5, prod6, prod7) ); } + + // Decay table size. + int sizeChannels() const {return channels.size();} + + // Gain access to a channel in the decay table. + DecayChannel& channel(int i){return channels[i];} + const DecayChannel& channel(int i) const {return channels[i];} + + // Rescale sum of branching ratios to unity. + void rescaleBR(double newSumBR = 1.); + + // Random choice of decay channel according to branching ratios. + bool preparePick(int idSgn, double mHat = 0., int idInFlav = 0); + DecayChannel& pickChannel(); + + // Access methods stored in ResonanceWidths. + void setResonancePtr(ResonanceWidths* resonancePtrIn); + ResonanceWidths* getResonancePtr() {return resonancePtr;} + void resInit(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, CoupSM* coupSMPtrIn); + double resWidth(int idSgn, double mHat, int idIn = 0, + bool openOnly = false, bool setBR = false); + double resWidthOpen(int idSgn, double mHat, int idIn = 0); + double resWidthStore(int idSgn, double mHat, int idIn = 0); + double resOpenFrac(int idSgn); + double resWidthRescaleFactor(); + double resWidthChan(double mHat, int idAbs1 = 0, int idAbs2 = 0); + +private: + + // Constants: could only be changed in the code itself. + static const int INVISIBLENUMBER, INVISIBLETABLE[38]; + static const double MAXTAU0FORDECAY,MINMASSRESONANCE, NARROWMASS, + CONSTITUENTMASSTABLE[6]; + + // Particle data. + int idSave; + string nameSave, antiNameSave; + int spinTypeSave, chargeTypeSave, colTypeSave; + double m0Save, mWidthSave, mMinSave, mMaxSave, tau0Save, + constituentMassSave; + bool hasAntiSave, isResonanceSave, mayDecaySave, doExternalDecaySave, + isVisibleSave, doForceWidthSave, hasChangedSave; + + // Extra data for mass selection according to a Breit-Wigner. + int modeBWnow; + double atanLow, atanDif, mThr; + + // A vector containing all the decay channels of the particle. + vector channels; + + // Summed branching ratio of currently open channels. + double currentBRSum; + + // Pointer to ResonanceWidths object; only used for some particles. + ResonanceWidths* resonancePtr; + + // Pointer to the full particle data table. + ParticleData* particleDataPtr; + + // Set constituent mass. + void setConstituentMass(); + + // Useful functions for string handling. + string toLower(const string& nameConv); + +}; + +//========================================================================== + +// This class holds a map of all ParticleDataEntries. + +class ParticleData { + +public: + + // Constructor. + ParticleData() : isInit(false) {} + + // Initialize pointers. + void initPtr(Info* infoPtrIn, Settings* settingsPtrIn, Rndm* rndmPtrIn, + CoupSM* coupSMPtrIn) {infoPtr = infoPtrIn; settingsPtr = settingsPtrIn; + rndmPtr = rndmPtrIn; coupSMPtr = coupSMPtrIn;} + + // Read in database from specific file. + bool init(string startFile = "../xmldoc/ParticleData.xml") { + initCommon(); return readXML(startFile);} + + // Overwrite existing database by reading from specific file. + bool reInit(string startFile, bool xmlFormat = true) { initCommon(); + return (xmlFormat) ? readXML(startFile) : readFF(startFile);} + + // Initialize pointers, normal Breit-Wigners and special resonances. + void initWidths(vector resonancePtrs); + + // Read or list whole (or part of) database from/to an XML file. + bool readXML(string inFile, bool reset = true) ; + void listXML(string outFile); + + // Read or list whole (or part of) database from/to a free format file. + bool readFF(string inFile, bool reset = true) ; + void listFF(string outFile); + + // Read in one update from a single line. + bool readString(string lineIn, bool warn = true, ostream& os = cout) ; + + // Print out table of whole database, or of only part of it. + void listAll(ostream& os = cout) {list(false, true, os);} + void listChanged(ostream& os = cout) {list(true, false, os);} + void listChanged(bool changedRes, ostream& os = cout) { + list(true, changedRes, os);} + void list(bool changedOnly = false, bool changedRes = true, + ostream& os = cout); + + // Print out specified particles. + void list(int idList, ostream& os = cout) {vector idListTemp; + idListTemp.push_back(idList); list( idListTemp, os);} + void list(vector idList, ostream& os = cout); + + // Check that table makes sense, especially for decays. + void checkTable(ostream& os = cout) {checkTable(1, os);}; + void checkTable(int verbosity, ostream& os = cout) ; + + // Add new entry. + void addParticle(int idIn, string nameIn = " ", int spinTypeIn = 0, + int chargeTypeIn = 0, int colTypeIn = 0, double m0In = 0., + double mWidthIn = 0., double mMinIn = 0., double mMaxIn = 0., + double tau0In = 0.) { pdt[abs(idIn)] = ParticleDataEntry(idIn, + nameIn, spinTypeIn, chargeTypeIn, colTypeIn, m0In, mWidthIn, + mMinIn, mMaxIn, tau0In); } + void addParticle(int idIn, string nameIn, string antiNameIn, + int spinTypeIn = 0, int chargeTypeIn = 0, int colTypeIn = 0, + double m0In = 0., double mWidthIn = 0., double mMinIn = 0., + double mMaxIn = 0., double tau0In = 0.) { pdt[abs(idIn)] + = ParticleDataEntry(idIn, nameIn, antiNameIn, spinTypeIn, + chargeTypeIn, colTypeIn, m0In, mWidthIn, mMinIn, mMaxIn, tau0In); } + + // Reset all the properties of an entry in one go.. + void setAll(int idIn, string nameIn, string antiNameIn, + int spinTypeIn = 0, int chargeTypeIn = 0, int colTypeIn = 0, + double m0In = 0., double mWidthIn = 0., double mMinIn = 0., + double mMaxIn = 0.,double tau0In = 0.) { if (isParticle(idIn)) + pdt[abs(idIn)].setAll( nameIn, antiNameIn, spinTypeIn, chargeTypeIn, + colTypeIn, m0In, mWidthIn, mMinIn, mMaxIn, tau0In); } + + // Query existence of an entry. + bool isParticle(int idIn) { + if (pdt.find(abs(idIn)) == pdt.end()) return false; + if (idIn > 0 || pdt[abs(idIn)].hasAnti()) return true; + return false; } + + // Return the id of the sequentially next particle stored in table. + int nextId(int idIn) ; + + // Change current values one at a time (or set if not set before). + void name(int idIn, string nameIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setName(nameIn); } + void antiName(int idIn, string antiNameIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setAntiName(antiNameIn); } + void names(int idIn, string nameIn, string antiNameIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setNames(nameIn, antiNameIn); } + void spinType(int idIn, int spinTypeIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setSpinType(spinTypeIn); } + void chargeType(int idIn, int chargeTypeIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setChargeType(chargeTypeIn); } + void colType(int idIn, int colTypeIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setColType(colTypeIn); } + void m0(int idIn, double m0In) { + if (isParticle(idIn)) pdt[abs(idIn)].setM0(m0In); } + void mWidth(int idIn, double mWidthIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setMWidth(mWidthIn); } + void mMin(int idIn, double mMinIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setMMin(mMinIn); } + void mMax(int idIn, double mMaxIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setMMax(mMaxIn); } + void tau0(int idIn, double tau0In) { + if (isParticle(idIn)) pdt[abs(idIn)].setTau0(tau0In); } + void isResonance(int idIn, bool isResonanceIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setIsResonance(isResonanceIn); } + void mayDecay(int idIn, bool mayDecayIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setMayDecay(mayDecayIn); } + void doExternalDecay(int idIn, bool doExternalDecayIn) { + if (isParticle(idIn)) + pdt[abs(idIn)].setDoExternalDecay(doExternalDecayIn); } + void isVisible(int idIn, bool isVisibleIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setIsVisible(isVisibleIn); } + void doForceWidth(int idIn, bool doForceWidthIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setDoForceWidth(doForceWidthIn); } + void hasChanged(int idIn, bool hasChangedIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setHasChanged(hasChangedIn); } + + // Give back current values. + bool hasAnti(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].hasAnti() : false ; } + string name(int idIn) { + return (isParticle(abs(idIn))) ? pdt[abs(idIn)].name(idIn) : " "; } + int spinType(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].spinType() : 0 ; } + int chargeType(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].chargeType(idIn) : 0 ; } + double charge(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].charge(idIn) : 0 ; } + int colType(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].colType(idIn) : 0 ; } + double m0(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].m0() : 0. ; } + double mWidth(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].mWidth() : 0. ; } + double mMin(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].mMin() : 0. ; } + double m0Min(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].m0Min() : 0. ; } + double mMax(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].mMax() : 0. ; } + double m0Max(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].m0Max() : 0. ; } + double tau0(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].tau0() : 0. ; } + bool isResonance(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isResonance() : false ; } + bool mayDecay(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].mayDecay() : false ; } + bool doExternalDecay(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].doExternalDecay() : false ; } + bool isVisible(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isVisible() : false ; } + bool doForceWidth(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].doForceWidth() : false ; } + bool hasChanged(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].hasChanged() : false ; } + + // Give back special mass-related quantities. + bool useBreitWigner(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].useBreitWigner() : false ; } + double constituentMass(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].constituentMass() : 0. ; } + double mass(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].mass() : 0. ; } + double mRun(int idIn, double mH) { + return isParticle(idIn) ? pdt[abs(idIn)].mRun(mH) : 0. ; } + + // Give back other quantities. + bool canDecay(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].canDecay() : false ; } + bool isLepton(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isLepton() : false ; } + bool isQuark(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isQuark() : false ; } + bool isGluon(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isGluon() : false ; } + bool isDiquark(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isDiquark() : false ; } + bool isHadron(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isHadron() : false ; } + bool isMeson(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isMeson() : false ; } + bool isBaryon(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isBaryon() : false ; } + bool isOctetHadron(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].isOctetHadron() : false ; } + int heaviestQuark(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].heaviestQuark(idIn) : 0 ; } + int baryonNumberType(int idIn) { + return isParticle(idIn) ? pdt[abs(idIn)].baryonNumberType(idIn) : 0 ; } + + // Change branching ratios. + void rescaleBR(int idIn, double newSumBR = 1.) { + if (isParticle(idIn)) pdt[abs(idIn)].rescaleBR(newSumBR); } + + // Access methods stored in ResonanceWidths. + void setResonancePtr(int idIn, ResonanceWidths* resonancePtrIn) { + if (isParticle(idIn)) pdt[abs(idIn)].setResonancePtr( resonancePtrIn);} + void resInit(int idIn) { if (isParticle(idIn)) + pdt[abs(idIn)].resInit(infoPtr, settingsPtr, this, coupSMPtr);} + double resWidth(int idIn, double mHat, int idInFlav = 0, + bool openOnly = false, bool setBR = false) { + return isParticle(idIn) ? pdt[abs(idIn)].resWidth(idIn, mHat, + idInFlav, openOnly, setBR) : 0.;} + double resWidthOpen(int idIn, double mHat, int idInFlav = 0) { + return isParticle(idIn) ? pdt[abs(idIn)].resWidthOpen(idIn, mHat, + idInFlav) : 0.;} + double resWidthStore(int idIn, double mHat, int idInFlav = 0) { + return isParticle(idIn) ? pdt[abs(idIn)].resWidthStore(idIn, mHat, + idInFlav) : 0.;} + double resOpenFrac(int id1In, int id2In = 0, int id3In = 0); + double resWidthRescaleFactor(int idIn) { return isParticle(idIn) + ? pdt[abs(idIn)].resWidthRescaleFactor() : 0.;} + double resWidthChan(int idIn, double mHat, int idAbs1 = 0, + int idAbs2 = 0) { return isParticle(idIn) + ? pdt[abs(idIn)].resWidthChan( mHat, idAbs1, idAbs2) : 0.;} + + // Return pointer to entry. + ParticleDataEntry* particleDataEntryPtr(int idIn) { + return (isParticle(idIn)) ? &pdt[abs(idIn)] : &pdt[0]; } + +private: + + // Common data, accessible for the individual particles. + int modeBreitWigner; + double maxEnhanceBW, mQRun[7], Lambda5Run; + + // The individual particle need access to the full database. + friend class ParticleDataEntry; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointer to Standard Model couplings. + CoupSM* coupSMPtr; + + // All particle data stored in a map. + map pdt; + + // Pointer to current particle (e.g. when reading decay channels). + ParticleDataEntry* particlePtr; + + // Flag that initialization has been performed. + bool isInit; + + // Method for common setting of particle-specific info. + void initCommon(); + + // Useful functions for string handling. + string toLower(const string& name); + bool boolString(string tag); + string attributeValue(string line, string attribute); + bool boolAttributeValue(string line, string attribute); + int intAttributeValue(string line, string attribute); + double doubleAttributeValue(string line, string attribute); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_ParticleData_H diff --git a/PYTHIA8/pythia8140/include/ParticleDecays.h b/PYTHIA8/pythia8140/include/ParticleDecays.h new file mode 100644 index 00000000000..7b89066e529 --- /dev/null +++ b/PYTHIA8/pythia8140/include/ParticleDecays.h @@ -0,0 +1,146 @@ +// ParticleDecays.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the classes to perform a particle decay. +// DecayHandler: base class for external handling of decays. +// ParticleDecays: decay a particle. + +#ifndef Pythia8_ParticleDecays_H +#define Pythia8_ParticleDecays_H + +#include "Basics.h" +#include "Event.h" +#include "FragmentationFlavZpT.h" +#include "Info.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" +#include "TimeShower.h" + +namespace Pythia8 { + +//========================================================================== + +// DecayHandler is base class for the external handling of decays. +// There is only one pure virtual method, that should do the decay. + +class DecayHandler { + +public: + + // A pure virtual method, wherein the derived class method does a decay. + virtual bool decay(vector& idProd, vector& mProd, + vector& pProd, int iDec, const Event& event) = 0; + +protected: + + // Destructor. + virtual ~DecayHandler() {} + +}; + +//========================================================================== + +// The ParticleDecays class contains the routines to decay a particle. + +class ParticleDecays { + +public: + + // Constructor. + ParticleDecays() {} + + // Initialize: store pointers and find settings + void init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + TimeShower* timesDecPtrIn, StringFlav* flavSelPtrIn, + DecayHandler* decayHandlePtrIn, vector handledParticles); + + // Perform a decay of a single particle. + bool decay(int iDec, Event& event); + + // Did decay result in new partons to hadronize? + bool moreToDo() const {return hasPartons && keepPartons;} + +private: + + // Constants: could only be changed in the code itself. + static const int NTRYDECAY, NTRYPICK, NTRYMEWT, NTRYDALITZ; + static const double MSAFEDALITZ, WTCORRECTION[11]; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to timelike showers, for decays to partons (e.g. Upsilon). + TimeShower* timesDecPtr; + + // Pointer to class for flavour generation; needed when to pick hadrons. + StringFlav* flavSelPtr; + + // Pointer to a handler of external decays. + DecayHandler* decayHandlePtr; + + // Initialization data, read from Settings. + bool limitTau0, limitTau, limitRadius, limitCylinder, limitDecay, + mixB, doFSRinDecays; + double mSafety, tau0Max, tauMax, rMax, xyMax, zMax, xBdMix, xBsMix, + sigmaSoft, multIncrease, multRefMass, multGoffset, colRearrange, + stopMass, sRhoDal, wRhoDal; + + // Multiplicity. Decay products positions and masses. + bool hasPartons, keepPartons; + int idDec, meMode, mult; + double scale; + vector iProd, idProd, cols, acols, idPartons; + vector mProd, mInv, rndmOrd; + vector pInv, pProd; + vector flavEnds; + + // Pointer to particle data for currently decaying particle + ParticleDataEntry* decDataPtr; + + // Check whether a decay is allowed, given the upcoming decay vertex. + bool checkVertex(Particle& decayer); + + // Check for oscillations B0 <-> B0bar or B_s0 <-> B_s0bar. + bool oscillateB(Particle& decayer); + + // Do a one-body decay. + bool oneBody(Event& event); + + // Do a two-body decay; + bool twoBody(Event& event); + + // Do a three-body decay; + bool threeBody(Event& event); + + // Do a multibody decay using the M-generator algorithm. + bool mGenerator(Event& event); + + // Select mass of lepton pair in a Dalitz decay. + bool dalitzMass(); + + // Do kinematics of gamma* -> l- l+ in Dalitz decay. + bool dalitzKinematics(Event& event); + + // Translate a partonic content into a set of actual hadrons. + bool pickHadrons(); + + // Set colour flow and scale in a decay explicitly to partons. + bool setColours(Event& event); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_ParticleDecays_H diff --git a/PYTHIA8/pythia8140/include/PartonDistributions.h b/PYTHIA8/pythia8140/include/PartonDistributions.h new file mode 100644 index 00000000000..f3030ac5ba2 --- /dev/null +++ b/PYTHIA8/pythia8140/include/PartonDistributions.h @@ -0,0 +1,455 @@ +// PartonDistributions.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for parton densities. +// PDF: base class. +// LHAPDF: derived class for interface to the LHAPDF library. +// GRV94L: derived class for the GRV 94L parton densities. +// CTEQ5L: derived class for the CTEQ 5L parton densities. +// MSTWpdf: derived class for MRST LO*, LO**, MSTW 2008 LO, NLO. +// CTEQ6pdf: derived class for CTEQ 6L, 6L1, 66, CT09 MC1, MC2, (MCS?). +// ProtonPoint: unresolved proton with equivalent photon spectrum. +// GRVpiL: derived class for the GRV LO pion parton densities. +// PomFix: derived class for Q2-independent Pomeron parton densities. +// PomH1FitAB: derived class for the H1 2006 Fit A and Fit B Pomeron PDFs. +// PomH1Jets: derived class for the H1 2007 Jets Pomeron PDFs. +// Lepton: derived class for parton densities inside a lepton. +// LeptonPoint: derived class for unresolved lepton (mainly dummy). + +#ifndef Pythia8_PartonDistributions_H +#define Pythia8_PartonDistributions_H + +#include "Basics.h" +#include "Info.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// Base class for parton distribution functions. + +class PDF { + +public: + + // Constructor. + PDF(int idBeamIn = 2212) {idBeam = idBeamIn; idBeamAbs = abs(idBeam); + setValenceContent(); idSav = 9; xSav = -1.; Q2Sav = -1.; + xu = 0.; xd = 0.; xs = 0.; xubar = 0.; xdbar = 0.; xsbar = 0.; xc = 0.; + xb = 0.; xg = 0.; xlepton = 0.; xgamma = 0.; xuVal = 0.; xuSea = 0.; + xdVal = 0.; xdSea = 0.; isSet = true; isInit = false;} + + // Destructor. + virtual ~PDF() {} + + // Confirm that PDF has been set up (important for LHAPDF and H1 Pomeron). + bool isSetup() {return isSet;} + + // Dynamic choice of meson valence flavours for pi0, K0S, K0L, Pomeron. + void newValenceContent(int idVal1In, int idVal2In) { + idVal1 = idVal1In; idVal2 = idVal2In;} + + // Allow extrapolation beyond boundaries. This is optional. + virtual void setExtrapolate(bool) {} + + // Read out parton density + double xf(int id, double x, double Q2); + + // Read out valence and sea part of parton densities. + double xfVal(int id, double x, double Q2); + double xfSea(int id, double x, double Q2); + +protected: + + // Store relevant quantities. + int idBeam, idBeamAbs, idSav, idVal1, idVal2; + double xSav, Q2Sav; + double xu, xd, xs, xubar, xdbar, xsbar, xc, xb, xg, xlepton, xgamma, + xuVal, xuSea, xdVal, xdSea; + bool isSet, isInit; + + // Resolve valence content for assumed meson. Possibly modified later. + void setValenceContent(); + + // Update parton densities. + virtual void xfUpdate(int id, double x, double Q2) = 0; + +}; + +//========================================================================== + +// Provide interface to the LHAPDF library of parton densities. + +class LHAPDF : public PDF { + +public: + + // Constructor. + LHAPDF(int idBeamIn, string setName, int member, int nSetIn = 1, + Info* infoPtr = 0) : PDF(idBeamIn), nSet(nSetIn) + {init( setName, member, infoPtr);} + + // Allow extrapolation beyond boundaries. This is optional. + void setExtrapolate(bool extrapol); + +private: + + // Initialization of PDF set. + void init(string setName, int member, Info* infoPtr); + + // Update all PDF values. + void xfUpdate(int , double x, double Q2); + + // Current set and pdf values. + int nSet; + double xfArray[13]; + double xPhoton; + + // Keep track of latest initialized PDF, so does not have to repeat. + static string latestSetName; + static int latestMember, latestNSet; + +}; + +//========================================================================== + +// Gives the GRV 94L (leading order) parton distribution function set +// in parametrized form. Authors: M. Glueck, E. Reya and A. Vogt. + +class GRV94L : public PDF { + +public: + + // Constructor. + GRV94L(int idBeamIn = 2212) : PDF(idBeamIn) {} + +private: + + // Update PDF values. + void xfUpdate(int id, double x, double Q2); + + // Auxiliary routines used during the updating. + double grvv (double x, double n, double ak, double bk, double a, + double b, double c, double d); + double grvw (double x, double s, double al, double be, double ak, + double bk, double a, double b, double c, double d, double e, double es); + double grvs (double x, double s, double sth, double al, double be, + double ak, double ag, double b, double d, double e, double es); + +}; + +//========================================================================== + +// Gives the CTEQ 5L (leading order) parton distribution function set +// in parametrized form. Parametrization by J. Pumplin. Authors: CTEQ. + +class CTEQ5L : public PDF { + +public: + + // Constructor. + CTEQ5L(int idBeamIn = 2212) : PDF(idBeamIn) {} + +private: + + // Update PDF values. + void xfUpdate(int id, double x, double Q2); + +}; + +//========================================================================== + +// The MSTWpdf class. +// MRST LO*(*) and MSTW 2008 PDF's, specifically the LO one. +// Original C++ version by Jeppe Andersen. +// Modified by Graeme Watt . +// Sets available: +// iFit = 1 : MRST LO* (2007). +// iFit = 2 : MRST LO** (2008). +// iFit = 3 : MSTW 2008 LO, central member. +// iFit = 4 : MSTW 2008 NLO, central member. (Warning!) + +class MSTWpdf : public PDF { + +public: + + // Constructor. + MSTWpdf(int idBeamIn = 2212, int iFitIn = 1, string xmlPath = "../xmldoc/", + Info* infoPtr = 0) : PDF(idBeamIn) {init( iFitIn, xmlPath, infoPtr);} + +private: + + // Constants: could only be changed in the code itself. + static const int np, nx, nq, nqc0, nqb0; + static const double xmin, xmax, qsqmin, qsqmax, xxInit[65], qqInit[49]; + + // Data read in from grid file or set at initialization. + int iFit, alphaSorder, alphaSnfmax; + double mCharm, mBottom, alphaSQ0, alphaSMZ, distance, tolerance, + xx[65], qq[49], c[13][64][48][5][5]; + + // Initialization of data array. + void init( int iFitIn, string xmlPath, Info* infoPtr); + + // Update PDF values. + void xfUpdate(int id, double x, double Q2); + + // Evaluate PDF of one flavour species. + double parton(int flavour,double x,double q); + double parton_interpolate(int flavour,double xxx,double qqq); + double parton_extrapolate(int flavour,double xxx,double qqq); + + // Auxiliary routines for evaluation. + int locate(double xx[],int n,double x); + double polderivative1(double x1, double x2, double x3, double y1, + double y2, double y3); + double polderivative2(double x1, double x2, double x3, double y1, + double y2, double y3); + double polderivative3(double x1, double x2, double x3, double y1, + double y2, double y3); + +}; + +//========================================================================== + +// The CTEQ6pdf class. +// Sets available: +// iFit = 1 : CTEQ6L +// iFit = 2 : CTEQ6L1 +// iFit = 3 : CTEQ66.00 (NLO, central member) +// iFit = 4 : CT09MC1 +// iFit = 5 : CT09MC2 +// iFit = 6 : CT09MCS (not yet implemented) + +class CTEQ6pdf : public PDF { + +public: + + // Constructor. + CTEQ6pdf(int idBeamIn = 2212, int iFitIn = 1, string xmlPath = "../xmldoc/", + Info* infoPtr = 0) : PDF(idBeamIn) {init( iFitIn, xmlPath, infoPtr);} + +private: + + // Constants: could only be changed in the code itself. + static const double EPSILON, XPOWER; + + // Data read in from grid file or set at initialization. + int iFit, order, nQuark, nfMx, mxVal, nX, nT, nG, + iGridX, iGridQ, iGridLX, iGridLQ; + double lambda, mQ[7], qIni, qMax, tv[26], xMin, xv[202], upd[57773], + xvpow[202], xMinEps, xMaxEps, qMinEps, qMaxEps, fVec[5], + tConst[9], xConst[9], xLast, qLast; + + // Initialization of data array. + void init( int iFitIn, string xmlPath, Info* infoPtr); + + // Update PDF values. + void xfUpdate(int id, double x, double Q2); + + // Evaluate PDF of one flavour species. + double parton6(int iParton, double x, double q); + + // Interpolation in grid. + double polint4F(double xgrid[], double fgrid[], double xin); + +}; + +//========================================================================== + +// SA Unresolved proton: equivalent photon spectrum from +// V.M. Budnev, I.F. Ginzburg, G.V. Meledin and V.G. Serbo, +// Phys. Rept. 15 (1974/1975) 181. + +class ProtonPoint : public PDF { + +public: + + // Constructor. + ProtonPoint(int idBeamIn = 2212, Info* infoPtrIn = 0) : + PDF(idBeamIn), m_infoPtr(infoPtrIn) {} + +private: + + // Stored value for PDF choice. + static const double ALPHAEM, Q2MAX, Q20, A, B, C; + + // Update PDF values. + void xfUpdate(int id, double x, double Q2); + + // phi function from Q2 integration. + double phiFunc(double x, double Q); + + // Info and errors + Info* m_infoPtr; + +}; + +//========================================================================== + +// Gives the GRV 1992 pi+ (leading order) parton distribution function set +// in parametrized form. Authors: Glueck, Reya and Vogt. + +class GRVpiL : public PDF { + +public: + + // Constructor. + GRVpiL(int idBeamIn = 221) : PDF(idBeamIn) {} + +private: + + // Update PDF values. + void xfUpdate(int id, double x, double Q2); + +}; + +//========================================================================== + +// Gives generic Q2-independent Pomeron PDF. + +class PomFix : public PDF { + +public: + + // Constructor. + PomFix(int idBeamIn = 990, double PomGluonAIn = 0., + double PomGluonBIn = 0., double PomQuarkAIn = 0., + double PomQuarkBIn = 0., double PomQuarkFracIn = 0., + double PomStrangeSuppIn = 0.) : PDF(idBeamIn), + PomGluonA(PomGluonAIn), PomGluonB(PomGluonBIn), + PomQuarkA(PomQuarkAIn), PomQuarkB(PomQuarkBIn), + PomQuarkFrac(PomQuarkFracIn), PomStrangeSupp(PomStrangeSuppIn) + {init();} + +private: + + // Stored value for PDF choice. + double PomGluonA, PomGluonB, PomQuarkA, PomQuarkB, PomQuarkFrac, + PomStrangeSupp, normGluon, normQuark; + + // Initialization of some constants. + void init(); + + // Update PDF values. + void xfUpdate(int id, double x, double); + +}; + +//========================================================================== + +// The H1 2006 Fit A and Fit B Pomeron parametrization. +// H1 Collaboration, A. Aktas et al., "Measurement and QCD Analysis of +// the Diffractive Deep-Inelastic Scattering Cross Section at HERA", +// DESY-06-049, Eur. Phys. J. C48 (2006) 715. e-Print: hep-ex/0606004. + +class PomH1FitAB : public PDF { + +public: + + // Constructor. + PomH1FitAB(int idBeamIn = 990, int iFit = 1, double rescaleIn = 1., + string xmlPath = "../xmldoc/", Info* infoPtr = 0) : PDF(idBeamIn) + {rescale = rescaleIn; init( iFit, xmlPath, infoPtr);} + +private: + + // Limits for grid in x, in Q2, and data in (x, Q2). + int nx, nQ2; + double rescale, xlow, xupp, dx, Q2low, Q2upp, dQ2; + double gluonGrid[100][30]; + double quarkGrid[100][30]; + + // Initialization of data array. + void init( int iFit, string xmlPath, Info* infoPtr); + + // Update PDF values. + void xfUpdate(int id, double x, double ); + +}; + +//========================================================================== + +// The H1 2007 Jets Pomeron parametrization.. +// H1 Collaboration, A. Aktas et al., "Dijet Cross Sections and Parton +// Densities in Diffractive DIS at HERA", DESY-07-115, Aug 2007. 33pp. +// Published in JHEP 0710:042,2007. e-Print: arXiv:0708.3217 [hep-ex] + +class PomH1Jets : public PDF { + +public: + + // Constructor. + PomH1Jets(int idBeamIn = 990, double rescaleIn = 1., + string xmlPath = "../xmldoc/", Info* infoPtr = 0) : PDF(idBeamIn) + {rescale = rescaleIn; init( xmlPath, infoPtr);} + +private: + + // Arrays for grid in x, in Q2, and data in (x, Q2). + double rescale; + double xGrid[100]; + double Q2Grid[88]; + double gluonGrid[100][88]; + double singletGrid[100][88]; + double charmGrid[100][88]; + + // Initialization of data array. + void init( string xmlPath, Info* infoPtr); + + // Update PDF values. + void xfUpdate(int id, double x, double ); + +}; + +//========================================================================== + +// Gives electron (or muon, or tau) parton distribution. + +class Lepton : public PDF { + +public: + + // Constructor. + Lepton(int idBeamIn = 11) : PDF(idBeamIn) {} + +private: + + // Constants: could only be changed in the code itself. + static const double ALPHAEM, ME, MMU, MTAU; + + // Update PDF values. + void xfUpdate(int id, double x, double Q2); + + // The squared lepton mass, set at initialization. + double m2Lep; + +}; + +//========================================================================== + +// Gives electron (or other lepton) parton distribution when unresolved. + +class LeptonPoint : public PDF { + +public: + + // Constructor. + LeptonPoint(int idBeamIn = 11) : PDF(idBeamIn) {} + +private: + + // Update PDF values in trivial way. + void xfUpdate(int , double , double ) {xlepton = 1; xgamma = 0.;} + +}; + +} // end namespace Pythia8 + +//========================================================================== + +#endif // Pythia8_PartonDistributions_H diff --git a/PYTHIA8/pythia8140/include/PartonLevel.h b/PYTHIA8/pythia8140/include/PartonLevel.h new file mode 100644 index 00000000000..6f5bee4ece1 --- /dev/null +++ b/PYTHIA8/pythia8140/include/PartonLevel.h @@ -0,0 +1,163 @@ +// PartonLevel.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the main class for parton-level event generation +// PartonLevel: administrates showers, multiple interactions and remnants. + +#ifndef Pythia8_PartonLevel_H +#define Pythia8_PartonLevel_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "BeamRemnants.h" +#include "Event.h" +#include "Info.h" +#include "MultipleInteractions.h" +#include "ParticleData.h" +#include "PartonSystems.h" +#include "PythiaStdlib.h" +#include "Settings.h" +#include "SigmaTotal.h" +#include "SpaceShower.h" +#include "StandardModel.h" +#include "TimeShower.h" +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// The PartonLevel class contains the top-level routines to generate +// the partonic activity of an event. + +class PartonLevel { + +public: + + // Constructor. + PartonLevel() : userHooksPtr(0) {} + + // Initialization of all classes at the parton level. + bool init( Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + BeamParticle* beamPomAPtrIn, BeamParticle* beamPomBPtrIn, + CoupSM* coupSMPtrIn, PartonSystems* partonSystemsPtrIn, + SigmaTotal* sigmaTotPtr, TimeShower* timesDecPtrIn, + TimeShower* timesPtrIn, SpaceShower* spacePtrIn, + UserHooks* userHooksPtrIn); + + // Generate the next parton-level process. + bool next( Event& process, Event& event); + + // Tell whether failure was due to vetoing. + bool hasVetoed() const {return doVeto;} + + // Accumulate and print statistics. + void accumulate() {multiPtr->accumulate();} + void statistics(bool reset = false) { + if (doMI) multiMB.statistics(reset);} + // For now no separate statistics for diffraction?? + //if (doMISDA && doDiffraction) multiSDA.statistics(reset); + //if (doMISDB && doDiffraction) multiSDB.statistics(reset);} + +private: + + // Constants: could only be changed in the code itself. + static const int NTRY; + + // Initialization data, mainly read from Settings. + bool doMinBias, doDiffraction, doMI, doMIMB, doMISDA, doMISDB, doMIinit, + doISR, doFSRduringProcess, doFSRafterProcess, doFSRinResonances, + doRemnants, doSecondHard, hasLeptonBeams, hasPointLeptons, + canVetoPT, canVetoStep, canVetoMIStep, canSetScale; + double mMinDiff, mWidthDiff; + + // Event generation strategy. Number of steps. Maximum pT scales. + bool doVeto; + int nMI, nISR, nFSRinProc, nFSRinRes, nISRhard, nFSRhard, + typeLatest, nVetoStep, typeVetoStep, nVetoMIStep, iSysNow; + double pTsaveMI, pTsaveISR, pTsaveFSR, pTvetoPT; + + // Current event properties. + bool isMinBias, isDiffA, isDiffB, isDiff, isSingleDiff, isDoubleDiff, + isResolved, isResolvedA, isResolvedB; + int sizeProcess, sizeEvent; + double eCMsave; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to the two incoming beams. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + + // Spare copies of normal pointers. Pointers to Pomeron beam-inside-beam. + BeamParticle* beamHadAPtr; + BeamParticle* beamHadBPtr; + BeamParticle* beamPomAPtr; + BeamParticle* beamPomBPtr; + + // Pointers to Standard Model couplings. + CoupSM* coupSMPtr; + + // Pointer to information on subcollision parton locations. + PartonSystems* partonSystemsPtr; + + // Pointer to userHooks object for user interaction with program. + UserHooks* userHooksPtr; + + // Pointers to timelike showers for resonance decays and the rest. + TimeShower* timesDecPtr; + TimeShower* timesPtr; + + // Pointer to spacelike showers. + SpaceShower* spacePtr; + + // The generator classes for multiple interactions. + MultipleInteractions multiMB; + MultipleInteractions multiSDA; + MultipleInteractions multiSDB; + MultipleInteractions* multiPtr; + + // The generator class to construct beam-remnant kinematics. + BeamRemnants remnants; + + // Resolved diffraction: find how many systems should have it. + int decideResolvedDiff( Event& process); + + // Set up an unresolved process, i.e. elastic or diffractive. + bool setupUnresolvedSys( Event& process, Event& event); + + // Set up the hard process, excluding subsequent resonance decays. + void setupHardSys( int iHardLoop, Event& process, Event& event); + // Keep track of how much of hard process has been handled. + int nHardDone; + + // Resolved diffraction: pick whether to have it and set up for it. + void setupResolvedDiff( int iHardLoop, Event& process); + + // Resolved diffraction: restore normal behaviour. + void leaveResolvedDiff( int iHardLoop, Event& event); + + // Perform showers in resonance decay chains. + bool resonanceShowers( Event& process, Event& event); + + // Position in main event record of hard partons before showers. + vector iPosBefShow; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_PartonLevel_H diff --git a/PYTHIA8/pythia8140/include/PartonSystems.h b/PYTHIA8/pythia8140/include/PartonSystems.h new file mode 100644 index 00000000000..e6e1fddd2e6 --- /dev/null +++ b/PYTHIA8/pythia8140/include/PartonSystems.h @@ -0,0 +1,95 @@ +// PartonSystems.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains auxiliary classes for the parton-level processes. +// PartonSystem contains info on a single partonic subcollision. +// PartonSystems describes the set of subcollisions in the whole event. + +#ifndef Pythia8_PartonSystems_H +#define Pythia8_PartonSystems_H + +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// The PartonSystem class contains info on an individual singlet. +// Only to be used inside PartonSystems, so no private members. + +class PartonSystem { + +public: + + // Constructors. + PartonSystem() : iInA(0), iInB(0), sHat(0.) {iOut.reserve(10);} + + // Stored quantities. + int iInA, iInB; + vector iOut; + double sHat; + +}; + +//========================================================================== + +// The PartonSystems class describes the whole set of subcollisions. + +class PartonSystems { + +public: + + // Constructor. + PartonSystems() {systems.resize(0);} + + // Reset system list to empty. + void clear() {systems.resize(0);} + + // Add new subsystem to list; return its index. Number of subsystems. + int addSys() {systems.push_back(PartonSystem()); + return systems.size() - 1;} + int sizeSys() const {return systems.size();} + + // Set, add or replace info to one system. + void setInA(int iSys, int iPos) {systems[iSys].iInA = iPos;} + void setInB(int iSys, int iPos) {systems[iSys].iInB = iPos;} + void addOut(int iSys, int iPos) {systems[iSys].iOut.push_back(iPos);} + void setOut(int iSys, int iMem, int iPos) {systems[iSys].iOut[iMem] = iPos;} + void replace(int iSys, int iPosOld, int iPosNew); + void setSHat(int iSys, double sHatIn) {systems[iSys].sHat = sHatIn;} + + // Get info on one system. + bool hasInAB(int iSys) const {return ( (systems[iSys].iInA > 0) + || (systems[iSys].iInB > 0) ) ;} + int getInA(int iSys) const {return systems[iSys].iInA;} + int getInB(int iSys) const {return systems[iSys].iInB;} + int sizeOut(int iSys) const {return systems[iSys].iOut.size();} + int getOut(int iSys, int iMem) const {return systems[iSys].iOut[iMem];} + int sizeAll(int iSys) const {return (hasInAB(iSys)) + ? systems[iSys].iOut.size() + 2 : systems[iSys].iOut.size();} + int getAll(int iSys, int iMem) const; + double getSHat(int iSys) const {return systems[iSys].sHat;} + + // Find system of given outgoing parton, optionally also incoming one. + int getSystemOf(int iPos, bool alsoIn = false) const; + + // Find iOut index of given system and event record index + int getIndexOfOut(int iSys, int iPos) const; + + // List all current systems. + void list(ostream& os = cout) const; + +private: + + // List of all separate partonic subsystems. + vector systems; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_PartonSystems_H diff --git a/PYTHIA8/pythia8140/include/PhaseSpace.h b/PYTHIA8/pythia8140/include/PhaseSpace.h new file mode 100644 index 00000000000..f1437570c5b --- /dev/null +++ b/PYTHIA8/pythia8140/include/PhaseSpace.h @@ -0,0 +1,514 @@ +// PhaseSpace.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for phase space generators in kinematics selection. +// PhaseSpace: base class for phase space generators. +// Base class for derived classes> 2 ->1 , 2 -> 2, 2 -> 2 elastic/diffractive, +// 2 -> 2 minbias, 2 -> 3, Les Houches. + +#ifndef Pythia8_PhaseSpace_H +#define Pythia8_PhaseSpace_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Info.h" +#include "LesHouches.h" +#include "MultipleInteractions.h" +#include "ParticleData.h" +#include "PartonDistributions.h" +#include "PythiaStdlib.h" +#include "SigmaProcess.h" +#include "SigmaTotal.h" +#include "Settings.h" +#include "StandardModel.h" +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// Forward reference to the UserHooks class. +class UserHooks; + +//========================================================================== + +// PhaseSpace is a base class for phase space generators +// used in the selection of hard-process kinematics. + +class PhaseSpace { + +public: + + // Destructor. + virtual ~PhaseSpace() {} + + // Perform simple initialization and store pointers. + void init(bool isFirst, SigmaProcess* sigmaProcessPtrIn, + Info* infoPtrIn, Settings* settingsPtrIn, ParticleData* particleDataPtrIn, + Rndm* rndmPtrIn, BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + CoupSM* coupSMPtrIn, SigmaTotal* sigmaTotPtrIn, UserHooks* userHooksPtrIn); + + // Update the CM energy of the event. + void newECM(double eCMin) {eCM = eCMin; s = eCM * eCM;} + + // Store or replace Les Houches pointer. + void setLHAPtr(LHAup* lhaUpPtrIn) {lhaUpPtr = lhaUpPtrIn;} + + // A pure virtual method, wherein an optimization procedure + // is used to determine how phase space should be sampled. + virtual bool setupSampling() = 0; + + // A pure virtual method, wherein a trial event kinematics + // is to be selected in the derived class + virtual bool trialKin(bool inEvent = true, bool repeatSame = false) = 0; + + // A pure virtual method, wherein the accepted event kinematics + // is to be constructed in the derived class + virtual bool finalKin() = 0; + + // Allow for nonisotropic decays when ME's available. + void decayKinematics( Event& process); + + // Give back current or maximum cross section, or set latter. + double sigmaNow() const {return sigmaNw;} + double sigmaMax() const {return sigmaMx;} + bool newSigmaMax() const {return newSigmaMx;} + void setSigmaMax(double sigmaMaxIn) {sigmaMx = sigmaMaxIn;} + + // For Les Houches with negative event weight needs + virtual double sigmaSumSigned() const {return sigmaMx;} + + // Give back constructed four-vectors and known masses. + Vec4 p(int i) const {return pH[i];} + double m(int i) const {return mH[i];} + + // Give back other event properties. + double ecm() const {return eCM;} + double x1() const {return x1H;} + double x2() const {return x2H;} + double sHat() const {return sH;} + double tHat() const {return tH;} + double uHat() const {return uH;} + double pTHat() const {return pTH;} + double thetaHat() const {return theta;} + double phiHat() const {return phi;} + double runBW3() const {return runBW3H;} + double runBW4() const {return runBW4H;} + double runBW5() const {return runBW5H;} + + // Inform whether beam particles are resolved in partons or scatter directly. + virtual bool isResolved() const {return true;} + +protected: + + // Constructor. + PhaseSpace() {} + + // Constants: could only be changed in the code itself. + static const int NMAXTRY, NTRY3BODY; + static const double SAFETYMARGIN, TINY, EVENFRAC, SAMESIGMA, WIDTHMARGIN, + SAMEMASS, MASSMARGIN, EXTRABWWTMAX, THRESHOLDSIZE, + THRESHOLDSTEP, YRANGEMARGIN, LEPTONXMIN, LEPTONXMAX, + LEPTONXLOGMIN, LEPTONXLOGMAX, LEPTONTAUMIN, + SHATMINZ, PT2RATMINZ, WTCORRECTION[11]; + + // Pointer to cross section. + SigmaProcess* sigmaProcessPtr; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to incoming beams. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + + // Pointer to Standard Model couplings. + CoupSM* coupSMPtr; + + // Pointer to the total/elastic/diffractive cross section object. + SigmaTotal* sigmaTotPtr; + + // Pointer to userHooks object for user interaction with program. + UserHooks* userHooksPtr; + + // Pointer to LHAup for generating external events. + LHAup* lhaUpPtr; + + // Initialization data, normally only set once. + bool useBreitWigners, doEnergySpread, showSearch, showViolation, + increaseMaximum; + int gmZmodeGlobal; + double mHatGlobalMin, mHatGlobalMax, pTHatGlobalMin, pTHatGlobalMax, + pTHatMinDiverge, minWidthBreitWigners; + + // Information on incoming beams. + int idA, idB; + double mA, mB, eCM, s; + bool hasLeptonBeams, hasPointLeptons; + + // Cross section information. + bool newSigmaMx, canModifySigma; + int gmZmode; + double wtBW, sigmaNw, sigmaMx, sigmaPos, sigmaNeg; + + // Process-specific kinematics properties, almost always available. + double mHatMin, mHatMax, sHatMin, sHatMax, pTHatMin, pTHatMax, + pT2HatMin, pT2HatMax; + + // Event-specific kinematics properties, almost always available. + double x1H, x2H, m3, m4, m5, s3, s4, s5, mHat, sH, tH, uH, pAbs, p2Abs, + pTH, theta, phi, betaZ; + Vec4 pH[6]; + double mH[6]; + + // Reselect decay products momenta isotropically in phase space. + void decayKinematicsStep( Event& process, int iRes); + + // Much common code for normal 2 -> 1, 2 -> 2 and 2 -> 3 cases: + + // Determine how phase space should be sampled. + void setup3Body(); + bool setupSampling123(bool is2, bool is3, ostream& os = cout); + + // Select a trial kinematics phase space point. + bool trialKin123(bool is2, bool is3, bool inEvent = true, ostream& os = cout); + + // Presence and properties of any s-channel resonances. + int idResA, idResB; + double mResA, mResB, GammaResA, GammaResB, tauResA, tauResB, widResA, + widResB; + bool sameResMass; + + // Kinematics properties specific to 2 -> 1/2/3. + bool useMirrorWeight; + double tau, y, z, tauMin, tauMax, yMax, zMin, zMax, ratio34, unity34, + zNeg, zPos, wtTau, wtY, wtZ, wt3Body, runBW3H, runBW4H, runBW5H, + intTau0, intTau1, intTau2, intTau3, intTau4, intTau5, intTau6, + intY0, intY12, intY34, intY56, mTchan1, sTchan1, mTchan2, sTchan2, + frac3Flat, frac3Pow1, frac3Pow2; + Vec4 p3cm, p4cm, p5cm; + + // Coefficients for optimized selection in 2 -> 1/2/3. + int nTau, nY, nZ; + double tauCoef[8], yCoef[8], zCoef[8], tauCoefSum[8], yCoefSum[8], + zCoefSum[8]; + + // Calculate kinematical limits for 2 -> 1/2/3. + bool limitTau(bool is2, bool is3); + bool limitY(); + bool limitZ(); + + // Select kinematical variable between defined limits for 2 -> 1/2/3. + void selectTau(int iTau, double tauVal, bool is2); + void selectY(int iY, double yVal); + void selectZ(int iZ, double zVal); + bool select3Body(); + + // Solve equation system for better phase space coefficients in 2 -> 1/2/3. + void solveSys( int n, int bin[8], double vec[8], double mat[8][8], + double coef[8], ostream& os = cout); + + // Properties specific to resonance mass selection in 2 -> 2 and 2 -> 3. + bool useBW[6]; + int idMass[6]; + double mPeak[6], sPeak[6], mWidth[6], mMin[6], mMax[6], mw[6], wmRat[6], + mLower[6], mUpper[6], sLower[6], sUpper[6], fracFlat[6], fracInv[6], + fracInv2[6], atanLower[6], atanUpper[6], intBW[6], intFlat[6], + intInv[6], intInv2[6]; + + // Setup mass selection for one resonance at a time. Split in two parts. + void setupMass1(int iM); + void setupMass2(int iM, double distToThresh); + + // Do mass selection and find the associated weight. + void trialMass(int iM); + double weightMass(int iM); + +}; + +//========================================================================== + +// A derived class with 2 -> 1 kinematics set up in tau, y. + +class PhaseSpace2to1tauy : public PhaseSpace { + +public: + + // Constructor. + PhaseSpace2to1tauy() {} + + // Optimize subsequent kinematics selection. + virtual bool setupSampling() {if (!setupMass()) return false; + return setupSampling123(false, false);} + + // Construct the trial kinematics. + virtual bool trialKin(bool inEvent = true, bool = false) {wtBW = 1.; + return trialKin123(false, false, inEvent);} + + // Construct the final event kinematics. + virtual bool finalKin(); + +private: + + // Set up allowed mass range. + bool setupMass(); + +}; + +//========================================================================== + +// A derived class with 2 -> 2 kinematics set up in tau, y, z = cos(theta). + +class PhaseSpace2to2tauyz : public PhaseSpace { + +public: + + // Constructor. + PhaseSpace2to2tauyz() {} + + // Optimize subsequent kinematics selection. + virtual bool setupSampling() {if (!setupMasses()) return false; + return setupSampling123(true, false);} + + // Construct the trial kinematics. + virtual bool trialKin(bool inEvent = true, bool = false) { + if (!trialMasses()) return false; + return trialKin123(true, false, inEvent);} + + // Construct the final event kinematics. + virtual bool finalKin(); + +private: + + // Set up for fixed or Breit-Wigner mass selection. + bool setupMasses(); + + // Select fixed or Breit-Wigner-distributed masses. + bool trialMasses(); + + // Pick off-shell initialization masses when on-shell not allowed. + bool constrainedM3M4(); + bool constrainedM3(); + bool constrainedM4(); + +}; + +//========================================================================== + +// A derived class with 2 -> 2 kinematics set up for elastic scattering. + +class PhaseSpace2to2elastic : public PhaseSpace { + +public: + + // Constructor. + PhaseSpace2to2elastic() {} + + // Construct the trial or final event kinematics. + virtual bool setupSampling(); + virtual bool trialKin(bool inEvent = true, bool = false); + virtual bool finalKin(); + + // Are beam particles resolved in partons or scatter directly? + virtual bool isResolved() const {return false;} + +private: + + // Constants: could only be changed in the code itself. + static const double EXPMAX, CONVERTEL; + + // Kinematics properties specific to 2 -> 2 elastic. + bool useCoulomb; + double s1, s2, bSlope, lambda12S, tLow, tUpp, tAux, sigmaTot, rho, + lambda, tAbsMin, phaseCst, alphaEM0, sigmaNuc, sigmaCou, signCou; + + // Calculation of alphaElectromagnetic. + AlphaEM alphaEM; + +}; + +//========================================================================== + +// A derived class with 2 -> 2 kinematics set up for diffractive scattering. + +class PhaseSpace2to2diffractive : public PhaseSpace { + +public: + + // Constructor. + PhaseSpace2to2diffractive(bool isDiffAin = false, bool isDiffBin = false) + : isDiffA(isDiffAin), isDiffB(isDiffBin) {} + + // Construct the trial or final event kinematics. + virtual bool setupSampling(); + virtual bool trialKin(bool inEvent = true, bool = false); + virtual bool finalKin(); + + // Are beam particles resolved in partons or scatter directly? + virtual bool isResolved() const {return false;} + +private: + + // Constants: could only be changed in the code itself. + static const int NTRY; + static const double EXPMAX, DIFFMASSMAX; + + // Initialization data, in constructor or read from Settings. + bool isDiffA, isDiffB; + int PomFlux; + double epsilonPF, alphaPrimePF; + + // Initialization: kinematics properties specific to 2 -> 2 diffractive. + double m3ElDiff, m4ElDiff, s1, s2, lambda12, lambda34, tLow, tUpp, + cRes, sResXB, sResAX, sProton, bMin, bSlope, bSlope1, bSlope2, + probSlope1, xIntPF, xtCorPF, mp24DL, coefDL, tAux, tAux1, tAux2; + +}; + +//========================================================================== + +// A derived class for minumum bias events. Hardly does anything, since +// the real action is taken care of by the MultipleInteractions class. + +class PhaseSpace2to2minbias : public PhaseSpace { + +public: + + // Constructor. + PhaseSpace2to2minbias() {} + + // Construct the trial or final event kinematics. + virtual bool setupSampling() {sigmaNw = sigmaProcessPtr->sigmaHat(); + sigmaMx = sigmaNw; return true;} + virtual bool trialKin( bool , bool = false) {return true;} + virtual bool finalKin() {return true;} + +private: + +}; + +//========================================================================== + +// A derived class with 2 -> 3 kinematics 1 + 2 -> 3 + 4 + 5 set up in +// tau, y, pT2_4, pT2_5, phi_4, phi_5 and y_3 (partial cylindrical symmetry). + +class PhaseSpace2to3tauycyl : public PhaseSpace { + +public: + + // Constructor. + PhaseSpace2to3tauycyl() {} + + // Optimize subsequent kinematics selection. + virtual bool setupSampling() {if (!setupMasses()) return false; + setup3Body(); return setupSampling123(false, true);} + + // Construct the trial kinematics. + virtual bool trialKin(bool inEvent = true, bool = false) { + if (!trialMasses()) return false; + return trialKin123(false, true, inEvent);} + + // Construct the final event kinematics. + virtual bool finalKin(); + +private: + + // Constants: could only be changed in the code itself. + static const int NITERNR; + + // Set up for fixed or Breit-Wigner mass selection. + bool setupMasses(); + + // Select fixed or Breit-Wigner-distributed masses. + bool trialMasses(); + +}; + +//========================================================================== + +// A derived class with 2 -> 3 kinematics 1 + 2 -> 3 + 4 + 5 set up in +// y3, y4, y5, pT2_3, pT2_5, phi_3 and phi_5, and with R separation cut. +// Intended specifically for (essentially massless) 2 -> 3 QCD processes. + +class PhaseSpace2to3yyycyl : public PhaseSpace { + +public: + + // Constructor. + PhaseSpace2to3yyycyl() {} + + // Optimize subsequent kinematics selection. + virtual bool setupSampling(); + + // Construct the trial kinematics. + virtual bool trialKin(bool inEvent = true, bool = false); + + // Construct the final event kinematics. + virtual bool finalKin(); + +private: + + // Phase space cuts specifically for 2 -> 3 QCD processes. + double pTHat3Min, pTHat3Max, pTHat5Min, pTHat5Max, RsepMin, R2sepMin; + bool hasBaryonBeams; + + // Event kinematics choices. + double pT3Min, pT3Max, pT5Min, pT5Max, y3Max, y4Max, y5Max, + pT3, pT4, pT5, phi3, phi4, phi5, y3, y4, y5, dphi; + Vec4 pInSum; + +}; + +//========================================================================== + +// A derived class for Les Houches events. + +class PhaseSpaceLHA : public PhaseSpace { + +public: + + // Constructor. + PhaseSpaceLHA() {idProcSave = 0;} + + // Find maximal cross section for comparison with internal processes. + virtual bool setupSampling(); + + // Construct the next process, by interface to Les Houches class. + virtual bool trialKin( bool , bool repeatSame = false); + + // Set scale, alpha_s and alpha_em if not done. + virtual bool finalKin() {sigmaProcessPtr->setScale(); return true;} + + // For Les Houches with negative event weight needs + virtual double sigmaSumSigned() const {return sigmaSgn;} + +private: + + // Constants. + static const double CONVERTPB2MB; + + // Local properties. + int strategy, stratAbs, nProc, idProcSave; + double xMaxAbsSum, xSecSgnSum, sigmaSgn; + vector idProc; + vector xMaxAbsProc; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_PhaseSpace_H + diff --git a/PYTHIA8/pythia8140/include/ProcessContainer.h b/PYTHIA8/pythia8140/include/ProcessContainer.h new file mode 100644 index 00000000000..f9e9fc6691d --- /dev/null +++ b/PYTHIA8/pythia8140/include/ProcessContainer.h @@ -0,0 +1,180 @@ +// ProcessContainer.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the collected machinery of a process. +// ProcessContainer: contains information on a particular process. +// SetupContainers: administrates the selection/creation of processes. + +#ifndef Pythia8_ProcessContainer_H +#define Pythia8_ProcessContainer_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Event.h" +#include "Info.h" +#include "ParticleData.h" +#include "PartonDistributions.h" +#include "PhaseSpace.h" +#include "PythiaStdlib.h" +#include "ResonanceDecays.h" +#include "Settings.h" +#include "SigmaProcess.h" +#include "SigmaTotal.h" +#include "StandardModel.h" +#include "SusyCouplings.h" +#include "SusyLesHouches.h" +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// The ProcessContainer class combines pointers to matrix element and +// phase space generator with general generation info. + +class ProcessContainer { + +public: + + // Constructor. + ProcessContainer(SigmaProcess* sigmaProcessPtrIn = 0, + bool externalPtrIn = false) : sigmaProcessPtr(sigmaProcessPtrIn), + externalPtr(externalPtrIn), phaseSpacePtr(0) {} + + // Destructor. Do not destroy external sigmaProcessPtr. + ~ProcessContainer() {delete phaseSpacePtr; + if (!externalPtr) delete sigmaProcessPtr;} + + // Initialize phase space and counters. + bool init(bool isFirst, Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, BeamParticle* beamAPtr, + BeamParticle* beamBPtr, CoupSM* coupSMPtr, SigmaTotal* sigmaTotPtr, + CoupSUSY* coupSUSYPtr, ResonanceDecays* resDecaysPtrIn, + SusyLesHouches* slhaPtr, UserHooks* userHooksPtr); + + // Store or replace Les Houches pointer. + void setLHAPtr( LHAup* lhaUpPtrIn) {lhaUpPtr = lhaUpPtrIn; + if (sigmaProcessPtr > 0) sigmaProcessPtr->setLHAPtr(lhaUpPtr); + if (phaseSpacePtr > 0) phaseSpacePtr->setLHAPtr(lhaUpPtr);} + + // Update the CM energy of the event. + void newECM(double eCM) {phaseSpacePtr->newECM(eCM);} + + // Generate a trial event; accepted or not. + bool trialProcess(); + + // Give the hard subprocess (with option for a second hard subprocess). + bool constructProcess( Event& process, bool isHardest = true); + + // Do resonance decays. + bool decayResonances( Event& process); + + // Accumulate statistics after user veto. + void accumulate() {++nAcc;} + + // Reset statistics on events generated so far. + void reset(); + + // Process name and code, and the number of final-state particles. + string name() const {return sigmaProcessPtr->name();} + int code() const {return sigmaProcessPtr->code();} + int nFinal() const {return sigmaProcessPtr->nFinal();} + bool isSUSY() const {return sigmaProcessPtr->isSUSY();} + + // Member functions for info on generation process. + bool newSigmaMax() const {return newSigmaMx;} + double sigmaMax() const {return sigmaMx;} + long nTried() const {return nTry;} + long nSelected() const {return nSel;} + long nAccepted() const {return nAcc;} + double sigmaSelMC() {if (nTry > nTryStat) sigmaDelta(); return sigmaAvg;} + double sigmaMC() {if (nTry > nTryStat) sigmaDelta(); return sigmaFin;} + double deltaMC() {if (nTry > nTryStat) sigmaDelta(); return deltaFin;} + + // Some kinematics quantities. + int id1() const {return sigmaProcessPtr->id(1);} + int id2() const {return sigmaProcessPtr->id(2);} + double x1() const {return phaseSpacePtr->x1();} + double x2() const {return phaseSpacePtr->x2();} + double Q2Fac() const {return sigmaProcessPtr->Q2Fac();} + double mHat() const {return sqrtpos(phaseSpacePtr->sHat());} + double pTHat() const {return phaseSpacePtr->pTHat();} + + // Tell whether container is for Les Houches events. + bool isLHAContainer() const {return isLHA;} + + // When two hard processes set or get info whether process is matched. + void isSame( bool isSameIn) { isSameSave = isSameIn;} + bool isSame() const {return isSameSave;} + +private: + + // Constants: could only be changed in the code itself. + static const int N12SAMPLE, N3SAMPLE; + + // Pointer to the subprocess matrix element. Mark if external. + SigmaProcess* sigmaProcessPtr; + bool externalPtr; + + // Pointer to the phase space generator. + PhaseSpace* phaseSpacePtr; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointer to ResonanceDecays object for sequential resonance decays. + ResonanceDecays* resDecaysPtr; + + // Pointer to LHAup for generating external events. + LHAup* lhaUpPtr; + + // Info on process. + bool isLHA, isMinBias, isResolved, isDiffA, isDiffB, isQCD3body, + allowNegSig, hasOctetOnium, isSameSave, increaseMaximum; + int lhaStrat, lhaStratAbs; + + // Statistics on generation process. (Long integers just in case.) + bool newSigmaMx; + long nTry, nSel, nAcc, nTryStat; + double sigmaMx, sigmaSgn, sigmaSum, sigma2Sum, sigmaNeg, sigmaAvg, + sigmaFin, deltaFin; + + // Estimate integrated cross section and its uncertainty. + void sigmaDelta(); + +}; + +//========================================================================== + +// The SetupContainers class turns the list of user-requested processes +// into a vector of ProcessContainer objects, each with a process. + +class SetupContainers { + +public: + + // Constructor. + SetupContainers() {} + + // Initialization assuming all necessary data already read. + bool init(vector& containerPtrs, Settings& settings, + ParticleData* particleDataPtr, CoupSUSY& coupSUSY); + + // Initialization of a second hard process. + bool init2(vector& container2Ptrs, Settings& settings); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_ProcessContainer_H diff --git a/PYTHIA8/pythia8140/include/ProcessLevel.h b/PYTHIA8/pythia8140/include/ProcessLevel.h new file mode 100644 index 00000000000..941c7623279 --- /dev/null +++ b/PYTHIA8/pythia8140/include/ProcessLevel.h @@ -0,0 +1,152 @@ +// ProcessLevel.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the main class for process-level event generation. +// ProcessLevel: administrates the selection of "hard" process. + +#ifndef Pythia8_ProcessLevel_H +#define Pythia8_ProcessLevel_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Event.h" +#include "Info.h" +#include "ParticleData.h" +#include "PartonDistributions.h" +#include "ProcessContainer.h" +#include "PythiaStdlib.h" +#include "ResonanceDecays.h" +#include "Settings.h" +#include "SigmaTotal.h" +#include "SusyCouplings.h" +#include "SusyLesHouches.h" +#include "StandardModel.h" +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// The ProcessLevel class contains the top-level routines to generate +// the characteristic "hard" process of an event. + +class ProcessLevel { + +public: + + // Constructor. + ProcessLevel() : iLHACont(-1) {} + + // Destructor to delete processes in containers. + ~ProcessLevel(); + + // Initialization. + bool init( Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, CoupSM* CoupSMPtrIn, + SigmaTotal* sigmaTotPtrIn, bool doLHAin, SusyLesHouches* slhaPtrIn, + UserHooks* userHooksPtrIn, vector& sigmaPtrs, + ostream& os = cout); + + // Store or replace Les Houches pointer. + void setLHAPtr( LHAup* lhaUpPtrIn) {lhaUpPtr = lhaUpPtrIn; + if (iLHACont >= 0) containerPtrs[iLHACont]->setLHAPtr(lhaUpPtr);} + + // Generate the next "hard" process. + bool next( Event& process); + + // Accumulate and update statistics (after possible user veto). + void accumulate(); + + // Print statistics on cross sections and number of events. + void statistics(bool reset = false, ostream& os = cout); + + // Add any junctions to the process event record list. + void findJunctions( Event& junEvent); + +private: + + // Constants: could only be changed in the code itself. + static const int MAXLOOP; + + // Generic info for process generation. + bool doSecondHard, doSameCuts, allHardSame, noneHardSame, + someHardSame, cutsAgree, cutsOverlap, doResDecays; + int nImpact, startColTag; + double mHatMin1, mHatMax1, pTHatMin1, pTHatMax1, mHatMin2, mHatMax2, + pTHatMin2, pTHatMax2, sigmaND, sumImpactFac, sum2ImpactFac; + + // Vector of containers of internally-generated processes. + vector containerPtrs; + int iContainer, iLHACont; + double sigmaMaxSum; + + // Ditto for optional choice of a second hard process. + vector container2Ptrs; + int i2Container; + double sigma2MaxSum; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to the two incoming beams. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + + // Pointer to Standard Model couplings, including alphaS and alphaEM. + CoupSM* coupSMPtr; + + // Pointer to SigmaTotal object needed to handle soft QCD processes. + SigmaTotal* sigmaTotPtr; + + // The CoupSUSY object needed to handle SUSY processes. + CoupSUSY coupSUSY; + + // Pointer to SusyLesHouches object for interface to SUSY spectra. + SusyLesHouches* slhaPtr; + + // Pointer to userHooks object for user interaction with program. + UserHooks* userHooksPtr; + + // Pointer to LHAup for generating external events. + LHAup* lhaUpPtr; + + // Initialization routine for SUSY spectra. + bool initSLHA(Settings& settings); + + // ResonanceDecay object does sequential resonance decays. + ResonanceDecays resonanceDecays; + + // Generate the next event with one interaction. + bool nextOne( Event& process); + + // Generate the next event with two hard interactions. + bool nextTwo( Event& process); + + // Append the second to the first process list. + void combineProcessRecords( Event& process, Event& process2); + + // Check that colours match up. + bool checkColours( Event& process); + + // Print statistics when two hard processes allowed. + void statistics2(bool reset, ostream& os = cout); + + // Statistics for Les Houches event classification. + vector codeLHA, nEvtLHA; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_ProcessLevel_H diff --git a/PYTHIA8/pythia8140/include/Pythia.h b/PYTHIA8/pythia8140/include/Pythia.h new file mode 100644 index 00000000000..e59c35afafc --- /dev/null +++ b/PYTHIA8/pythia8140/include/Pythia.h @@ -0,0 +1,303 @@ +// Pythia.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the main class for event generation. +// Pythia: provide the main user interface to everything else. + +#ifndef Pythia8_Pythia_H +#define Pythia8_Pythia_H + +#include "Analysis.h" +#include "Basics.h" +#include "BeamParticle.h" +#include "BeamShape.h" +#include "Event.h" +#include "FragmentationFlavZpT.h" +#include "HadronLevel.h" +#include "Info.h" +#include "LesHouches.h" +#include "PartonLevel.h" +#include "ParticleData.h" +#include "PartonDistributions.h" +#include "PartonSystems.h" +#include "ProcessLevel.h" +#include "PythiaStdlib.h" +#include "ResonanceWidths.h" +#include "Settings.h" +#include "SigmaTotal.h" +#include "SpaceShower.h" +#include "StandardModel.h" +#include "SusyLesHouches.h" +#include "TimeShower.h" +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// The Pythia class contains the top-level routines to generate an event. + +class Pythia { + +public: + + // Constructor. (See Pythia.cc file.) + Pythia(string xmlDir = "../xmldoc"); + + // Destructor. (See Pythia.cc file.) + ~Pythia(); + + // Read in one update for a setting or particle data from a single line. + bool readString(string, bool warn = true); + + // Read in updates for settings or particle data from user-defined file. + bool readFile(string fileName, bool warn = true, + int subrun = SUBRUNDEFAULT); + bool readFile(string fileName, int subrun) { + return readFile(fileName, true, subrun);} + bool readFile(istream& is = cin, bool warn = true, + int subrun = SUBRUNDEFAULT); + bool readFile(istream& is, int subrun) { + return readFile(is, true, subrun);} + + // Possibility to pass in pointers to PDF's. + bool setPDFPtr( PDF* pdfAPtrIn, PDF* pdfBPtrIn, PDF* pdfHardAPtrIn = 0, + PDF* pdfHardBPtrIn = 0, PDF* pdfPomAPtrIn = 0, PDF* pdfPomBPtrIn = 0); + + // Possibility to pass in pointer for external handling of some decays. + bool setDecayPtr( DecayHandler* decayHandlePtrIn, + vector handledParticlesIn) {decayHandlePtr = decayHandlePtrIn; + handledParticles.resize(0); + for(int i = 0; i < int(handledParticlesIn.size()); ++i) + handledParticles.push_back( handledParticlesIn[i] ); return true;} + + // Possibility to pass in pointer for external random number generation. + bool setRndmEnginePtr( RndmEngine* rndmEnginePtrIn) + { return rndm.rndmEnginePtr( rndmEnginePtrIn);} + + // Possibility to pass in pointer for user hooks. + bool setUserHooksPtr( UserHooks* userHooksPtrIn) + { userHooksPtr = userHooksPtrIn; return true;} + + // Possibility to pass in pointer for beam shape. + bool setBeamShapePtr( BeamShape* beamShapePtrIn) + { beamShapePtr = beamShapePtrIn; return true;} + + // Possibility to pass in pointer(s) for external cross section. + bool setSigmaPtr( SigmaProcess* sigmaPtrIn) + { sigmaPtrs.push_back( sigmaPtrIn); return true;} + + // Possibility to pass in pointer(s) for external resonance. + bool setResonancePtr( ResonanceWidths* resonancePtrIn) + { resonancePtrs.push_back( resonancePtrIn); return true;} + + // Possibility to pass in pointer for external showers. + bool setShowerPtr( TimeShower* timesDecPtrIn, + TimeShower* timesPtrIn = 0, SpaceShower* spacePtrIn = 0) + { timesDecPtr = timesDecPtrIn; timesPtr = timesPtrIn; + spacePtr = spacePtrIn; return true;} + + // Initialize tunes to e+e- and pp/ppbar data. + void initTunes(int eeTune = 0, int ppTune = 0); + + // Initialization in the CM frame. + bool init( int idAin, int idBin, double eCMin); + + // Initialization with two collinear beams, including fixed target. + bool init( int idAin, int idBin, double eAin, double eBin); + + // Initialization with two acollinear beams. + bool init( int idAin, int idBin, double pxAin, double pyAin, + double pzAin, double pxBin, double pyBin, double pzBin); + + // Initialization by a Les Houches Event File. + bool init( string LesHouchesEventFile, bool skipInit = false); + + // Initialization using the Main beam variables. + bool init(); + + // Initialization according to the Les Houches Accord. + bool init( LHAup* lhaUpPtrIn); + + // Generate the next event. + bool next(); + + // Generate only the hadronization/decay stage. + bool forceHadronLevel(); + + // Special routine to allow more decays if on/off switches changed. + bool moreDecays() {return hadronLevel.moreDecays(event);} + + // List the current Les Houches event. + void LHAeventList(ostream& os = cout) { + if (lhaUpPtr > 0) lhaUpPtr->listEvent(os);} + + // Skip a number of Les Houches events at input. + bool LHAeventSkip(int nSkip) { + if (lhaUpPtr > 0) return lhaUpPtr->skipEvent(nSkip); return false;} + + // Main routine to provide final statistics on generation. + void statistics(bool all = false, bool reset = false); + + // Read in settings values: shorthand, not new functionality. + bool flag(string key) {return settings.flag(key);} + int mode(string key) {return settings.mode(key);} + double parm(string key) {return settings.parm(key);} + string word(string key) {return settings.word(key);} + + // The event record for the parton-level central process. + Event process; + + // The event record for the complete event history. + Event event; + + // Information on the generation: current subprocess and error statistics. + Info info; + + // Settings: databases of flags/modes/parms/words to control run. + Settings settings; + + // ParticleData: the particle data table/database. + ParticleData particleData; + + // Random number generator. + Rndm rndm; + + // Standard Model couplings, including alphaS and alphaEM. + CoupSM coupSM; + + // SusyLesHouches - SLHA object for interface to SUSY spectra. + SusyLesHouches slha; + + // The partonic content of each subcollision system (auxiliary to event). + PartonSystems partonSystems; + +private: + + // Constants: could only be changed in the code itself. + static const int NTRY, SUBRUNDEFAULT; + + // Initialization data, extracted from database. + string xmlPath; + bool doProcessLevel, doPartonLevel, doHadronLevel, checkEvent, + doDiffraction; + int nErrList; + double epTolErr, epTolWarn; + + // Initialization data, extracted from init(...) call. + bool isConstructed, isInit; + int idA, idB, frameType; + double mA, mB, pxA, pxB, pyA, pyB, pzA, pzB, eA, eB, + pzAcm, pzBcm, eCM, betaZ, gammaZ; + Vec4 pAinit, pBinit, pAnow, pBnow; + RotBstMatrix MfromCM, MtoCM; + + // information for error checkout. + int nErrEvent; + vector iErrId, iErrCol, iErrNan, iErrNanVtx; + + // Pointers to the parton distributions of the two incoming beams. + PDF* pdfAPtr; + PDF* pdfBPtr; + + // Extra PDF pointers to be used in hard processes only. + PDF* pdfHardAPtr; + PDF* pdfHardBPtr; + + // Extra Pomeron PDF pointers to be used in diffractive processes only. + PDF* pdfPomAPtr; + PDF* pdfPomBPtr; + + // Keep track when "new" has been used and needs a "delete" for PDF's. + bool useNewPdfA, useNewPdfB, useNewPdfHard, useNewPdfPomA, useNewPdfPomB; + + // The two incoming beams. + BeamParticle beamA; + BeamParticle beamB; + + // Alternative Pomeron beam-inside-beam. + BeamParticle beamPomA; + BeamParticle beamPomB; + + // LHAup object for generating external events. + bool doLHA, useNewLHA; + LHAup* lhaUpPtr; + + // Pointer to external decay handler and list of particles it handles. + DecayHandler* decayHandlePtr; + vector handledParticles; + + // Pointer to UserHooks object for user interaction with program. + UserHooks* userHooksPtr; + bool hasUserHooks, doVetoProcess, doVetoPartons; + + // Pointer to BeamShape object for beam momentum and interaction vertex. + BeamShape* beamShapePtr; + bool useNewBeamShape, doMomentumSpread, doVertexSpread; + + // Pointers to external processes derived from the Pythia base classes. + vector sigmaPtrs; + + // Pointers to external calculation of resonance widths. + vector resonancePtrs; + + // Pointers to timelike and spacelike showers. + TimeShower* timesDecPtr; + TimeShower* timesPtr; + SpaceShower* spacePtr; + bool useNewTimes, useNewSpace; + + // The main generator class to define the core process of the event. + ProcessLevel processLevel; + + // The main generator class to produce the parton level of the event. + PartonLevel partonLevel; + + // The main generator class to produce the hadron level of the event. + HadronLevel hadronLevel; + + // The total cross section class is used both on process and parton level. + SigmaTotal sigmaTot; + + // Write the Pythia banner, with symbol and version information. + void banner(ostream& os = cout); + + // Check for lines in file that mark the beginning of new subrun. + int readSubrun(string line, bool warn = true, ostream& os = cout); + + // Initialization routine to set up the whole generation machinery. + bool initInternal(); + + // Check that combinations of settings are allowed; change if not. + void checkSettings(); + + // Check that beams and beam combination can be handled. + bool checkBeams(); + + // Calculate kinematics at initialization. + bool initKinematics(); + + // Set up pointers to PDFs. + bool initPDFs(); + + // Recalculate kinematics for each event when beam momentum has a spread. + void nextKinematics(); + + // Boost from CM frame to lab frame, or inverse. Set production vertex. + void boostAndVertex(bool toLab, bool setVertex); + + // Check that the final event makes sense. + bool check(ostream& os = cout); + + // Auxiliary to set parton densities among list of possibilities. + PDF* getPDFPtr(int idIn, int sequence = 1); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_Pythia_H diff --git a/PYTHIA8/pythia8140/include/PythiaComplex.h b/PYTHIA8/pythia8140/include/PythiaComplex.h new file mode 100644 index 00000000000..22703cbfd44 --- /dev/null +++ b/PYTHIA8/pythia8140/include/PythiaComplex.h @@ -0,0 +1,21 @@ +// PythiaComplex.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for typedef'd double precision complex numbers. + +#ifndef Pythia8_PythiaComplex_H +#define Pythia8_PythiaComplex_H + +// Stdlib header for complex numbers. +# include + +namespace Pythia8 { + +// Convenient typedef for double precision complex numbers. +typedef std::complex complex; + +} // end namespace Pythia8 + +#endif // Pythia8_PythiaComplex_H diff --git a/PYTHIA8/pythia8140/include/PythiaStdlib.h b/PYTHIA8/pythia8140/include/PythiaStdlib.h new file mode 100644 index 00000000000..b25db6ab113 --- /dev/null +++ b/PYTHIA8/pythia8140/include/PythiaStdlib.h @@ -0,0 +1,88 @@ +// PythiaStdlib.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for functionality pulled in from Stdlib, +// plus a few useful utilities (small powers; positive square root, +// Gamma function). + +#ifndef Pythia8_PythiaStdlib_H +#define Pythia8_PythiaStdlib_H + +// Stdlib header files for mathematics. +#include +#include + +// Stdlib header files for strings and containers. +#include +#include +#include +#include + +// Stdlib header file for input and output. +#include +#include +#include +#include + +// Define pi if not yet done. +#ifndef M_PI +#define M_PI 3.1415926535897932385 +#endif + +// By this declaration you do not need to use std:: qualifier everywhere. +using namespace std; + +// Alternatively you can specify exactly which std:: methods will be used. +/* +namespace Pythia8 { +// Generic utilities and mathematical functions. +using std::swap; +using std::max; +using std::min; +using std::abs; +// Strings and containers. +using std::string; +using std::vector; +using std::map; +using std::deque; +// Input/output streams. +using std::cin; +using std::cout; +using std::cerr; +using std::istream; +using std::ostream; +using std::ifstream; +using std::ofstream; +using std::istringstream; +using std::ostringstream; +// Input/output formatting. +using std::endl; +using std::fixed; +using std::scientific; +using std::left; +using std::right; +using std::setw; +using std::setprecision; +} // end namespace Pythia8 +*/ + +namespace Pythia8 { + +// Powers of small integers - for balance speed/code clarity. +inline double pow2(const double& x) {return x*x;} +inline double pow3(const double& x) {return x*x*x;} +inline double pow4(const double& x) {return x*x*x*x;} +inline double pow5(const double& x) {return x*x*x*x*x;} +inline double pow6(const double& x) {return x*x*x*x*x*x;} + +// Avoid problem with negative square root argument (from roundoff). +inline double sqrtpos(const double& x) {return sqrt( max( 0., x));} + +// The Gamma function for real argument. +double GammaReal(double x); + +} // end namespace Pythia8 + +#endif // Pythia8_PythiaStdlib_H diff --git a/PYTHIA8/pythia8140/include/ResonanceDecays.h b/PYTHIA8/pythia8140/include/ResonanceDecays.h new file mode 100644 index 00000000000..8a9a65d3d3b --- /dev/null +++ b/PYTHIA8/pythia8140/include/ResonanceDecays.h @@ -0,0 +1,80 @@ +// ResonanceDecays.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the main class for performing resonance decays. +// ResonanceDecays: handles the sequential decay of resonances in process. + +#ifndef Pythia8_ResonanceDecays_H +#define Pythia8_ResonanceDecays_H + +#include "Basics.h" +#include "Event.h" +#include "Info.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "ResonanceWidths.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// The ResonanceDecays class handles the sequential decay of resonances +// that are part of the hard process (t, W, Z, H, SUSY,...). + +class ResonanceDecays { + +public: + + // Constructor. + ResonanceDecays() {} + + // Store pointers to Info and Rndm for error messages and random numbers. + void init(Info* infoPtrIn, ParticleData* particleDataPtrIn, + Rndm* rndmPtrIn) {infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; rndmPtr = rndmPtrIn;} + + // Generate the next decay sequence. + bool next( Event& process); + +private: + + // Constants: could only be changed in the code itself. + static const int NTRYCHANNEL, NTRYMASSES; + static const double MSAFETY, WIDTHCUT, TINY, TINYBWRANGE, + WTCORRECTION[11]; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Select masses of decay products. + bool pickMasses(); + + // Select colours of decay products. + bool pickColours(int iDec, Event& process); + + // Select kinematics isotropic in phase space. + bool pickKinematics(); + + // Flavour, colour and momentum information. + int id0, mult; + double m0; + vector idProd, cols, acols; + vector mProd; + vector pProd; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_ResonanceDecays_H diff --git a/PYTHIA8/pythia8140/include/ResonanceWidths.h b/PYTHIA8/pythia8140/include/ResonanceWidths.h new file mode 100644 index 00000000000..bb423c4e8f0 --- /dev/null +++ b/PYTHIA8/pythia8140/include/ResonanceWidths.h @@ -0,0 +1,670 @@ +// ResonanceWidths.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for resonance properties: dynamical widths etc. +// ResonanceWidths: base class for all resonances. +// ResonanceGmZ, ...: derived classes for individual resonances. + +#ifndef Pythia8_ResonanceWidths_H +#define Pythia8_ResonanceWidths_H + +#include "Basics.h" +#include "Info.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" +#include "StandardModel.h" + +namespace Pythia8 { + +//========================================================================== + +// Forward references to ParticleData and StandardModel classes. +class DecayChannel; +class ParticleData; +class ParticleDataEntry; +class CoupSM; + +//========================================================================== + +// The ResonanceWidths is the base class. Also used for generic resonaces. + +class ResonanceWidths { + +public: + + // Destructor. + virtual ~ResonanceWidths() {} + + // Set up standard properties. + void initBasic(int idResIn, bool isGenericIn = false) { + idRes = idResIn; isGeneric = isGenericIn;} + + // Calculate and store partial and total widths at the nominal mass. + bool init(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, CoupSM* coupSMPtrIn); + + // Return identity of particle species. + int id() const {return idRes;} + + // Calculate the total/open width for given mass, charge and instate. + double width(int idSgn, double mHatIn, int idInFlavIn = 0, + bool openOnly = false, bool setBR = false, int idOutFlav1 = 0, + int idOutFlav2 = 0); + + // Special case to calculate open final-state width. + double widthOpen(int idSgn, double mHatIn, int idIn = 0) { + return width( idSgn, mHatIn, idIn, true, false);} + + // Special case to store open final-state widths for channel selection. + double widthStore(int idSgn, double mHatIn, int idIn = 0) { + return width( idSgn, mHatIn, idIn, true, true);} + + // Return fraction of width open for particle and antiparticle. + double openFrac(int idSgn) {return (idSgn > 0) ? openPos : openNeg;} + + // Return forced rescaling factor of resonance width. + double widthRescaleFactor() {return forceFactor;} + + // Special case to calculate one final-state width. + // Currently only used for Higgs -> qqbar, g g or gamma gamma. + double widthChan(double mHatIn, int idOutFlav1, int idOutFlav2) { + return width( 1, mHatIn, 0, false, false, idOutFlav1, idOutFlav2);} + +protected: + + // Constructor. + ResonanceWidths() {} + + // Constants: could only be changed in the code itself. + static const int NPOINT; + static const double MASSMARGIN; + + // Particle properties always present. + int idRes, hasAntiRes; + bool doForceWidth, isGeneric; + double minWidth, minThreshold, mRes, GammaRes, m2Res, GamMRat, + openPos, openNeg, forceFactor; + + // Properties for currently studied decay channel(s). + int iChannel, onMode, meMode, mult, id1, id2, id3, id1Abs, + id2Abs, id3Abs, idInFlav; + double widNow, mHat, mf1, mf2, mf3, mr1, mr2, mr3, ps, kinFac, + alpEM, alpS, colQ, preFac; + + // Pointer to properties of the particle species. + ParticleDataEntry* particlePtr; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to Standard Model couplings. + CoupSM* coupSMPtr; + + // Initialize constants. + virtual void initConstants() {} + + // Calculate various common prefactors for the current mass. + // Optional argument calledFromInit only used for Z0. + virtual void calcPreFac(bool = false) {} + + // Calculate width for currently considered channel. + // Optional argument calledFromInit only used for Z0. + virtual void calcWidth(bool = false) {} + + // Simple routines for matrix-element integration over Breit-Wigners. + double numInt1BW(double mHatIn, double m1, double Gamma1, double mMin1, + double m2, int psMode = 1); + double numInt2BW(double mHatIn, double m1, double Gamma1, double mMin1, + double m2, double Gamma2, double mMin2, int psMode = 1); + +}; + +//========================================================================== + +// The ResonanceGeneric class handles a generic resonance. +// Only needs a constructor; for the rest uses defaults in base class. + +class ResonanceGeneric : public ResonanceWidths { + +public: + + // Constructor. + ResonanceGeneric(int idResIn) {initBasic(idResIn, true);} + +}; + +//========================================================================== + +// The ResonanceGmZ class handles the gamma*/Z0 resonance. + +class ResonanceGmZ : public ResonanceWidths { + +public: + + // Constructor. + ResonanceGmZ(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + int gmZmode; + double thetaWRat, ei2, eivi, vi2ai2, gamNorm, intNorm, resNorm; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool calledFromInit = false); + +}; + +//========================================================================== + +// The ResonanceW class handles the W+- resonance. + +class ResonanceW : public ResonanceWidths { + +public: + + // Constructor. + ResonanceW(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double thetaWRat, alpEM; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceTop class handles the top/antitop resonance. + +class ResonanceTop : public ResonanceWidths { + +public: + + // Constructor. + ResonanceTop(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double thetaWRat, m2W; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceFour class handles fourth-generation resonances. + +class ResonanceFour : public ResonanceWidths { + +public: + + // Constructor. + ResonanceFour(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double thetaWRat, m2W; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceH class handles the SM and BSM Higgs resonance. +// higgsType = 0 : SM H; = 1: h^0/H_1; = 2 : H^0/H_2; = 3 : A^0/A_3. + +class ResonanceH : public ResonanceWidths { + +public: + + // Constructor. + ResonanceH(int higgsTypeIn, int idResIn) : higgsType(higgsTypeIn) + {initBasic(idResIn);} + +private: + + // Constants: could only be changed in the code itself. + static const double MASSMIN, GAMMAMARGIN; + + // Higgs type in current instance. + int higgsType; + + // Locally stored properties and couplings. + bool useCubicWidth, useRunLoopMass; + double sin2tW, cos2tW, mT, mZ, mW, mHchg, GammaT, GammaZ, GammaW, + coup2d, coup2u, coup2l, coup2Z, coup2W, coup2Hchg, coup2H1H1, + coup2A3A3, coup2H1Z, coup2A3Z, coup2A3H1, coup2HchgW, + kinFacT[101], kinFacZ[101], kinFacW[101]; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + + // Sum up loop contributions in Higgs -> g + g. + double eta2gg(); + + // Sum up loop contributions in Higgs -> gamma + gamma. + double eta2gaga(); + + // Sum up loop contributions in Higgs -> gamma + Z0. + double eta2gaZ(); + +}; + +//========================================================================== + +// The ResonanceHchg class handles the H+- resonance. + +class ResonanceHchg : public ResonanceWidths { + +public: + + // Constructor. + ResonanceHchg(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + bool useCubicWidth; + double thetaWRat, mW, tanBeta, tan2Beta, coup2H1W; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceZprime class handles the gamma*/Z0 /Z'^0 resonance. + +class ResonanceZprime : public ResonanceWidths { + +public: + + // Constructor. + ResonanceZprime(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + int gmZmode; + double sin2tW, cos2tW, thetaWRat, mZ, GammaZ, m2Z, GamMRatZ, afZp[20], + vfZp[20], coupZpWW, ei2, eivi, vai2, eivpi, vaivapi, vapi2, + gamNorm, gamZNorm, ZNorm, gamZpNorm, ZZpNorm, ZpNorm; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool calledFromInit = false); + +}; + +//========================================================================== + +// The ResonanceWprime class handles the W'+- resonance. + +class ResonanceWprime : public ResonanceWidths { + +public: + + // Constructor. + ResonanceWprime(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double thetaWRat, cos2tW, alpEM, aqWp, vqWp, alWp, vlWp, coupWpWZ; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceRhorizontal class handles the R^0 resonance. + +class ResonanceRhorizontal : public ResonanceWidths { + +public: + + // Constructor. + ResonanceRhorizontal(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double thetaWRat; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceExcited class handles excited-fermion resonances. + +class ResonanceExcited : public ResonanceWidths { + +public: + + // Constructor. + ResonanceExcited(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double Lambda, coupF, coupFprime, coupFcol, sin2tW, cos2tW; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceGraviton class handles the excited Graviton resonance. + +class ResonanceGraviton : public ResonanceWidths { + +public: + + // Constructor. + ResonanceGraviton(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + bool m_smbulk; + double kappaMG; + + // Couplings between graviton and SM (map from particle id to coupling). + double m_coupling[26]; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceKKgluon class handles the excited kk-gluon resonance. + +class ResonanceKKgluon : public ResonanceWidths { + +public: + + // Constructor. + ResonanceKKgluon(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + bool m_smbulk; + + // Couplings between KK gluon and SM (map from particle id to coupling). + double m_coupling[10]; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + + +//========================================================================== + +// The ResonanceLeptoquark class handles the LQ/LQbar resonance. + +class ResonanceLeptoquark : public ResonanceWidths { + +public: + + // Constructor. + ResonanceLeptoquark(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double kCoup; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceNuRight class handles righthanded Majorana neutrinos. + +class ResonanceNuRight : public ResonanceWidths { + +public: + + // Constructor. + ResonanceNuRight(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double thetaWRat, mWR; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceZRight class handles the Z_R^0 resonance. + +class ResonanceZRight : public ResonanceWidths { + +public: + + // Constructor. + ResonanceZRight(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double sin2tW, thetaWRat; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceWRight class handles the W_R+- resonance. + +class ResonanceWRight : public ResonanceWidths { + +public: + + // Constructor. + ResonanceWRight(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double thetaWRat; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceHchgchgLeft class handles the H++/H-- (left) resonance. + +class ResonanceHchgchgLeft : public ResonanceWidths { + +public: + + // Constructor. + ResonanceHchgchgLeft(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + double yukawa[4][4], gL, vL, mW; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +// The ResonanceHchgchgRight class handles the H++/H-- (right) resonance. + +class ResonanceHchgchgRight : public ResonanceWidths { + +public: + + // Constructor. + ResonanceHchgchgRight(int idResIn) {initBasic(idResIn);} + +private: + + // Locally stored properties and couplings. + int idWR; + double yukawa[4][4], gR; + + // Initialize constants. + virtual void initConstants(); + + // Calculate various common prefactors for the current mass. + virtual void calcPreFac(bool = false); + + // Caclulate width for currently considered channel. + virtual void calcWidth(bool = false); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_ResonanceWidths_H diff --git a/PYTHIA8/pythia8140/include/Settings.h b/PYTHIA8/pythia8140/include/Settings.h new file mode 100644 index 00000000000..3587d4a2852 --- /dev/null +++ b/PYTHIA8/pythia8140/include/Settings.h @@ -0,0 +1,234 @@ +// Settings.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for the settings database. +// Flag: helper class with bool flags. +// Mode: helper class with int modes. +// Parm: (short for parameter) helper class with double parameters. +// Word: helper class with string words. +// Settings: maps of flags, modes, parms and words with input/output. + +#ifndef Pythia8_Settings_H +#define Pythia8_Settings_H + +#include "Info.h" +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// Class for bool flags. + +class Flag { + +public: + + // Constructor + Flag(string nameIn = " ", bool defaultIn = false) : name(nameIn), + valNow(defaultIn) , valDefault(defaultIn) { } + + // Data members. + string name; + bool valNow, valDefault; + +}; + +//========================================================================== + +// Class for integer modes. + +class Mode { + +public: + + // Constructor + Mode(string nameIn = " ", int defaultIn = 0, bool hasMinIn = false, + bool hasMaxIn = false, int minIn = 0, int maxIn = 0) : name(nameIn), + valNow(defaultIn), valDefault(defaultIn), hasMin(hasMinIn), + hasMax(hasMaxIn), valMin(minIn), valMax(maxIn) { } + + // Data members. + string name; + int valNow, valDefault; + bool hasMin, hasMax; + int valMin, valMax; + +}; + +//========================================================================== + +// Class for double parms (where parm is shorthand for parameter). + +class Parm { + +public: + + // Constructor + Parm(string nameIn = " ", double defaultIn = 0., + bool hasMinIn = false, bool hasMaxIn = false, double minIn = 0., + double maxIn = 0.) : name(nameIn), valNow(defaultIn), + valDefault(defaultIn), hasMin(hasMinIn), hasMax(hasMaxIn), + valMin(minIn), valMax(maxIn) { } + + // Data members. + string name; + double valNow, valDefault; + bool hasMin, hasMax; + double valMin, valMax; + +}; + +//========================================================================== + +// Class for string words. + +class Word { + +public: + + // Constructor + Word(string nameIn = " ", string defaultIn = " ") : name(nameIn), + valNow(defaultIn) , valDefault(defaultIn) { } + + // Data members. + string name, valNow, valDefault; + +}; + +//========================================================================== + +// This class holds info on flags (bool), modes (int), +// parms (double) and words (string). + +class Settings { + +public: + + // Constructor. + Settings() : isInit(false) {} + + // Initialize Info pointer. + void initPtr(Info* infoPtrIn) {infoPtr = infoPtrIn;} + + // Read in database from specific file. + bool init(string startFile = "../xmldoc/Index.xml", bool append = false, + ostream& os = cout) ; + + // Overwrite existing database by reading from specific file. + bool reInit(string startFile = "../xmldoc/Index.xml", ostream& os = cout) ; + + // Read in one update from a single line. + bool readString(string line, bool warn = true, ostream& os = cout) ; + + // Write updates or everything to user-defined file. + bool writeFile(string toFile, bool writeAll = false) ; + bool writeFile(ostream& os = cout, bool writeAll = false) ; + + // Print out table of database, either all or only changed ones, + // or ones containing a given string. + void listAll(ostream& os = cout) { + list( true, false, " ", os); } + void listChanged(ostream& os = cout) { + list (false, false, " ", os); } + void list(string match, ostream& os = cout) { + list (false, true, match, os); } + + // Reset all values to their defaults. + void resetAll() ; + + // Query existence of an entry. + bool isFlag(string keyIn) { + return (flags.find(toLower(keyIn)) != flags.end()); } + bool isMode(string keyIn) { + return (modes.find(toLower(keyIn)) != modes.end()); } + bool isParm(string keyIn) { + return (parms.find(toLower(keyIn)) != parms.end()); } + bool isWord(string keyIn) { + return (words.find(toLower(keyIn)) != words.end()); } + + // Add new entry. + void addFlag(string keyIn, bool defaultIn) { + flags[toLower(keyIn)] = Flag(keyIn, defaultIn); } + void addMode(string keyIn, int defaultIn, bool hasMinIn, + bool hasMaxIn, int minIn, int maxIn) { modes[toLower(keyIn)] + = Mode(keyIn, defaultIn, hasMinIn, hasMaxIn, minIn, maxIn); } + void addParm(string keyIn, double defaultIn, bool hasMinIn, + bool hasMaxIn, double minIn, double maxIn) { parms[toLower(keyIn)] + = Parm(keyIn, defaultIn, hasMinIn, hasMaxIn, minIn, maxIn); } + void addWord(string keyIn, string defaultIn) { + words[toLower(keyIn)] = Word(keyIn, defaultIn); } + + // Give back current value, with check that key exists. + bool flag(string keyIn); + int mode(string keyIn); + double parm(string keyIn); + string word(string keyIn); + + // Change current value, respecting limits. + void flag(string keyIn, bool nowIn); + void mode(string keyIn, int nowIn); + void parm(string keyIn, double nowIn); + void word(string keyIn, string nowIn); + + // Change current value, disregarding limits. + void forceMode(string keyIn, int nowIn) { + if (isMode(keyIn)) modes[toLower(keyIn)].valNow = nowIn; } + void forceParm(string keyIn, double nowIn) { + if (isParm(keyIn)) parms[toLower(keyIn)].valNow = nowIn; } + + // Restore current value to default. + void resetFlag(string keyIn) { + if (isFlag(keyIn)) flags[toLower(keyIn)].valNow + = flags[toLower(keyIn)].valDefault ; } + void resetMode(string keyIn) { + if (isMode(keyIn)) modes[toLower(keyIn)].valNow + = modes[toLower(keyIn)].valDefault ; } + void resetParm(string keyIn) { + if (isParm(keyIn)) parms[toLower(keyIn)].valNow + = parms[toLower(keyIn)].valDefault ; } + void resetWord(string keyIn) { + if (isWord(keyIn)) words[toLower(keyIn)].valNow + = words[toLower(keyIn)].valDefault ; } + +private: + + // Pointer to various information on the generation. + Info* infoPtr; + + // Map for bool flags. + map flags; + + // Map for integer modes. + map modes; + + // Map for double parms. + map parms; + + // Map for string words. + map words; + + // Flag that initialization has been performed. + bool isInit; + + // Print out table of database, called from listAll and listChanged. + void list(bool doListAll, bool doListString, string match, + ostream& os = cout); + + // Useful functions for string handling. + string toLower(const string& name); + bool boolString(string tag); + string attributeValue(string line, string attribute); + bool boolAttributeValue(string line, string attribute); + int intAttributeValue(string line, string attribute); + double doubleAttributeValue(string line, string attribute); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_Settings_H diff --git a/PYTHIA8/pythia8140/include/SigmaCompositeness.h b/PYTHIA8/pythia8140/include/SigmaCompositeness.h new file mode 100644 index 00000000000..1df25390ebb --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaCompositeness.h @@ -0,0 +1,270 @@ +// SigmaCompositeness.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for compositiness-process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma(1/2)Process. + +#ifndef Pythia8_SigmaCompositeness_H +#define Pythia8_SigmaCompositeness_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for q g -> q^* (excited quark state). + +class Sigma1qg2qStar : public Sigma1Process { + +public: + + // Constructor. + Sigma1qg2qStar(int idqIn) : idq(idqIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for q* decay angles (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int resonanceA() const {return idRes;} + +private: + + // Parameters set at initialization or for current kinematics. + int idq, idRes, codeSave; + string nameSave; + double mRes, GammaRes, m2Res, GamMRat, Lambda, coupFcol, widthIn, sigBW; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* qStarPtr; + +}; + +//========================================================================== + +// A derived class for l gamma -> q^* (excited lepton state). + +class Sigma1lgm2lStar : public Sigma1Process { + +public: + + // Constructor. + Sigma1lgm2lStar(int idlIn) : idl(idlIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for l* decay angles (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "fgm";} + virtual int resonanceA() const {return idRes;} + +private: + + // Parameters set at initialization or for current kinematics. + int idl, idRes, codeSave; + string nameSave; + double mRes, GammaRes, m2Res, GamMRat, Lambda, coupChg, widthIn, sigBW; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* qStarPtr; + +}; + +//========================================================================== + +// A derived class for q q' -> q^* q' (excited quark state). + +class Sigma2qq2qStarq : public Sigma2Process { + +public: + + // Constructor. + Sigma2qq2qStarq(int idqIn) : idq(idqIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qq";} + virtual int id3Mass() const {return idRes;} + +private: + + // Parameters set at initialization or for current kinematics. + int idq, idRes, codeSave; + string nameSave; + double Lambda, preFac, openFracPos, openFracNeg, sigmaA, sigmaB; + +}; + +//========================================================================== + +// A derived class for q qbar -> l^* lbar (excited lepton state). + +class Sigma2qqbar2lStarlbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2lStarlbar(int idlIn) : idl(idlIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idRes;} + +private: + + // Parameters set at initialization or for current kinematics. + int idl, idRes, codeSave; + string nameSave; + double Lambda, preFac, openFracPos, openFracNeg, sigma; + +}; + +//========================================================================== + +// A derived class for q q -> q q (quark contact interactions). +// Based on, Sigma2qq2qq (QCD). + +class Sigma2QCqq2qq : public Sigma2Process { + +public: + + // Constructor. + Sigma2QCqq2qq(){} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q q(bar)' -> (QC) -> q q(bar)'";} + virtual int code() const {return 4201;} + virtual string inFlux() const {return "qq";} + + private: + + // Values stored for colour flow selection. + double sigT, sigU, sigTU, sigST, sigSum, sigQCSTU, sigQCUTS; + + // Compositeness parameters. + double m_Lambda2; + int m_etaLL, m_etaRR, m_etaLR; + +}; + +//========================================================================== + +// A derived class for q qbar -> q' qbar' (quark contact interactions). +// Based on, Sigma2qqbar2qqbarNew(QCD). +// Note: This process give the same contributions for q == q' and q != q'. + +class Sigma2QCqqbar2qqbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2QCqqbar2qqbar(){} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> (QC) -> q' qbar' (uds)";} + virtual int code() const {return 4202;} + virtual string inFlux() const {return "qqbarSame";} + + private: + + // Number of outgoing quark flavours to be considered, given that + // matrix elements are calculated in the massless approximation. + int m_nQuarkNew; + + // Values stored for colour flow selection. + int idNew; + double mNew, m2New, sigS, sigma; + + // Compositeness parameters. + double m_Lambda2; + int m_etaLL, m_etaRR, m_etaLR; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaCompositeness_H diff --git a/PYTHIA8/pythia8140/include/SigmaEW.h b/PYTHIA8/pythia8140/include/SigmaEW.h new file mode 100644 index 00000000000..cf28add042f --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaEW.h @@ -0,0 +1,1057 @@ +// SigmaEW.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for electroweak process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma(1/2)Process. + +#ifndef Pythia8_SigmaEW_H +#define Pythia8_SigmaEW_H + +#include "PythiaComplex.h" +#include "SigmaProcess.h" + +namespace Pythia8 { + + +//========================================================================== + +// A derived class for q g -> q gamma (q = u, d, s, c, b). +// Use massless approximation also for Q since no alternative. + +class Sigma2qg2qgamma : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2qgamma() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g -> q gamma (udscb)";} + virtual int code() const {return 201;} + virtual string inFlux() const {return "qg";} + +private: + + // Values stored for later use. + double mNew, m2New, sigUS, sigma0; + +}; + +//========================================================================== + +// A derived class for q qbar -> g gamma. + +class Sigma2qqbar2ggamma : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2ggamma() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> g gamma";} + virtual int code() const {return 202;} + virtual string inFlux() const {return "qqbarSame";} + +private: + + // Values stored for later use. + double sigma0; + +}; + +//========================================================================== + +// A derived class for g g -> g gamma. + +class Sigma2gg2ggamma : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2ggamma() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> g gamma";} + virtual int code() const {return 203;} + virtual string inFlux() const {return "gg";} + +private: + + // Values stored for later use. + double chargeSum, sigma; + +}; + +//========================================================================== + +// A derived class for f fbar -> gamma gamma. + +class Sigma2ffbar2gammagamma : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2gammagamma() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> gamma gamma";} + virtual int code() const {return 204;} + virtual string inFlux() const {return "ffbarSame";} + +private: + + // Values stored for later use. + double sigTU, sigma0; + +}; + +//========================================================================== + +// A derived class for g g -> gamma gamma. + +class Sigma2gg2gammagamma : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2gammagamma() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> gamma gamma";} + virtual int code() const {return 205;} + virtual string inFlux() const {return "gg";} + +private: + + double charge2Sum, sigma; + +}; + +//========================================================================== + +// A derived class for f f' -> f f' via t-channel gamma*/Z0 exchange. + +class Sigma2ff2fftgmZ : public Sigma2Process { + +public: + + // Constructor. + Sigma2ff2fftgmZ() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f f' -> f f' (t-channel gamma*/Z0)";} + virtual int code() const {return 211;} + virtual string inFlux() const {return "ff";} + +private: + + // Z parameters for propagator. + int gmZmode; + double mZ, mZS, thetaWRat, sigmagmgm, sigmagmZ, sigmaZZ; + +}; + +//========================================================================== + +// A derived class for f_1 f_2 -> f_3 f_4 via t-channel W+- exchange. + +class Sigma2ff2fftW : public Sigma2Process { + +public: + + // Constructor. + Sigma2ff2fftW() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f_1 f_2 -> f_3 f_4 (t-channel W+-)";} + virtual int code() const {return 212;} + virtual string inFlux() const {return "ff";} + +private: + + // W parameters for propagator. + double mW, mWS, thetaWRat, sigma0; + +}; + +//========================================================================== + +// A derived class for q q' -> Q q" via t-channel W+- exchange. +// Related to Sigma2ff2fftW class, but with massive matrix elements. + +class Sigma2qq2QqtW : public Sigma2Process { + +public: + + // Constructor. + Sigma2qq2QqtW(int idIn, int codeIn) : idNew(idIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angles in top decay (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ff";} + virtual int id3Mass() const {return idNew;} + +private: + + // Values stored for process type. W parameters for propagator. + int idNew, codeSave; + string nameSave; + double mW, mWS, thetaWRat, sigma0, openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for f fbar -> gamma*/Z0. + +class Sigma1ffbar2gmZ : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2gmZ() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for Z decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> gamma*/Z0";} + virtual int code() const {return 221;} + virtual string inFlux() const {return "ffbarSame";} + virtual int resonanceA() const {return 23;} + +private: + + // Parameters set at initialization or for each new event. + int gmZmode; + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, + gamSum, intSum, resSum, gamProp, intProp, resProp; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +// A derived class for f fbar' -> W+-. + +class Sigma1ffbar2W : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2W() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar' -> W+-";} + virtual int code() const {return 222;} + virtual string inFlux() const {return "ffbarChg";} + virtual int resonanceA() const {return 24;} + +private: + + // Parameters set at initialization. + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, sigma0Pos, sigma0Neg; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +// A derived class for f fbar -> gamma* -> f' fbar', summed over light f'. +// Allows pT-ordered evolution for multiple interactions. + +class Sigma2ffbar2ffbarsgm : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2ffbarsgm() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const { + return "f fbar -> f' fbar' (s-channel gamma*)";} + virtual int code() const {return 223;} + virtual string inFlux() const {return "ffbarSame";} + virtual bool isSChannel() const {return true;} + +private: + + // Values stored for later use. + int idNew; + double sigma0; + +}; + +//========================================================================== + +// A derived class for f fbar -> gamma*/Z0 -> F Fbar, for one heavy F. +// Allows pT cuts as for other 2 -> 2 processes. + +class Sigma2ffbar2FFbarsgmZ : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2FFbarsgmZ(int idIn, int codeIn) : idNew(idIn), + codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angles in top decay (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarSame";} + virtual bool isSChannel() const {return true;} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idNew;} + virtual int resonanceA() const {return 23;} + +private: + + // Values stored for process type. Z parameters for propagator. + int idNew, codeSave, gmZmode; + string nameSave; + bool isPhysical; + double ef, vf, af, mRes, GammaRes, m2Res, GamMRat, thetaWRat, + mr, betaf, cosThe, gamProp, intProp, resProp, openFracPair; + +}; + +//========================================================================== + +// A derived class for f fbar' -> W+- -> F fbar", for one or two heavy F. +// Allows pT cuts as for other 2 -> 2 processes. + +class Sigma2ffbar2FfbarsW : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2FfbarsW(int idIn, int idIn2, int codeIn) : idNew(idIn), + idNew2(idIn2), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angles in top decay (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarChg";} + virtual bool isSChannel() const {return true;} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idPartner;} + virtual int resonanceA() const {return 24;} + +private: + + // Values stored for process type. W parameters for propagator. + int idNew, idNew2, codeSave, idPartner; + string nameSave; + bool isPhysical; + double V2New, mRes, GammaRes, m2Res, GamMRat, thetaWRat, sigma0, + openFracPos, openFracNeg; + +}; + +//========================================================================== + +// An intermediate class for f fbar -> gamma*/Z0/W+- gamma*/Z0/W-+. + +class Sigma2ffbargmZWgmZW : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbargmZWgmZW() {} + +protected: + + // Internal products. + Vec4 pRot[7]; + complex hA[7][7]; + complex hC[7][7]; + + // Calculate and store internal products. + void setupProd( Event& process, int i1, int i2, int i3, int i4, + int i5, int i6); + + // Evaluate the F function of Gunion and Kunszt. + complex fGK(int i1, int i2, int i3, int i4, int i5, int i6); + + // Evaluate the Xi function of Gunion and Kunszt. + double xiGK( double tHnow, double uHnow); + + // Evaluate the Xj function of Gunion and Kunszt. + double xjGK( double tHnow, double uHnow); + +private: + +}; + +//========================================================================== + +// A derived class for f fbar -> gamma*/Z0 gamma*/Z0. + +class Sigma2ffbar2gmZgmZ : public Sigma2ffbargmZWgmZW { + +public: + + // Constructor. + Sigma2ffbar2gmZgmZ() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for simultaneous flavour choices. + virtual double weightDecayFlav( Event& process); + + // Evaluate weight for decay angles of the two gamma*/Z0. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> gamma*/Z0 gamma*/Z0";} + virtual int code() const {return 231;} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return 23;} + virtual int id4Mass() const {return 23;} + +private: + + // Parameters set at initialization or for each new event. + int gmZmode, i1, i2, i3, i4, i5, i6; + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, sigma0, + gamSum3, intSum3, resSum3, gamProp3, intProp3, resProp3, + gamSum4, intSum4, resSum4, gamProp4, intProp4, resProp4, + c3LL, c3LR, c3RL, c3RR, c4LL, c4LR, c4RL, c4RR, flavWt; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +// A derived class for f fbar' -> Z0 W+-. (Here pure Z0, unfortunately.) + +class Sigma2ffbar2ZW : public Sigma2ffbargmZWgmZW { + +public: + + // Constructor. + Sigma2ffbar2ZW() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for Z0 and W+- decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar' -> Z0 W+- (no gamma*!)";} + virtual int code() const {return 232;} + virtual string inFlux() const {return "ffbarChg";} + virtual int id3Mass() const {return 23;} + virtual int id4Mass() const {return 24;} + virtual int resonanceA() const {return 24;} + +private: + + // Store W+- mass and width, and couplings. + double mW, widW, mWS, mwWS, sin2thetaW, cos2thetaW, thetaWRat, cotT, + thetaWpt, thetaWmm, lun, lde, sigma0, openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for f fbar -> W+ W-. + +class Sigma2ffbar2WW : public Sigma2ffbargmZWgmZW { + +public: + + // Constructor. + Sigma2ffbar2WW() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W+ and W- decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> W+ W-";} + virtual int code() const {return 233;} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return 24;} + virtual int id4Mass() const {return -24;} + virtual int resonanceA() const {return 23;} + +private: + + // Store Z0 mass and width. + double mZ, widZ, mZS, mwZS, thetaWRat, sigma0, cgg, cgZ, cZZ, cfg, + cfZ, cff, gSS, gTT, gST, gUU, gSU, openFracPair; + +}; + +//========================================================================== + +// An intermediate class for f fbar -> gamma*/Z0 g/gamma and permutations. + +class Sigma2ffbargmZggm : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbargmZggm() {} + + // Initialize process. + virtual void initProc(); + + // Evaluate weight for gamma&/Z0 decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + +protected: + + // Parameters set at initialization or for each new event. + int gmZmode; + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, + gamSum, intSum, resSum, gamProp, intProp, resProp; + + // Evaluate current sum of flavour couplings times phase space. + void flavSum(); + + // Evaluate current propagator terms of cross section. + void propTerm(); + +private: + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +// A derived class for q qbar -> gamma*/Z0 g. + +class Sigma2qqbar2gmZg : public Sigma2ffbargmZggm { + +public: + + // Constructor. + Sigma2qqbar2gmZg() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> gamma*/Z0 g";} + virtual int code() const {return 241;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return 23;} + +private: + + // Values stored for later use. + double sigma0; + +}; + +//========================================================================== + +// A derived class for q g -> gamma*/Z0 q. + +class Sigma2qg2gmZq : public Sigma2ffbargmZggm { + +public: + + // Constructor. + Sigma2qg2gmZq() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g-> gamma*/Z0 q";} + virtual int code() const {return 242;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return 23;} + +private: + + // Values stored for later use. + double sigma0; + +}; + +//========================================================================== + +// A derived class for f fbar' -> gamma*/Z0 gamma. + +class Sigma2ffbar2gmZgm : public Sigma2ffbargmZggm { + +public: + + // Constructor. + Sigma2ffbar2gmZgm() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> gamma*/Z0 gamma";} + virtual int code() const {return 243;} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return 23;} + +private: + + // Values stored for later use. + double sigma0; + +}; + +//========================================================================== + +// A derived class for f gamma -> gamma*/Z0 f. + +class Sigma2fgm2gmZf : public Sigma2ffbargmZggm { + +public: + + // Constructor. + Sigma2fgm2gmZf() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f gamma -> gamma*/Z0 f";} + virtual int code() const {return 244;} + virtual string inFlux() const {return "fgm";} + virtual int id3Mass() const {return 23;} + +private: + + // Values stored for later use. + double sigma0; + +}; + +//========================================================================== + +// An intermediate class for f fbar -> W+- g/gamma and permutations. + +class Sigma2ffbarWggm : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbarWggm() {} + + // Evaluate weight for gamma&/Z0 decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + +private: + +}; + +//========================================================================== + +// A derived class for q qbar' -> W+- g. + +class Sigma2qqbar2Wg : public Sigma2ffbarWggm { + +public: + + // Constructor. + Sigma2qqbar2Wg() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar' -> W+- g";} + virtual int code() const {return 251;} + virtual string inFlux() const {return "ffbarChg";} + virtual int id3Mass() const {return 24;} + +private: + + // Values stored for later use. + double sigma0, openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for q g -> W+- q'. + +class Sigma2qg2Wq : public Sigma2ffbarWggm { + +public: + + // Constructor. + Sigma2qg2Wq() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g-> W+- q'";} + virtual int code() const {return 252;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return 24;} + +private: + + // Values stored for later use. + double sigma0, openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for f fbar' -> W+- gamma. + +class Sigma2ffbar2Wgm : public Sigma2ffbarWggm { + +public: + + // Constructor. + Sigma2ffbar2Wgm() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f fbar' -> W+- gamma";} + virtual int code() const {return 253;} + virtual string inFlux() const {return "ffbarChg";} + virtual int id3Mass() const {return 24;} + +private: + + // Values stored for later use. + double sigma0, openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for f gamma -> W+- f'. + +class Sigma2fgm2Wf : public Sigma2ffbarWggm { + +public: + + // Constructor. + Sigma2fgm2Wf() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f gamma -> W+- f'";} + virtual int code() const {return 254;} + virtual string inFlux() const {return "fgm";} + virtual int id3Mass() const {return 24;} + +private: + + // Values stored for later use. + double sigma0, openFracPos, openFracNeg; + +}; +//========================================================================== + +// A derived class for gamma gamma -> f fbar. + +class Sigma2gmgm2ffbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2gmgm2ffbar(int idIn, int codeIn) : idNew(idIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gmgm";} + virtual int id3Mass() const {return idMass;} + virtual int id4Mass() const {return idMass;} + +private: + + // Member variables. + int idNew, codeSave, idMass, idNow; + string nameSave; + double ef4, s34Avg, sigTU, sigma, openFracPair; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaEW_H diff --git a/PYTHIA8/pythia8140/include/SigmaExtraDim.h b/PYTHIA8/pythia8140/include/SigmaExtraDim.h new file mode 100644 index 00000000000..d60b117c935 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaExtraDim.h @@ -0,0 +1,729 @@ +// SigmaExtraDim.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// Copyright (C) 2010 Stefan Ask for the *LED* routines. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for extra-dimensional-process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma(1/2)Process. + +#ifndef Pythia8_SigmaExtraDim_H +#define Pythia8_SigmaExtraDim_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for g g -> G^* (excited graviton state). + +class Sigma1gg2GravitonStar : public Sigma1Process { + +public: + + // Constructor. + Sigma1gg2GravitonStar() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for G* decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "g g -> G*";} + virtual int code() const {return 5001;} + virtual string inFlux() const {return "gg";} + virtual int resonanceA() const {return idGstar;} + +private: + + // Parameters set at initialization or for current kinematics. + bool m_smbulk; + int idGstar; + double mRes, GammaRes, m2Res, GamMRat, kappaMG, sigma; + + // Couplings between graviton and SM (indexed by particle id). + double m_coupling[26]; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* gStarPtr; + +}; + +//========================================================================== + +// A derived class for f fbar -> G^* (excited graviton state). + +class Sigma1ffbar2GravitonStar : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2GravitonStar() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for G* decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> G*";} + virtual int code() const {return 5002;} + virtual string inFlux() const {return "ffbarSame";} + virtual int resonanceA() const {return idGstar;} + +private: + + // Parameters set at initialization or for current kinematics. + bool m_smbulk; + int idGstar; + double mRes, GammaRes, m2Res, GamMRat, kappaMG, sigma0; + + // Couplings between graviton and SM (indexed by particle id). + double m_coupling[26]; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* gStarPtr; + +}; + +//========================================================================== + +// A derived class for q qbar -> KK-gluon^* (excited kk-gluon state). + +class Sigma1qqbar2KKgluonStar : public Sigma1Process { + +public: + + // Constructor. + Sigma1qqbar2KKgluonStar() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for g* decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> KK-gluon*";} + virtual int code() const {return 5006;} + virtual string inFlux() const {return "qqbarSame";} + virtual int resonanceA() const {return idKKgluon;} + +private: + + // Parameters set at initialization or for current kinematics. + int idKKgluon; + double mRes, GammaRes, m2Res, GamMRat, sigma0; + + // Couplings between graviton and SM (indexed by particle id). + double m_coupling[10]; + + // Pointer to properties of the particle species, to access decay + // channels. + ParticleDataEntry* gStarPtr; + +}; + +//========================================================================== + +// A derived class for g g -> G^* g (excited graviton state). + +class Sigma2gg2GravitonStarg : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2GravitonStarg() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight: currently isotropic (except secondary top decay).. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "g g -> G* g";} + virtual int code() const {return 5003;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idGstar;} + +private: + + // Parameters set at initialization or for current kinematics. + int idGstar; + double mRes, GammaRes, m2Res, GamMRat, kappaMG, openFrac, sigma; + +}; + +//========================================================================== + +// A derived class for q g -> G^* q (excited graviton state). + +class Sigma2qg2GravitonStarq : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2GravitonStarq() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight: currently isotropic (except secondary top decay). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "q g -> G* q";} + virtual int code() const {return 5004;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return idGstar;} + +private: + + // Parameters set at initialization or for current kinematics. + int idGstar; + double mRes, GammaRes, m2Res, GamMRat, kappaMG, openFrac, sigma; + +}; + +//========================================================================== + +// A derived class for q qbar -> G^* g (excited graviton state). + +class Sigma2qqbar2GravitonStarg : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2GravitonStarg() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight: currently isotropic (except secondary top decay). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> G* g";} + virtual int code() const {return 5005;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idGstar;} + +private: + + // Parameters set at initialization or for current kinematics. + int idGstar; + double mRes, GammaRes, m2Res, GamMRat, kappaMG, openFrac, sigma; + +}; + +//========================================================================== + +// NOAM: A derived class for, f fbar -> (gamma/Z)_KKTower -> F Fbar, +// for one heavy F. +// Process provided by N. Hod et al. and is described in arXiv:XXXX.YYYY + +class Sigma2ffbar2TEVffbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2TEVffbar(int idIn) : idNew(idIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angles in top decay (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return 5011;} + virtual string inFlux() const {return "ffbarSame";} + virtual bool isSChannel() const {return true;} + virtual int idSChannel() const {return 5000023;} + virtual int resonanceA() const {return 23;} + virtual int resonanceB() const {return 5000023;} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idNew;} + // Add phase-space sampling also around the Z_KK resonance. + virtual int resonanceA(); + virtual int resonanceB(); + +private: + + // Values stored for process type. + string nameSave; + int idNew, gmZmode, n_excitation_max; + bool isPhysical; + double gPlusf, gMinusf, gPlusF, gMinusF, gPlusTop, gMinusTop, + gPlus, gMinus, gf, gF; + double mRes, m2Res, mStar, mTop, m2Top, mZKKn, m2ZKKn, m2gmKKn, mgmKKn, + alphaem_fixed; + double helicityME2, coefTot, coefAngular; + double mr, betaf, cosThe, openFracPair; + double wgmKKFactor, wgmKKn, wZKKn, + wZ0, ttbar_wZKKn, ttbar_wgmKKn, + ttbar_wFactorA, ttbar_wFactorB; + double phaseSpace_mHatMin, phaseSpace_mHatMax; + complex gammaProp, resProp, gmPropKK, ZPropKK, totalProp; + complex M_I; +}; + +//========================================================================== + +// A derived class for g g -> U/G g (real graviton emission in +// large extra dimensions or unparticle emission). + +class Sigma2gg2LEDUnparticleg : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2gg2LEDUnparticleg( bool Graviton ) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "g g -> G g" : "g g -> U g") ;} + virtual int code() const {return (m_graviton ? 5021 : 5045);} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return 5000039;} + virtual int id4Mass() const {return 21;} + +private: + + bool m_graviton; + int m_spin, m_nGrav, m_idG, m_cutoff; + double mG, mGS, m_sigma0, m_dU, m_LambdaU, m_lambda, m_constantTerm, + m_tff, m_cf; + +}; + +//========================================================================== + +// A derived class for q g -> U/G q (real graviton emission in +// large extra dimensions or unparticle emission). + +class Sigma2qg2LEDUnparticleq : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2qg2LEDUnparticleq( bool Graviton) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "q g -> G q" : "q g -> U q") ;} + virtual int code() const {return (m_graviton ? 5022 : 5046);} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return 5000039;} + +private: + + bool m_graviton; + int m_spin, m_nGrav, m_idG, m_cutoff; + double mG, mGS, m_sigma0, m_dU, m_LambdaU, m_lambda, m_constantTerm, + m_tff, m_gf, m_cf; + +}; + +//========================================================================== + +// A derived class for q qbar -> U/G g (real graviton emission in +// large extra dimensions or unparticle emission). + +class Sigma2qqbar2LEDUnparticleg : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2qqbar2LEDUnparticleg( bool Graviton) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "q qbar -> G g" : "q qbar -> U g") ;} + virtual int code() const {return (m_graviton ? 5023 : 5047);} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return 5000039;} + virtual int id4Mass() const {return 21;} + +private: + + bool m_graviton; + int m_spin, m_nGrav, m_idG, m_cutoff; + double mG, mGS, m_sigma0, m_dU, m_LambdaU, m_lambda, m_constantTerm, + m_tff, m_gf, m_cf; + +}; + +//========================================================================== + +// A derived class for f fbar -> U/G Z (real graviton emission in +// large extra dimensions or unparticle emission). + +class Sigma2ffbar2LEDUnparticleZ : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2ffbar2LEDUnparticleZ( bool Graviton) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "f fbar -> G Z" : "f fbar -> U Z") ;} + virtual int code() const {return (m_graviton ? 5024 : 5041);} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return 5000039;} + virtual int id4Mass() const {return 23;} + virtual int resonanceA() const {return 23;} + virtual int gmZmode() const {return 2;} + +private: + + // Constants: could only be changed in the code itself. + static const double FIXRATIO; + + int m_spin, m_nGrav, m_cutoff, m_idG; + bool m_graviton; + double m_dU, m_LambdaU, m_lambda, m_ratio, m_lambdaPrime, + m_tff, m_constantTerm; + double sHS, tHS, uHS, tHC, uHC, tHQ, uHQ, tHuH, mU, mUS, mZ, widZ, + mZS, mwZS, thetaWRat, m_sigma0; + +}; + +//========================================================================== + +// A derived class for f fbar -> U/G gamma (real graviton emission in +// large extra dimensions or unparticle emission). + +class Sigma2ffbar2LEDUnparticlegamma : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2ffbar2LEDUnparticlegamma( bool Graviton) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "f fbar -> G gamma" : "f fbar -> U gamma") ;} + virtual int code() const {return (m_graviton ? 5025 : 5042);} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return 5000039;} + virtual int id4Mass() const {return 22;} + +private: + + // Constants: could only be changed in the code itself. + static const double FIXRATIO; + + int m_spin, m_nGrav, m_cutoff, m_idG; + bool m_graviton; + double m_dU, m_LambdaU, m_lambda, m_ratio, m_lambdaPrime, + m_tff, m_constantTerm; + double sHS, tHS, uHS, tHC, uHC, tHQ, uHQ, tHuH, mU, mUS, mZ, widZ, + mZS, mwZS, thetaWRat, m_sigma0; + +}; + +//========================================================================== + +// A derived class for f fbar -> (LED G*/U*) -> gamma gamma +// (virtual graviton/unparticle exchange). + +class Sigma2ffbar2LEDgammagamma : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2ffbar2LEDgammagamma( bool Graviton) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "f fbar -> (LED G*) -> gamma gamma" + : "f fbar -> (U*) -> gamma gamma") ;} + virtual int code() const {return (m_graviton ? 5026 : 5043);} + virtual string inFlux() const {return "ffbarSame";} + +private: + + int m_spin, m_cutoff, m_nGrav; + bool m_graviton; + double m_dU, m_LambdaU, m_lambda, m_lambda2chi, + m_term1, m_term2, m_term3, m_tff; + +}; + +//========================================================================== + +// A derived class for g g -> (LED G*/U*) -> gamma gamma +// (virtual graviton/unparticle exchange). + +class Sigma2gg2LEDgammagamma : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2gg2LEDgammagamma( bool Graviton) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return (m_graviton + ? "g g -> (LED G*) -> gamma gamma" : "g g -> (U*) -> gamma gamma") ;} + virtual int code() const {return (m_graviton ? 5027 : 5044);} + virtual string inFlux() const {return "gg";} + +private: + + int m_spin, m_cutoff, m_nGrav; + bool m_graviton; + double m_dU, m_LambdaU, m_lambda, m_lambda2chi, m_sigma0, m_tff; + +}; + +//========================================================================== + +// A derived class for f fbar -> (LED G*/U*) -> l lbar +// (virtual graviton/unparticle exchange). +// Does not include t-channel contributions relevant for e^+e^- to e^+e^- + +class Sigma2ffbar2LEDllbar : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2ffbar2LEDllbar( bool Graviton) : m_graviton(Graviton) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "f fbar -> (LED G*) -> l l" : "f fbar -> (U*) -> l l") ;} + virtual int code() const {return (m_graviton ? 5028 : 5048);} + virtual string inFlux() const {return "ffbarSame";} + virtual bool isSChannel() const {return true;} + +private: + + int m_spin, m_cutoff, m_nGrav,m_nxx, m_nxy; + bool m_graviton; + double m_dU, m_LambdaU, m_lambda, m_lambda2chi, m_tff, + m_mZ, m_mZS, m_GZ, m_GZS, m_absMeU, m_denomPropZ, m_rePropGamma, + m_rePropZ, m_imPropZ, m_absAS, m_reA, m_reABW, m_poly1, m_poly2, + m_poly3; + +}; + +//========================================================================== + +// A derived class for g g -> (LED G*/U*) -> l lbar +// (virtual graviton/unparticle exchange). + +class Sigma2gg2LEDllbar : public Sigma2Process { + +public: + + // Constructor: bool Graviton = true, to use LED graviton settings. + Sigma2gg2LEDllbar( bool Graviton) : m_graviton(Graviton) {} + + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section; + // first step when inflavours unknown. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat); second step for given inflavours. + virtual double sigmaHat() {return m_sigma0;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return + (m_graviton ? "g g -> (LED G*) -> l l" : "g g -> (U*) -> l l") ;} + virtual int code() const {return (m_graviton ? 5029 : 5049);} + virtual string inFlux() const {return "gg";} + +private: + + int m_spin, m_cutoff, m_nGrav; + bool m_graviton; + double m_dU, m_LambdaU, m_lambda, m_lambda2chi, m_sigma0, m_tff; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaExtraDim_H diff --git a/PYTHIA8/pythia8140/include/SigmaGeneric.h b/PYTHIA8/pythia8140/include/SigmaGeneric.h new file mode 100644 index 00000000000..bc373dab32b --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaGeneric.h @@ -0,0 +1,148 @@ +// SigmaGeneric.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Johan Bijnens,Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for various generic production processes, to be used as +// building blocks for some BSM processes. +// Currently represented by QCD pair production of colour triplet objects, +// with spin either 0, 1/2 or 1. + +#ifndef Pythia8_SigmaGeneric_H +#define Pythia8_SigmaGeneric_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for g g -> qG qGbar (generic quark of spin 0, 1/2 or 1). + +class Sigma2gg2qGqGbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2qGqGbar(int idIn, int codeIn, int spinIn, + string nameIn = "g g -> qG qGbar") : idNew(idIn), codeSave(codeIn), + spinSave(spinIn), nameSave(nameIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idNew;} + +private: + + // Values stored for process type and colour flow selection. + int idNew, codeSave, spinSave, nCHV; + string nameSave; + bool hasKappa; + double openFracPair, sigma, sigTS, sigUS, sigSum, kappam1; + +}; + +//========================================================================== + +// A derived class for q qbar -> qG qGbar (generic quark of spin 0, 1/2 or 1). + +class Sigma2qqbar2qGqGbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2qGqGbar(int idIn, int codeIn, int spinIn, + string nameIn = "q qbar -> qG qGbar") : idNew(idIn), codeSave(codeIn), + spinSave(spinIn), nameSave(nameIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idNew;} + +private: + + // Values stored for process type and colour flow selection. + int idNew, codeSave, spinSave, nCHV; + string nameSave; + double openFracPair, sigma, sigTS, sigUS, sigSum, kappa; + +}; + +//========================================================================== + +// A derived class for f fbar -> fG fGbar (generic particle of spin 0, 1/2 or 1) +// via gamma^*/Z^* s-channel exchange. Still under development!! ?? + +class Sigma2ffbar2fGfGbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2fGfGbar(int idIn, int codeIn, int spinIn, + string nameIn = "q qbar -> qG qGbar") : idNew(idIn), codeSave(codeIn), + spinSave(spinIn), nameSave(nameIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idNew;} + +private: + + // Values stored for process type and colour flow selection. + int idNew, codeSave, spinSave, nCHV; + string nameSave; + bool hasColour; + double eQHV2, openFracPair, sigma0, sigTS, sigUS, sigSum, kappa, colFac; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaGeneric_H diff --git a/PYTHIA8/pythia8140/include/SigmaHiggs.h b/PYTHIA8/pythia8140/include/SigmaHiggs.h new file mode 100644 index 00000000000..defcc91b7a4 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaHiggs.h @@ -0,0 +1,812 @@ +// SigmaHiggs.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// Part of code written by Marc Montull, CERN summer student 2007. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for Higgs process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma2Process. + +#ifndef Pythia8_SigmaHiggs_H +#define Pythia8_SigmaHiggs_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for f fbar -> H0 (SM), H1, H2 or A3 (BSM). + +class Sigma1ffbar2H : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2H(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarSame";} + virtual int resonanceA() const {return idRes;} + +private: + + // An H0, H1, H2 or A3 resonance object provides coupling + // and propagator expressions. + ParticleDataEntry* HResPtr; + double mRes, GammaRes, m2Res, GamMRat, sigBW, widthOut; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for g g -> H0 (SM), H1, H2 or A3 (BSM). + +class Sigma1gg2H : public Sigma1Process { + +public: + + // Constructor. + Sigma1gg2H(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave ;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int resonanceA() const {return idRes;} + +private: + + // A H0, H1, H2 or A3 resonance object provides coupling + // and propagator expressions. + ParticleDataEntry* HResPtr; + double mRes, GammaRes, m2Res, GamMRat, sigma; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for gamma gamma -> H0 (SM Higgs), H1, H2 or A3 (BSM Higgs). + +class Sigma1gmgm2H : public Sigma1Process { + +public: + + // Constructor. + Sigma1gmgm2H(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gmgm";} + virtual int resonanceA() const {return idRes;} + +private: + + // A H0, H1, H2 or A3 resonance object provides coupling + // and propagator expressions. + ParticleDataEntry* HResPtr; + double mRes, GammaRes, m2Res, GamMRat, sigma; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for f fbar -> H Z0. +// (H can be H0 SM or H1, H2, A3 from BSM). +class Sigma2ffbar2HZ : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2HZ(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarSame";} + virtual bool isSChannel() const {return true;} + virtual int id3Mass() const {return idRes;} + virtual int id4Mass() const {return 23;} + virtual int resonanceA() const {return 23;} + virtual int gmZmode() const {return 2;} + +private: + + // Store Z0 mass and width. + double mZ, widZ, mZS, mwZS, thetaWRat, sigma0, openFracPair, coup2Z; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for f fbar -> H W+- (Standard Model Higgs). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma2ffbar2HW : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2HW(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarChg";} + virtual bool isSChannel() const {return true;} + virtual int id3Mass() const {return idRes;} + virtual int id4Mass() const {return 24;} + virtual int resonanceA() const {return 24;} + +private: + + // Store W+- mass and width, and couplings. + double mW, widW, mWS, mwWS, thetaWRat, sigma0, openFracPairPos, + openFracPairNeg, coup2W; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for f f' -> H f f' (Z0 Z0 fusion of SM or BSM Higgs). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma3ff2HfftZZ : public Sigma3Process { + +public: + + // Constructor. + Sigma3ff2HfftZZ(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ff";} + virtual int id3Mass() const {return idRes;} + + // Instructions for 3-body phase space with t-channel propagators. + virtual int idTchan1() const {return 23;} + virtual int idTchan2() const {return 23;} + virtual double tChanFracPow1() const {return 0.05;} + virtual double tChanFracPow2() const {return 0.9;} + virtual bool useMirrorWeight() const {return true;} + +private: + + // Store standard factors. + double mZS, prefac, sigma1, sigma2, openFrac, coup2Z; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for f_1 f_2 -> H f_3 f_4 (W+ W- fusion of SM or BSM Higgs). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma3ff2HfftWW : public Sigma3Process { + +public: + + // Constructor. + Sigma3ff2HfftWW(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ff";} + virtual int id3Mass() const {return idRes;} + + // Instructions for 3-body phase space with t-channel propagators. + virtual int idTchan1() const {return 24;} + virtual int idTchan2() const {return 24;} + virtual double tChanFracPow1() const {return 0.05;} + virtual double tChanFracPow2() const {return 0.9;} + virtual bool useMirrorWeight() const {return true;} + +private: + + // Store standard prefactor. + double mWS, prefac, sigma0, openFrac, coup2W; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for g g -> H Q Qbar (Q Qbar fusion of SM or BSM Higgs). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma3gg2HQQbar : public Sigma3Process { + +public: + + // Constructor. + Sigma3gg2HQQbar(int idIn, int higgsTypeIn) : idNew(idIn), + higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idRes;} + virtual int id4Mass() const {return idNew;} + virtual int id5Mass() const {return idNew;} + + // Instructions for 3-body phase space with t-channel propagators. + virtual int idTchan1() const {return idNew;} + virtual int idTchan2() const {return idNew;} + virtual double tChanFracPow1() const {return 0.4;} + virtual double tChanFracPow2() const {return 0.2;} + virtual bool useMirrorWeight() const {return false;} + +private: + + // Store flavour-specific process information and standard prefactor. + double prefac, sigma, openFracTriplet, coup2Q; + int idNew, higgsType, codeSave, idRes; + string nameSave; + +}; + +//========================================================================== + +// A derived class for q qbar -> H Q Qbar (Q Qbar fusion of SM or BSM Higgs). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma3qqbar2HQQbar : public Sigma3Process { + +public: + + // Constructor. + Sigma3qqbar2HQQbar(int idIn, int higgsTypeIn) : idNew(idIn), + higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idRes;} + virtual int id4Mass() const {return idNew;} + virtual int id5Mass() const {return idNew;} + + // Instructions for 3-body phase space with t-channel propagators. + virtual int idTchan1() const {return idNew;} + virtual int idTchan2() const {return idNew;} + virtual double tChanFracPow1() const {return 0.4;} + virtual double tChanFracPow2() const {return 0.2;} + virtual bool useMirrorWeight() const {return false;} + +private: + + // Store flavour-specific process information and standard prefactor. + double prefac, sigma, openFracTriplet, coup2Q; + int idNew, higgsType, codeSave, idRes; + string nameSave; + +}; + +//========================================================================== + +// A derived class for q g -> H q (SM or BSM Higgs). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma2qg2Hq : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2Hq(int idIn, int higgsTypeIn) : idNew(idIn), + higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return idRes;} + virtual int id4Mass() const {return idNew;} + +private: + + // Store flavour-specific process information and standard prefactor. + double m2W, thetaWRat, sigma, openFrac; + int idNew, higgsType, codeSave, idRes; + string nameSave; + +}; + +//========================================================================== + +// A derived class for g g -> H0 g (SM or BSM Higgs via heavy top loop). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma2gg2Hglt : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2Hglt(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idRes;} + +private: + + // Store standard prefactor. + double widHgg, sigma, openFrac; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for q g -> H q (SM or BSM Higgs via heavy top loop). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma2qg2Hqlt : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2Hqlt(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return idRes;} + +private: + + // Store standard prefactor. + double widHgg, sigma, openFrac; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for q qbar -> H g (SM or BSM Higgs via heavy top loop). +// (H can be H0 SM or H1, H2, A3 from BSM). + +class Sigma2qqbar2Hglt : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2Hglt(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idRes;} + +private: + + // Store standard prefactor. + double widHgg, sigma, openFrac; + int higgsType, codeSave, idRes; + string nameSave; +}; + +//========================================================================== + +// A derived class for f fbar' -> H+-. + +class Sigma1ffbar2Hchg : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2Hchg() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar' -> H+-";} + virtual int code() const {return 961;} + virtual string inFlux() const {return "ffbarChg";} + virtual int resonanceA() const {return 37;} + +private: + + // A H0 resonance object provides coupling and propagator expressions. + ParticleDataEntry* HResPtr; + double mRes, GammaRes, m2Res, GamMRat, m2W, thetaWRat, tan2Beta, sigBW, + widthOutPos, widthOutNeg; + +}; + +//========================================================================== + +// A derived class for q g -> H+- q'. + +class Sigma2qg2Hchgq : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2Hchgq(int idIn, int codeIn, string nameIn) : idNew(idIn), + codeSave(codeIn), nameSave(nameIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return 37;} + virtual int id4Mass() const {return idNew;} + +private: + + // Store flavour-specific process information and standard prefactor. + int idNew, codeSave, idOld, idUp, idDn; + string nameSave; + double m2W, thetaWRat, tan2Beta, sigma, openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for f fbar -> A0(H_3) h0(H_1) or A0(H_3) H0(H_2). + +class Sigma2ffbar2A3H12 : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2A3H12(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return 36;} + virtual int id4Mass() const {return higgs12;} + +private: + + // Store flavour-specific process information and standard prefactor. + int higgsType, higgs12, codeSave; + string nameSave; + double coupZA3H12, m2Z, mGammaZ, thetaWRat, openFrac, sigma0; + +}; + +//========================================================================== + +// A derived class for f fbar -> H+- h0(H_1) or H+- H0(H_2). + +class Sigma2ffbar2HchgH12 : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2HchgH12(int higgsTypeIn) : higgsType(higgsTypeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarChg";} + virtual int id3Mass() const {return 37;} + virtual int id4Mass() const {return higgs12;} + +private: + + // Store flavour-specific process information and standard prefactor. + int higgsType, higgs12, codeSave; + string nameSave; + double coupWHchgH12, m2W, mGammaW, thetaWRat, openFracPos, openFracNeg, + sigma0; + +}; + +//========================================================================== + +// A derived class for f fbar -> H+ H-. + +class Sigma2ffbar2HposHneg : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2HposHneg() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> H+ H-";} + virtual int code() const {return 1085;} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return 37;} + virtual int id4Mass() const {return 37;} + +private: + + // Store flavour-specific process information and standard prefactor. + double m2Z, mGammaZ, thetaWRat, eH, lH, openFrac, gamSig, intSig, resSig; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaHiggs_H diff --git a/PYTHIA8/pythia8140/include/SigmaLeftRightSym.h b/PYTHIA8/pythia8140/include/SigmaLeftRightSym.h new file mode 100644 index 00000000000..f7ea6fd7121 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaLeftRightSym.h @@ -0,0 +1,275 @@ +// SigmaLeftRightSym.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for left-rights-symmetry differential cross sections. +// Contains classes derived from SigmaProcess via Sigma(1/2/3)Process. + +#ifndef Pythia8_SigmaLeftRightSym_H +#define Pythia8_SigmaLeftRightSym_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for f fbar -> Z_R^0 (righthanded gauge boson). + +class Sigma1ffbar2ZRight : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2ZRight() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for G* decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> Z_R^0";} + virtual int code() const {return 3101;} + virtual string inFlux() const {return "ffbarSame";} + virtual int resonanceA() const {return idZR;} + +private: + + // Parameters set at initialization or for current kinematics. + int idZR; + double mRes, GammaRes, m2Res, GamMRat, sin2tW, sigma0; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* ZRPtr; + +}; + +//========================================================================== + +// A derived class for f fbar' -> W_R^+- (righthanded gauge boson). + +class Sigma1ffbar2WRight : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2WRight() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar' -> W_R^+-";} + virtual int code() const {return 3102;} + virtual string inFlux() const {return "ffbarChg";} + virtual int resonanceA() const {return idWR;} + +private: + + // Parameters set at initialization. + int idWR; + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, sigma0Pos, sigma0Neg; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +// A derived class for l l -> H_L^++-- or H_R^++-- (doubly charged Higgs). + +class Sigma1ll2Hchgchg : public Sigma1Process { + +public: + + // Constructor. + Sigma1ll2Hchgchg(int leftRightIn ) : leftRight(leftRightIn) {} + + // Initialize process. + virtual void initProc(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ff";} + virtual int resonanceA() const {return idHLR;} + +private: + + // Parameters set at initialization. + int leftRight, idHLR, codeSave; + string nameSave; + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, yukawa[4][4]; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +// A derived class for l- gamma -> H_(L/R)^-- l+ (doubly charged Higgs). + +class Sigma2lgm2Hchgchgl : public Sigma2Process { + +public: + + // Constructor. + Sigma2lgm2Hchgchgl(int leftRightIn, int idLepIn ) : leftRight(leftRightIn), + idLep(idLepIn) {} + + // Initialize process. + virtual void initProc(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "fgm";} + virtual int resonanceA() const {return idHLR;} + +private: + + // Parameters set at initialization. + int leftRight, idHLR, idLep, codeSave; + string nameSave; + double yukawa[4], openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for f_1 f_2 -> H_(L/R)^++-- f_3 f_4 (W+- W+- fusion). + +class Sigma3ff2HchgchgfftWW : public Sigma3Process { + +public: + + // Constructor. + Sigma3ff2HchgchgfftWW(int leftRightIn) : leftRight(leftRightIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for decay angles. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ff";} + virtual int id3Mass() const {return idHLR;} + + // Instructions for 3-body phase space with t-channel propagators. + virtual int idTchan1() const {return 9900024;} + virtual int idTchan2() const {return 9900024;} + virtual double tChanFracPow1() const {return 0.05;} + virtual double tChanFracPow2() const {return 0.9;} + virtual bool useMirrorWeight() const {return true;} + +private: + + // Store standard prefactor. + int leftRight, idHLR, codeSave; + string nameSave; + double mWS, prefac, sigma0TU, sigma0T, openFracPos, openFracNeg; + +}; + +//========================================================================== + +// A derived class for f fbar -> H_(L/R)^++ H_(L/R)^-- (doubly charged Higgs). + +class Sigma2ffbar2HchgchgHchgchg : public Sigma2Process { + +public: + + // Constructor. + Sigma2ffbar2HchgchgHchgchg(int leftRightIn) : leftRight(leftRightIn) {} + + // Initialize process. + virtual void initProc(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "ffbarSame";} + virtual int id3Mass() const {return idHLR;} + virtual int id4Mass() const {return idHLR;} + virtual int resonanceA() const {return 23;} + +private: + + // Parameters set at initialization. + int leftRight, idHLR, codeSave; + string nameSave; + double mRes, GammaRes, m2Res, GamMRat, sin2tW, preFac, yukawa[4][4], + openFrac; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaLeftRightSym_H diff --git a/PYTHIA8/pythia8140/include/SigmaLeptoquark.h b/PYTHIA8/pythia8140/include/SigmaLeptoquark.h new file mode 100644 index 00000000000..f951c08f530 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaLeptoquark.h @@ -0,0 +1,176 @@ +// SigmaLeptoquark.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for leptoquark-process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma(1/2)Process. +// Note: since leptoquark assumed scalar no need for decay-angles routines. + +#ifndef Pythia8_SigmaLeptoquark_H +#define Pythia8_SigmaLeptoquark_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for q l -> LQ (leptoquark). + +class Sigma1ql2LeptoQuark : public Sigma1Process { + +public: + + // Constructor. + Sigma1ql2LeptoQuark() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q l -> LQ (leptoquark)";} + virtual int code() const {return 3201;} + virtual string inFlux() const {return "ff";} + virtual int resonanceA() const {return 42;} + +private: + + // Parameters set at initialization or for current kinematics. + int idQuark, idLepton; + double mRes, GammaRes, m2Res, GamMRat, kCoup, widthIn, sigBW; + + // Pointer to properties of the particle species, to access decay channel. + ParticleDataEntry* LQPtr; + +}; + +//========================================================================== + +// A derived class for q g -> LQ l (leptoquark). + +class Sigma2qg2LeptoQuarkl : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2LeptoQuarkl() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g -> LQ l (leptoquark)";} + virtual int code() const {return 3202;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return 42;} + +private: + + // Parameters set at initialization or for current kinematics. + int idQuark, idLepton; + double mRes, GammaRes, m2Res, GamMRat, kCoup, openFracPos, openFracNeg, + sigma0; + +}; + +//========================================================================== + +// A derived class for g g -> LQ LQbar (leptoquark). + +class Sigma2gg2LQLQbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2LQLQbar() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> LQ LQbar (leptoquark)";} + virtual int code() const {return 3203;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return 42;} + virtual int id4Mass() const {return 42;} + +private: + + // Parameters set at initialization or for current kinematics. + double mRes, GammaRes, m2Res, GamMRat, openFrac, sigma; + +}; + +//========================================================================== + +// A derived class for q qbar -> LQ LQbar (leptoquark). + +class Sigma2qqbar2LQLQbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2LQLQbar() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat() { + return (abs(id1) == idQuark) ? sigmaSame : sigmaDiff;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> LQ LQbar (leptoquark)";} + virtual int code() const {return 3204;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return 42;} + virtual int id4Mass() const {return 42;} + +private: + + // Parameters set at initialization or for current kinematics. + int idQuark; + double mRes, GammaRes, m2Res, GamMRat, kCoup, openFrac, sigmaDiff, + sigmaSame; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaLeptoquark_H diff --git a/PYTHIA8/pythia8140/include/SigmaNewGaugeBosons.h b/PYTHIA8/pythia8140/include/SigmaNewGaugeBosons.h new file mode 100644 index 00000000000..1c25c21d6cc --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaNewGaugeBosons.h @@ -0,0 +1,185 @@ +// SigmaNewGaugeBosons.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for new-gauge-boson-process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma1Process. + +#ifndef Pythia8_SigmaNewGaugeBosons_H +#define Pythia8_SigmaNewGaugeBosons_H + +#include "PythiaComplex.h" +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// An intermediate class for f fbar -> Z'/W' -> WW/WZ -> 4 fermions. +// Copied from SigmaEW for gauge-boson-pair production. + +class Sigma1ffbarZprimeWprime: public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbarZprimeWprime() {} + +protected: + + // Internal products. + Vec4 pRot[7]; + complex hA[7][7]; + complex hC[7][7]; + + // Calculate and store internal products. + void setupProd( Event& process, int i1, int i2, int i3, int i4, + int i5, int i6); + + // Evaluate the F function of Gunion and Kunszt. + complex fGK(int i1, int i2, int i3, int i4, int i5, int i6); + + // Evaluate the Xi function of Gunion and Kunszt. + double xiGK( double tHnow, double uHnow, double s3now, double s4now); + + // Evaluate the Xj function of Gunion and Kunszt. + double xjGK( double tHnow, double uHnow, double s3now, double s4now); + +private: + +}; + +//========================================================================== + +// A derived class for f fbar -> gamma*/Z0/Z'0. + +class Sigma1ffbar2gmZZprime : public Sigma1ffbarZprimeWprime { + +public: + + // Constructor. + Sigma1ffbar2gmZZprime() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for Z' decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar -> gamma*/Z0/Zprime0";} + virtual int code() const {return 3001;} + virtual string inFlux() const {return "ffbarSame";} + virtual int resonanceA() const {return 23;} + virtual int resonanceB() const {return 32;} + +private: + + // Parameters set at initialization or for each new event. + int gmZmode; + double mRes, GammaRes, m2Res, GamMRat, sin2tW, cos2tW, thetaWRat, + mZ, GammaZ, m2Z, GamMRatZ, afZp[20], vfZp[20], coupZpWW, + anglesZpWW, gamSum, gamZSum, ZSum, gamZpSum, ZZpSum, ZpSum, + gamNorm, gamZNorm, ZNorm, gamZpNorm, ZZpNorm, ZpNorm; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +// A derived class for f fbar' -> W'+-. + +class Sigma1ffbar2Wprime : public Sigma1ffbarZprimeWprime { + +public: + + // Constructor. + Sigma1ffbar2Wprime() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angle. + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return "f fbar' -> W'+-";} + virtual int code() const {return 3021;} + virtual string inFlux() const {return "ffbarChg";} + virtual int resonanceA() const {return 34;} + +private: + + // Parameters set at initialization. + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, sigma0Pos, sigma0Neg, + aqWp, vqWp, alWp, vlWp, coupWpWZ, anglesWpWZ; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; +//========================================================================== + +// A derived class for f fbar' -> R^0 (horizontal gauge boson). + +class Sigma1ffbar2Rhorizontal : public Sigma1Process { + +public: + + // Constructor. + Sigma1ffbar2Rhorizontal() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate sigmaHat(sHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "f fbar' -> R^0";} + virtual int code() const {return 3041;} + virtual string inFlux() const {return "ffbar";} + virtual int resonanceA() const {return 41;} + +private: + + // Parameters set at initialization. + double mRes, GammaRes, m2Res, GamMRat, thetaWRat, sigma0Pos, sigma0Neg; + + // Pointer to properties of the particle species, to access decay channels. + ParticleDataEntry* particlePtr; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia_SigmaNewGaugeBosons_H diff --git a/PYTHIA8/pythia8140/include/SigmaOnia.h b/PYTHIA8/pythia8140/include/SigmaOnia.h new file mode 100644 index 00000000000..01b85de2586 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaOnia.h @@ -0,0 +1,294 @@ +// SigmaOnia.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for charmonia/bottomonia process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma2Process. + +#ifndef Pythia8_SigmaOnia_H +#define Pythia8_SigmaOnia_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for g g -> QQbar[3S1(1)] g (Q = c or b). + +class Sigma2gg2QQbar3S11g : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2QQbar3S11g(int idIn, int codeIn) : idNew(idIn), + codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idHad;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, idHad, codeSave; + string nameSave; + double oniumME, sigma; + +}; + +//========================================================================== + +// A derived class for g g -> QQbar[3PJ(1)] g (Q = c or b, J = 0, 1 or 2). + +class Sigma2gg2QQbar3PJ1g : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2QQbar3PJ1g(int idIn, int jIn, int codeIn) : idNew(idIn), + jSave(jIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idHad;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, idHad, jSave, codeSave; + string nameSave; + double oniumME, sigma; + +}; + +//========================================================================== + +// A derived class for q g -> QQbar[3PJ(1)] q (Q = c or b, J = 0, 1 or 2). + +class Sigma2qg2QQbar3PJ1q : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2QQbar3PJ1q(int idIn, int jIn, int codeIn) : idNew(idIn), + jSave(jIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return idHad;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, idHad, jSave, codeSave; + string nameSave; + double oniumME, sigma; + +}; + +//========================================================================== + +// A derived class for q qbar -> QQbar[3PJ(1)] g (Q = c or b, J = 0, 1 or 2). + +class Sigma2qqbar2QQbar3PJ1g : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2QQbar3PJ1g(int idIn, int jIn, int codeIn) : idNew(idIn), + jSave(jIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idHad;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, idHad, jSave, codeSave; + string nameSave; + double oniumME, sigma; + +}; + +//========================================================================== + +// A derived class for g g -> QQbar[X(8)] g (Q = c or b, X = 3S1, 1S0 or 3PJ). + +class Sigma2gg2QQbarX8g : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2QQbarX8g(int idIn, int stateIn, int codeIn) : idNew(idIn), + stateSave(stateIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idHad;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, idHad, stateSave, codeSave; + string nameSave; + double oniumME, sigma; + +}; + +//========================================================================== + +// A derived class for q g -> QQbar[X(8)] q (Q = c or b, X = 3S1, 1S0 or 3PJ). + +class Sigma2qg2QQbarX8q : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2QQbarX8q(int idIn, int stateIn, int codeIn) : idNew(idIn), + stateSave(stateIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return idHad;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, idHad, stateSave, codeSave; + string nameSave; + double oniumME, sigma; + +}; + +//========================================================================== + +// A derived class for q qbar -> QQbar[X(8)] g (Q = c or b, +// X = 3S1, 1S0 or 3PJ). + +class Sigma2qqbar2QQbarX8g : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2QQbarX8g(int idIn, int stateIn, int codeIn) : idNew(idIn), + stateSave(stateIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idHad;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, idHad, stateSave, codeSave; + string nameSave; + double oniumME, sigma; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaOnia_H diff --git a/PYTHIA8/pythia8140/include/SigmaProcess.h b/PYTHIA8/pythia8140/include/SigmaProcess.h new file mode 100644 index 00000000000..c4d21bf565d --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaProcess.h @@ -0,0 +1,585 @@ +// SigmaProcess.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for hard-process differential cross sections. +// SigmaProcess: base class for cross sections. +// Sigma0Process: base class for unresolved processes, derived from above. +// Sigma1Process: base class for 2 -> 1 processes, derived from above. +// Sigma2Process: base class for 2 -> 2 processes, derived from above. +// Sigma3Process: base class for 2 -> 3 processes, derived from above. +// SigmaLHAProcess: wrapper class for Les Houches Accord external input. +// Actual physics processes are found in separate files: +// SigmaQCD for QCD processes; +// SigmaEW for electroweak processes (including photon production); +// SigmaOnia for charmonium and bottomonium processes; +// SigmaHiggs for Higgs processes; +// SigmaSUSY for supersymmetric production; +// SigmaLeftRightSym for processes in left-right-symmetric scenarios; +// SigmaLeptoquark for leptoquark production. +// SigmaExtraDim for processes in scenarios for extra dimensions; +// SigmaGeneric for generic scalar/fermion/vector pair production. + +#ifndef Pythia8_SigmaProcess_H +#define Pythia8_SigmaProcess_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Event.h" +#include "Info.h" +#include "LesHouches.h" +#include "ParticleData.h" +#include "PartonDistributions.h" +#include "PythiaStdlib.h" +#include "ResonanceWidths.h" +#include "Settings.h" +#include "SigmaTotal.h" +#include "StandardModel.h" +#include "SusyCouplings.h" +#include "SusyLesHouches.h" + +namespace Pythia8 { + +//========================================================================== + +// InBeam is a simple helper class for partons and their flux in a beam. + +class InBeam { + +public: + + // Constructor. + InBeam( int idIn = 0) : id(idIn), pdf(0.) {} + + // Values. + int id; + double pdf; + +}; + +//========================================================================== + +// InPair is a simple helper class for colliding parton pairs and their flux. + +class InPair { + +public: + + // Constructor. + InPair( int idAIn = 0, int idBIn = 0) : idA(idAIn), idB(idBIn), + pdfA(0.), pdfB(0.), pdfSigma(0.) {} + + // Values. + int idA, idB; + double pdfA, pdfB, pdfSigma; + +}; + +//========================================================================== + +// SigmaProcess is the base class for cross section calculations. + +class SigmaProcess { + +public: + + // Destructor. + virtual ~SigmaProcess() {} + + // Perform simple initialization and store pointers. + void init(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, CoupSM* coupSMPtrIn, + SigmaTotal* sigmaTotPtrIn = 0, CoupSUSY* coupSUSYPtrIn = 0, + SusyLesHouches* slhaPtrIn = 0); + + // Store or replace Les Houches pointer. + void setLHAPtr( LHAup* lhaUpPtrIn) {lhaUpPtr = lhaUpPtrIn;} + + // Initialize process. Only used for some processes. + virtual void initProc() {} + + // Set up allowed flux of incoming partons. Default is no flux. + virtual bool initFlux(); + + // Input and complement kinematics for resolved 2 -> 1 process. + // Usage: set1Kin( x1in, x2in, sHin). + virtual void set1Kin( double , double , double ) {} + + // Input and complement kinematics for resolved 2 -> 2 process. + // Usage: set2Kin( x1in, x2in, sHin, tHin, m3in, m4in, runBW3in, runBW4in). + virtual void set2Kin( double , double , double , double , double , + double, double, double ) {} + + // Ditto, but for Multiple Interactions applications, so different input. + // Usage: set2KinMI( x1in, x2in, sHin, tHin, uHin, + // alpSin, alpEMin, needMasses, m3in, m4in) + virtual void set2KinMI( double , double , double , double , + double , double , double , bool , double , double ) {} + + // Input and complement kinematics for resolved 2 -> 3 process. + // Usage: set3Kin( x1in, x2in, sHin, p3prel, p4prel, p5prel, + // m3in, m4in, m5in, runBW3in, runBW4in, runBW5in); + virtual void set3Kin( double , double , double , Vec4 , Vec4 , Vec4 , + double , double , double , double , double , double ) {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin() {} + + // Evaluate sigma for unresolved, sigmaHat(sHat) for 2 -> 1 processes, + // d(sigmaHat)/d(tHat) for (resolved) 2 -> 2 processes, and |M|^2 for + // 2 -> 3 processes. Answer in "native" units, either mb or GeV^-2. + virtual double sigmaHat() {return 0.;} + + // Wrapper to sigmaHat, to (a) store current incoming flavours and + // (b) convert from GeV^-2 to mb where required. + // For 2 -> 2 also (c) convert from from |M|^2 to d(sigmaHat)/d(tHat). + virtual double sigmaHatWrap(int id1in = 0, int id2in = 0) { + id1 = id1in; id2 = id2in; + return ( convert2mb() ? CONVERT2MB * sigmaHat() : sigmaHat() ); } + + // Convolute above with parton flux and K factor. Sum over open channels. + virtual double sigmaPDF(); + + // Select incoming parton channel and extract parton densities (resolved). + void pickInState(int id1in = 0, int id2in = 0); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol() {} + + // Perform kinematics for a Multiple Interaction, in its rest frame. + virtual bool final2KinMI( int = 0, int = 0, Vec4 = 0., Vec4 = 0., + double = 0., double = 0.) {return true;} + + // Evaluate weight for simultaneous flavours (only gamma*/Z0 gamma*/Z0). + // Usage: weightDecayFlav( process). + virtual double weightDecayFlav( Event&) {return 1.;} + + // Evaluate weight for decay angular configuration. + // Usage: weightDecay( process, iResBeg, iResEnd), where + // iResBeg <= i < iResEnd is range of sister partons to test decays of. + virtual double weightDecay( Event&, int, int) {return 1.;} + + // Set scale, when that is missing for an external LHA process. + virtual void setScale() {} + + // Process name and code, and the number of final-state particles. + virtual string name() const {return "unnamed process";} + virtual int code() const {return 0;} + virtual int nFinal() const {return 2;} + + // Need to know which incoming partons to set up interaction for. + virtual string inFlux() const {return "unknown";} + + // Need to know whether to convert cross section answer from GeV^-2 to mb. + virtual bool convert2mb() const {return true;} + + // For 2 -> 2 process optional conversion from |M|^2 to d(sigmaHat)/d(tHat). + virtual bool convertM2() const {return false;} + + // Special treatment needed for Les Houches processes. + virtual bool isLHA() const {return false;} + + // Special treatment needed for elastic and diffractive processes. + virtual bool isMinBias() const {return false;} + virtual bool isResolved() const {return true;} + virtual bool isDiffA() const {return false;} + virtual bool isDiffB() const {return false;} + + // Special treatment needed for SUSY processes. + virtual bool isSUSY() const {return false;} + + // Special treatment needed if negative cross sections allowed. + virtual bool allowNegativeSigma() const {return false;} + + // Flavours in 2 -> 2/3 processes where masses needed from beginning. + // (For a light quark masses will be used in the final kinematics, + // but not at the matrix-element level. For a gluon no masses at all.) + virtual int id3Mass() const {return 0;} + virtual int id4Mass() const {return 0;} + virtual int id5Mass() const {return 0;} + + // Special treatment needed if process contains an s-channel resonance. + virtual int resonanceA() const {return 0;} + virtual int resonanceB() const {return 0;} + + // 2 -> 2 and 2 -> 3 processes only through s-channel exchange. + virtual bool isSChannel() const {return false;} + + // NOAM: Insert an intermediate resonance in 2 -> 1 -> 2 (or 3) listings. + virtual int idSChannel() const {return 0;} + + // QCD 2 -> 3 processes need special phase space selection machinery. + virtual bool isQCD3body() const {return false;} + + // Special treatment in 2 -> 3 with two massive propagators. + virtual int idTchan1() const {return 0;} + virtual int idTchan2() const {return 0;} + virtual double tChanFracPow1() const {return 0.3;} + virtual double tChanFracPow2() const {return 0.3;} + virtual bool useMirrorWeight() const {return false;} + + // Special process-specific gamma*/Z0 choice if >=0 (e.g. f fbar -> H0 Z0). + virtual int gmZmode() const {return -1;} + + // Tell whether tHat and uHat are swapped (= same as swap 3 and 4). + bool swappedTU() const {return swapTU;} + + // Give back particle properties: flavours, colours, masses, or all. + int id(int i) const {return idSave[i];} + int col(int i) const {return colSave[i];} + int acol(int i) const {return acolSave[i];} + double m(int i) const {return mSave[i];} + Particle getParton(int i) const {return parton[i];} + + // Give back couplings and parton densities. Not all known for minbias. + double Q2Ren() const {return Q2RenSave;} + double alphaEMRen() const {return alpEM;} + double alphaSRen() const {return alpS;} + double Q2Fac() const {return Q2FacSave;} + double pdf1() const {return pdf1Save;} + double pdf2() const {return pdf2Save;} + + // Give back angles; relevant only for multipe-interactions processes. + double thetaMI() const {return atan2( sinTheta, cosTheta);} + double phiMI() const {return phi;} + double sHBetaMI() const {return sHBeta;} + double pT2MI() const {return pT2Mass;} + double pTMIFin() const {return pTFin;} + +protected: + + // Constructor. + SigmaProcess() {for (int i = 0; i < 6; ++i) mSave[i] = 0.;} + + // Constants: could only be changed in the code itself. + static const double CONVERT2MB, MASSMARGIN; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to incoming beams. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + + // Pointer to Standard Model couplings, including alphaS and alphaEM. + CoupSM* coupSMPtr; + + // Pointer to the total/elastic/diffractive cross section object. + SigmaTotal* sigmaTotPtr; + + // Pointer to SUSY couplings. + CoupSUSY* coupSUSYPtr; + + // Pointer to the SLHA object. + SusyLesHouches* slhaPtr; + + // Pointer to LHAup for generating external events. + LHAup* lhaUpPtr; + + // Initialization data, normally only set once. + int nQuarkIn, renormScale1, renormScale2, renormScale3, renormScale3VV, + factorScale1, factorScale2, factorScale3, factorScale3VV; + double Kfactor, renormMultFac, renormFixScale, factorMultFac, + factorFixScale; + + // CP violation parameters for Higgs sector, normally only set once. + int higgsH1parity, higgsH2parity, higgsA3parity; + double higgsH1eta, higgsH2eta, higgsA3eta; + + // Information on incoming beams. + int idA, idB; + double mA, mB; + bool isLeptonA, isLeptonB, hasLeptonBeams; + + // Partons in beams, with PDF's. + vector inBeamA; + vector inBeamB; + void addBeamA(int idIn) {inBeamA.push_back(InBeam(idIn));} + void addBeamB(int idIn) {inBeamB.push_back(InBeam(idIn));} + int sizeBeamA() const {return inBeamA.size();} + int sizeBeamB() const {return inBeamB.size();} + + // Allowed colliding parton pairs, with pdf's. + vector inPair; + void addPair(int idAIn, int idBIn) { + inPair.push_back(InPair(idAIn, idBIn));} + int sizePair() const {return inPair.size();} + + // Store Q2 renormalization and factorization scales, and related values. + double Q2RenSave, alpEM, alpS, Q2FacSave, x1Save, x2Save, pdf1Save, + pdf2Save, sigmaSumSave; + + // Store flavour, colour, anticolour, mass, angles and the whole particle. + int id1, id2, id3, id4, id5; + int idSave[6], colSave[6], acolSave[6]; + double mSave[6], cosTheta, sinTheta, phi, sHMass, sHBeta, pT2Mass, pTFin; + Particle parton[6]; + + // Store modified masses and four-vectors intended for matrix elements. + double mME[5]; + Vec4 pME[5]; + + // Store whether tHat and uHat are swapped (= same as swap 3 and 4). + bool swapTU; + + // Set flavour, colour and anticolour. + void setId( int id1in = 0, int id2in = 0, int id3in = 0, int id4in = 0, + int id5in = 0) {idSave[1] = id1in; idSave[2] = id2in; idSave[3] = id3in; + idSave[4] = id4in; idSave[5] = id5in;} + void setColAcol( int col1 = 0, int acol1 = 0, + int col2 = 0, int acol2 = 0, int col3 = 0, int acol3 = 0, + int col4 = 0, int acol4 = 0, int col5 = 0, int acol5 = 0) { + colSave[1] = col1; acolSave[1] = acol1; colSave[2] = col2; + acolSave[2] = acol2; colSave[3] = col3; acolSave[3] = acol3; + colSave[4] = col4; acolSave[4] = acol4; colSave[5] = col5; + acolSave[5] = acol5; } + void swapColAcol() { swap(colSave[1], acolSave[1]); + swap(colSave[2], acolSave[2]); swap(colSave[3], acolSave[3]); + swap(colSave[4], acolSave[4]); swap(colSave[5], acolSave[5]);} + void swapCol1234() { swap(colSave[1], colSave[2]); + swap(colSave[3], colSave[4]); swap(acolSave[1], acolSave[2]); + swap(acolSave[3], acolSave[4]);} + void swapCol12() { swap(colSave[1], colSave[2]); + swap(acolSave[1], acolSave[2]);} + void swapCol34() { swap(colSave[3], colSave[4]); + swap(acolSave[3], acolSave[4]);} + + // Common code for top and Higgs secondary decay angular weights. + double weightTopDecay( Event& process, int iResBeg, int iResEnd); + double weightHiggsDecay( Event& process, int iResBeg, int iResEnd); + +}; + +//========================================================================== + +// Sigma0Process is the base class for unresolved and minimum-bias processes. +// It is derived from SigmaProcess. + +class Sigma0Process : public SigmaProcess { + +public: + + // Destructor. + virtual ~Sigma0Process() {} + + // Number of final-state particles. + virtual int nFinal() const {return 2;}; + + // No partonic flux to be set up. + virtual bool initFlux() {return true;} + + // Evaluate sigma for unresolved processes. + virtual double sigmaHat() {return 0.;} + + // Since no PDF's there is no difference from above. + virtual double sigmaPDF() {return sigmaHat();} + + // Answer for these processes already in mb, so do not convert. + virtual bool convert2mb() const {return false;} + +protected: + + // Constructor. + Sigma0Process() {} + +}; + +//========================================================================== + +// Sigma1Process is the base class for 2 -> 1 processes. +// It is derived from SigmaProcess. + +class Sigma1Process : public SigmaProcess { + +public: + + // Destructor. + virtual ~Sigma1Process() {} + + // Number of final-state particles. + virtual int nFinal() const {return 1;}; + + // Input and complement kinematics for resolved 2 -> 1 process. + virtual void set1Kin( double x1in, double x2in, double sHin) { + store1Kin( x1in, x2in, sHin); sigmaKin();} + + // Evaluate sigmaHat(sHat) for resolved 2 -> 1 processes. + virtual double sigmaHat() {return 0.;} + +protected: + + // Constructor. + Sigma1Process() {} + + // Store kinematics and set scales for resolved 2 -> 1 process. + virtual void store1Kin( double x1in, double x2in, double sHin); + + // Store subprocess kinematics quantities. + double mH, sH, sH2; + +}; + +//========================================================================== + +// Sigma2Process is the base class for 2 -> 2 processes. +// It is derived from SigmaProcess. + +class Sigma2Process : public SigmaProcess { + +public: + + // Destructor. + virtual ~Sigma2Process() {} + + // Number of final-state particles. + virtual int nFinal() const {return 2;}; + + // Input and complement kinematics for resolved 2 -> 2 process. + virtual void set2Kin( double x1in, double x2in, double sHin, + double tHin, double m3in, double m4in, double runBW3in, + double runBW4in) { store2Kin( x1in, x2in, sHin, tHin, m3in, m4in, + runBW3in, runBW4in); sigmaKin();} + + // Ditto, but for Multiple Interactions applications, so different input. + virtual void set2KinMI( double x1in, double x2in, double sHin, + double tHin, double uHin, double alpSin, double alpEMin, + bool needMasses, double m3in, double m4in) { + store2KinMI( x1in, x2in, sHin, tHin, uHin, alpSin, alpEMin, + needMasses, m3in, m4in); sigmaKin();} + + // Evaluate d(sigmaHat)/d(tHat) for resolved 2 -> 2 processes. + virtual double sigmaHat() {return 0.;} + + // Wrapper to sigmaHat, to (a) store current incoming flavours, + // (b) convert from GeV^-2 to mb where required, and + // (c) convert from from |M|^2 to d(sigmaHat)/d(tHat) where required. + virtual double sigmaHatWrap(int id1in = 0, int id2in = 0) { + id1 = id1in; id2 = id2in; double sigmaTmp = sigmaHat(); + if (convertM2()) sigmaTmp /= 16. * M_PI * sH2; + if (convert2mb()) sigmaTmp *= CONVERT2MB; return sigmaTmp;} + + // Perform kinematics for a Multiple Interaction, in its rest frame. + virtual bool final2KinMI( int i1Res = 0, int i2Res = 0, Vec4 p1Res = 0., + Vec4 p2Res = 0., double m1Res = 0., double m2Res = 0.); + +protected: + + // Constructor. + Sigma2Process() {} + + // Store kinematics and set scales for resolved 2 -> 2 process. + virtual void store2Kin( double x1in, double x2in, double sHin, + double tHin, double m3in, double m4in, double runBW3in, + double runBW4in); + virtual void store2KinMI( double x1in, double x2in, double sHin, + double tHin, double uHin, double alpSin, double alpEMin, + bool needMasses, double m3in, double m4in); + + // Store subprocess kinematics quantities. + double mH, sH, tH, uH, sH2, tH2, uH2, m3, s3, m4, s4, pT2, runBW3, runBW4; + +}; + +//========================================================================== + +// Sigma3Process is the base class for 2 -> 3 processes. +// It is derived from SigmaProcess. + +class Sigma3Process : public SigmaProcess { + +public: + + // Destructor. + virtual ~Sigma3Process() {} + + // Number of final-state particles. + virtual int nFinal() const {return 3;}; + + // Input and complement kinematics for resolved 2 -> 3 process. + virtual void set3Kin( double x1in, double x2in, double sHin, + Vec4 p3cmIn, Vec4 p4cmIn, Vec4 p5cmIn, double m3in, double m4in, + double m5in, double runBW3in, double runBW4in, double runBW5in) { + store3Kin( x1in, x2in, sHin, p3cmIn, p4cmIn, p5cmIn, m3in, m4in, m5in, + runBW3in, runBW4in, runBW5in); sigmaKin();} + + // Evaluate d(sigmaHat)/d(tHat) for resolved 2 -> 3 processes. + virtual double sigmaHat() {return 0.;} + +protected: + + // Constructor. + Sigma3Process() {} + + // Store kinematics and set scales for resolved 2 -> 3 process. + virtual void store3Kin( double x1in, double x2in, double sHin, + Vec4 p3cmIn, Vec4 p4cmIn, Vec4 p5cmIn, double m3in, double m4in, + double m5in, double runBW3in, double runBW4in, double runBW5in); + + // Store subprocess kinematics quantities. + double mH, sH, m3, s3, m4, s4, m5, s5, runBW3, runBW4, runBW5; + Vec4 p3cm, p4cm, p5cm; + +}; + +//========================================================================== + +// SigmaLHAProcess is a wrapper class for Les Houches Accord external input. +// It is derived from SigmaProcess. + +class SigmaLHAProcess : public SigmaProcess { + +public: + + // Constructor. + SigmaLHAProcess() {} + + // Destructor. + virtual ~SigmaLHAProcess() {} + + // No partonic flux to be set up. + virtual bool initFlux() {return true;} + + // Dummy function: action is put in PhaseSpaceLHA. + virtual double sigmaPDF() {return 1.;} + + // Set scale, when that is missing for an external LHA process. + virtual void setScale(); + + // Info on the subprocess. + virtual string name() const {return "Les Houches User Process(es)";} + virtual int code() const {return 9999;} + + // Number of final-state particles depends on current process choice. + virtual int nFinal() const; + + // Answer for these processes not in GeV^-2, so do not do this conversion. + virtual bool convert2mb() const {return false;} + + // Ensure special treatment of Les Houches processes. + virtual bool isLHA() const {return true;} + + // Special treatment needed if negative cross sections allowed. + virtual bool allowNegativeSigma() const { + return (lhaUpPtr->strategy() < 0);} + +private: + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaProcess_H + diff --git a/PYTHIA8/pythia8140/include/SigmaQCD.h b/PYTHIA8/pythia8140/include/SigmaQCD.h new file mode 100644 index 00000000000..ba9dc7e8629 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaQCD.h @@ -0,0 +1,848 @@ +// SigmaQCD.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for QCD process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma(0/2)Process. + +#ifndef Pythia8_SigmaQCD_H +#define Pythia8_SigmaQCD_H + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for minimum-bias (inelastic, nondiffractive) events. + +class Sigma0minBias : public Sigma0Process { + +public: + + // Constructor. + Sigma0minBias() {} + + // Evaluate sigma. + virtual double sigmaHat() {return sigmaTotPtr->sigmaND();} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol() {} + + // Info on the subprocess. + virtual string name() const {return "minimum bias";} + virtual int code() const {return 101;} + virtual bool isMinBias() const {return true;} + +private: + +}; + +//========================================================================== + +// A derived class for elastic scattering A B -> A B. + +class Sigma0AB2AB : public Sigma0Process { + +public: + + // Constructor. + Sigma0AB2AB() {} + + // Evaluate sigma. + virtual double sigmaHat() {return sigmaTotPtr->sigmaEl();} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "A B -> A B elastic";} + virtual int code() const {return 102;} + virtual bool isResolved() const {return false;} + +private: + +}; + +//========================================================================== + +// A derived class for single diffractive scattering A B -> X B. + +class Sigma0AB2XB : public Sigma0Process { + +public: + + // Constructor. + Sigma0AB2XB() {} + + // Evaluate sigma. + virtual double sigmaHat() {return sigmaTotPtr->sigmaXB();} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "A B -> X B single diffractive";} + virtual int code() const {return 103;} + virtual bool isResolved() const {return false;} + virtual bool isDiffA() const {return true;}; + +private: + +}; + +//========================================================================== + +// A derived class for single diffractive scattering A B -> A X. + +class Sigma0AB2AX : public Sigma0Process { + +public: + + // Constructor. + Sigma0AB2AX() {} + + // Evaluate sigma. + virtual double sigmaHat() {return sigmaTotPtr->sigmaAX();} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "A B -> A X single diffractive";} + virtual int code() const {return 104;} + virtual bool isResolved() const {return false;} + virtual bool isDiffB() const {return true;}; + +private: + +}; + +//========================================================================== + +// A derived class for double diffractive scattering A B -> X X. + +class Sigma0AB2XX : public Sigma0Process { + +public: + + // Constructor. + Sigma0AB2XX() {} + + // Evaluate sigma. + virtual double sigmaHat() {return sigmaTotPtr->sigmaXX();} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "A B -> X X double diffractive";} + virtual int code() const {return 105;} + virtual bool isResolved() const {return false;} + virtual bool isDiffA() const {return true;}; + virtual bool isDiffB() const {return true;}; + +private: + +}; + +//========================================================================== + +// A derived class for g g -> g g. + +class Sigma2gg2gg : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2gg() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> g g";} + virtual int code() const {return 111;} + virtual string inFlux() const {return "gg";} + +private: + + // Values stored for colour flow selection. + double sigTS, sigUS, sigTU, sigSum, sigma; + +}; + +//========================================================================== + +// A derived class for g g -> q qbar (q = u, d, s, i.e. almost massless). + +class Sigma2gg2qqbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2qqbar() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> q qbar (uds)";} + virtual int code() const {return 112;} + virtual string inFlux() const {return "gg";} + +private: + + // Number of quarks to be considered in massless approximation. + int nQuarkNew; + + // Values stored for colour flow selection. + int idNew; + double mNew, m2New, sigTS, sigUS, sigSum, sigma; + +}; + +//========================================================================== + +// A derived class for q g -> q g (q = u, d, s, c, b). +// Use massless approximation also for Q since no alternative. + +class Sigma2qg2qg : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2qg() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g -> q g";} + virtual int code() const {return 113;} + virtual string inFlux() const {return "qg";} + +private: + + // Values stored for colour flow selection. + double mNew, m2New, sigTS, sigTU, sigSum, sigma; + +}; + +//========================================================================== + +// A derived class for q qbar' -> q qbar' or q q' -> q q' +// (qbar qbar' -> qbar qbar'), q' may be same as q. + +class Sigma2qq2qq : public Sigma2Process { + +public: + + // Constructor. + Sigma2qq2qq() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q q(bar)' -> q q(bar)'";} + virtual int code() const {return 114;} + virtual string inFlux() const {return "qq";} + + private: + + // Values stored for colour flow selection. + double sigT, sigU, sigTU, sigST, sigSum; + +}; + +//========================================================================== + +// A derived class for q qbar -> g g. + +class Sigma2qqbar2gg : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2gg() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> g g";} + virtual int code() const {return 115;} + virtual string inFlux() const {return "qqbarSame";} + + private: + + // Values stored for colour flow selection. + double sigTS, sigUS, sigSum, sigma; + +}; + +//========================================================================== + +// A derived class for q qbar -> q' qbar'. + +class Sigma2qqbar2qqbarNew : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2qqbarNew() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> q' qbar' (uds)";} + virtual int code() const {return 116;} + virtual string inFlux() const {return "qqbarSame";} + + private: + + // Number of quarks to be considered in massless approximation. + int nQuarkNew; + + // Values stored for colour flow selection. + int idNew; + double mNew, m2New, sigS, sigma; + +}; + +//========================================================================== + +// A derived class for g g -> Q Qbar (Q = c, b or t). + +class Sigma2gg2QQbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2QQbar(int idIn, int codeIn) : idNew(idIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angles in top decay (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idNew;} + + private: + + // Values stored for process type and colour flow selection. + int idNew, codeSave; + string nameSave; + double sigTS, sigUS, sigSum, sigma, openFracPair; + +}; + +//========================================================================== + +// A derived class for q qbar -> Q Qbar (Q = c, b or t). + +class Sigma2qqbar2QQbar : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2QQbar(int idIn, int codeIn) : idNew(idIn), codeSave(codeIn) {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Evaluate weight for W decay angles in top decay (else inactive). + virtual double weightDecay( Event& process, int iResBeg, int iResEnd); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return idNew;} + virtual int id4Mass() const {return idNew;} + + private: + + // Values stored for process type. + int idNew, codeSave; + string nameSave; + double sigma, openFracPair; + +}; + +//========================================================================== + +// A derived class for g g -> g g g. + +class Sigma3gg2ggg : public Sigma3Process { + +public: + + // Constructor. + Sigma3gg2ggg() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> g g g";} + virtual int code() const {return 131;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "gg";} + virtual bool isQCD3body() const {return true;} + +private: + + // Values stored for colour flow selection. + double sigma; + + // Intermediate storage and calculation of four-products. + double pp[6][6]; + double cycle(int i1, int i2, int i3, int i4, int i5) {return + pp[i1][i2] * pp[i2][i3] * pp[i3][i4] * pp[i4][i5] * pp[i5][i1];} + +}; + +//========================================================================== + +// A derived class for q qbar -> g g g. + +class Sigma3qqbar2ggg : public Sigma3Process { + +public: + + // Constructor. + Sigma3qqbar2ggg() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> g g g";} + virtual int code() const {return 132;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qqbarSame";} + virtual bool isQCD3body() const {return true;} + +protected: + + // Pick/map a random final state configuration + int config; + inline void pickFinal() { config = int( 6 * rndmPtr->flat() ); } + inline void mapFinal(); + + // |M|^2 calculation + inline double m2Calc(); + + // Four-vectors for |M|^2 calculation + Vec4 pCM[5]; + + // Intermediate storage and calculation of four-products + double a[3], b[3], pp[3][3], ab[3][3]; + + // Values stored for colour flow selection. + double sigma; + +}; + +//========================================================================== + +// A derived class for q g -> q g g +// Derived from Sigma3qqbar2ggg + +class Sigma3qg2qgg : public Sigma3qqbar2ggg { + +public: + + // Constructor. + Sigma3qg2qgg() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g -> q g g";} + virtual int code() const {return 133;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qg";} + virtual bool isQCD3body() const {return true;} + +private: + + // Sigma for (qg) and (gq) incoming + double sigma[2]; + +}; + +//========================================================================== + +// A derived class for g g -> q qbar g +// Derived from Sigma3qqbar2ggg + +class Sigma3gg2qqbarg : public Sigma3qqbar2ggg { + +public: + + // Constructor. + Sigma3gg2qqbarg() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> q qbar g";} + virtual int code() const {return 138;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "gg";} + virtual bool isQCD3body() const {return true;} + +private: + + // Number of quarks to be considered in massless approximation. + int nQuarkNew; + +}; + +//========================================================================== + +// A derived class for q q' -> q q' g + +class Sigma3qq2qqgDiff : public Sigma3Process { + +public: + + // Constructor. + Sigma3qq2qqgDiff() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const + {return "q(bar) q(bar)' -> q(bar) q(bar)' g";} + virtual int code() const {return 134;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qq";} + virtual bool isQCD3body() const {return true;} + +protected: + + // Pick/map a random final state configuration + int config; + inline void pickFinal() { config = int( 6 * rndmPtr->flat() ); } + inline void mapFinal(); + + // |M|^2 calculation + inline double m2Calc(); + + // Kinematic configuration + Vec4 pCM[5]; + + // Four-products + double s, t, u, sp, tp, up; + + // Cross section + double sigma; + +}; + +//========================================================================== + +// A derived class for q qbar -> q' qbar' g +// Derived from Sigma3qq2qqgDiff + +class Sigma3qqbar2qqbargDiff : public Sigma3qq2qqgDiff { + +public: + + // Constructor. + Sigma3qqbar2qqbargDiff() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> q' qbar' g";} + virtual int code() const {return 136;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qqbarSame";} + virtual bool isQCD3body() const {return true;} + +private: + + // Number of quarks to be considered in massless approximation. + int nQuarkNew; + +}; + +//========================================================================== + +// A derived class for q g -> q q' qbar' +// Derived from Sigma3qq2qqgDiff + +class Sigma3qg2qqqbarDiff : public Sigma3qq2qqgDiff { + +public: + + // Constructor. + Sigma3qg2qqqbarDiff() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g -> q q' qbar'";} + virtual int code() const {return 139;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qg";} + virtual bool isQCD3body() const {return true;} + +private: + + // Number of quarks to be considered in massless approximation. + int nQuarkNew; + + // gq and qg incoming + double sigma[2]; + +}; + +//========================================================================== + +// A derived class for q q -> q q g + +class Sigma3qq2qqgSame : public Sigma3Process { + +public: + + // Constructor. + Sigma3qq2qqgSame() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const + {return "q(bar) q(bar) -> q(bar) q(bar) g";} + virtual int code() const {return 135;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qq";} + virtual bool isQCD3body() const {return true;} + +protected: + + // Pick/map a random final state configuration + int config; + inline void pickFinal() { config = int( 6 * rndmPtr->flat() ); } + inline void mapFinal(); + + // |M|^2 calculation + inline double m2Calc(); + + // Kinematic configuration + Vec4 pCM[5]; + + // Four-products + double s, t, u, sp, tp, up; + double ssp, ttp, uup, s_sp, t_tp, u_up; + + // Cross section + double sigma; + +}; + +//========================================================================== + +// A derived class for q q -> q q g +// Derived from Sigma3qq2qqgSame + +class Sigma3qqbar2qqbargSame : public Sigma3qq2qqgSame { + +public: + + // Constructor. + Sigma3qqbar2qqbargSame() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> q qbar g";} + virtual int code() const {return 137;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qqbarSame";} + virtual bool isQCD3body() const {return true;} + +private: + +}; + +//========================================================================== + +// A derived class for q g -> q qbar q; same flavour. +// Derived from Sigma3qq2qqgSame + +class Sigma3qg2qqqbarSame : public Sigma3qq2qqgSame { + +public: + + // Constructor. + Sigma3qg2qqqbarSame() {} + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q g -> q q qbar";} + virtual int code() const {return 140;} + virtual int nFinal() const {return 3;} + virtual string inFlux() const {return "qg";} + virtual bool isQCD3body() const {return true;} + +private: + + // gq and qg incoming + double sigma[2]; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaQCD_H diff --git a/PYTHIA8/pythia8140/include/SigmaSUSY.h b/PYTHIA8/pythia8140/include/SigmaSUSY.h new file mode 100644 index 00000000000..2eef2c29d3c --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaSUSY.h @@ -0,0 +1,598 @@ +// SigmaSUSY.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Peter Skands, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for Supersymmetric process differential cross sections. +// Contains classes derived from SigmaProcess via Sigma2Process. + +#ifndef Pythia8_SigmaSUSY_H +#define Pythia8_SigmaSUSY_H + +#include "PhaseSpace.h" +#include "PythiaComplex.h" +#include "SigmaProcess.h" +#include "SusyCouplings.h" +#include "SusyLesHouches.h" + +namespace Pythia8 { + +//========================================================================== + +// A derived class for q qbar -> neutralino_i neutralino_j. + +class Sigma2qqbar2chi0chi0 : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2chi0chi0() { }; + + // Constructor. + Sigma2qqbar2chi0chi0(int id3chiIn, int id4chiIn, int codeIn) { + + // Save ordering indices and process code + id3chi = id3chiIn; + id4chi = id4chiIn; + codeSave = codeIn; + + // Construct id codes from ordering indices. + id3 = 1000022; + if (id3chi == 2) id3 = 1000023; + if (id3chi == 3) id3 = 1000025; + if (id3chi == 4) id3 = 1000035; + if (id3chi == 5) id3 = 1000045; + id4 = 1000022; + if (id4chi == 2) id4 = 1000023; + if (id4chi == 3) id4 = 1000025; + if (id4chi == 4) id4 = 1000035; + if (id4chi == 5) id4 = 1000045; + + } + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qq";} + virtual int id3Mass() const {return abs(id3);} + virtual int id4Mass() const {return abs(id4);} + virtual int resonanceA() const {return 23;} + virtual bool isSUSY() const {return true;} + + protected: + + // Basic process information + int id3chi, id4chi, codeSave; + string nameSave; + + // Values stored for later use + double sigma0, ui, uj, ti, tj, openFracPair; + complex propZ; + +}; + +//========================================================================== + +// A derived class for q qbar -> neutralino_i chargino_j. + +class Sigma2qqbar2charchi0 : public Sigma2qqbar2chi0chi0 { + +public: + + // Constructor. + Sigma2qqbar2charchi0(int id3chiIn, int id4chiIn, int codeIn) { + + // Save ordering indices and process code + id3chi = id3chiIn; + id4chi = id4chiIn; + codeSave = codeIn; + + // Construct id codes from ordering indices. + id3 = (abs(id3chi) == 2) ? 1000037 : 1000024; + if (id3chi < 0) id3 = -id3; + + id4 = 1000022; + if (id4chi == 2) id4 = 1000023; + if (id4chi == 3) id4 = 1000025; + if (id4chi == 4) id4 = 1000035; + if (id4chi == 5) id4 = 1000045; + + } + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + virtual int resonanceA() const {return 24;} + +protected : + + complex propW; + +}; + +//========================================================================== + +// A derived class for q qbar -> chargino+_i chargino-_j. + +class Sigma2qqbar2charchar : public Sigma2qqbar2chi0chi0 { + +public: + + // Constructor. + Sigma2qqbar2charchar(int id3chiIn, int id4chiIn, int codeIn) { + + // Save ordering indices and process code + id3chi = id3chiIn; + id4chi = id4chiIn; + codeSave = codeIn; + + // Construct id codes from ordering indices. + id3 = (abs(id3chi) == 2) ? 1000037 : 1000024; + id4 = (abs(id4chi) == 2) ? -1000037 : -1000024; + + } + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + +}; + +//========================================================================== + +// A derived class for q g -> neutralino_i squark_j (and cc) + +class Sigma2qg2chi0squark : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2chi0squark() { }; + + // Constructor. + Sigma2qg2chi0squark(int id3chiIn, int id4sqIn, bool isUp, int codeIn) { + + // Save ordering indices and process code + id3chi = id3chiIn; + id4sq = id4sqIn; + codeSave = codeIn; + + // Construct id codes from ordering indices. + id3 = 1000022; + if (id3chi == 2) id3 = 1000023; + if (id3chi == 3) id3 = 1000025; + if (id3chi == 4) id3 = 1000035; + if (id3chi == 5) id3 = 1000045; + id4 = 1000001 + (isUp ? 1 : 0); + if (id4sq == 2) id4 = 1000003 + (isUp ? 1 : 0); + if (id4sq == 3) id4 = 1000005 + (isUp ? 1 : 0); + if (id4sq == 4) id4 = 2000001 + (isUp ? 1 : 0); + if (id4sq == 5) id4 = 2000003 + (isUp ? 1 : 0); + if (id4sq == 6) id4 = 2000005 + (isUp ? 1 : 0); + + } + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return abs(id3);} + virtual int id4Mass() const {return abs(id4);} + virtual bool isSUSY() const {return true;} + + protected: + + // Basic process information + int id3chi, id4sq, codeSave; + string nameSave; + + // Values stored for later use + double sigma0, ui, uj, ti, tj, openFracPair; + +}; + +//========================================================================== + +// A derived class for q g -> chargino_i squark_j (incl cc) + +class Sigma2qg2charsquark : public Sigma2qg2chi0squark { + +public: + + // Constructor. + Sigma2qg2charsquark(int id3chiIn, int id4sqIn, bool isUp, int codeIn) { + + // Save ordering indices and process code + id3chi = id3chiIn; + id4sq = id4sqIn; + codeSave = codeIn; + + // Construct id codes from ordering indices. + id3Sav = 1000024; + if (abs(id3chi) == 2) id3Sav = 1000037; + if (isUp) id3Sav = -id3Sav; + id4Sav = 1000001 + (isUp ? 1 : 0); + if (id4sq == 2) id4Sav = 1000003 + (isUp ? 1 : 0); + if (id4sq == 3) id4Sav = 1000005 + (isUp ? 1 : 0); + if (id4sq == 4) id4Sav = 2000001 + (isUp ? 1 : 0); + if (id4sq == 5) id4Sav = 2000003 + (isUp ? 1 : 0); + if (id4sq == 6) id4Sav = 2000005 + (isUp ? 1 : 0); + + // Initial values, can be swapped to charge conjugates event by event. + id3 = id3Sav; + id4 = id4Sav; + + } + + // Initialize process. + virtual void initProc(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + private: + + // Basic process information + int id3Sav, id4Sav; + +}; + +//========================================================================== + +// A derived class for q q' -> ~q_i ~q_j + +class Sigma2qq2squarksquark : public Sigma2Process { + +public: + + // Constructor. + Sigma2qq2squarksquark() {} + + // Constructor. + Sigma2qq2squarksquark(int id3In, int id4In, int codeIn) { + + // Save ordering indices and process code + id3Sav = id3In; + id4Sav = id4In; + codeSave = codeIn; + // Initial values (flipped for c.c.) + id3 = id3Sav; + id4 = id4Sav; + + } + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qq";} + virtual int id3Mass() const {return abs(id3Sav);} + virtual int id4Mass() const {return abs(id4Sav);} + virtual bool isSUSY() const {return true;} + +private: + + // Basic process information + int id3Sav, id4Sav, codeSave, iGen3, iGen4, nNeut; + string nameSave; + bool isUD; + + // Storage of mass squares + double m2Glu; + vector m2Neut, m2Char; + + // Flavor-independent prefactors. + double sigmaChar, sigmaNeut, sigmaGlu; + double sigmaCharNeut, sigmaCharGlu, sigmaNeutGlu; + double openFracPair; + + // Point-by-point info + double tGlu, uGlu; + vector tNeut, uNeut, tChar, uChar; + double sumCt, sumCu, sumNt, sumNu, sumGt, sumGu, sumInterference; + +}; + +//========================================================================== + +// A derived class for q qbar' -> ~q_i ~q*_j + +class Sigma2qqbar2squarkantisquark : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2squarkantisquark() {} + + // Constructor. + Sigma2qqbar2squarkantisquark(int id3In, int id4In, int codeIn) { + + // Save ordering indices and process code + // (always store squark first, antisquark second) + id3Sav = abs(id3In); + id4Sav = -abs(id4In); + codeSave = codeIn; + // Initial values + id3 = id3Sav; + id4 = id4Sav; + + } + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qq";} + virtual int id3Mass() const {return abs(id3Sav);} + virtual int id4Mass() const {return abs(id4Sav);} + virtual bool isSUSY() const {return true;} + +private: + + // Basic process information + int id3Sav, id4Sav, codeSave, iGen3, iGen4, nNeut; + string nameSave; + bool isUD, isCC; + + // Storage of mass squares + double m2Glu; + vector m2Neut; + + // Flavor-independent prefactors: EW, strong, and interference + double xW; + double openFracPair; + double sigmaEW, sigmaGlu, sigmaEWG; + + // Point-by-point info + double tGlu, uGlu; + vector tNeut, uNeut; + complex propZW; + double sumColS, sumColT, sumColSCC, sumColTCC, sumInterference; + +}; + +//========================================================================== + +// A derived class for g g -> ~q ~q* + +class Sigma2gg2squarkantisquark : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2squarkantisquark() {} + + // Constructor. + Sigma2gg2squarkantisquark(int id34In, int codeIn) { + + // Save ordering indices and process code + // (always store squark first, antisquark second) + id3Sav = abs(id34In); + id4Sav = -abs(id34In); + codeSave = codeIn; + // Initial values + id3 = id3Sav; + id4 = id4Sav; + + } + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return abs(id3Sav);} + virtual int id4Mass() const {return abs(id4Sav);} + virtual bool isSUSY() const {return true;} + +private: + + // Basic process information + int id3Sav, id4Sav, codeSave; + string nameSave; + double sigma, m2Sq, openFracPair; + + // Color flow info + double sumColT, sumColU, sumInterference; + +}; + +//========================================================================== + +// A derived class for q g -> ~q ~g + +class Sigma2qg2squarkgluino : public Sigma2Process { + +public: + + // Constructor. + Sigma2qg2squarkgluino() {} + + // Constructor. + Sigma2qg2squarkgluino(int id3In, int codeIn) { + + // Save ordering indices and process code + id3Sav = abs(id3In); + codeSave = codeIn; + // Initial values + id3 = id3Sav; + id4 = 1000021; + + } + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return nameSave;} + virtual int code() const {return codeSave;} + virtual string inFlux() const {return "qg";} + virtual int id3Mass() const {return abs(id3Sav);} + virtual int id4Mass() const {return 1000021;} + virtual bool isSUSY() const {return true;} + +private: + + // Basic process information + int id3Sav, codeSave; + string nameSave; + double sigmaA, sigmaB, comFac, m2Glu, m2Sq, openFracPair; + +}; + +//========================================================================== + +// A derived class for g g -> gluino gluino. + +class Sigma2gg2gluinogluino : public Sigma2Process { + +public: + + // Constructor. + Sigma2gg2gluinogluino() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat() {return sigma;} + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "g g -> gluino gluino";} + virtual int code() const {return 1201;} + virtual string inFlux() const {return "gg";} + virtual int id3Mass() const {return 1000021;} + virtual int id4Mass() const {return 1000021;} + virtual bool isSUSY() const {return true;} + +private: + + // Values stored for process type and colour flow selection. + double sigTS, sigUS, sigTU, sigSum, sigma, openFracPair; + +}; + +//========================================================================== + +// A derived class for q qbar -> gluino gluino. + +class Sigma2qqbar2gluinogluino : public Sigma2Process { + +public: + + // Constructor. + Sigma2qqbar2gluinogluino() {} + + // Initialize process. + virtual void initProc(); + + // Calculate flavour-independent parts of cross section. + virtual void sigmaKin(); + + // Evaluate d(sigmaHat)/d(tHat). + virtual double sigmaHat(); + + // Select flavour, colour and anticolour. + virtual void setIdColAcol(); + + // Info on the subprocess. + virtual string name() const {return "q qbar -> gluino gluino";} + virtual int code() const {return 1202;} + virtual string inFlux() const {return "qqbarSame";} + virtual int id3Mass() const {return 1000021;} + virtual int id4Mass() const {return 1000021;} + virtual bool isSUSY() const {return true;} + +private: + + // Values stored for process type and colour flow selection. + double openFracPair, s34Avg, sigS, tHG, uHG, tHG2, uHG2; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaSUSY_H + diff --git a/PYTHIA8/pythia8140/include/SigmaTotal.h b/PYTHIA8/pythia8140/include/SigmaTotal.h new file mode 100644 index 00000000000..ddf014c7fad --- /dev/null +++ b/PYTHIA8/pythia8140/include/SigmaTotal.h @@ -0,0 +1,99 @@ +// SigmaTotal.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the class for cross section parametrizations. +// SigmaTotal: total and partial cross section in hadron-hadron collisions. + +#ifndef Pythia8_SigmaTotal_H +#define Pythia8_SigmaTotal_H + +#include "Info.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// The SigmaTotal class contains parametrizations of total, elastic and +// diffractive cross sections, and of the respective slope parameter. + +class SigmaTotal { + +public: + + // Constructor. + SigmaTotal() : isCalc(false) {}; + + // Store pointers and initialize data members. + void init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn ); + + // Calculate, or recalculate for new beams or new energy. + bool calc(int idA, int idB, double eCM); + + // Confirm that initialization worked. + bool hasSigmaTot() const {return isCalc;} + + // Read out total and partial cross sections. + double sigmaTot() const {return sigTot;} + double sigmaEl() const {return sigEl;} + double sigmaXB() const {return sigXB;} + double sigmaAX() const {return sigAX;} + double sigmaXX() const {return sigXX;} + double sigmaND() const {return sigND;} + + // Read out slope b in exp(b*t) dependence. + double bSlopeEl() const {return bEl;} + double bSlopeXB(double sX) const { return 2.*bB + alP2 * log(s/sX) ;} + double bSlopeAX(double sX) const { return 2.*bA + alP2 * log(s/sX) ;} + double bSlopeXX(double sX1, double sX2) const { + return alP2 * log( exp(4.) + s * s0 / (sX1 * sX2) ) ;} + + // Read out parameters of diffractive mass spectra. + double mMinXB() const {return mMinXBsave;} + double mMinAX() const {return mMinAXsave;} + double cRes() const {return CRES;} + double mResXB() const {return mResXBsave;} + double mResAX() const {return mResAXsave;} + double sProton() const {return SPROTON;} + + // Read out parameters of trial t spectra. + double bMinSlopeXB() const { return max(2., 2. * bB);} + double bMinSlopeAX() const { return max(2., 2. * bA);} + double bMinSlopeXX() const { return alP2 * 4.;} + +private: + + // Constants: could only be changed in the code itself. + static const int IHADATABLE[], IHADBTABLE[], ISDTABLE[], IDDTABLE[]; + static const double MMIN, EPSILON, ETA, X[], Y[], BETA0[], BHAD[], + ALPHAPRIME, CONVERTEL, CONVERTSD, CONVERTDD, MMIN0, + CRES, MRES0, CSD[10][8], CDD[10][9], SPROTON; + + // Initialization data, normally only set once. + bool isCalc, setTotal, doDampen, setElastic; + double sigTotOwn, sigElOwn, sigXBOwn, sigAXOwn, sigXXOwn, + maxXBOwn, maxAXOwn, maxXXOwn, bSlope, rho, lambda, tAbsMin, + alphaEM0, sigmaPomP; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Store values found by calc. + double sigTot, sigEl, sigXB, sigAX, sigXX, sigND, bEl, s, bA, bB, + alP2, s0, exp4, mMinXBsave, mMinAXsave, mResXBsave, mResAXsave; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SigmaTotal_H diff --git a/PYTHIA8/pythia8140/include/SpaceShower.h b/PYTHIA8/pythia8140/include/SpaceShower.h new file mode 100644 index 00000000000..f1a6b7a9252 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SpaceShower.h @@ -0,0 +1,223 @@ +// SpaceShower.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for the spacelike initial-state showers. +// SpaceDipoleEnd: radiating dipole end in ISR. +// SpaceShower: handles the showering description. + +#ifndef Pythia8_SpaceShower_H +#define Pythia8_SpaceShower_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Event.h" +#include "Info.h" +#include "ParticleData.h" +#include "PartonSystems.h" +#include "PythiaStdlib.h" +#include "Settings.h" +#include "StandardModel.h" +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// Data on radiating dipole ends, only used inside SpaceShower. + +class SpaceDipoleEnd { + +public: + + // Constructor. + SpaceDipoleEnd( int systemIn = 0, int sideIn = 0, int iRadiatorIn = 0, + int iRecoilerIn = 0, double pTmaxIn = 0., int colTypeIn = 0, + int chgTypeIn = 0, int MEtypeIn = 0, bool normalRecoilIn = true) : + system(systemIn), side(sideIn), iRadiator(iRadiatorIn), + iRecoiler(iRecoilerIn), pTmax(pTmaxIn), colType(colTypeIn), + chgType(chgTypeIn), MEtype(MEtypeIn), normalRecoil(normalRecoilIn), + nBranch(0) { } + + // Store values for trial emission. + void store( int idDaughterIn, int idMotherIn, int idSisterIn, + double x1In, double x2In, double m2DipIn, double pT2In, double zIn, + double xMoIn, double Q2In, double mSisterIn, double m2SisterIn, + double pT2corrIn) {idDaughter = idDaughterIn; idMother = idMotherIn; + idSister = idSisterIn; x1 = x1In; x2 = x2In; m2Dip = m2DipIn; + pT2 = pT2In; z = zIn; xMo = xMoIn; Q2 = Q2In; mSister = mSisterIn; + m2Sister = m2SisterIn; pT2corr = pT2corrIn;} + + // Basic properties related to evolution and matrix element corrections. + int system, side, iRadiator, iRecoiler; + double pTmax; + int colType, chgType, MEtype; + bool normalRecoil; + + // Properties specific to current trial emission. + int nBranch, idDaughter, idMother, idSister, iFinPol; + double x1, x2, m2Dip, pT2, z, xMo, Q2, mSister, m2Sister, pT2corr, + pT2Old, zOld, asymPol; + +} ; + +//========================================================================== + +// The SpaceShower class does spacelike showers. + +class SpaceShower { + +public: + + // Constructor. + SpaceShower() {} + + // Destructor. + virtual ~SpaceShower() {} + + // Initialize various pointers. + // (Separated from rest of init since not virtual.) + void initPtr(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + PartonSystems* partonSystemsPtrIn, UserHooks* userHooksPtrIn) { + infoPtr = infoPtrIn; settingsPtr = settingsPtrIn; + particleDataPtr = particleDataPtrIn; rndmPtr = rndmPtrIn; + partonSystemsPtr = partonSystemsPtrIn; userHooksPtr = userHooksPtrIn;} + + // Initialize generation. Possibility to force re-initialization by hand. + virtual void init(BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn); + + // New beams possible for handling of hard diffraction. (Not virtual.) + void reassignBeamPtrs( BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn) + {beamAPtr = beamAPtrIn; beamBPtr = beamBPtrIn;} + + // Find whether to limit maximum scale of emissions, and whether to dampen. + virtual bool limitPTmax( Event& event, double Q2Fac = 0., + double Q2Ren = 0.); + + // Potential enhancement factor of pTmax scale for hardest emission. + virtual double enhancePTmax() const {return pTmaxFudge;} + + // Prepare system for evolution; identify ME. + virtual void prepare( int iSys, Event& event, bool limitPTmaxIn = true); + + // Update dipole list after each FSR emission. Currently superfluous. + // Usage: update( iSys, event). + virtual void update( int , Event& ) {} + + // Select next pT in downwards evolution. + virtual double pTnext( Event& event, double pTbegAll, double pTendAll, + int nRadIn = -1); + + // ME corrections and kinematics that may give failure. + virtual bool branch( Event& event); + + // Tell which system was the last processed one. + int system() const {return iSysSel;} + + // Flag for failure in branch(...) that will force a retry of parton level. + bool doRestart() const {return rescatterFail;} + + // Print dipole list; for debug mainly. + virtual void list(ostream& os = cout) const; + +protected: + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to the two incoming beams. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + + // Pointer to information on subcollision parton locations. + PartonSystems* partonSystemsPtr; + + // Pointer to userHooks object for user interaction with program. + UserHooks* userHooksPtr; + + // Store properties to be returned by methods. + bool rescatterFail; + int iSysSel; + double pTmaxFudge; + +private: + + // Constants: could only be changed in the code itself. + static const bool DEBUG; + static const int MAXLOOPTINYPDF; + static const double CTHRESHOLD, BTHRESHOLD, EVALPDFSTEP, TINYPDF, + TINYKERNELPDF, TINYPT2, HEAVYPT2EVOL, HEAVYXEVOL, EXTRASPACEQ, + LAMBDA3MARGIN, LEPTONXMIN, LEPTONXMAX, LEPTONPT2MIN, LEPTONFUDGE; + + // Initialization data, normally only set once. + bool doQCDshower, doQEDshowerByQ, doQEDshowerByL, useSamePTasMI, + doMEcorrections, doPhiPolAsym, doPhiIntAsym, doRapidityOrder, + canVetoEmission; + int pTmaxMatch, pTdampMatch, alphaSorder, alphaEMorder, nQuarkIn, + enhanceScreening; + double pTdampFudge, mc, mb, m2c, m2b, alphaSvalue, alphaS2pi, + Lambda3flav, Lambda4flav, Lambda5flav, Lambda3flav2, Lambda4flav2, + Lambda5flav2, pT0Ref, ecmRef, ecmPow, pTmin, sCM, eCM, pT0, + pTminChgQ, pTminChgL, pT20, pT2min, pT2minChgQ, pT2minChgL, + pTmaxFudgeMI, strengthIntAsym; + + // alphaStrong and alphaEM calculations. + AlphaStrong alphaS; + AlphaEM alphaEM; + + // Some current values. + bool sideA, dopTdamp; + int iNow, iRec, idDaughter, nRad, idResFirst, idResSecond; + double xDaughter, x1Now, x2Now, m2Dip, m2Rec, pT2damp, pTbegRef; + + // All dipole ends + vector dipEnd; + + // Pointers to the current and hardest (so far) dipole ends. + int iDipNow, iSysNow; + SpaceDipoleEnd* dipEndNow; + int iDipSel; + SpaceDipoleEnd* dipEndSel; + + // Evolve a QCD dipole end. + void pT2nextQCD( double pT2begDip, double pT2endDip); + + // Evolve a QCD dipole end near heavy quark threshold region. + void pT2nearQCDthreshold( BeamParticle& beam, double m2Massive, + double m2Threshold, double xMaxAbs, double zMinAbs, + double zMaxMassive); + + // Evolve a QED dipole end. + void pT2nextQED( double pT2begDip, double pT2endDip); + + // Find class of ME correction. + int findMEtype( int iSys, Event& event); + + // Provide maximum of expected ME weight; for preweighting of evolution. + double calcMEmax( int MEtype, int idMother, int idDaughterIn); + + // Provide actual ME weight for current branching. + double calcMEcorr(int MEtype, int idMother, int idDaughterIn, double M2, + double z, double Q2); + + // Find coefficient of azimuthal asymmetry from gluon polarization. + void findAsymPol( Event& event, SpaceDipoleEnd* dip); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SpaceShower_H diff --git a/PYTHIA8/pythia8140/include/StandardModel.h b/PYTHIA8/pythia8140/include/StandardModel.h new file mode 100644 index 00000000000..7fbbe14e283 --- /dev/null +++ b/PYTHIA8/pythia8140/include/StandardModel.h @@ -0,0 +1,176 @@ +// StandardModel.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file gives access to some Standard Model parameters. +// AlphaStrong: fix or first- or second-order running alpha_strong. + +#ifndef Pythia8_StandardModel_H +#define Pythia8_StandardModel_H + +#include "ParticleData.h" +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// The AlphaStrong class calculates the alpha_strong value at an arbitrary +// scale, given the value at m_Z, to zeroth, first or second order. + +class AlphaStrong { + +public: + + // Constructors. + AlphaStrong() : isInit(false) {} + AlphaStrong(double valueIn, int orderIn = 1) { + init( valueIn, orderIn) ;} + + // Initialization for given value at M_Z and given order. + void init(double valueIn = 0.12, int orderIn = 1); + + // alpha_S value and Lambda values. + double alphaS(double scale2); + double alphaS1Ord(double scale2); + double alphaS2OrdCorr(double scale2); + double Lambda3() const { return Lambda3Save; } + double Lambda4() const { return Lambda4Save; } + double Lambda5() const { return Lambda5Save; } + +protected: + + // Initialization data member; protected to allow inheritance. + bool isInit; + +private: + + // Constants: could only be changed in the code itself. + static const int NITER; + static const double MC, MB, MZ, SAFETYMARGIN1, SAFETYMARGIN2; + + // Data members. + bool lastCallToFull; + int order; + double valueRef, valueNow, scale2Now, scale2Min, Lambda3Save, + Lambda4Save, Lambda5Save, Lambda3Save2, Lambda4Save2, + Lambda5Save2, mc, mb, mZ, mc2, mb2; + +}; + +//========================================================================== + +// The AlphaEM class calculates the alpha_electromagnetic value at an +// arbitrary scale, given the value at 0 and m_Z, to zeroth or first order. + +class AlphaEM { + +public: + + // Constructors. + AlphaEM() {} + + // Initialization for a given order. + void init(int orderIn, Settings* settingsPtr); + + // alpha_EM value. + double alphaEM(double scale2); + +private: + + // Constants: could only be changed in the code itself. + static const double MZ, Q2STEP[5], BRUNDEF[5]; + + // Data members. + int order; + double alpEM0, alpEMmZ, mZ2, bRun[5], alpEMstep[5]; + +}; + +//========================================================================== + +// The CoupSM class stores and returns electroweak couplings, +// including Cabibbo-Kobayashi-Maskawa mass mixing matrix elements. + +class CoupSM { + +public: + + // Constructor. + CoupSM() {} + + // Initialize, normally from Pythia::init(). + void init(Settings& settings, Rndm* rndmPtrIn); + + // alpha_S value and Lambda values. + double alphaS(double scale2) {return alphaSlocal.alphaS(scale2);} + double alphaS1Ord(double scale2) {return alphaSlocal.alphaS1Ord(scale2);} + double alphaS2OrdCorr(double scale2) { + return alphaSlocal.alphaS2OrdCorr(scale2);} + double Lambda3() const {return alphaSlocal.Lambda3();} + double Lambda4() const {return alphaSlocal.Lambda4();} + double Lambda5() const {return alphaSlocal.Lambda5();} + + // Return alpha_EM value. + double alphaEM(double scale2) {return alphaEMlocal.alphaEM(scale2);} + + // Return electroweak mixing angle. + double sin2thetaW() {return s2tW;} + double cos2thetaW() {return c2tW;} + double sin2thetaWbar() {return s2tWbar;} + + // Return electroweak couplings of quarks and leptons. + double ef(int idAbs) {return efSave[idAbs];} + double vf(int idAbs) {return vfSave[idAbs];} + double af(int idAbs) {return afSave[idAbs];} + double t3f(int idAbs) {return 0.5*afSave[idAbs];} + double lf(int idAbs) {return lfSave[idAbs];} + double rf(int idAbs) {return rfSave[idAbs];} + + // Return some squared couplings and other combinations. + double ef2(int idAbs) {return ef2Save[idAbs];} + double vf2(int idAbs) {return vf2Save[idAbs];} + double af2(int idAbs) {return af2Save[idAbs];} + double efvf(int idAbs) {return efvfSave[idAbs];} + double vf2af2(int idAbs) {return vf2af2Save[idAbs];} + + // Return CKM value or square: + // first index 1/2/3/4 = u/c/t/t', second 1/2/3/4 = d/s/b/b'. + double VCKMgen(int genU, int genD) {return VCKMsave[genU][genD];} + double V2CKMgen(int genU, int genD) {return V2CKMsave[genU][genD];} + + // Return CKM value or square for incoming flavours (sign irrelevant). + double VCKMid(int id1, int id2); + double V2CKMid(int id1, int id2); + + // Return CKM sum of squares for given inflavour, or random outflavour. + double V2CKMsum(int id) {return V2CKMout[abs(id)];} + int V2CKMpick(int id); + +private: + + // Constants: could only be changed in the code itself. + static const double efSave[20], afSave[20]; + + // Couplings and VCKM matrix (index 0 not used). + double s2tW, c2tW, s2tWbar, vfSave[20], lfSave[20], rfSave[20], + ef2Save[20], vf2Save[20], af2Save[20], efvfSave[20], + vf2af2Save[20], VCKMsave[5][5], V2CKMsave[5][5], V2CKMout[20]; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // An AlphaStrong instance for general use (but not MI, ISR, FSR). + AlphaStrong alphaSlocal; + + // An AlphaEM instance for general use (but not MI, ISR, FSR). + AlphaEM alphaEMlocal; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_StandardModel_H diff --git a/PYTHIA8/pythia8140/include/StringFragmentation.h b/PYTHIA8/pythia8140/include/StringFragmentation.h new file mode 100644 index 00000000000..a891ac9d540 --- /dev/null +++ b/PYTHIA8/pythia8140/include/StringFragmentation.h @@ -0,0 +1,174 @@ +// StringFragmentation.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// This file contains the classes for string fragmentation. +// StringEnd: keeps track of the fragmentation step. +// StringFragmentation: is the top-level class. + +#ifndef Pythia8_StringFragmentation_H +#define Pythia8_StringFragmentation_H + +#include "Basics.h" +#include "Event.h" +#include "Info.h" +#include "FragmentationFlavZpT.h" +#include "FragmentationSystems.h" +#include "ParticleData.h" +#include "PythiaStdlib.h" +#include "Settings.h" + +namespace Pythia8 { + +//========================================================================== + +// The StringEnd class contains the information related to +// one of the current endpoints of the string system. +// Only to be used inside StringFragmentation, so no private members. + +class StringEnd { + +public: + + // Constructor. + StringEnd() {} + + // Save pointers. + void init( ParticleData* particleDataPtrIn, StringFlav* flavSelPtrIn, + StringPT* pTSelPtrIn, StringZ* zSelPtrIn) { + particleDataPtr = particleDataPtrIn; flavSelPtr = flavSelPtrIn; + pTSelPtr = pTSelPtrIn; zSelPtr = zSelPtrIn;} + + // Set up initial endpoint values from input. + void setUp(bool fromPosIn, int iEndIn, int idOldIn, int iMaxIn, + double pxIn, double pyIn, double GammaIn, double xPosIn, double xNegIn); + + // Fragment off one hadron from the string system, in flavour and pT. + void newHadron(); + + // Fragment off one hadron from the string system, in momentum space, + // by taking steps either from positive or from negative end. + Vec4 kinematicsHadron(StringSystem& system); + + // Update string end information after a hadron has been removed. + void update(); + + // Constants: could only be changed in the code itself. + static const double TINY, PT2SAME; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointers to classes for flavour, pT and z generation. + StringFlav* flavSelPtr; + StringPT* pTSelPtr; + StringZ* zSelPtr; + + // Data members. + bool fromPos; + int iEnd, iMax, idHad, iPosOld, iNegOld, iPosNew, iNegNew; + double pxOld, pyOld, pxNew, pyNew, pxHad, pyHad, mHad, mT2Had, zHad, + GammaOld, GammaNew, xPosOld, xPosNew, xPosHad, xNegOld, xNegNew, + xNegHad; + FlavContainer flavOld, flavNew; + Vec4 pHad, pSoFar; + +}; + +//========================================================================== + +// The StringFragmentation class contains the top-level routines +// to fragment a colour singlet partonic system. + +class StringFragmentation { + +public: + + // Constructor. + StringFragmentation() {} + + // Initialize and save pointers. + void init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + StringFlav* flavSelPtrIn, StringPT* pTSelPtrIn, StringZ* zSelPtrIn); + + // Do the fragmentation: driver routine. + bool fragment( int iSub, ColConfig& colConfig, Event& event); + + // Find the boost matrix to the rest frame of a junction. + RotBstMatrix junctionRestFrame(Vec4& p0, Vec4& p1, Vec4& p2); + +private: + + // Constants: could only be changed in the code itself. + static const int NTRYFLAV, NTRYJOIN, NSTOPMASS, NTRYJNREST, + NTRYJNMATCH, NTRYJRFEQ; + static const double FACSTOPMASS, CLOSEDM2MAX, CLOSEDM2FRAC, EXPMAX, + MATCHPOSNEG, EJNWEIGHTMAX, CONVJNREST, M2MAXJRF, + CONVJRFEQ; + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to classes for flavour, pT and z generation. + StringFlav* flavSelPtr; + StringPT* pTSelPtr; + StringZ* zSelPtr; + + // Initialization data, read from Settings. + double stopMass, stopNewFlav, stopSmear, eNormJunction, + eBothLeftJunction, eMaxLeftJunction, eMinLeftJunction, bLund; + + // Data members. + bool hasJunction, isClosed; + int iPos, iNeg; + double w2Rem, stopMassNow; + Vec4 pSum, pRem, pJunctionHadrons; + + // List of partons in string system. + vector iParton; + + // Temporary event record for the produced particles. + Event hadrons; + + // Information on the system of string regions. + StringSystem system, systemMin, systemMid; + + // Information on the two current endpoints of the fragmenting system. + StringEnd posEnd, negEnd; + + // Find region where to put first string break for closed gluon loop. + vector findFirstRegion(vector& iPartonIn, Event& event); + + // Set flavours and momentum position for initial string endpoints. + void setStartEnds(int idPos, int idNeg, StringSystem systemNow); + + // Check remaining energy-momentum whether it is OK to continue. + bool energyUsedUp(bool fromPos); + + // Produce the final two partons to complete the system. + bool finalTwo(bool fromPos); + + // Construct a special joining region for the final two hadrons. + StringRegion finalRegion(); + + // Store the hadrons in the normal event record, ordered from one end. + void store(Event& event); + + // Fragment off two of the string legs in to a junction. + bool fragmentToJunction(Event& event); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_StringFragmentation_H diff --git a/PYTHIA8/pythia8140/include/SusyCouplings.h b/PYTHIA8/pythia8140/include/SusyCouplings.h new file mode 100644 index 00000000000..3579036e826 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SusyCouplings.h @@ -0,0 +1,139 @@ +// SusyCouplings.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Peter Skands, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for setup of common SUSY couplings. + +#ifndef Pythia8_SusyCouplings_H +#define Pythia8_SusyCouplings_H + +#include "PythiaComplex.h" +#include "Settings.h" +#include "StandardModel.h" +#include "SusyLesHouches.h" + +namespace Pythia8 { + +//========================================================================== + +// CoupSUSY +// Auxiliary class to compute and store various SM and SUSY couplings. + +class CoupSUSY { + +public: + + // Constructor + CoupSUSY() {isInit=false; isNMSSM = false;} + + // Initialize + void init(SusyLesHouches* slhaPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, CoupSM* coupSMPtrIn); + + // Status flag. Flag for NMSSM. + bool isInit, isNMSSM; + + // Z and W pole masses and widths + double mWpole, wWpole, mZpole, wZpole; + + // Running masses and weak mixing angle + // (default to pole values if no running available) + double mW, mZ, sin2W, sinW, cosW; + + // Tanbeta + double tanb, cosb, sinb; + + // ~qq~g couplings + complex LsddG[7][4], RsddG[7][4]; + complex LsuuG[7][4], RsuuG[7][4]; + // Assume generation index for Squark. Translate if PDG code instead. + complex getLsqqG(int iGenSq, int idQ) {if (abs(iGenSq) > 1000000) + iGenSq = 3*(abs(iGenSq)/2000000) + (abs(iGenSq)%10+1)/2; + return (abs(idQ)%2 == 0) ? LsuuG[iGenSq][abs(idQ)/2] + : LsddG[iGenSq][(abs(idQ)+1)/2] ;} + complex getRsqqG(int iGenSq, int idQ) {if (abs(iGenSq) > 1000000) + iGenSq = 3*(abs(iGenSq)/2000000) + (abs(iGenSq)%10+1)/2; + return (abs(idQ)%2 == 0) ? RsuuG[iGenSq][abs(idQ)/2] + : RsddG[iGenSq][(abs(idQ)+1)/2] ;} + + // ~chi0~chi0Z couplings + complex OLpp[6][6], ORpp[6][6]; + + // ~chi+~chi-Z couplings + complex OLp[3][3], ORp[3][3]; + + // ~chi0~chi+W couplings + complex OL[6][3], OR[6][3]; + + // qqZ couplings + double LqqZ[7], RqqZ[7]; + + // ~q~qZ couplings + complex LsdsdZ[7][7], RsdsdZ[7][7]; + complex LsusuZ[7][7], RsusuZ[7][7]; + complex getLsqsqZ(int idSq1, int idSq2) { + if (abs(idSq1)%2 != abs(idSq2)%2) return complex(0.0,0.0); + int iGen1 = 3*(abs(idSq1)/2000000) + (abs(idSq1)%10+1)/2; + int iGen2 = 3*(abs(idSq2)/2000000) + (abs(idSq2)%10+1)/2; + return (abs(idSq1)%2 == 0) ? LsusuZ[iGen1][iGen2] : LsdsdZ[iGen1][iGen2];} + complex getRsqsqZ(int idSq1, int idSq2) { + if (abs(idSq1)%2 != abs(idSq2)%2) return complex(0.0,0.0); + int iGen1 = 3*(abs(idSq1)/2000000) + (abs(idSq1)%10+1)/2; + int iGen2 = 3*(abs(idSq2)/2000000) + (abs(idSq2)%10+1)/2; + return (abs(idSq1)%2 == 0) ? RsusuZ[iGen1][iGen2] : RsdsdZ[iGen1][iGen2];} + + // udW couplings + complex LudW[4][4], RudW[4][4]; + + // ~u~dW couplings + complex LsusdW[7][7], RsusdW[7][7]; + + // ~qq~chi0 couplings + complex LsddX[7][4][6], RsddX[7][4][6]; + complex LsuuX[7][4][6], RsuuX[7][4][6]; + complex getLsqqX(int iSq, int idQ, int iNeut) {return (abs(idQ)%2 == 0) + ? LsuuX[iSq][abs(idQ)/2][iNeut] : LsddX[iSq][(abs(idQ)+1)/2][iNeut] ;} + complex getRsqqX(int iSq, int idQ, int iNeut) {return (abs(idQ)%2 == 0) + ? RsuuX[iSq][abs(idQ)/2][iNeut] : RsddX[iSq][(abs(idQ)+1)/2][iNeut] ;} + + // ~du~chi+ couplings + complex LsduX[7][4][3], RsduX[7][4][3]; + + // ~ud~chi+ couplings + complex LsudX[7][4][3], RsudX[7][4][3]; + + // Return neutralino, chargino, sup, sdown and slepton flavour codes. + int idNeut(int idChi); + int idChar(int idChi); + int idSup(int iSup); + int idSdown(int iSdown); + int idSlep(int iSlep); + + // Return a particle name, given the PDG code. + string getName(int pdgCode); + +private: + + // Debug flag + static const bool DEBUG; + + // Pointer to SLHA instance + SusyLesHouches* slhaPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the Standard Models couplings. + CoupSM* coupSMPtr; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_SusyCouplings_H diff --git a/PYTHIA8/pythia8140/include/SusyLesHouches.h b/PYTHIA8/pythia8140/include/SusyLesHouches.h new file mode 100644 index 00000000000..543b62899d0 --- /dev/null +++ b/PYTHIA8/pythia8140/include/SusyLesHouches.h @@ -0,0 +1,603 @@ +// SusyLesHouches.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Peter Skands, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for SUSY Les Houches Accord Interface +// Is independent of the rest of the Pythia implementation and thus could +// be re-used stand-alone or merged into other applications, subject to +// the MCnet Guidelines mentioned above. + +#ifndef SLHA_H +#define SLHA_H + +// Stdlib header files for string and character manipulation. +#include +#include +// Stdlib header files for containers. +#include +#include +// Stdlib header files for input/output. +#include +#include +#include +#include +// Stdlib header files for mathematics. +#include +#include + +// Stdlib namespace +using namespace std; + +class SusyLesHouches { + +public: + + //Constructor, with and without filename. + SusyLesHouches(int verboseIn=1) : verbose(verboseIn), + headerPrinted(false), footerPrinted(false), + slhaRead(false), lhefRead(false), lhefSlha(false) {}; + SusyLesHouches(string filename, int verboseIn=1) : verbose(verboseIn), + headerPrinted(false), footerPrinted(false), + slhaRead(true), lhefRead(false), lhefSlha(false) {readFile(filename);}; + + //***************************** SLHA FILE I/O *****************************// + // Read and write SLHA files + int readFile(string slhaFileIn="slha.spc",int verboseIn=1); + //int writeFile(string filename): write SLHA file on filename + + //Output utilities + void printHeader(); // print Header + void printFooter(); // print Footer + void printSpectrum(); // print Spectrum + + // Check spectrum and decays + int checkSpectrum(); + int checkDecays(); + + // File Name (can be either SLHA or LHEF) + string slhaFile; + + // Class for SLHA data entry + class Entry { + + public: + //Constructor. + Entry() : isIntP(false), isDoubleP(false), + isStringP(false), n(0), d(0.0), s(""), commentP("") {} + + // Generic functions to inquire whether an int, double, or string + bool isInt(){return isIntP;} + bool isDouble(){return isDoubleP;} + bool isString(){return isStringP;} + + // = Overloading: Set entry to int, double, or string + Entry& operator=(double& val) { + d=val;isIntP=false;isDoubleP=true;isStringP=false; + return *this; + }; + Entry& operator=(int& val) { + n=val;isIntP=true;isDoubleP=false;isStringP=false; + return *this; + }; + Entry& operator=(string& val) { + s=val;isIntP=false;isDoubleP=false;isStringP=true; + return *this; + }; + + // Set and Get comment + void setComment(string comment) {commentP=comment;} + void getComment(string comment) {comment=commentP;} + + // Generic functions to get value + bool get(int& val) {val=n; return isIntP;} + bool get(double& val) {val=d; return isDoubleP;} + bool get(string& val) {val=s; return isStringP;} + + private: + bool isIntP, isDoubleP, isStringP; + int n; + double d; + string s; + string commentP; + + }; + + //***************************** SLHA CLASSES *****************************// + + + //class block: the generic SLHA block (see below for matrices) + //Explicit typing required, e.g. block minpar; + template class block { + + public: + + //Constructor. + block() : idnow(0) { } ; + + //Does block exist? + bool exists() { return int(entry.size()) == 0 ? false : true ; }; + //Clear block + void clear() { entry.clear(); }; + + //set: set block entry values. + //Possible return values from set: + // 0: normal return. Entry did not previously exist and has been created. + // 1: normal return. Entry did previously exist and has been overwritten. + //-1: failure. + int set(int iIn,T valIn) { + int alreadyexisting=exists(iIn)?1:0; + entry[iIn]=valIn; + return alreadyexisting; + }; + // Read index and value from SLHA data line + int set(istringstream& linestream) { + linestream >> i >> val; + return linestream ? set(i,val) : -1; + }; + // With i already given, read value from remaining SLHA data line + int set(int iIn,istringstream& linestream) { + linestream >> val; + return linestream ? set(iIn,val) : -1; + }; + // Shorthand for entry[0]. Used e.g. for block ALPHA. + void set(T valIn) { entry[0]=valIn; }; + + // Does entry i already exist in this block? + bool exists(int iIn) {return entry.find(iIn) != entry.end() + ? true : false;}; + + // Indexing with (). Output only. + T operator()(int iIn=0) { + if (exists(iIn)) {return entry[iIn];} else {T dummy(0); return dummy;}; + }; + + // Size of map + int size() {return int(entry.size());}; + + // First and next key code + int first() { idnow = entry.begin()->first; return idnow; }; + int next() { + typename map::iterator itnow; + itnow = ++entry.find(idnow); + if ( itnow == entry.end() ) itnow=entry.begin(); + return idnow = itnow->first; + }; + + // Simple print utility + void print() { + bool finished=false; + int ibegin=first(); + i=ibegin; + while (!finished) { + cout << " "<< i << " " << entry[i] < entry; + int idnow; + double qDRbar; + //Auxiliary vars + int i; + T val; + }; + + // class matrixblock: the generic SLHA matrix + // Explicit sizing required, e.g. matrixblock<4> nmix; + template class matrixblock { + public: + //Constructor. Set uninitialized and explicitly zero. + matrixblock() { + initialized=false; + for (i=1;i<=size;i++) { + for (j=1;j<=size;j++) { + entry[i][j]=0.0; + }; + }; + }; + + // Assignment + matrixblock& operator=(const matrixblock& m) { + if (this != &m) { + for (i=0;i0 && jIn>0 && iIn<=size && jIn<=size) { + entry[iIn][jIn]=valIn; + initialized=true; + return 0; + } else { + return -1; + }; + }; + + // Set entry from linestream (used during file read) + int set(istringstream& linestream) { + linestream >> i >> j >> val; + return linestream ? set(i,j,val) : -1; + }; + + // () Overloading: Get entry + double operator()(int iIn, int jIn) const { + return (iIn <= size && jIn <= size && iIn > 0 && jIn > 0) ? + entry[iIn][jIn] : 0.0; + }; + + // Set and get scale for DRbar running blocks. + void setq(double qIn) { qDRbar=qIn; } + double q() { return qDRbar; } + + // Simple print utility, to be elaborated on. + void print() { + for (i=1;i<=size;i++) { + cout << " "< rvlam; + template class tensor3block { + public: + //Constructor. Set uninitialized and explicitly zero. + tensor3block() { + initialized=false; + for (i=1;i<=size;i++) { + for (j=1;j<=size;j++) { + for (k=1;k<=size;k++) { + entry[i][j][k]=0.0; + }; + }; + }; + }; + + // Assignment + tensor3block& operator=(const tensor3block& m) { + if (this != &m) { + for (i=0;i0 && jIn>0 && kIn>0 && iIn<=size && jIn<=size && kIn<=size) { + entry[iIn][jIn][kIn]=valIn; + initialized=true; + return 0; + } else { + return -1; + }; + }; + + // Set entry from linestream (used during file read) + int set(istringstream& linestream) { + linestream >> i >> j >> k >> val; + return linestream ? set(i,j,k,val) : -1; + }; + + // () Overloading: Get entry + double operator()(int iIn, int jIn, int kIn) const { + return (iIn <= size && jIn <= size && kIn <= size && iIn > 0 + && jIn > 0 && kIn > 0) ? entry[iIn][jIn][kIn] : 0.0; + }; + + // Set and get scale for DRbar running blocks. + void setq(double qIn) { qDRbar=qIn; } + double q() { return qDRbar; } + + // Simple print utility, to be elaborated on. + void print() { + for (i=1;i<=size;i++) { + for (j=1;j<=size;j++) { + cout << " "< idDaIn, string cIn="") { + setChannel(bratIn,nDaIn,idDaIn,cIn); + } + + // Functions to set decay channel information + void setChannel(double bratIn, int nDaIn, vector idDaIn, string cIn="") { + brat = bratIn; + for (int i=0; i<=nDaIn; i++) { + if (i < int(idDaIn.size())) idDa.push_back(idDaIn[i]); + comment = cIn; + } + } + void setBrat(double bratIn) {brat=bratIn;} + void setIdDa(vector idDaIn) {idDa = idDaIn;} + + // Functions to get decay channel information + double getBrat() {return brat;} + int getNDa() {return int(idDa.size());} + vector getIdDa() {return idDa;} + string getComment() {return comment;} + + private: + double brat; + vector idDa; + string comment; + + }; + + class decayTable { + public: + + decayTable() : id(0), width(0.0) {}; + decayTable(int idIn) : id(idIn), width(0.0) {}; + decayTable(int idIn, double widthIn) : id(idIn), width(widthIn) {}; + + // Functions to get PDG code (id) and width + int getId() {return id;} + double getWidth() {return width;} + + // Functions to set PDG code (id) and width + void setId(int idIn) {id = idIn;} + void setWidth(double widthIn) {width=widthIn;} + + // Function to reset size and width (width -> 0 by default) + void reset(double widthIn=0.0) {table.resize(0); width=widthIn;} + + // Function to add another decay channel + void addChannel(decayChannel channelIn) {table.push_back(channelIn);} + void addChannel(double bratIn, int nDaIn, vector idDaIn, string cIn="") { + decayChannel newChannel(bratIn, nDaIn, idDaIn, cIn); + table.push_back(newChannel); + } + + // Function to return number of decay channels + int size() {return int(table.size());} + + // Function to return a branching ratio + double getBrat(int iChannel) { + if (iChannel >= 0 && iChannel < int(table.size())) { + return table[iChannel].getBrat(); + } else { + return 0.0; + } + } + // Function to return daughter PDG codes + vector getIdDa(int iChannel) { + if (iChannel >= 0 && iChannel < int(table.size())) { + return table[iChannel].getIdDa(); + } else { + vector dum; + return dum; + } + } + // Function to return a decay channel + decayChannel getChannel(int iChannel) { + if (iChannel >= 0 && iChannel < int(table.size())) { + return table[iChannel]; + } else { + decayChannel dum; + return dum; + } + } + + private: + int id; + double width; + vector table; + + }; + + //*************************** THE SLHA1 BLOCKS ***************************// + //blocks for model definition: + block modsel; + block modsel21; + block modsel12; + block minpar; + block extpar; + block sminputs; + //blocks for RGE program specific output + block spinfo; + block spinfo3; + block spinfo4; + //blocks for DCY program specific output + block dcinfo; + block dcinfo3; + block dcinfo4; + //blocks for mass and coupling spectrum + block mass; + matrixblock<4> nmix; + matrixblock<2> umix; + matrixblock<2> vmix; + matrixblock<2> stopmix; + matrixblock<2> sbotmix; + matrixblock<2> staumix; + block alpha; + block hmix; + block gauge; + block msoft; + matrixblock<3> au; + matrixblock<3> ad; + matrixblock<3> ae; + matrixblock<3> yu; + matrixblock<3> yd; + matrixblock<3> ye; + + //************************ THE SLHA1 DECAY TABLES ************************// + vector decays; + map decayIndices; + + //*************************** THE SLHA2 BLOCKS ***************************// + //Additions to SLHA1 + block qextpar; + + //FLV Input + block vckmin; // The input CKM Wolfenstein parms. + block upmnsin; // The input PMNS PDG parms. + matrixblock<3> msq2in; // The input upper off-diagonal msq2 + matrixblock<3> msu2in; // The input upper off-diagonal msu2 + matrixblock<3> msd2in; // The input upper off-diagonal msd2 + matrixblock<3> msl2in; // The input upper off-diagonal msl2 + matrixblock<3> mse2in; // The input upper off-diagonal mse2 + matrixblock<3> tuin; // The input upper off-diagonal TU + matrixblock<3> tdin; // The input upper off-diagonal TD + matrixblock<3> tein; // The input upper off-diagonal TE + //FLV Output + matrixblock<3> vckm; // The output DRbar running Re{VCKM} at Q + matrixblock<3> upmns; // The output DRbar running Re{UPMNS} at Q + matrixblock<3> msq2; // The output DRbar running msq2 at Q + matrixblock<3> msu2; // The output DRbar running msu2 at Q + matrixblock<3> msd2; // The output DRbar running msd2 at Q + matrixblock<3> msl2; // The output DRbar running msl2 at Q + matrixblock<3> mse2; // The output DRbar running mse2 at Q + matrixblock<3> tu; // The output DRbar running TU at Q + matrixblock<3> td; // The output DRbar running TD at Q + matrixblock<3> te; // The output DRbar running TE at Q + matrixblock<6> usqmix; // The Re{} up squark mixing matrix + matrixblock<6> dsqmix; // The Re{} down squark mixing matrix + matrixblock<6> selmix; // The Re{} selectron mixing matrix + matrixblock<3> snumix; // The Re{} sneutrino mixing matrix + matrixblock<3> snsmix; // The scalar sneutrino mixing matrix + matrixblock<3> snamix; // The pseudoscalar neutrino mixing matrix + + //RPV Input + tensor3block<3> rvlamllein; // The input LNV lambda couplings + tensor3block<3> rvlamlqdin; // The input LNV lambda' couplings + tensor3block<3> rvlamuddin; // The input BNV lambda'' couplings + tensor3block<3> rvtllein; // The input LNV T couplings + tensor3block<3> rvtlqdin; // The input LNV T' couplings + tensor3block<3> rvtuddin; // The input BNV T'' couplings + block rvkappain; // The input LNV kappa couplings + block rvdin; // The input LNV D terms + block rvm2lh1in; // The input LNV m2LH1 couplings + block rvsnvevin; // The input LNV sneutrino vevs + //RPV Output + tensor3block<3> rvlamlle; // The output LNV lambda couplings + tensor3block<3> rvlamlqd; // The output LNV lambda' couplings + tensor3block<3> rvlamudd; // The output BNV lambda'' couplings + tensor3block<3> rvtlle; // The output LNV T couplings + tensor3block<3> rvtlqd; // The output LNV T' couplings + tensor3block<3> rvtudd; // The output BNV T'' couplings + block rvkappa; // The output LNV kappa couplings + block rvd; // The output LNV D terms + block rvm2lh1; // The output LNV m2LH1 couplings + block rvsnvev; // The output LNV sneutrino vevs + matrixblock<7> rvnmix; // The RPV neutralino mixing matrix + matrixblock<5> rvumix; // The RPV chargino L mixing matrix + matrixblock<5> rvvmix; // The RPV chargino R mixing matrix + matrixblock<5> rvhmix; // The RPV neutral scalar mixing matrix + matrixblock<5> rvamix; // The RPV neutral pseudoscalar mixing matrix + matrixblock<7> rvlmix; // The RPV charged fermion mixing matrix + + //CPV Input + block imminpar; + block imextpar; + //CPV Output + matrixblock<4> cvhmix; // The CPV Higgs mixing matrix + matrixblock<4> imcvhmix; // Optional: imaginary components + matrixblock<3> imau,imad,imae; // Im{} of AU, AD, AE + block imhmix; + block immsoft; + + //CPV + FLV Input + matrixblock<3> immsq2in; // The Im{} input upper off-diagonal msq2 + matrixblock<3> immsu2in; // The Im{} input upper off-diagonal msu2 + matrixblock<3> immsd2in; // The Im{} input upper off-diagonal msd2 + matrixblock<3> immsl2in; // The Im{} input upper off-diagonal msl2 + matrixblock<3> immse2in; // The Im{} input upper off-diagonal mse2 + matrixblock<3> imtuin,imtdin,imtein; // The Im{} input upper off-diagonal T + //CPV + FLV Output + matrixblock<3> imvckm; // The output DRbar running Im{VCKM} at Q + matrixblock<3> imupmns; // The output DRbar running Im{UPMNS} at Q + matrixblock<3> immsq2; // The output DRbar running msq2 at Q + matrixblock<3> immsu2; // The output DRbar running msu2 at Q + matrixblock<3> immsd2; // The output DRbar running msd2 at Q + matrixblock<3> immsl2; // The output DRbar running msl2 at Q + matrixblock<3> immse2; // The output DRbar running mse2 at Q + matrixblock<3> imtu,imtd,imte; // Im{} of TU, TD, TE + matrixblock<6> imusqmix;// The Im{} up squark mixing matrix + matrixblock<6> imdsqmix; // The Im{} down squark mixing matrix + matrixblock<6> imselmix; // The Im{} selectron mixing matrix + matrixblock<3> imsnumix; // The Im{} sneutrino mixing matrix + matrixblock<4> imnmix; // The Im{} neutralino mixing matrix + matrixblock<4> imumix; // The Im{} chargino L mixing matrix + matrixblock<4> imvmix; // The Im{} chargino R mixing matrix + + //NMSSM Input + // All input is in EXTPAR + //NMSSM Output + block nmssmrun; // The block of NMSSM running parameters + matrixblock<3> nmhmix; // The NMSSM scalar Higgs mixing + matrixblock<3> nmamix; // The NMSSM pseudoscalar Higgs mixing + matrixblock<5> nmnmix; // The NMSSM neutralino mixing + matrixblock<5> imnmnmix; // Im{} (for future use) + + //*************************** SET BLOCK VALUE ****************************// + template int set(string,T); + template int set(string,int,T); + template int set(string,int,int,T); + template int set(string,int,int,int,T); + + //***************************** SLHA PRIVATE *****************************// +private: + //SLHA I/O + void message(int, string,string ,int line=0); + int verbose; + bool headerPrinted, footerPrinted; + bool slhaRead, lhefRead, lhefSlha; + +}; + +#endif + + diff --git a/PYTHIA8/pythia8140/include/TimeShower.h b/PYTHIA8/pythia8140/include/TimeShower.h new file mode 100644 index 00000000000..7dbcc5ca076 --- /dev/null +++ b/PYTHIA8/pythia8140/include/TimeShower.h @@ -0,0 +1,252 @@ +// TimeShower.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file for the timelike final-state showers. +// TimeDipoleEnd: data on a radiating dipole end. +// TimeShower: handles the showering description. + +#ifndef Pythia8_TimeShower_H +#define Pythia8_TimeShower_H + +#include "Basics.h" +#include "BeamParticle.h" +#include "Event.h" +#include "Info.h" +#include "ParticleData.h" +#include "PartonSystems.h" +#include "PythiaStdlib.h" +#include "Settings.h" +#include "StandardModel.h" +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// Data on radiating dipole ends; only used inside TimeShower class. + +class TimeDipoleEnd { + +public: + + // Constructors. + TimeDipoleEnd() : iRadiator(-1), iRecoiler(-1), pTmax(0.), colType(0), + chgType(0), gamType(0), isrType(0), system(0), systemRec(0), MEtype(0), + iMEpartner(-1), isOctetOnium(false), isHiddenValley(false), colvType(0), + MEmix(0.), MEorder(true), MEsplit(true), MEgluinoRec(false) { } + TimeDipoleEnd(int iRadiatorIn, int iRecoilerIn, double pTmaxIn = 0., + int colIn = 0, int chgIn = 0, int gamIn = 0, int isrIn = 0, + int systemIn = 0, int MEtypeIn = 0, int iMEpartnerIn = -1, + bool isOctetOniumIn = false, bool isHiddenValleyIn = false, + int colvTypeIn = 0, double MEmixIn = 0., bool MEorderIn = true, + bool MEsplitIn = true, bool MEgluinoRecIn = false) : + iRadiator(iRadiatorIn), iRecoiler(iRecoilerIn), pTmax(pTmaxIn), + colType(colIn), chgType(chgIn), gamType(gamIn), isrType(isrIn), + system(systemIn), systemRec(systemIn) , MEtype(MEtypeIn), + iMEpartner(iMEpartnerIn), isOctetOnium(isOctetOniumIn), + isHiddenValley(isHiddenValleyIn), colvType(colvTypeIn), MEmix(MEmixIn), + MEorder (MEorderIn), MEsplit(MEsplitIn), MEgluinoRec(MEgluinoRecIn) { } + + // Basic properties related to dipole and matrix element corrections. + int iRadiator, iRecoiler; + double pTmax; + int colType, chgType, gamType, isrType, system, systemRec, + MEtype, iMEpartner; + bool isOctetOnium, isHiddenValley; + int colvType; + double MEmix; + bool MEorder, MEsplit, MEgluinoRec; + + // Properties specific to current trial emission. + int flavour, iAunt; + double mRad, m2Rad, mRec, m2Rec, mDip, m2Dip, m2DipCorr, + pT2, m2, z, mFlavour, asymPol; + +} ; + +//========================================================================== + +// The TimeShower class does timelike showers. + +class TimeShower { + +public: + + // Constructor. + TimeShower() {beamOffset = 0;} + + // Destructor. + virtual ~TimeShower() {} + + // Initialize various pointers. + // (Separated from rest of init since not virtual.) + void initPtr(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + CoupSM* coupSMPtrIn, PartonSystems* partonSystemsPtrIn, + UserHooks* userHooksPtrIn) { infoPtr = infoPtrIn; + settingsPtr = settingsPtrIn; particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; coupSMPtr = coupSMPtrIn; + partonSystemsPtr = partonSystemsPtrIn; userHooksPtr = userHooksPtrIn;} + + // Initialize alphaStrong and related pTmin parameters. + virtual void init( BeamParticle* beamAPtrIn = 0, + BeamParticle* beamBPtrIn = 0); + + // New beams possible for handling of hard diffraction. (Not virtual.) + void reassignBeamPtrs( BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + int beamOffsetIn = 0) {beamAPtr = beamAPtrIn; beamBPtr = beamBPtrIn; + beamOffset = beamOffsetIn;} + + // Find whether to limit maximum scale of emissions, and whether to dampen. + virtual bool limitPTmax( Event& event, double Q2Fac = 0., + double Q2Ren = 0.); + + // Potential enhancement factor of pTmax scale for hardest emission. + double enhancePTmax() {return pTmaxFudge;} + + // Top-level routine to do a full time-like shower in resonance decay. + virtual int shower( int iBeg, int iEnd, Event& event, double pTmax, + int nBranchMax = 0); + + // Provide the pT scale of the last branching in the above shower. + double pTLastInShower() {return pTLastBranch;} + + // Prepare system for evolution after each new interaction; identify ME. + virtual void prepare( int iSys, Event& event, bool limitPTmaxIn = true); + + // Update dipole list after a multiple interactions rescattering. + virtual void rescatterUpdate( int iSys, Event& event); + + // Update dipole list after each ISR emission. + virtual void update( int iSys, Event& event); + + // Select next pT in downwards evolution. + virtual double pTnext( Event& event, double pTbegAll, double pTendAll); + + // ME corrections and kinematics that may give failure. + virtual bool branch( Event& event, bool isInterleaved = false); + + // Tell which system was the last processed one. + int system() const {return iSysSel;}; + + // Print dipole list; for debug mainly. + virtual void list( ostream& os = cout) const; + +protected: + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointer to Standard Model couplings. + CoupSM* coupSMPtr; + + // Pointers to the two incoming beams. Offset their location in event. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + int beamOffset; + + // Pointer to information on subcollision parton locations. + PartonSystems* partonSystemsPtr; + + // Pointer to userHooks object for user interaction with program. + UserHooks* userHooksPtr; + + // Store properties to be returned by methods. + int iSysSel; + double pTmaxFudge, pTLastBranch; + +private: + + // Constants: could only be changed in the code itself. + static const double SIMPLIFYROOT, XMARGIN, XMARGINCOMB, TINYPDF, LARGEM2, + THRESHM2, LAMBDA3MARGIN; + // Rescatter: try to fix up recoil between systems + static const bool FIXRESCATTER, VETONEGENERGY; + static const double MAXVIRTUALITYFRACTION, MAXNEGENERGYFRACTION; + + // Initialization data, normally only set once. + bool doQCDshower, doQEDshowerByQ, doQEDshowerByL, doQEDshowerByGamma, + doMEcorrections, doPhiPolAsym, doInterleave, allowBeamRecoil, + dampenBeamRecoil, allowRescatter, canVetoEmission, doHVshower; + int pTmaxMatch, pTdampMatch, alphaSorder, nGluonToQuark, + alphaEMorder, nGammaToQuark, nGammaToLepton, nCHV; + double pTdampFudge, mc, mb, m2c, m2b, alphaSvalue, alphaS2pi, + Lambda3flav, Lambda4flav, Lambda5flav, Lambda3flav2, Lambda4flav2, + Lambda5flav2, pTcolCutMin, pTcolCut, pT2colCut, pTchgQCut, + pT2chgQCut, pTchgLCut, pT2chgLCut, mMaxGamma, m2MaxGamma, + octetOniumFraction, octetOniumColFac, mZ, gammaZ, thetaWRat, + CFHV, alphaHVfix, pThvCut, pT2hvCut, pTmaxFudgeMI; + + // alphaStrong and alphaEM calculations. + AlphaStrong alphaS; + AlphaEM alphaEM; + + // Some current values. + bool dopTdamp; + double pT2damp; + + // All dipole ends and a pointer to the selected hardest dipole end. + vector dipEnd; + TimeDipoleEnd* dipSel; + int iDipSel; + + // Setup a dipole end, either QCD, QED/photon or Hidden Valley one. + void setupQCDdip( int iSys, int i, int colTag, int colSign, Event& event, + bool isOctetOnium = false, bool limitPTmaxIn = true); + void setupQEDdip( int iSys, int i, int chgType, int gamType, Event& event, + bool limitPTmaxIn = true); + void setupHVdip( int iSys, int i, Event& event, bool limitPTmaxIn = true); + + // Evolve a QCD dipole end. + void pT2nextQCD( double pT2begDip, double pT2sel, TimeDipoleEnd& dip, + Event& event); + + // Evolve a QED dipole end, either charged or photon. + void pT2nextQED( double pT2begDip, double pT2sel, TimeDipoleEnd& dip, + Event& event); + + // Evolve a Hidden Valley dipole end. + void pT2nextHV( double pT2begDip, double pT2sel, TimeDipoleEnd& dip, + Event& ); + + // Find kind of QCD ME correction. + void findMEtype( Event& event, TimeDipoleEnd& dip); + + // Find type of particle; used by findMEtype. + int findMEparticle( int id, bool isHiddenColour = false); + + // Find mixture of V and A in gamma/Z: energy- and flavour-dependent. + double gammaZmix( Event& event, int iRes, int iDau1, int iDau2); + + // Set up to calculate QCD ME correction with calcMEcorr. + double findMEcorr(TimeDipoleEnd* dip, Particle& rad, Particle& partner, + Particle& emt); + + // Calculate value of QCD ME correction. + double calcMEcorr( int kind, int combiIn, double mixIn, double x1, + double x2, double r1, double r2); + + // Find coefficient of azimuthal asymmetry from gluon polarization. + void findAsymPol( Event& event, TimeDipoleEnd* dip); + + // Rescatter: propagate dipole recoil to internal lines connecting systems. + bool rescatterPropagateRecoil( Event& event, Vec4& pNew); + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_TimeShower_H diff --git a/PYTHIA8/pythia8140/include/UserHooks.h b/PYTHIA8/pythia8140/include/UserHooks.h new file mode 100644 index 00000000000..30b22a1433a --- /dev/null +++ b/PYTHIA8/pythia8140/include/UserHooks.h @@ -0,0 +1,216 @@ +// UserHooks.h is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Header file to allow user access to program at different stages. +// UserHooks: almost empty base class, with user to write the rela code. +// MyUserHooks: derived class, only intended as an example. + +#ifndef Pythia8_UserHooks_H +#define Pythia8_UserHooks_H + +#include "Event.h" +#include "PartonSystems.h" +#include "PhaseSpace.h" +#include "PythiaStdlib.h" +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// Forward reference to the PhaseSpace class. +class PhaseSpace; + +//========================================================================== + +// UserHooks is base class for user access to program execution. + +class UserHooks { + +public: + + // Destructor. + virtual ~UserHooks() {} + + // Initialize pointers and workEvent. Note: not virtual. + void initPtr( Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + BeamParticle* beamPomAPtrIn, BeamParticle* beamPomBPtrIn, + CoupSM* coupSMPtrIn, PartonSystems* partonSystemsPtrIn, + SigmaTotal* sigmaTotPtrIn) { infoPtr = infoPtrIn; + settingsPtr = settingsPtrIn; particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; beamAPtr = beamAPtrIn; beamBPtr = beamBPtrIn; + beamPomAPtr = beamPomAPtrIn; beamPomBPtr = beamPomBPtrIn; + coupSMPtr = coupSMPtrIn; partonSystemsPtr = partonSystemsPtrIn; + sigmaTotPtr = sigmaTotPtrIn; + workEvent.init("(work event)", particleDataPtr);} + + // Possibility to modify cross section of process. + virtual bool canModifySigma() {return false;} + + // Multiplicative factor modifying the cross section of a hard process. + virtual double multiplySigmaBy(const SigmaProcess* sigmaProcessPtr, + const PhaseSpace* phaseSpacePtr, bool inEvent); + + // Possibility to veto event after process-level selection. + virtual bool canVetoProcessLevel() {return false;} + + // Decide whether to veto current process or not, based on process record. + // Usage: doVetoProcessLevel( process). + virtual bool doVetoProcessLevel(Event& ) {return false;} + + // Possibility to veto MI + ISR + FSR evolution and kill event, + // making decision at a fixed pT scale. Useful for MLM-style matching. + virtual bool canVetoPT() {return false;} + + // Transverse-momentum scale for veto test. + virtual double scaleVetoPT() {return 0.;} + + // Decide whether to veto current event or not, based on event record. + // Usage: doVetoPT( iPos, event), where iPos = 0: no emissions so far; + // iPos = 1/2/3 joint evolution, latest step was MI/ISR/FSR; + // iPos = 4: FSR only afterwards; iPos = 5: FSR in resonance decay. + virtual bool doVetoPT( int , const Event& ) {return false;} + + // Possibility to veto MI + ISR + FSR evolution and kill event, + // making decision after fixed number of ISR or FSR steps. + virtual bool canVetoStep() {return false;} + + // Up to how many ISR + FSR steps of hardest interaction should be checked. + virtual int numberVetoStep() {return 1;} + + // Decide whether to veto current event or not, based on event record. + // Usage: doVetoStep( iPos, nISR, nFSR, event), where iPos as above, + // nISR and nFSR number of emissions so far for hard interaction only. + virtual bool doVetoStep( int , int , int , const Event& ) {return false;} + + // Possibility to veto MI + ISR + FSR evolution and kill event, + // making decision after fixed number of MI steps. + virtual bool canVetoMIStep() {return false;} + + // Up to how many MI steps should be checked. + virtual int numberVetoMIStep() {return 1;} + + // Decide whether to veto current event or not, based on event record. + // Usage: doVetoMIStep( nMI, event), where nMI is number of MI's so far. + virtual bool doVetoMIStep( int , const Event& ) {return false;} + + // Possibility to veto event after parton-level selection. + virtual bool canVetoPartonLevel() {return false;} + + // Decide whether to veto current partons or not, based on event record. + // Usage: doVetoPartonLevel( event). + virtual bool doVetoPartonLevel( const Event& ) {return false;} + + // Possibility to set initial scale in TimeShower for resonance decay. + virtual bool canSetResonanceScale() {return false;} + + // Initial scale for TimeShower evolution. + // Usage: scaleResonance( iRes, event), where iRes is location + // of decaying resonance in the event record. + virtual double scaleResonance( const int, const Event& ) {return 0.;} + + // Possibility to veto an emission in the ISR machinery. + virtual bool canVetoISREmission() {return false;} + + // Decide whether to veto current emission or not, based on event record. + // Usage: doVetoISREmission( sizeOld, event) where sizeOld is size + // of event record before current emission-to-be-scrutinized was added. + virtual bool doVetoISREmission( const int, const Event& ) {return false;} + + // Possibility to veto an emission in the FSR machinery. + virtual bool canVetoFSREmission() {return false;} + + // Decide whether to veto current emission or not, based on event record. + // Usage: doVetoFSREmission( sizeOld, event) where sizeOld is size + // of event record before current emission-to-be-scrutinized was added. + virtual bool doVetoFSREmission( const int, const Event& ) {return false;} + +protected: + + // Constructor. + UserHooks() {} + + // Pointer to various information on the generation. + Info* infoPtr; + + // Pointer to the settings database. + Settings* settingsPtr; + + // Pointer to the particle data table. + ParticleData* particleDataPtr; + + // Pointer to the random number generator. + Rndm* rndmPtr; + + // Pointers to the two incoming beams and to Pomeron beam-inside-beam. + BeamParticle* beamAPtr; + BeamParticle* beamBPtr; + BeamParticle* beamPomAPtr; + BeamParticle* beamPomBPtr; + + // Pointers to Standard Model couplings. + CoupSM* coupSMPtr; + + // Pointer to information on subcollision parton locations. + PartonSystems* partonSystemsPtr; + + // Pointer to the total/elastic/diffractive cross sections. + SigmaTotal* sigmaTotPtr; + + // omitResonanceDecays omits resonance decay chains from process record. + void omitResonanceDecays(const Event& process); + + // subEvent extracts currently resolved partons in the hard process. + void subEvent(const Event& event, bool isHardest = true); + + // Have one event object around as work area. + Event workEvent; + +}; + +//========================================================================== + +// SuppressSmallPT is a derived class for user access to program execution. +// It is a simple example, illustrating how to suppress the cross section +// of 2 -> 2 processes by a factor pT^4 / (pT0^2 + pT^2)^2, with pT0 input, +// and also modify alpha_strong scale similarly. + +class SuppressSmallPT : public UserHooks { + +public: + + // Constructor. + SuppressSmallPT( double pT0timesMIIn = 1., int numberAlphaSIn = 0, + bool useSameAlphaSasMIIn = true) {isInit = false; + pT0timesMI = pT0timesMIIn; numberAlphaS = numberAlphaSIn; + useSameAlphaSasMI = useSameAlphaSasMIIn;} + + // Possibility to modify cross section of process. + virtual bool canModifySigma() {return true;} + + // Multiplicative factor modifying the cross section of a hard process. + // Usage: inEvent is true for event generation, false for initialization. + virtual double multiplySigmaBy(const SigmaProcess* sigmaProcessPtr, + const PhaseSpace* phaseSpacePtr, bool ); + +private: + + // Save input properties and the squared pT0 scale. + bool isInit, useSameAlphaSasMI; + int numberAlphaS; + double pT0timesMI, pT20; + + // Alpha_strong calculation. + AlphaStrong alphaS; + +}; + +//========================================================================== + +} // end namespace Pythia8 + +#endif // Pythia8_UserHooks_H diff --git a/PYTHIA8/pythia8140/src/Analysis.cxx b/PYTHIA8/pythia8140/src/Analysis.cxx new file mode 100644 index 00000000000..3187eafc47a --- /dev/null +++ b/PYTHIA8/pythia8140/src/Analysis.cxx @@ -0,0 +1,892 @@ +// Analysis.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// Sphericity, Thrust, ClusJet and CellJet classes. + +#include "Analysis.h" + +namespace Pythia8 { + +//========================================================================== + +// Sphericity class. +// This class finds sphericity-related properties of an event. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Minimum number of particles to perform study. +const int Sphericity::NSTUDYMIN = 2; + +// Maximum number of times that an error warning will be printed. +const int Sphericity::TIMESTOPRINT = 1; + +// Assign mimimum squared momentum in weight to avoid division by zero. +const double Sphericity::P2MIN = 1e-20; + +// Second eigenvalue not too low or not possible to find eigenvectors. +const double Sphericity::EIGENVALUEMIN = 1e-10; + +//-------------------------------------------------------------------------- + +// Analyze event. + +bool Sphericity::analyze(const Event& event, ostream& os) { + + // Initial values, tensor and counters zero. + eVal1 = eVal2 = eVal3 = 0.; + eVec1 = eVec2 = eVec3 = 0.; + double tt[4][4]; + for (int j = 1; j < 4; ++j) + for (int k = j; k < 4; ++k) tt[j][k] = 0.; + int nStudy = 0; + double denom = 0.; + + // Loop over desired particles in the event. + for (int i = 0; i < event.size(); ++i) + if (event[i].isFinal()) { + if (select > 2 && event[i].isNeutral() ) continue; + if (select == 2 && !event[i].isVisible() ) continue; + ++nStudy; + + // Calculate matrix to be diagonalized. Special cases for speed. + double pNow[4]; + pNow[1] = event[i].px(); + pNow[2] = event[i].py(); + pNow[3] = event[i].pz(); + double p2Now = pNow[1]*pNow[1] + pNow[2]*pNow[2] + pNow[3]*pNow[3]; + double pWeight = 1.; + if (powerInt == 1) pWeight = 1. / sqrt(max(P2MIN, p2Now)); + else if (powerInt == 0) pWeight = pow( max(P2MIN, p2Now), powerMod); + for (int j = 1; j < 4; ++j) + for (int k = j; k < 4; ++k) tt[j][k] += pWeight * pNow[j] * pNow[k]; + denom += pWeight * p2Now; + } + + // Very low multiplicities (0 or 1) not considered. + if (nStudy < NSTUDYMIN) { + if (nFew < TIMESTOPRINT) os << " PYTHIA Error in " << + "Sphericity::analyze: too few particles" << endl; + ++nFew; + return false; + } + + // Normalize tensor to trace = 1. + for (int j = 1; j < 4; ++j) + for (int k = j; k < 4; ++k) tt[j][k] /= denom; + + // Find eigenvalues to matrix (third degree equation). + double qCoef = ( tt[1][1] * tt[2][2] + tt[1][1] * tt[3][3] + + tt[2][2] * tt[3][3] - pow2(tt[1][2]) - pow2(tt[1][3]) + - pow2(tt[2][3]) ) / 3. - 1./9.; + double qCoefRt = sqrt( -qCoef); + double rCoef = -0.5 * ( qCoef + 1./9. + tt[1][1] * pow2(tt[2][3]) + + tt[2][2] * pow2(tt[1][3]) + tt[3][3] * pow2(tt[1][2]) + - tt[1][1] * tt[2][2] * tt[3][3] ) + + tt[1][2] * tt[1][3] * tt[2][3] + 1./27.; + double pTemp = max( min( rCoef / pow3(qCoefRt), 1.), -1.); + double pCoef = cos( acos(pTemp) / 3.); + double pCoefRt = sqrt( 3. * (1. - pow2(pCoef)) ); + eVal1 = 1./3. + qCoefRt * max( 2. * pCoef, pCoefRt - pCoef); + eVal3 = 1./3. + qCoefRt * min( 2. * pCoef, -pCoefRt - pCoef); + eVal2 = 1. - eVal1 - eVal3; + + // Begin find first and last eigenvector. + for (int iVal = 0; iVal < 2; ++iVal) { + double eVal = (iVal == 0) ? eVal1 : eVal3; + + // If all particles are back-to-back then only first axis meaningful. + if (iVal > 1 && eVal2 < EIGENVALUEMIN) { + if (nBack < TIMESTOPRINT) os << " PYTHIA Error in " + "Sphericity::analyze: particles too back-to-back" << endl; + ++nBack; + return false; + } + + // Set up matrix to diagonalize. + double dd[4][4]; + for (int j = 1; j < 4; ++j) { + dd[j][j] = tt[j][j] - eVal; + for (int k = j + 1; k < 4; ++k) { + dd[j][k] = tt[j][k]; + dd[k][j] = tt[j][k]; + } + } + + // Find largest = pivotal element in matrix. + int jMax = 0; + int kMax = 0; + double ddMax = 0.; + for (int j = 1; j < 4; ++j) + for (int k = 1; k < 4; ++k) + if (abs(dd[j][k]) > ddMax) { + jMax = j; + kMax = k; + ddMax = abs(dd[j][k]); + } + + // Subtract one row from the other two; find new largest element. + int jMax2 = 0; + ddMax = 0.; + for (int j = 1; j < 4; ++j) + if ( j != jMax) { + double pivot = dd[j][kMax] / dd[jMax][kMax]; + for (int k = 1; k < 4; ++k) { + dd[j][k] -= pivot * dd[jMax][k]; + if (abs(dd[j][k]) > ddMax) { + jMax2 = j; + ddMax = abs(dd[j][k]); + } + } + } + + // Construct eigenvector. Normalize to unit length; sign irrelevant. + int k1 = kMax + 1; if (k1 > 3) k1 -= 3; + int k2 = kMax + 2; if (k2 > 3) k2 -= 3; + double eVec[4]; + eVec[k1] = -dd[jMax2][k2]; + eVec[k2] = dd[jMax2][k1]; + eVec[kMax] = (dd[jMax][k1] * dd[jMax2][k2] + - dd[jMax][k2] * dd[jMax2][k1]) / dd[jMax][kMax]; + double length = sqrt( pow2(eVec[1]) + pow2(eVec[2]) + + pow2(eVec[3]) ); + + // Store eigenvectors. + if (iVal == 0) eVec1 = Vec4( eVec[1] / length, + eVec[2] / length, eVec[3] / length, 0.); + else eVec3 = Vec4( eVec[1] / length, + eVec[2] / length, eVec[3] / length, 0.); + } + + // Middle eigenvector is orthogonal to the other two; sign irrelevant. + eVec2 = cross3( eVec1, eVec3); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Provide a listing of the info. + +void Sphericity::list(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA Sphericity Listing -------- \n"; + if (powerInt !=2) os << " Nonstandard momentum power = " + << fixed << setprecision(3) << setw(6) << power << "\n"; + os << "\n no lambda e_x e_y e_z \n"; + + // The three eigenvalues and eigenvectors. + os << setprecision(5); + os << " 1" << setw(11) << eVal1 << setw(11) << eVec1.px() + << setw(10) << eVec1.py() << setw(10) << eVec1.pz() << "\n"; + os << " 2" << setw(11) << eVal2 << setw(11) << eVec2.px() + << setw(10) << eVec2.py() << setw(10) << eVec2.pz() << "\n"; + os << " 3" << setw(11) << eVal3 << setw(11) << eVec3.px() + << setw(10) << eVec3.py() << setw(10) << eVec3.pz() << "\n"; + + // Listing finished. + os << "\n -------- End PYTHIA Sphericity Listing ----" << endl; + +} + + +//========================================================================== + +// Thrust class. +// This class finds thrust-related properties of an event. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Minimum number of particles to perform study. +const int Thrust::NSTUDYMIN = 2; + +// Maximum number of times that an error warning will be printed. +const int Thrust::TIMESTOPRINT = 1; + +// Major not too low or not possible to find major axis. +const double Thrust::MAJORMIN = 1e-10; + +//-------------------------------------------------------------------------- + +// Analyze event. + +bool Thrust::analyze(const Event& event, ostream& os) { + + // Initial values and counters zero. + eVal1 = eVal2 = eVal3 = 0.; + eVec1 = eVec2 = eVec3 = 0.; + int nStudy = 0; + vector pOrder; + Vec4 pSum, nRef, pPart, pFull, pMax; + + // Loop over desired particles in the event. + for (int i = 0; i < event.size(); ++i) + if (event[i].isFinal()) { + if (select > 2 && event[i].isNeutral() ) continue; + if (select == 2 && !event[i].isVisible() ) continue; + ++nStudy; + + // Store momenta. Use energy component for absolute momentum. + Vec4 pNow = event[i].p(); + pNow.e(pNow.pAbs()); + pSum += pNow; + pOrder.push_back(pNow); + } + + // Very low multiplicities (0 or 1) not considered. + if (nStudy < NSTUDYMIN) { + if (nFew < TIMESTOPRINT) os << " PYTHIA Error in " << + "Thrust::analyze: too few particles" << endl; + ++nFew; + return false; + } + + // Try all combinations of reference vector orthogonal to two particles. + for (int i1 = 0; i1 < nStudy - 1; ++i1) + for (int i2 = i1 + 1; i2 < nStudy; ++i2) { + nRef = cross3( pOrder[i1], pOrder[i2]); + nRef /= nRef.pAbs(); + pPart = 0.; + + // Add all momenta with sign; two choices for each reference particle. + for (int i = 0; i < nStudy; ++i) if (i != i1 && i != i2) { + if (dot3(pOrder[i], nRef) > 0.) pPart += pOrder[i]; + else pPart -= pOrder[i]; + } + for (int j = 0; j < 4; ++j) { + if (j == 0) pFull = pPart + pOrder[i1] + pOrder[i2]; + else if (j == 1) pFull = pPart + pOrder[i1] - pOrder[i2]; + else if (j == 2) pFull = pPart - pOrder[i1] + pOrder[i2]; + else pFull = pPart - pOrder[i1] - pOrder[i2]; + pFull.e(pFull.pAbs()); + if (pFull.e() > pMax.e()) pMax = pFull; + } + } + + // Maximum gives thrust axis and value. + eVal1 = pMax.e() / pSum.e(); + eVec1 = pMax / pMax.e(); + eVec1.e(0.); + + // Subtract momentum along thrust axis. + double pAbsSum = 0.; + for (int i = 0; i < nStudy; ++i) { + pOrder[i] -= dot3( eVec1, pOrder[i]) * eVec1; + pOrder[i].e(pOrder[i].pAbs()); + pAbsSum += pOrder[i].e(); + } + + // Simpleminded major and minor axes if too little transverse left. + if (pAbsSum < MAJORMIN * pSum.e()) { + if ( abs(eVec1.pz()) > 0.5) eVec2 = Vec4( 1., 0., 0., 0.); + else eVec2 = Vec4( 0., 0., 1., 0.); + eVec2 -= dot3( eVec1, eVec2) * eVec1; + eVec2 /= eVec2.pAbs(); + eVec3 = cross3( eVec1, eVec2); + return true; + } + + // Try all reference vectors orthogonal to one particles. + pMax = 0.; + for (int i1 = 0; i1 < nStudy; ++i1) { + nRef = cross3( pOrder[i1], eVec1); + nRef /= nRef.pAbs(); + pPart = 0.; + + // Add all momenta with sign; two choices for each reference particle. + for (int i = 0; i < nStudy; ++i) if (i != i1) { + if (dot3(pOrder[i], nRef) > 0.) pPart += pOrder[i]; + else pPart -= pOrder[i]; + } + pFull = pPart + pOrder[i1]; + pFull.e(pFull.pAbs()); + if (pFull.e() > pMax.e()) pMax = pFull; + pFull = pPart - pOrder[i1]; + pFull.e(pFull.pAbs()); + if (pFull.e() > pMax.e()) pMax = pFull; + } + + // Maximum gives major axis and value. + eVal2 = pMax.e() / pSum.e(); + eVec2 = pMax / pMax.e(); + eVec2.e(0.); + + // Orthogonal direction gives minor axis, and from there value. + eVec3 = cross3( eVec1, eVec2); + pAbsSum = 0.; + for (int i = 0; i < nStudy; ++i) + pAbsSum += abs( dot3(eVec3, pOrder[i]) ); + eVal3 = pAbsSum / pSum.e(); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Provide a listing of the info. + +void Thrust::list(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA Thrust Listing ------------ \n" + << "\n value e_x e_y e_z \n"; + + // The thrust, major and minor values and related event axes. + os << setprecision(5); + os << " Thr" << setw(11) << eVal1 << setw(11) << eVec1.px() + << setw(10) << eVec1.py() << setw(10) << eVec1.pz() << "\n"; + os << " Maj" << setw(11) << eVal2 << setw(11) << eVec2.px() + << setw(10) << eVec2.py() << setw(10) << eVec2.pz() << "\n"; + os << " Min" << setw(11) << eVal3 << setw(11) << eVec3.px() + << setw(10) << eVec3.py() << setw(10) << eVec3.pz() << "\n"; + + // Listing finished. + os << "\n -------- End PYTHIA Thrust Listing --------" << endl; + +} + +//========================================================================== + +// SingleClusterJet class. +// Simple helper class to ClusterJet for a jet and its contents. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Assign minimal pAbs to avoid division by zero. +const double SingleClusterJet::PABSMIN = 1e-10; + +//-------------------------------------------------------------------------- + +// Distance measures between two SingleClusterJet objects. + +double dist2Fun(int measure, const SingleClusterJet& j1, + const SingleClusterJet& j2) { + + // JADE distance. + if (measure == 2) return 2. * j1.pJet.e() * j2.pJet.e() + * (1. - dot3( j1.pJet, j2.pJet) / (j1.pAbs * j2.pAbs) ); + + // Durham distance. + if (measure == 3) return 2. * pow2( min( j1.pJet.e(), j2.pJet.e() ) ) + * (1. - dot3( j1.pJet, j2.pJet) / (j1.pAbs * j2.pAbs) ); + + // Lund distance; "default". + return (j1.pAbs * j2.pAbs - dot3( j1.pJet, j2.pJet)) + * 2. * j1.pAbs * j2.pAbs / pow2(j1.pAbs + j2.pAbs); + +} + +//========================================================================== + +// ClusterJet class. +// This class performs a jet clustering according to different +// distance measures: Lund, JADE or Durham. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Maximum number of times that an error warning will be printed. +const int ClusterJet::TIMESTOPRINT = 1; + +// Assume the pi+- mass for all particles exceptthe photon in one option. +const double ClusterJet::PIMASS = 0.13957; + +// Assign minimal pAbs to avoid division by zero. +const double ClusterJet::PABSMIN = 1e-10; + +// Initial pT/m preclustering scale as fraction of clustering one. +const double ClusterJet::PRECLUSTERFRAC = 0.1; + +// Step with which pT/m is reduced if preclustering gives too few jets. +const double ClusterJet::PRECLUSTERSTEP = 0.8; + +//-------------------------------------------------------------------------- + +// Analyze event. + +bool ClusterJet::analyze(const Event& event, double yScaleIn, + double pTscaleIn, int nJetMinIn, int nJetMaxIn, ostream& os) { + + // Input values. Initial values zero. + yScale = yScaleIn; + pTscale = pTscaleIn; + nJetMin = nJetMinIn; + nJetMax = nJetMaxIn; + particles.resize(0); + jets.resize(0); + Vec4 pSum; + distances.clear(); + + // Loop over desired particles in the event. + for (int i = 0; i < event.size(); ++i) + if (event[i].isFinal()) { + if (select > 2 && event[i].isNeutral() ) continue; + if (select == 2 && !event[i].isVisible() ) continue; + + // Store them, possibly with modified mass => new energy. + Vec4 pTemp = event[i].p(); + if (massSet == 0 || massSet == 1) { + double mTemp = (massSet == 0 || event[i].id() == 22) + ? 0. : PIMASS; + double eTemp = sqrt(pTemp.pAbs2() + pow2(mTemp)); + pTemp.e(eTemp); + } + particles.push_back( SingleClusterJet(pTemp, i) ); + pSum += pTemp; + } + + // Very low multiplicities not considered. + nParticles = particles.size(); + if (nParticles < nJetMin) { + if (nFew < TIMESTOPRINT) os << " PYTHIA Error in " << + "ClusterJet::analyze: too few particles" << endl; + ++nFew; + return false; + } + + // Squared maximum distance in GeV^2 for joining. + double p2Sum = pSum.m2Calc(); + dist2Join = max( yScale * p2Sum, pow2(pTscale)); + dist2BigMin = 2. * max( dist2Join, p2Sum); + + // Do preclustering if desired and possible. + if (doPrecluster && nParticles > nJetMin + 2) { + precluster(); + if (doReassign) reassign(); + } + + // If no preclustering: each particle is a starting jet. + else for (int i = 0; i < nParticles; ++i) { + jets.push_back( SingleClusterJet(particles[i]) ); + particles[i].daughter = i; + } + + // Begin iteration towards fewer jets. + for ( ; ; ) { + + // Find the two closest jets. + double dist2Min = dist2BigMin; + int jMin = 0; + int kMin = 0; + for (int j = 0; j < int(jets.size()) - 1; ++j) + for (int k = j + 1; k < int(jets.size()); ++k) { + double dist2 = dist2Fun( measure, jets[j], jets[k]); + if (dist2 < dist2Min) { + dist2Min = dist2; + jMin = j; + kMin = k; + } + } + + // Stop if no pair below cut and not more jets than allowed. + if ( dist2Min > dist2Join + && (nJetMax < nJetMin || int(jets.size()) <= nJetMax) ) break; + + // Stop if reached minimum allowed number of jets. Else continue. + if (int(jets.size()) <= nJetMin) break; + + // Join two closest jets. + jets[jMin].pJet += jets[kMin].pJet; + jets[jMin].pAbs = max( PABSMIN, jets[jMin].pJet.pAbs()); + jets[jMin].multiplicity += jets[kMin].multiplicity; + for (int i = 0; i < nParticles; ++i) + if (particles[i].daughter == kMin) particles[i].daughter = jMin; + + // Save the last 5 distances. + distances.push_front(dist2Min); + if (distances.size() > 5) distances.pop_back(); + + // Move up last jet to empty slot to shrink list. + jets[kMin] = jets.back(); + jets.pop_back(); + int iEnd = jets.size(); + for (int i = 0; i < nParticles; ++i) + if (particles[i].daughter == iEnd) particles[i].daughter = kMin; + + // Do reassignments of particles to nearest jet if desired. + if (doReassign) reassign(); + } + + // Order jets in decreasing energy. + for (int j = 0; j < int(jets.size()) - 1; ++j) + for (int k = int(jets.size()) - 1; k > j; --k) + if (jets[k].pJet.e() > jets[k-1].pJet.e()) { + swap( jets[k], jets[k-1]); + for (int i = 0; i < nParticles; ++i) { + if (particles[i].daughter == k) particles[i].daughter = k-1; + else if (particles[i].daughter == k-1) particles[i].daughter = k; + } + } + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Precluster nearby particles to save computer time. + +void ClusterJet::precluster() { + + // Begin iteration over preclustering scale. + distPre = PRECLUSTERFRAC * sqrt(dist2Join) / PRECLUSTERSTEP; + for ( ; ;) { + distPre *= PRECLUSTERSTEP; + dist2Pre = pow2(distPre); + for (int i = 0; i < nParticles; ++i) { + particles[i].daughter = -1; + particles[i].isAssigned = false; + } + + // Sum up low-momentum region. Jet if enough momentum. + Vec4 pCentral; + int multCentral = 0; + for (int i = 0; i < nParticles; ++i) + if (particles[i].pAbs < 2. * distPre) { + pCentral += particles[i].pJet; + multCentral += particles[i].multiplicity; + particles[i].isAssigned = true; + } + if (pCentral.pAbs() > 2. * distPre) { + jets.push_back( SingleClusterJet(pCentral) ); + jets.back().multiplicity = multCentral; + for (int i = 0; i < nParticles; ++i) + if (particles[i].isAssigned) particles[i].daughter = 0; + } + + // Find fastest remaining particle until none left. + for ( ; ;) { + int iMax = -1; + double pMax = 0.; + for (int i = 0; i < nParticles; ++i) + if ( !particles[i].isAssigned && particles[i].pAbs > pMax) { + iMax = i; + pMax = particles[i].pAbs; + } + if (iMax == -1) break; + + // Sum up precluster around it according to distance function. + Vec4 pPre; + int multPre = 0; + int nRemain = 0; + for (int i = 0; i < nParticles; ++i) + if ( !particles[i].isAssigned) { + double dist2 = dist2Fun( measure, particles[iMax], + particles[i]); + if (dist2 < dist2Pre) { + pPre += particles[i].pJet; + ++multPre; + particles[i].isAssigned = true; + particles[i].daughter = jets.size(); + } else ++nRemain; + } + jets.push_back( SingleClusterJet(pPre) ); + jets.back().multiplicity = multPre; + + // Decide whether sensible starting configuration or iterate. + if (int(jets.size()) + nRemain < nJetMin) break; + } + if (int(jets.size()) >= nJetMin) break; + } + +} + +//-------------------------------------------------------------------------- + +// Reassign particles to nearest jet to correct misclustering. + +void ClusterJet::reassign() { + + // Reset clustered momenta. + for (int j = 0; j < int(jets.size()); ++j) { + jets[j].pTemp = 0.; + jets[j].multiplicity = 0; + } + + // Loop through particles to find closest jet. + for (int i = 0; i < nParticles; ++i) { + particles[i].daughter = -1; + double dist2Min = dist2BigMin; + int jMin = 0; + for (int j = 0; j < int(jets.size()); ++j) { + double dist2 = dist2Fun( measure, particles[i], jets[j]); + if (dist2 < dist2Min) { + dist2Min = dist2; + jMin = j; + } + } + jets[jMin].pTemp += particles[i].pJet; + ++jets[jMin].multiplicity; + particles[i].daughter = jMin; + } + + // Replace old by new jet momenta. + for (int j = 0; j < int(jets.size()); ++j) { + jets[j].pJet = jets[j].pTemp; + jets[j].pAbs = max( PABSMIN, jets[j].pJet.pAbs()); + } + + // Check that no empty clusters after reassignments. + for ( ; ; ) { + + // If no empty jets then done. + int jEmpty = -1; + for (int j = 0; j < int(jets.size()); ++j) + if (jets[j].multiplicity == 0) jEmpty = j; + if (jEmpty == -1) return; + + // Find particle assigned to jet with largest distance to it. + int iSplit = -1; + double dist2Max = 0.; + for (int i = 0; i < nParticles; ++i) { + int j = particles[i].daughter; + double dist2 = dist2Fun( measure, particles[i], jets[j]); + if (dist2 > dist2Max) { + iSplit = i; + dist2Max = dist2; + } + } + + // Let this particle form new jet and subtract off from existing. + int jSplit = particles[iSplit].daughter; + jets[jEmpty] = SingleClusterJet( particles[iSplit].pJet ); + jets[jSplit].pJet -= particles[iSplit].pJet; + jets[jSplit].pAbs = max( PABSMIN,jets[jSplit].pJet.pAbs()); + particles[iSplit].daughter = jEmpty; + --jets[jSplit].multiplicity; + } + +} + +//-------------------------------------------------------------------------- + +// Provide a listing of the info. + +void ClusterJet::list(ostream& os) const { + + // Header. + string method = (measure == 1) ? "Lund pT" + : ( (measure == 2) ? "JADE m" : "Durham kT" ) ; + os << "\n -------- PYTHIA ClusterJet Listing, " << setw(9) << method + << " =" << fixed << setprecision(3) << setw(7) << sqrt(dist2Join) + << " GeV --- \n \n no mult p_x p_y p_z " + << " e m \n"; + + // The jets. + for (int i = 0; i < int(jets.size()); ++i) { + os << setw(4) << i << setw(6) << jets[i].multiplicity << setw(11) + << jets[i].pJet.px() << setw(11) << jets[i].pJet.py() + << setw(11) << jets[i].pJet.pz() << setw(11) + << jets[i].pJet.e() << setw(11) << jets[i].pJet.mCalc() + << "\n"; + } + + // Listing finished. + os << "\n -------- End PYTHIA ClusterJet Listing ---------------" + << "--------" << endl; +} + +//========================================================================== + +// CellJet class. +// This class performs a cone jet search in (eta, phi, E_T) space. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Minimum number of particles to perform study. +const int CellJet::TIMESTOPRINT = 1; + +//-------------------------------------------------------------------------- + +// Analyze event. + +bool CellJet::analyze(const Event& event, double eTjetMinIn, + double coneRadiusIn, double eTseedIn, ostream& ) { + + // Input values. Initial values zero. + eTjetMin = eTjetMinIn; + coneRadius = coneRadiusIn; + eTseed = eTseedIn; + jets.resize(0); + vector cells; + + // Loop over desired particles in the event. + for (int i = 0; i < event.size(); ++i) + if (event[i].isFinal()) { + if (select > 2 && event[i].isNeutral() ) continue; + if (select == 2 && !event[i].isVisible() ) continue; + + // Find particle position in (eta, phi, pT) space. + double etaNow = event[i].eta(); + if (abs(etaNow) > etaMax) continue; + double phiNow = event[i].phi(); + double pTnow = event[i].pT(); + int iEtaNow = max(1, min( nEta, 1 + int(nEta * 0.5 + * (1. + etaNow / etaMax) ) ) ); + int iPhiNow = max(1, min( nPhi, 1 + int(nPhi * 0.5 + * (1. + phiNow / M_PI) ) ) ); + int iCell = nPhi * iEtaNow + iPhiNow; + + // Add pT to cell already hit or book a new cell. + bool found = false; + for (int j = 0; j < int(cells.size()); ++j) { + if (iCell == cells[j].iCell) { + found = true; + ++cells[j].multiplicity; + cells[j].eTcell += pTnow; + continue; + } + } + if (!found) { + double etaCell = (etaMax / nEta) * (2 * iEtaNow - 1 - nEta); + double phiCell = (M_PI / nPhi) * (2 * iPhiNow - 1 - nPhi); + cells.push_back( SingleCell( iCell, etaCell, phiCell, pTnow, 1) ); + } + } + + // Smear true bin content by calorimeter resolution. + if (smear > 0 && rndmPtr > 0) + for (int j = 0; j < int(cells.size()); ++j) { + double eTeConv = (smear < 2) ? 1. : cosh( cells[j].etaCell ); + double eBef = cells[j].eTcell * eTeConv; + double eAft = 0.; + do eAft = eBef + resolution * sqrt(eBef) * rndmPtr->gauss(); + while (eAft < 0 || eAft > upperCut * eBef); + cells[j].eTcell = eAft / eTeConv; + } + + // Remove cells below threshold for seed or for use at all. + for (int j = 0; j < int(cells.size()); ++j) { + if (cells[j].eTcell < eTseed) cells[j].canBeSeed = false; + if (cells[j].eTcell < threshold) cells[j].isUsed = true; + } + + // Find seed cell: the one with highest pT of not yet probed ones. + for ( ; ; ) { + int jMax = 0; + double eTmax = 0.; + for (int j = 0; j < int(cells.size()); ++j) + if (cells[j].canBeSeed && cells[j].eTcell > eTmax) { + jMax = j; + eTmax = cells[j].eTcell; + } + + // If too small cell eT then done, else start new trial jet. + if (eTmax < eTseed) break; + double etaCenterNow = cells[jMax].etaCell; + double phiCenterNow = cells[jMax].phiCell; + double eTjetNow = 0.; + + // Sum up unused cells within required distance of seed. + for (int j = 0; j < int(cells.size()); ++j) { + if (cells[j].isUsed) continue; + double dEta = abs( cells[j].etaCell - etaCenterNow ); + if (dEta > coneRadius) continue; + double dPhi = abs( cells[j].phiCell - phiCenterNow ); + if (dPhi > M_PI) dPhi = 2. * M_PI - dPhi; + if (dPhi > coneRadius) continue; + if (pow2(dEta) + pow2(dPhi) > pow2(coneRadius)) continue; + cells[j].isAssigned = true; + eTjetNow += cells[j].eTcell; + } + + // Reject cluster below minimum ET. + if (eTjetNow < eTjetMin) { + cells[jMax].canBeSeed = false; + for (int j = 0; j < int(cells.size()); ++j) + cells[j].isAssigned = false; + + // Else find new jet properties. + } else { + double etaWeightedNow = 0.; + double phiWeightedNow = 0.; + int multiplicityNow = 0; + Vec4 pMassiveNow; + for (int j = 0; j < int(cells.size()); ++j) + if (cells[j].isAssigned) { + cells[j].canBeSeed = false; + cells[j].isUsed = true; + cells[j].isAssigned = false; + etaWeightedNow += cells[j].eTcell * cells[j].etaCell; + double phiCell = cells[j].phiCell; + if (abs(phiCell - phiCenterNow) > M_PI) + phiCell += (phiCenterNow > 0.) ? 2. * M_PI : -2. * M_PI; + phiWeightedNow += cells[j].eTcell * phiCell; + multiplicityNow += cells[j].multiplicity; + pMassiveNow += cells[j].eTcell * Vec4( + cos(cells[j].phiCell), sin(cells[j].phiCell), + sinh(cells[j].etaCell), cosh(cells[j].etaCell) ); + } + etaWeightedNow /= eTjetNow; + phiWeightedNow /= eTjetNow; + + // Bookkeep new jet, in decreasing ET order. + jets.push_back( SingleCellJet( eTjetNow, etaCenterNow, phiCenterNow, + etaWeightedNow, phiWeightedNow, multiplicityNow, pMassiveNow) ); + for (int i = int(jets.size()) - 1; i > 0; --i) { + if (jets[i-1].eTjet > jets[i].eTjet) break; + swap( jets[i-1], jets[i]); + } + } + } + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Provide a listing of the info. + +void CellJet::list(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA CellJet Listing, eTjetMin = " + << fixed << setprecision(3) << setw(8) << eTjetMin + << ", coneRadius = " << setw(5) << coneRadius + << " ------------------------------ \n \n no " + << " eTjet etaCtr phiCtr etaWt phiWt mult p_x" + << " p_y p_z e m \n"; + + // The jets. + for (int i = 0; i < int(jets.size()); ++i) { + os << setw(4) << i << setw(10) << jets[i].eTjet << setw(8) + << jets[i].etaCenter << setw(8) << jets[i].phiCenter << setw(8) + << jets[i].etaWeighted << setw(8) << jets[i].phiWeighted + << setw(5) << jets[i].multiplicity << setw(11) + << jets[i].pMassive.px() << setw(11) << jets[i].pMassive.py() + << setw(11) << jets[i].pMassive.pz() << setw(11) + << jets[i].pMassive.e() << setw(11) + << jets[i].pMassive.mCalc() << "\n"; + } + + // Listing finished. + os << "\n -------- End PYTHIA CellJet Listing ------------------" + << "-------------------------------------------------" + << endl; +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/Basics.cxx b/PYTHIA8/pythia8140/src/Basics.cxx new file mode 100644 index 00000000000..f8cfa922ba5 --- /dev/null +++ b/PYTHIA8/pythia8140/src/Basics.cxx @@ -0,0 +1,1214 @@ +// Basics.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the Rndm, Vec4, +// RotBstMatrix and Hist classes, and some related global functions. + +#include "Basics.h" + +// Access time information. +#include + +namespace Pythia8 { + +//========================================================================== + +// Rndm class. +// This class handles random number generation according to the +// Marsaglia-Zaman-Tsang algorithm + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// The default seed, i.e. the Marsaglia-Zaman random number sequence. +const int Rndm::DEFAULTSEED = 19780503; + +//-------------------------------------------------------------------------- + +// Method to pass in pointer for external random number generation. + +bool Rndm::rndmEnginePtr( RndmEngine* rndmEngPtrIn) { + + // Save pointer. + if (rndmEngPtrIn == 0) return false; + rndmEngPtr = rndmEngPtrIn; + useExternalRndm = true; + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Initialize, normally at construction or in first call. + +void Rndm::init(int seedIn) { + + // Pick seed in convenient way. Assure it to be non-negative. + int seed = seedIn; + if (seedIn < 0) seed = DEFAULTSEED; + else if (seedIn == 0) seed = int(time(0)); + if (seed < 0) seed = -seed; + + // Unpack seed. + int ij = (seed/30082) % 31329; + int kl = seed % 30082; + int i = (ij/177) % 177 + 2; + int j = ij % 177 + 2; + int k = (kl/169) % 178 + 1; + int l = kl % 169; + + // Initialize random number array. + for (int ii = 0; ii < 97; ++ii) { + double s = 0.; + double t = 0.5; + for (int jj = 0; jj < 48; ++jj) { + int m = (( (i*j)%179 )*k) % 179; + i = j; + j = k; + k = m; + l = (53*l+1) % 169; + if ( (l*m) % 64 >= 32) s += t; + t *= 0.5; + } + u[ii] = s; + } + + // Initialize other variables. + double twom24 = 1.; + for (int i24 = 0; i24 < 24; ++i24) twom24 *= 0.5; + c = 362436. * twom24; + cd = 7654321. * twom24; + cm = 16777213. * twom24; + i97 = 96; + j97 = 32; + + // Finished. + initRndm = true; + seedSave = seed; + sequence = 0; + +} + +//-------------------------------------------------------------------------- + +// Generate next random number uniformly between 0 and 1. + +double Rndm::flat() { + + // Use external random number generator if such has been linked. + if (useExternalRndm) return rndmEngPtr->flat(); + + // Ensure that already initialized. + if (!initRndm) init(DEFAULTSEED); + + // Find next random number and update saved state. + ++sequence; + double uni; + do { + uni = u[i97] - u[j97]; + if (uni < 0.) uni += 1.; + u[i97] = uni; + if (--i97 < 0) i97 = 96; + if (--j97 < 0) j97 = 96; + c -= cd; + if (c < 0.) c += cm; + uni -= c; + if(uni < 0.) uni += 1.; + } while (uni <= 0. || uni >= 1.); + return uni; + +} + +//-------------------------------------------------------------------------- + +// Pick one option among vector of (positive) probabilities. + +int Rndm::pick(const vector& prob) { + + double work = 0.; + for (int i = 0; i < int(prob.size()); ++i) work += prob[i]; + work *= flat(); + int index = -1; + do work -= prob[++index]; + while (work > 0. && index < int(prob.size())); + return index; + +} + +//-------------------------------------------------------------------------- + +// Save current state of the random number generator to a binary file. + +bool Rndm::dumpState(string fileName) { + + // Open file as output stream. + const char* fn = fileName.c_str(); + ofstream ofs(fn, ios::binary); + + if (!ofs.good()) { + cout << " Rndm::dumpState: could not open output file" << endl; + return false; + } + + // Write the state of the generator on the file. + ofs.write((char *) &seedSave, sizeof(int)); + ofs.write((char *) &sequence, sizeof(long)); + ofs.write((char *) &i97, sizeof(int)); + ofs.write((char *) &j97, sizeof(int)); + ofs.write((char *) &c, sizeof(double)); + ofs.write((char *) &cd, sizeof(double)); + ofs.write((char *) &cm, sizeof(double)); + ofs.write((char *) &u, sizeof(double) * 97); + + // Write confirmation on cout. + cout << " PYTHIA Rndm::dumpState: seed = " << seedSave + << ", sequence no = " << sequence << endl; + return true; + +} + +//-------------------------------------------------------------------------- + +// Read in the state of the random number generator from a binary file. + +bool Rndm::readState(string fileName) { + + // Open file as input stream. + const char* fn = fileName.c_str(); + ifstream ifs(fn, ios::binary); + + if (!ifs.good()) { + cout << " Rndm::readState: could not open input file" << endl; + return false; + } + + // Read the state of the generator from the file. + ifs.read((char *) &seedSave, sizeof(int)); + ifs.read((char *) &sequence, sizeof(long)); + ifs.read((char *) &i97, sizeof(int)); + ifs.read((char *) &j97, sizeof(int)); + ifs.read((char *) &c, sizeof(double)); + ifs.read((char *) &cd, sizeof(double)); + ifs.read((char *) &cm, sizeof(double)); + ifs.read((char *) &u, sizeof(double) *97); + + // Write confirmation on cout. + cout << " PYTHIA Rndm::readState: seed " << seedSave + << ", sequence no = " << sequence << endl; + return true; + +} + +//========================================================================== + +// Vec4 class. +// This class implements four-vectors, in energy-momentum space. +// (But could also be used to hold space-time four-vectors.) + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Small number to avoid division by zero. +const double Vec4::TINY = 1e-20; + +//-------------------------------------------------------------------------- + +// Rotation (simple). + +void Vec4::rot(double thetaIn, double phiIn) { + + double cthe = cos(thetaIn); + double sthe = sin(thetaIn); + double cphi = cos(phiIn); + double sphi = sin(phiIn); + double tmpx = cthe * cphi * xx - sphi * yy + sthe * cphi * zz; + double tmpy = cthe * sphi * xx + cphi * yy + sthe * sphi * zz; + double tmpz = -sthe * xx + cthe * zz; + xx = tmpx; + yy = tmpy; + zz = tmpz; + +} + +//-------------------------------------------------------------------------- + +// Azimuthal rotation phi around an arbitrary axis (nz, ny, nz). + +void Vec4::rotaxis(double phiIn, double nx, double ny, double nz) { + + double norm = 1./sqrt(nx*nx + ny*ny + nz*nz); + nx *= norm; + ny *= norm; + nz *= norm; + double cphi = cos(phiIn); + double sphi = sin(phiIn); + double comb = (nx * xx + ny * yy + nz * zz) * (1. - cphi); + double tmpx = cphi * xx + comb * nx + sphi * (ny * zz - nz * yy); + double tmpy = cphi * yy + comb * ny + sphi * (nz * xx - nx * zz); + double tmpz = cphi * zz + comb * nz + sphi * (nx * yy - ny * xx); + xx = tmpx; + yy = tmpy; + zz = tmpz; + +} + +//-------------------------------------------------------------------------- + +// Azimuthal rotation phi around an arbitrary (3-vector component of) axis. + +void Vec4::rotaxis(double phiIn, const Vec4& n) { + + double nx = n.xx; + double ny = n.yy; + double nz = n.zz; + double norm = 1./sqrt(nx*nx + ny*ny + nz*nz); + nx *= norm; + ny *=norm; + nz *=norm; + double cphi = cos(phiIn); + double sphi = sin(phiIn); + double comb = (nx * xx + ny * yy + nz * zz) * (1. - cphi); + double tmpx = cphi * xx + comb * nx + sphi * (ny * zz - nz * yy); + double tmpy = cphi * yy + comb * ny + sphi * (nz * xx - nx * zz); + double tmpz = cphi * zz + comb * nz + sphi * (nx * yy - ny * xx); + xx = tmpx; + yy = tmpy; + zz = tmpz; + +} + +//-------------------------------------------------------------------------- + +// Boost (simple). + +void Vec4::bst(double betaX, double betaY, double betaZ) { + + double beta2 = betaX*betaX + betaY*betaY + betaZ*betaZ; + double gamma = 1. / sqrt(1. - beta2); + double prod1 = betaX * xx + betaY * yy + betaZ * zz; + double prod2 = gamma * (gamma * prod1 / (1. + gamma) + tt); + xx += prod2 * betaX; + yy += prod2 * betaY; + zz += prod2 * betaZ; + tt = gamma * (tt + prod1); + +} + +//-------------------------------------------------------------------------- + +// Boost (simple, given gamma). + +void Vec4::bst(double betaX, double betaY, double betaZ, double gamma) { + + double prod1 = betaX * xx + betaY * yy + betaZ * zz; + double prod2 = gamma * (gamma * prod1 / (1. + gamma) + tt); + xx += prod2 * betaX; + yy += prod2 * betaY; + zz += prod2 * betaZ; + tt = gamma * (tt + prod1); + +} + +//-------------------------------------------------------------------------- + +// Boost given by a Vec4 p. + +void Vec4::bst(const Vec4& pIn) { + + double betaX = pIn.xx / pIn.tt; + double betaY = pIn.yy / pIn.tt; + double betaZ = pIn.zz / pIn.tt; + double beta2 = betaX*betaX + betaY*betaY + betaZ*betaZ; + double gamma = 1. / sqrt(1. - beta2); + double prod1 = betaX * xx + betaY * yy + betaZ * zz; + double prod2 = gamma * (gamma * prod1 / (1. + gamma) + tt); + xx += prod2 * betaX; + yy += prod2 * betaY; + zz += prod2 * betaZ; + tt = gamma * (tt + prod1); + +} + +//-------------------------------------------------------------------------- + +// Boost given by a Vec4 p and double m. + +void Vec4::bst(const Vec4& pIn, double mIn) { + + double betaX = pIn.xx / pIn.tt; + double betaY = pIn.yy / pIn.tt; + double betaZ = pIn.zz / pIn.tt; + double gamma = pIn.tt / mIn; + double prod1 = betaX * xx + betaY * yy + betaZ * zz; + double prod2 = gamma * (gamma * prod1 / (1. + gamma) + tt); + xx += prod2 * betaX; + yy += prod2 * betaY; + zz += prod2 * betaZ; + tt = gamma * (tt + prod1); + +} + +//-------------------------------------------------------------------------- + +// Boost given by a Vec4 p; boost in opposite direction. + +void Vec4::bstback(const Vec4& pIn) { + + double betaX = -pIn.xx / pIn.tt; + double betaY = -pIn.yy / pIn.tt; + double betaZ = -pIn.zz / pIn.tt; + double beta2 = betaX*betaX + betaY*betaY + betaZ*betaZ; + double gamma = 1. / sqrt(1. - beta2); + double prod1 = betaX * xx + betaY * yy + betaZ * zz; + double prod2 = gamma * (gamma * prod1 / (1. + gamma) + tt); + xx += prod2 * betaX; + yy += prod2 * betaY; + zz += prod2 * betaZ; + tt = gamma * (tt + prod1); + +} + +//-------------------------------------------------------------------------- + +// Boost given by a Vec4 p and double m; boost in opposite direction. + +void Vec4::bstback(const Vec4& pIn, double mIn) { + + double betaX = -pIn.xx / pIn.tt; + double betaY = -pIn.yy / pIn.tt; + double betaZ = -pIn.zz / pIn.tt; + double gamma = pIn.tt / mIn; + double prod1 = betaX * xx + betaY * yy + betaZ * zz; + double prod2 = gamma * (gamma * prod1 / (1. + gamma) + tt); + xx += prod2 * betaX; + yy += prod2 * betaY; + zz += prod2 * betaZ; + tt = gamma * (tt + prod1); + +} + +//-------------------------------------------------------------------------- + +// Arbitrary combination of rotations and boosts defined by 4 * 4 matrix. + +void Vec4::rotbst(const RotBstMatrix& M) { + + double x = xx; double y = yy; double z = zz; double t = tt; + tt = M.M[0][0] * t + M.M[0][1] * x + M.M[0][2] * y + M.M[0][3] * z; + xx = M.M[1][0] * t + M.M[1][1] * x + M.M[1][2] * y + M.M[1][3] * z; + yy = M.M[2][0] * t + M.M[2][1] * x + M.M[2][2] * y + M.M[2][3] * z; + zz = M.M[3][0] * t + M.M[3][1] * x + M.M[3][2] * y + M.M[3][3] * z; + +} + +//-------------------------------------------------------------------------- + +// The invariant mass of two four-vectors. + +double m(const Vec4& v1, const Vec4& v2) { + double m2 = pow2(v1.tt + v2.tt) - pow2(v1.xx + v2.xx) + - pow2(v1.yy + v2.yy) - pow2(v1.zz + v2.zz); + return (m2 > 0.) ? sqrt(m2) : 0.; +} + +//-------------------------------------------------------------------------- + +// The squared invariant mass of two four-vectors. + +double m2(const Vec4& v1, const Vec4& v2) { + double m2 = pow2(v1.tt + v2.tt) - pow2(v1.xx + v2.xx) + - pow2(v1.yy + v2.yy) - pow2(v1.zz + v2.zz); + return m2; +} + +//-------------------------------------------------------------------------- + +// The scalar product of two three-vectors. + +double dot3(const Vec4& v1, const Vec4& v2) { + return v1.xx*v2.xx + v1.yy*v2.yy + v1.zz*v2.zz; +} + +//-------------------------------------------------------------------------- + +// The cross product of two three-vectors. + +Vec4 cross3(const Vec4& v1, const Vec4& v2) { + Vec4 v; + v.xx = v1.yy * v2.zz - v1.zz * v2.yy; + v.yy = v1.zz * v2.xx - v1.xx * v2.zz; + v.zz = v1.xx * v2.yy - v1.yy * v2.xx; return v; +} + +//-------------------------------------------------------------------------- + +// Opening angle between two three-vectors. + +double theta(const Vec4& v1, const Vec4& v2) { + double cthe = (v1.xx * v2.xx + v1.yy * v2.yy + v1.zz * v2.zz) + / sqrt( (v1.xx*v1.xx + v1.yy*v1.yy + v1.zz*v1.zz) + * (v2.xx*v2.xx + v2.yy*v2.yy + v2.zz*v2.zz) ); + cthe = max(-1., min(1., cthe)); + return acos(cthe); +} + +//-------------------------------------------------------------------------- + +// Cosine of the opening angle between two three-vectors. + +double costheta(const Vec4& v1, const Vec4& v2) { + double cthe = (v1.xx * v2.xx + v1.yy * v2.yy + v1.zz * v2.zz) + / sqrt( (v1.xx*v1.xx + v1.yy*v1.yy + v1.zz*v1.zz) + * (v2.xx*v2.xx + v2.yy*v2.yy + v2.zz*v2.zz) ); + cthe = max(-1., min(1., cthe)); + return cthe; +} + +//-------------------------------------------------------------------------- + +// Azimuthal angle between two three-vectors. + +double phi(const Vec4& v1, const Vec4& v2) { + double cphi = (v1.xx * v2.xx + v1.yy * v2.yy) / sqrt( max( Vec4::TINY, + (v1.xx*v1.xx + v1.yy*v1.yy) * (v2.xx*v2.xx + v2.yy*v2.yy) )); + cphi = max(-1., min(1., cphi)); + return acos(cphi); +} + +//-------------------------------------------------------------------------- + +// Cosine of the azimuthal angle between two three-vectors. + +double cosphi(const Vec4& v1, const Vec4& v2) { + double cphi = (v1.xx * v2.xx + v1.yy * v2.yy) / sqrt( max( Vec4::TINY, + (v1.xx*v1.xx + v1.yy*v1.yy) * (v2.xx*v2.xx + v2.yy*v2.yy) )); + cphi = max(-1., min(1., cphi)); + return cphi; +} + +//-------------------------------------------------------------------------- + +// Azimuthal angle between two three-vectors around a third. + +double phi(const Vec4& v1, const Vec4& v2, const Vec4& n) { + double nx = n.xx; double ny = n.yy; double nz = n.zz; + double norm = 1. / sqrt(nx*nx + ny*ny + nz*nz); + nx *= norm; ny *=norm; nz *=norm; + double v1s = v1.xx * v1.xx + v1.yy * v1.yy + v1.zz * v1.zz; + double v2s = v2.xx * v2.xx + v2.yy * v2.yy + v2.zz * v2.zz; + double v1v2 = v1.xx * v2.xx + v1.yy * v2.yy + v1.zz * v2.zz; + double v1n = v1.xx * nx + v1.yy * ny + v1.zz * nz; + double v2n = v2.xx * nx + v2.yy * ny + v2.zz * nz; + double cphi = (v1v2 - v1n * v2n) / sqrt( max( Vec4::TINY, + (v1s - v1n*v1n) * (v2s - v2n*v2n) )); + cphi = max(-1., min(1., cphi)); + return acos(cphi); +} + +//-------------------------------------------------------------------------- + +// Cosine of the azimuthal angle between two three-vectors around a third. + +double cosphi(const Vec4& v1, const Vec4& v2, const Vec4& n) { + double nx = n.xx; double ny = n.yy; double nz = n.zz; + double norm = 1. / sqrt(nx*nx + ny*ny + nz*nz); + nx *= norm; ny *=norm; nz *=norm; + double v1s = v1.xx * v1.xx + v1.yy * v1.yy + v1.zz * v1.zz; + double v2s = v2.xx * v2.xx + v2.yy * v2.yy + v2.zz * v2.zz; + double v1v2 = v1.xx * v2.xx + v1.yy * v2.yy + v1.zz * v2.zz; + double v1n = v1.xx * nx + v1.yy * ny + v1.zz * nz; + double v2n = v2.xx * nx + v2.yy * ny + v2.zz * nz; + double cphi = (v1v2 - v1n * v2n) / sqrt( max( Vec4::TINY, + (v1s - v1n*v1n) * (v2s - v2n*v2n) )); + cphi = max(-1., min(1., cphi)); + return cphi; +} + +//-------------------------------------------------------------------------- + +// Print a four-vector: also operator overloading with friend. + +ostream& operator<<(ostream& os, const Vec4& v) { + os << fixed << setprecision(3) << " " << setw(9) << v.xx << " " + << setw(9) << v.yy << " " << setw(9) << v.zz << " " << setw(9) + << v.tt << " (" << setw(9) << v.mCalc() << ")\n"; + return os; +} + +//========================================================================== + +// RotBstMatrix class. +// This class implements 4 * 4 matrices that encode an arbitrary combination +// of rotations and boosts, that can be applied to Vec4 four-vectors. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Small number to avoid division by zero. +const double RotBstMatrix::TINY = 1e-20; + +//-------------------------------------------------------------------------- + +// Rotate by polar angle theta and azimuthal angle phi. + +void RotBstMatrix::rot(double theta, double phi) { + + // Set up rotation matrix. + double cthe = cos(theta); + double sthe = sin(theta); + double cphi = cos(phi); + double sphi = sin(phi); + double Mrot[4][4] = { + {1., 0., 0., 0.}, + {0., cthe * cphi, - sphi, sthe * cphi}, + {0., cthe * sphi, cphi, sthe * sphi}, + {0., -sthe, 0., cthe } }; + + // Rotate current matrix accordingly. + double Mtmp[4][4]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + Mtmp[i][j] = M[i][j]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = Mrot[i][0] * Mtmp[0][j] + Mrot[i][1] * Mtmp[1][j] + + Mrot[i][2] * Mtmp[2][j] + Mrot[i][3] * Mtmp[3][j]; + +} + +//-------------------------------------------------------------------------- + +// Rotate so that vector originally along z axis becomes parallel with p. + +void RotBstMatrix::rot(const Vec4& p) { + + double theta = p.theta(); + double phi = p.phi(); + rot(0., -phi); + rot(theta, phi); + +} + +//-------------------------------------------------------------------------- + +// Boost with velocity vector (betaX, betaY, betaZ). + +void RotBstMatrix::bst(double betaX, double betaY, double betaZ) { + + // Set up boost matrix. + double gm = 1. / sqrt( max( TINY, 1. - betaX*betaX - betaY*betaY + - betaZ*betaZ ) ); + double gf = gm*gm / (1. + gm); + double Mbst[4][4] = { + { gm, gm*betaX, gm*betaY, gm*betaZ }, + { gm*betaX, 1. + gf*betaX*betaX, gf*betaX*betaY, gf*betaX*betaZ }, + { gm*betaY, gf*betaY*betaX, 1. + gf*betaY*betaY, gf*betaY*betaZ }, + { gm*betaZ, gf*betaZ*betaX, gf*betaZ*betaY, 1. + gf*betaZ*betaZ } }; + + // Boost current matrix correspondingly. + double Mtmp[4][4]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + Mtmp[i][j] = M[i][j]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = Mbst[i][0] * Mtmp[0][j] + Mbst[i][1] * Mtmp[1][j] + + Mbst[i][2] * Mtmp[2][j] + Mbst[i][3] * Mtmp[3][j]; + +} + +//-------------------------------------------------------------------------- + +// Boost so that vector originally at rest obtains same velocity as p. + +void RotBstMatrix::bst(const Vec4& p) { + double betaX = p.px() / p.e(); + double betaY = p.py() / p.e(); + double betaZ = p.pz() / p.e(); + bst(betaX, betaY, betaZ); +} + +//-------------------------------------------------------------------------- + +// Boost so vector originally with same velocity as p is brought to rest. + +void RotBstMatrix::bstback(const Vec4& p) { + double betaX = -p.px() / p.e(); + double betaY = -p.py() / p.e(); + double betaZ = -p.pz() / p.e(); + bst(betaX, betaY, betaZ); +} + +//-------------------------------------------------------------------------- + +// Boost that transforms p1 to p2, where p1^2 = p2^2 is assumed. + +void RotBstMatrix::bst(const Vec4& p1, const Vec4& p2) { + double eSum = p1.e() + p2.e(); + double betaX = (p2.px() - p1.px()) / eSum; + double betaY = (p2.py() - p1.py()) / eSum; + double betaZ = (p2.pz() - p1.pz()) / eSum; + double fac = 2. / (1. + betaX*betaX + betaY*betaY + betaZ*betaZ); + betaX *= fac; betaY *= fac; betaZ *= fac; + bst(betaX, betaY, betaZ); +} + +//-------------------------------------------------------------------------- + +// Boost and rotation that transforms from p1 and p2 +// to their rest frame with p1 along +z axis. + +void RotBstMatrix::toCMframe(const Vec4& p1, const Vec4& p2) { + Vec4 pSum = p1 + p2; + Vec4 dir = p1; + dir.bstback(pSum); + double theta = dir.theta(); + double phi = dir.phi(); + bstback(pSum); + rot(0., -phi); + rot(-theta, phi); +} + +//-------------------------------------------------------------------------- + +// Rotation and boost that transforms from rest frame of p1 and p2 +// with p1 along +z axis to actual frame of p1 and p2. (Inverse of above.) + +void RotBstMatrix::fromCMframe(const Vec4& p1, const Vec4& p2) { + Vec4 pSum = p1 + p2; + Vec4 dir = p1; + dir.bstback(pSum); + double theta = dir.theta(); + double phi = dir.phi(); + rot(0., -phi); + rot(theta, phi); + bst(pSum); +} + +//-------------------------------------------------------------------------- + +// Combine existing rotation/boost matrix with another one. + +void RotBstMatrix::rotbst(const RotBstMatrix& Mrb) { + double Mtmp[4][4]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + Mtmp[i][j] = M[i][j]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = Mrb.M[i][0] * Mtmp[0][j] + Mrb.M[i][1] * Mtmp[1][j] + + Mrb.M[i][2] * Mtmp[2][j] + Mrb.M[i][3] * Mtmp[3][j]; +} + +//-------------------------------------------------------------------------- + +// Invert the rotation and boost. + +void RotBstMatrix::invert() { + double Mtmp[4][4]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + Mtmp[i][j] = M[i][j]; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = ( (i == 0 && j > 0) || (i > 0 && j == 0) ) + ? - Mtmp[j][i] : Mtmp[j][i]; +} + +//-------------------------------------------------------------------------- + +// Reset to diagonal matrix. + +void RotBstMatrix::reset() { + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = (i==j) ? 1. : 0.; +} + +//-------------------------------------------------------------------------- + +// Crude estimate deviation from unit matrix. + +double RotBstMatrix::deviation() const { + double devSum = 0.; + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + devSum += (i==j) ? abs(M[i][j] - 1.) : abs(M[i][j]); + return devSum; +} + +//-------------------------------------------------------------------------- + +// Print a rotation and boost matrix: operator overloading with friend. + +ostream& operator<<(ostream& os, const RotBstMatrix& M) { + os << fixed << setprecision(5) << " Rotation/boost matrix: \n"; + for (int i = 0; i <4; ++i) + os << setw(10) << M.M[i][0] << setw(10) << M.M[i][1] + << setw(10) << M.M[i][2] << setw(10) << M.M[i][3] << "\n"; + return os; +} + +//========================================================================== + +// Hist class. +// This class handles a single histogram at a time +// (or a vector of histograms). + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Maximum number of bins in a histogram. +const int Hist::NBINMAX = 1000; + +// Maximum number of columns that can be printed for a histogram. +const int Hist::NCOLMAX = 100; + +// Maximum number of lines a histogram can use at output. +const int Hist::NLINES = 30; + +// Tolerance in deviation of xMin and xMax between two histograms. +const double Hist::TOLERANCE = 0.001; + +// Small number to avoid division by zero. +const double Hist::TINY = 1e-20; + +// When minbin/maxbin < SMALLFRAC the y scale goes down to zero. +const double Hist::SMALLFRAC = 0.1; + +// Constants for printout: fixed steps on y scale; filling characters. +const double DYAC[] = {0.04, 0.05, 0.06, 0.08, 0.10, + 0.12, 0.15, 0.20, 0.25, 0.30}; +const char NUMBER[] = {'0', '1', '2', '3', '4', '5', + '6', '7', '8', '9', 'X' }; + +//-------------------------------------------------------------------------- + +// Book a histogram. + +void Hist::book(string titleIn, int nBinIn, double xMinIn, + double xMaxIn) { + + title = titleIn; + nBin = nBinIn; + if (nBinIn < 1) nBin = 1; + if (nBinIn > NBINMAX) nBin = NBINMAX; + xMin = xMinIn; + xMax = xMaxIn; + dx = (xMax - xMin)/nBin; + res.resize(nBin); + null(); + +} + +//-------------------------------------------------------------------------- + +// Reset bin contents. + +void Hist::null() { + + nFill = 0; + under = 0.; + inside = 0.; + over = 0.; + for (int ix = 0; ix < nBin; ++ix) res[ix] = 0.; + +} + +//-------------------------------------------------------------------------- + +// Fill bin with weight. + +void Hist::fill(double x, double w) { + + ++nFill; + int iBin = int(floor((x - xMin)/dx)); + if (iBin < 0) under += w; + else if (iBin >= nBin) over += w; + else {inside += w; res[iBin] += w; } + +} + +//-------------------------------------------------------------------------- + +// Print a histogram: also operator overloading with friend. + +ostream& operator<<(ostream& os, const Hist& h) { + + // Do not print empty histograms. + if (h.nFill <= 0) return os; + + // Write time and title. + time_t t = time(0); + char date[18]; + strftime(date,18,"%Y-%m-%d %H:%M",localtime(&t)); + os << "\n\n " << date << " " << h.title << "\n\n"; + + // Group bins, where required, to make printout have fewer columns. + int nGroup = 1 + (h.nBin - 1) / Hist::NCOLMAX; + int nCol = 1 + (h.nBin - 1) / nGroup; + vector resCol(nCol); + for (int iCol = 0; iCol < nCol; ++iCol) { + resCol[iCol] = 0.; + for (int ix = nGroup * iCol; ix < min( h.nBin, nGroup * (iCol + 1)); ++ix) + resCol[iCol] += h.res[ix]; + } + + // Find minimum and maximum bin content. + double yMin = resCol[0]; + double yMax = resCol[0]; + for (int iCol = 1; iCol < nCol; ++iCol) { + if (resCol[iCol] < yMin) yMin = resCol[iCol]; + if (resCol[iCol] > yMax) yMax = resCol[iCol]; + } + + // Determine scale and step size for y axis. + if (yMax - yMin > Hist::NLINES * DYAC[0] * 1e-9) { + if (yMin > 0. && yMin < Hist::SMALLFRAC * yMax) yMin = 0.; + if (yMax < 0. && yMax > Hist::SMALLFRAC * yMin) yMax = 0.; + int iPowY = int(floor( log10(yMax - yMin) )); + if (yMax - yMin < Hist::NLINES * DYAC[0] * pow(10.,iPowY)) + iPowY = iPowY - 1; + if (yMax - yMin > Hist::NLINES * DYAC[9] * pow(10.,iPowY)) + iPowY = iPowY + 1; + double nLinePow = Hist::NLINES * pow(10.,iPowY); + double delY = DYAC[0]; + for (int idel = 0; idel < 9; ++idel) + if (yMax - yMin >= nLinePow * DYAC[idel]) delY = DYAC[idel+1]; + double dy = delY * pow(10.,iPowY); + + // Convert bin contents to integer form; fractional fill in top row. + vector row(nCol); + vector frac(nCol); + for (int iCol = 0; iCol < nCol ; ++iCol) { + double cta = abs(resCol[iCol]) / dy; + row[iCol] = int(cta + 0.95); + if(resCol[iCol] < 0.) row[iCol] = - row[iCol]; + frac[iCol] = int(10. * (cta + 1.05 - floor(cta + 0.95))); + } + int rowMin = int(abs(yMin)/dy + 0.95); + if ( yMin < 0) rowMin = - rowMin; + int rowMax = int(abs(yMax)/dy + 0.95); + if ( yMax < 0) rowMax = - rowMax; + + // Print histogram row by row. + os << fixed << setprecision(2); + for (int iRow = rowMax; iRow >= rowMin; iRow--) if (iRow != 0) { + os << " " << setw(10) << iRow*delY << "*10^" + << setw(2) << iPowY << " "; + for (int iCol = 0; iCol < nCol ; ++iCol) { + if (iRow == row[iCol]) os << NUMBER[frac[iCol]]; + else if (iRow * (row[iCol] - iRow) > 0) os << NUMBER[10]; + else os << " "; + } os << "\n"; + } os << "\n"; + + // Print sign and value of bin contents + double maxim = log10(max(yMax, -yMin)); + int iPowBin = int(floor(maxim + 0.0001)); + os << " Contents "; + for (int iCol = 0; iCol < nCol ; ++iCol) { + if (resCol[iCol] < - pow(10., iPowBin - 4)) os << "-"; + else os << " "; + row[iCol] = int(abs(resCol[iCol]) * pow(10., 3 - iPowBin) + 0.5); + } os << "\n"; + for (int iRow = 3; iRow >= 0; iRow--) { + os << " *10^" << setw(2) << iPowBin + iRow - 3 << " "; + int mask = int( pow(10., iRow) + 0.5); + for (int iCol = 0; iCol < nCol ; ++iCol) { + os << NUMBER[(row[iCol] / mask) % 10]; + } os << "\n"; + } os << "\n"; + + // Print sign and value of lower bin edge. + maxim = log10( max( -h.xMin, h.xMax - h.dx)); + int iPowExp = int(floor(maxim + 0.0001)); + os << " Low edge "; + for (int iCol = 0; iCol < nCol ; ++iCol) { + if (h.xMin + iCol * nGroup * h.dx < - pow(10., iPowExp - 3)) os << "-"; + else os << " "; + row[iCol] = int(abs(h.xMin + iCol * nGroup * h.dx) + * pow(10., 2 - iPowExp) + 0.5); + } os << "\n"; + for (int iRow = 2; iRow >= 0; iRow--) { + os << " *10^" << setw(2) << iPowExp + iRow - 2 << " "; + int mask = int( pow(10., iRow) + 0.5); + for (int iCol = 0; iCol < nCol ; ++iCol) + os << NUMBER[(row[iCol] / mask) % 10]; + os << "\n"; + } os << "\n"; + + // Print explanation if histogram cannot be shown. + } else os << " Histogram not shown since lowest value" << scientific + << setprecision(4) << setw(12) << yMin << " and highest value" + << setw(12) << yMax << " are too close \n \n"; + + // Calculate and print statistics. + double cSum = 0.; + double cxSum = 0.; + double cxxSum = 0.; + for (int ix = 0; ix < h.nBin ; ++ix) { + double cta = abs(h.res[ix]); + double x = h.xMin + (ix + 0.5) * h.dx; + cSum = cSum + cta; + cxSum = cxSum + cta * x; + cxxSum = cxxSum + cta * x * x; + } + double xmean = cxSum / max(cSum, Hist::TINY); + double rms = sqrtpos( cxxSum / max(cSum, Hist::TINY) - xmean*xmean ); + os << scientific << setprecision(4) + << " Entries =" << setw(12) << h.nFill + << " Mean =" << setw(12) << xmean + << " Underflow =" << setw(12) << h.under + << " Low edge =" << setw(12) << h.xMin << "\n" + << " All chan =" << setw(12) << h.inside + << " Rms =" << setw(12) << rms + << " Overflow =" << setw(12) << h.over + << " High edge =" << setw(12) << h.xMax << endl; + return os; +} + +//-------------------------------------------------------------------------- + +// Print histogram contents as a table (e.g. for Gnuplot). + +void Hist::table(ostream& os) const { + + // Print histogram vector bin by bin, with mean x as first column. + os << scientific << setprecision(4); + for (int ix = 0; ix < nBin; ++ix) + os << setw(12) << xMin + (ix + 0.5) * dx + << setw(12) << res[ix] << "\n"; + +} + +//-------------------------------------------------------------------------- + +// Get content of specific bin. +// Special values are bin 0 for underflow and bin nBin+1 for overflow. +// All other bins outside proper histogram range return 0. + +double Hist::getBinContent(int iBin) { + + if (iBin > 0 && iBin <= nBin) return res[iBin - 1]; + else if (iBin == 0) return under; + else if (iBin == nBin + 1) return over; + else return 0.; + +} + +//-------------------------------------------------------------------------- + +// Check whether another histogram has same size and limits. + +bool Hist::sameSize(const Hist& h) const { + + if (nBin == h.nBin && abs(xMin - h.xMin) < TOLERANCE * dx && + abs(xMax - h.xMax) < TOLERANCE * dx) return true; + else return false; + +} + +//-------------------------------------------------------------------------- + +// Take 10-logarithm or natural logarithm of contents bin by bin. + +void Hist::takeLog(bool tenLog) { + + // Find smallest positive bin content, and put min a bit below. + double yMin = 1e20; + for (int ix = 0; ix < nBin; ++ix) + if (res[ix] > 1e-20 && res[ix] < yMin ) yMin = res[ix]; + yMin *= 0.8; + + // Take 10-logarithm bin by bin, but ensure positivity. + if (tenLog) { + for (int ix = 0; ix < nBin; ++ix) + res[ix] = log10( max( yMin, res[ix]) ); + under = log10( max( yMin, under) ); + inside = log10( max( yMin, inside) ); + over = log10( max( yMin, over) ); + + // Take natural logarithm bin by bin, but ensure positivity. + } else { + for (int ix = 0; ix < nBin; ++ix) + res[ix] = log( max( yMin, res[ix]) ); + under = log( max( yMin, under) ); + inside = log( max( yMin, inside) ); + over = log( max( yMin, over) ); + } + +} + +//-------------------------------------------------------------------------- + +// Add histogram to existing one. + +Hist& Hist::operator+=(const Hist& h) { + if (!sameSize(h)) return *this; + nFill += h.nFill; + under += h.under; + inside += h.inside; + over += h.over; + for (int ix = 0; ix < nBin; ++ix) res[ix] += h.res[ix]; + return *this; +} + +//-------------------------------------------------------------------------- + +// Subtract histogram from existing one. + +Hist& Hist::operator-=(const Hist& h) { + if (!sameSize(h)) return *this; + nFill += h.nFill; + under -= h.under; + inside -= h.inside; + over -= h.over; + for (int ix = 0; ix < nBin; ++ix) res[ix] -= h.res[ix]; + return *this; +} + +//-------------------------------------------------------------------------- + +// Multiply existing histogram by another one. + +Hist& Hist::operator*=(const Hist& h) { + if (!sameSize(h)) return *this; + nFill += h.nFill; + under *= h.under; + inside *= h.inside; + over *= h.over; + for (int ix = 0; ix < nBin; ++ix) res[ix] *= h.res[ix]; + return *this; +} + +//-------------------------------------------------------------------------- + +// Divide existing histogram by another one. + +Hist& Hist::operator/=(const Hist& h) { + if (!sameSize(h)) return *this; + nFill += h.nFill; + under = (abs(h.under) < Hist::TINY) ? 0. : under/h.under; + inside = (abs(h.inside) < Hist::TINY) ? 0. : inside/h.inside; + over = (abs(h.over) < Hist::TINY) ? 0. : over/h.over; + for (int ix = 0; ix < nBin; ++ix) + res[ix] = (abs(h.res[ix]) < Hist::TINY) ? 0. : res[ix]/h.res[ix]; + return *this; +} + +//-------------------------------------------------------------------------- + +// Add constant offset to histogram. + +Hist& Hist::operator+=(double f) { + under += f; + inside += nBin * f; + over += f; + for (int ix = 0; ix < nBin; ++ix) res[ix] += f; + return *this; +} + +//-------------------------------------------------------------------------- + +// Subtract constant offset from histogram. + +Hist& Hist::operator-=(double f) { + under -= f; + inside -= nBin * f; + over -= f; + for (int ix = 0; ix < nBin; ++ix) res[ix] -= f; + return *this; +} + +//-------------------------------------------------------------------------- + +// Multiply histogram by constant + +Hist& Hist::operator*=(double f) { + under *= f; + inside *= f; + over *= f; + for (int ix = 0; ix < nBin; ++ix) res[ix] *= f; + return *this; +} + +//-------------------------------------------------------------------------- + +// Divide histogram by constant + +Hist& Hist::operator/=(double f) { + under /= f; + inside /= f; + over /= f; + for (int ix = 0; ix < nBin; ++ix) res[ix] /= f; + return *this; +} + +//-------------------------------------------------------------------------- + +// Implementation of operator overloading with friends. + +Hist operator+(double f, const Hist& h1) { + Hist h = h1; return h += f;} + +Hist operator+(const Hist& h1, double f) { + Hist h = h1; return h += f;} + +Hist operator+(const Hist& h1, const Hist& h2) { + Hist h = h1; return h += h2;} + +Hist operator-(double f, const Hist& h1) { + Hist h = h1; + h.under = f - h1.under; + h.inside = h1.nBin * f - h1.inside; + h.over = f - h1.over; + for (int ix = 0; ix < h1.nBin; ++ix) h.res[ix] = f - h1.res[ix]; + return h;} + +Hist operator-(const Hist& h1, double f) { + Hist h = h1; return h -= f;} + +Hist operator-(const Hist& h1, const Hist& h2) { + Hist h = h1; return h -= h2;} + +Hist operator*(double f, const Hist& h1) { + Hist h = h1; return h *= f;} + +Hist operator*(const Hist& h1, double f) { + Hist h = h1; return h *= f;} + +Hist operator*(const Hist& h1, const Hist& h2) { + Hist h = h1; return h *= h2;} + +Hist operator/(double f, const Hist& h1) { + Hist h = h1; + h.under = (abs(h1.under) < Hist::TINY) ? 0. : f/h1.under; + h.inside = (abs(h1.inside) < Hist::TINY) ? 0. : f/h1.inside; + h.over = (abs(h1.over) < Hist::TINY) ? 0. : f/h1.over; + for (int ix = 0; ix < h1.nBin; ++ix) + h.res[ix] = (abs(h1.res[ix]) < Hist::TINY) ? 0. : f/h1.res[ix]; + return h; +} + +Hist operator/(const Hist& h1, double f) { + Hist h = h1; return h /= f;} + +Hist operator/(const Hist& h1, const Hist& h2) { + Hist h = h1; return h /= h2;} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/BeamParticle.cxx b/PYTHIA8/pythia8140/src/BeamParticle.cxx new file mode 100644 index 00000000000..d13577fac99 --- /dev/null +++ b/PYTHIA8/pythia8140/src/BeamParticle.cxx @@ -0,0 +1,916 @@ +// BeamParticle.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// BeamParticle class. + +#include "BeamParticle.h" + +namespace Pythia8 { + +//========================================================================== + +// The BeamParticle class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// A lepton that takes (almost) the full beam energy does not leave a remnant. +const double BeamParticle::XMINUNRESOLVED = 1. - 1e-10; + +//-------------------------------------------------------------------------- + +// Initialize data on a beam particle and save pointers. + +void BeamParticle::init( int idIn, double pzIn, double eIn, double mIn, + Info* infoPtrIn, Settings& settings, ParticleData* particleDataPtrIn, + Rndm* rndmPtrIn,PDF* pdfInPtr, PDF* pdfHardInPtr, bool isUnresolvedIn, + StringFlav* flavSelPtrIn) { + + // Store input pointers (and one bool) for future use. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + pdfBeamPtr = pdfInPtr; + pdfHardBeamPtr = pdfHardInPtr; + isUnresolvedBeam = isUnresolvedIn; + flavSelPtr = flavSelPtrIn; + + // Maximum quark kind in allowed incoming beam hadrons. + maxValQuark = settings.mode("BeamRemnants:maxValQuark"); + + // Power of (1-x)^power/sqrt(x) for remnant valence quark distribution. + valencePowerMeson = settings.parm("BeamRemnants:valencePowerMeson"); + valencePowerUinP = settings.parm("BeamRemnants:valencePowerUinP"); + valencePowerDinP = settings.parm("BeamRemnants:valencePowerDinP"); + + // Enhancement factor of x of diquark. + valenceDiqEnhance = settings.parm("BeamRemnants:valenceDiqEnhance"); + + // Assume g(x) ~ (1-x)^power/x to constrain companion to sea quark. + companionPower = settings.mode("BeamRemnants:companionPower"); + + // Assume g(x) ~ (1-x)^power/x to constrain companion to sea quark. + companionPower = settings.mode("BeamRemnants:companionPower"); + + // Allow or not more than one valence quark to be kicked out. + allowJunction = settings.flag("BeamRemnants:allowJunction"); + + // For low-mass diffractive system kick out q/g = norm / mass^power. + pickQuarkNorm = settings.parm("Diffraction:pickQuarkNorm"); + pickQuarkPower = settings.parm("Diffraction:pickQuarkPower"); + + // Width of primordial kT distribution in low-mass diffractive systems. + diffPrimKTwidth = settings.parm("Diffraction:primKTwidth"); + + // Suppress large masses of beam remnant in low-mass diffractive systems. + diffLargeMassSuppress = settings.parm("Diffraction:largeMassSuppress"); + + // Store info on the incoming beam. + idBeam = idIn; + initBeamKind(); + pBeam = Vec4( 0., 0., pzIn, eIn); + mBeam = mIn; + +} + +//-------------------------------------------------------------------------- + +// Initialize kind and valence flavour content of incoming beam. +// For recognized hadrons one can generate multiple interactions. +// Dynamic choice of meson valence flavours in newValenceContent below. + +void BeamParticle::initBeamKind() { + + // Reset. + idBeamAbs = abs(idBeam); + isLeptonBeam = false; + isHadronBeam = false; + isMesonBeam = false; + isBaryonBeam = false; + nValKinds = 0; + + // Check for leptons. + if (idBeamAbs > 10 && idBeamAbs < 17) { + nValKinds = 1; + nVal[0] = 1; + idVal[0] = idBeam; + isLeptonBeam = true; + } + + // Done if cannot be lowest-lying hadron state. + if (idBeamAbs < 101 || idBeamAbs > 9999) return; + + // Resolve valence content for assumed Pomeron. + if (idBeamAbs == 990) { + isMesonBeam = true; + nValKinds = 2; + nVal[0] = 1 ; + nVal[1] = 1 ; + newValenceContent(); + + // Resolve valence content for assumed meson. Flunk unallowed codes. + } else if (idBeamAbs < 1000) { + int id1 = idBeamAbs/100; + int id2 = (idBeamAbs/10)%10; + if ( id1 < 1 || id1 > maxValQuark + || id2 < 1 || id2 > maxValQuark ) return; + isMesonBeam = true; + + // Store valence content of a confirmed meson. + nValKinds = 2; + nVal[0] = 1 ; + nVal[1] = 1; + if (id1%2 == 0) { + idVal[0] = id1; + idVal[1] = -id2; + } else { + idVal[0] = id2; + idVal[1] = -id1; + } + newValenceContent(); + + // Resolve valence content for assumed baryon. Flunk unallowed codes. + } else { + int id1 = idBeamAbs/1000; + int id2 = (idBeamAbs/100)%10; + int id3 = (idBeamAbs/10)%10; + if ( id1 < 1 || id1 > maxValQuark || id2 < 1 || id2 > maxValQuark + || id3 < 1 || id3 > maxValQuark) return; + if (id2 > id1 || id3 > id1) return; + isBaryonBeam = true; + + // Store valence content of a confirmed baryon. + nValKinds = 1; idVal[0] = id1; nVal[0] = 1; + if (id2 == id1) ++nVal[0]; + else { + nValKinds = 2; + idVal[1] = id2; + nVal[1] = 1; + } + if (id3 == id1) ++nVal[0]; + else if (id3 == id2) ++nVal[1]; + else { + idVal[nValKinds] = id3; + nVal[nValKinds] = 1; + ++nValKinds; + } + } + + // Flip flavours for antimeson or antibaryon, and then done. + if (idBeam < 0) for (int i = 0; i < nValKinds; ++i) idVal[i] = -idVal[i]; + isHadronBeam = true; + Q2ValFracSav = -1.; + +} + +//-------------------------------------------------------------------------- + + +// Dynamic choice of meson valence flavours for pi0, K0S, K0L, Pomeron. + +void BeamParticle::newValenceContent() { + + // A pi0 oscillates between d dbar and u ubar. + if (idBeam == 111) { + idVal[0] = (rndmPtr->flat() < 0.5) ? 1 : 2; + idVal[1] = -idVal[0]; + + // A K0S or K0L oscillates between d sbar and s dbar. + } else if (idBeam == 130 || idBeam == 310) { + idVal[0] = (rndmPtr->flat() < 0.5) ? 1 : 3; + idVal[1] = (idVal[0] == 1) ? -3 : -1; + + // For a Pomeron split gluon remnant into d dbar or u ubar. + } else if (idBeam == 990) { + idVal[0] = (rndmPtr->flat() < 0.5) ? 1 : 2; + idVal[1] = -idVal[0]; + + // Other hadrons so far do not require any event-by-event change. + } else return; + + // Propagate change to PDF routine(s). + pdfBeamPtr->newValenceContent( idVal[0], idVal[1]); + if (pdfHardBeamPtr != pdfBeamPtr && pdfHardBeamPtr != 0) + pdfHardBeamPtr->newValenceContent( idVal[0], idVal[1]); + +} + +//-------------------------------------------------------------------------- + +double BeamParticle::xMax(int iSkip) { + + // Minimum requirement on remaining energy > nominal mass for hadron. + double xLeft = 1.; + if (isHadron()) xLeft -= m() / e(); + if (size() == 0) return xLeft; + + // Subtract what was carried away by initiators (to date). + for (int i = 0; i < size(); ++i) + if (i != iSkip && resolved[i].isFromBeam()) xLeft -= resolved[i].x(); + return xLeft; + +} + +//-------------------------------------------------------------------------- + +// Parton distributions, reshaped to take into account previous +// multiple interactions. By picking a non-negative iSkip value, +// one particular interaction is skipped, as needed for ISR + +double BeamParticle::xfModified(int iSkip, int idIn, double x, double Q2) { + + // Initial values. + idSave = idIn; + iSkipSave = iSkip; + xqVal = 0.; + xqgSea = 0.; + xqCompSum = 0.; + + // Fast procedure for first interaction. + if (size() == 0) { + if (x >= 1.) return 0.; + bool canBeVal = false; + for (int i = 0; i < nValKinds; ++i) + if (idIn == idVal[i]) canBeVal = true; + if (canBeVal) { + xqVal = xfVal( idIn, x, Q2); + xqgSea = xfSea( idIn, x, Q2); + } + else xqgSea = xf( idIn, x, Q2); + + // More complicated procedure for non-first interaction. + } else { + + // Sum up the x already removed, and check that remaining x is enough. + double xUsed = 0.; + for (int i = 0; i < size(); ++i) + if (i != iSkip) xUsed += resolved[i].x(); + double xLeft = 1. - xUsed; + if (x >= xLeft) return 0.; + double xRescaled = x / xLeft; + + // Calculate total and remaining amount of x carried by valence quarks. + double xValTot = 0.; + double xValLeft = 0.; + for (int i = 0; i < nValKinds; ++i) { + nValLeft[i] = nVal[i]; + for (int j = 0; j < size(); ++j) + if (j != iSkip && resolved[j].isValence() + && resolved[j].id() == idVal[i]) --nValLeft[i]; + double xValNow = xValFrac(i, Q2); + xValTot += nVal[i] * xValNow; + xValLeft += nValLeft[i] * xValNow; + } + + // Calculate total amount of x carried by unmatched companion quarks. + double xCompAdded = 0.; + for (int i = 0; i < size(); ++i) + if (i != iSkip && resolved[i].isUnmatched()) xCompAdded + += xCompFrac( resolved[i].x() / (xLeft + resolved[i].x()) ) + // Typo warning: extrafactor missing in Skands&Sjostrand article; + // for companion refers to fraction of x left INCLUDING sea quark. + // To be modified further?? + * (1. + resolved[i].x() / xLeft); + + // Calculate total rescaling factor and pdf for sea and gluon. + double rescaleGS = max( 0., (1. - xValLeft - xCompAdded) + / (1. - xValTot) ); + xqgSea = rescaleGS * xfSea( idIn, xRescaled, Q2); + + // Find valence part and rescale it to remaining number of quarks. + for (int i = 0; i < nValKinds; ++i) + if (idIn == idVal[i] && nValLeft[i] > 0) + xqVal = xfVal( idIn, xRescaled, Q2) + * double(nValLeft[i]) / double(nVal[i]); + + // Find companion part, by adding all companion contributions. + for (int i = 0; i < size(); ++i) + if (i != iSkip && resolved[i].id() == -idIn + && resolved[i].isUnmatched()) { + double xsRescaled = resolved[i].x() / (xLeft + resolved[i].x()); + double xcRescaled = x / (xLeft + resolved[i].x()); + double xqCompNow = xCompDist( xcRescaled, xsRescaled); + resolved[i].xqCompanion( xqCompNow); + xqCompSum += xqCompNow; + } + } + + // Add total, but only return relevant part for ISR. More cases?? + // Watch out, e.g. g can come from either kind of quark.?? + xqgTot = xqVal + xqgSea + xqCompSum; + if (iSkip >= 0) { + if (resolved[iSkip].isValence()) return xqVal; + if (resolved[iSkip].isUnmatched()) return xqgSea + xqCompSum; + } + return xqgTot; + +} + +//-------------------------------------------------------------------------- + +// Decide whether a quark extracted from the beam is of valence, sea or +// companion kind; in the latter case also pick its companion. +// Assumes xfModified has already been called. + + int BeamParticle::pickValSeaComp() { + + // If parton already has a companion than reset code for this. + int oldCompanion = resolved[iSkipSave].companion(); + if (oldCompanion >= 0) resolved[oldCompanion].companion(-2); + + // Default assignment is sea. + int vsc = -2; + + // For gluons or photons no sense of valence or sea. + if (idSave == 21 || idSave == 22) vsc = -1; + + // For lepton beam assume same-kind lepton inside is valence. + else if (isLeptonBeam && idSave == idBeam) vsc = -3; + + // Decide if valence or sea quark. + else { + double xqRndm = xqgTot * rndmPtr->flat(); + if (xqRndm < xqVal) vsc = -3; + else if (xqRndm < xqVal + xqgSea) vsc = -2; + + // If not either, loop over all possible companion quarks. + else { + xqRndm -= xqVal + xqgSea; + for (int i = 0; i < size(); ++i) + if (i != iSkipSave && resolved[i].id() == -idSave + && resolved[i].isUnmatched()) { + xqRndm -= resolved[i].xqCompanion(); + if (xqRndm < 0.) vsc = i; + break; + } + } + } + + // Bookkeep assignment; for sea--companion pair both ways. + resolved[iSkipSave].companion(vsc); + if (vsc >= 0) resolved[vsc].companion(iSkipSave); + + // Done; return code for choice (to distinguish valence/sea in Info). + return vsc; + +} + +//-------------------------------------------------------------------------- + +// Fraction of hadron momentum sitting in a valence quark distribution. +// Based on hardcoded parametrizations of CTEQ 5L numbers. + +double BeamParticle::xValFrac(int j, double Q2) { + + // Only recalculate when required. + if (Q2 != Q2ValFracSav) { + Q2ValFracSav = Q2; + + // Q2-dependence of log-log form; assume fixed Lambda = 0.2. + double llQ2 = log( log( max( 1., Q2) / 0.04 )); + + // Fractions carried by u and d in proton. + uValInt = 0.48 / (1. + 1.56 * llQ2); + dValInt = 0.385 / (1. + 1.60 * llQ2); + } + + // Baryon with three different quark kinds: (2 * u + d) / 3 of proton. + if (isBaryonBeam && nValKinds == 3) return (2. * uValInt + dValInt) / 3.; + + // Baryon with one or two identical: like d or u of proton. + if (isBaryonBeam && nVal[j] == 1) return dValInt; + if (isBaryonBeam && nVal[j] == 2) return uValInt; + + // Meson: (2 * u + d) / 2 of proton so same total valence quark fraction. + return 0.5 * (2. * uValInt + dValInt); + +} + +//-------------------------------------------------------------------------- + +// The momentum integral of a companion quark, with its partner at x_s, +// using an approximate gluon density like (1 - x_g)^power / x_g. +// The value corresponds to an unrescaled range between 0 and 1 - x_s. + +double BeamParticle::xCompFrac(double xs) { + + // Select case by power of gluon (1-x_g) shape. + switch (companionPower) { + + case 0: + return xs * ( 5. + xs * (-9. - 2. * xs * (-3. + xs)) + 3. * log(xs) ) + / ( (-1. + xs) * (2. + xs * (-1. + 2. * xs)) ); + + case 1: + return -1. -3. * xs + ( 2. * pow2(-1. + xs) * (1. + xs + xs*xs)) + / ( 2. + xs*xs * (xs - 3.) + 3. * xs * log(xs) ); + + case 2: + return xs * ( (1. - xs) * (19. + xs * (43. + 4. * xs)) + + 6. * log(xs) * (1. + 6. * xs + 4.*xs*xs) ) / + ( 4. * ( (xs - 1.) * (1. + xs * (4. + xs) ) + - 3. * xs * log(xs) * (1 + xs) ) ); + + case 3: + return 3. * xs * ( (xs - 1.) * (7. + xs * (28. + 13. * xs)) + - 2. * log(xs) * (1. + xs * (9. + 2. * xs * (6. + xs))) ) + / ( 4. + 27. * xs - 31. * pow3(xs) + + 6. * xs * log(xs) * (3. + 2. * xs * (3.+xs)) ); + + default: + return ( -9. * xs * (xs*xs - 1.) * (5. + xs * (24. + xs)) + 12. * xs + * log(xs) * (1. + 2. * xs) * (1. + 2. * xs * (5. + 2. * xs)) ) + / ( 8. * (1. + 2. * xs) * ((xs - 1.) * (1. + xs * (10. + xs)) + - 6. * xs * log(xs) * (1. + xs)) ); + + } +} + +//-------------------------------------------------------------------------- + +// The x*f pdf of a companion quark at x_c, with its sea partner at x_s, +// using an approximate gluon density like (1 - x_g)^power / x_g. +// The value corresponds to an unrescaled range between 0 and 1 - x_s. + +double BeamParticle::xCompDist(double xc, double xs) { + + // Mother gluon momentum fraction. Check physical limit. + double xg = xc + xs; + if (xg > 1.) return 0.; + + // Common factor, including splitting kernel and part of gluon density + // (and that it is x_c * f that is coded). + double fac = 3. * xc * xs * (xc*xc + xs*xs) / pow4(xg); + + // Select case by power of gluon (1-x_g) shape. + switch (companionPower) { + + case 0: + return fac / ( 2. - xs * (3. - xs * (3. - 2. * xs)) ); + + case 1: + return fac * (1. - xg) / ( 2. + xs*xs * (-3. + xs) + 3. * xs * log(xs) ); + + case 2: + return fac * pow2(1. - xg) / ( 2. * ((1. - xs) * (1. + xs * (4. + xs)) + + 3. * xs * (1. + xs) * log(xs)) ); + + case 3: + return fac * pow3(1. - xg) * 2. / ( 4. + 27. * xs - 31. * pow3(xs) + + 6. * xs * log(xs) * (3. + 2. * xs * (3. + xs)) ); + + default: + return fac * pow4(1. - xg) / ( 2. * (1. + 2. * xs) * ((1. - xs) + * (1. + xs * (10. + xs)) + 6. * xs * log(xs) * (1. + xs)) ); + + } +} + +//-------------------------------------------------------------------------- + +// Add required extra remnant flavour content. Also initial colours. + +bool BeamParticle::remnantFlavours(Event& event) { + + // A baryon will have a junction, unless a diquark is formed later. + hasJunctionBeam = (isBaryon()); + + // Store how many hard-scattering partons were removed from beam. + nInit = size(); + + // Find remaining valence quarks. + for (int i = 0; i < nValKinds; ++i) { + nValLeft[i] = nVal[i]; + for (int j = 0; j < nInit; ++j) if (resolved[j].isValence() + && resolved[j].id() == idVal[i]) --nValLeft[i]; + // Add remaining valence quarks to record. Partly temporary values. + for (int k = 0; k < nValLeft[i]; ++k) append(0, idVal[i], 0., -3); + } + + // If at least two valence quarks left in baryon remnant then form diquark. + int nInitPlusVal = size(); + if (isBaryon() && nInitPlusVal - nInit >= 2) { + + // If three, pick two at random to form diquark, else trivial. + int iQ1 = nInit; + int iQ2 = nInit + 1; + if (nInitPlusVal - nInit == 3) { + double pickDq = 3. * rndmPtr->flat(); + if (pickDq > 1.) iQ2 = nInit + 2; + if (pickDq > 2.) iQ1 = nInit + 1; + } + + // Pick spin 0 or 1 according to SU(6) wave function factors. + int idDq = flavSelPtr->makeDiquark( resolved[iQ1].id(), + resolved[iQ2].id(), idBeam); + + // Overwrite with diquark flavour and remove one slot. No more junction. + resolved[iQ1].id(idDq); + if (nInitPlusVal - nInit == 3 && iQ2 == nInit + 1) + resolved[nInit + 1].id( resolved[nInit + 2].id() ); + resolved.pop_back(); + hasJunctionBeam = false; + } + + // Find companion quarks to unmatched sea quarks. + for (int i = 0; i < nInit; ++i) + if (resolved[i].isUnmatched()) { + + // Add companion quark to record; and bookkeep both ways. + append(0, -resolved[i].id(), 0., i); + resolved[i].companion(size() - 1); + } + + // If no other remnants found, add a gluon or photon to carry momentum. + if (size() == nInit) { + int idRemnant = (isHadronBeam) ? 21 : 22; + append(0, idRemnant, 0., -1); + } + + // Set initiator and remnant masses. + for (int i = 0; i < size(); ++i) { + if (i < nInit) resolved[i].m(0.); + else resolved[i].m( particleDataPtr->m0( resolved[i].id() ) ); + } + + // For debug purposes: reject beams with resolved junction topology. + if (hasJunctionBeam && !allowJunction) return false; + + // Pick initial colours for remnants. + for (int i = nInit; i < size(); ++i) { + int colType = particleDataPtr->colType( resolved[i].id() ); + int col = (colType == 1 || colType == 2) ? event.nextColTag() : 0; + int acol = (colType == -1 || colType == 2) ? event.nextColTag() : 0; + resolved[i].cols( col, acol); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Correlate all initiators and remnants to make a colour singlet. + +bool BeamParticle::remnantColours(Event& event, vector& colFrom, + vector& colTo) { + + // No colours in lepton beams so no need to do anything. + if (isLeptonBeam) return true; + + // Copy initiator colour info from the event record to the beam. + for (int i = 0; i < size(); ++i) { + int j = resolved[i].iPos(); + resolved[i].cols( event[j].col(), event[j].acol()); + } + + // Find number and position of valence quarks, of gluons, and + // of sea-companion pairs (counted as gluons) in the beam remnants. + // Skip gluons with same colour as anticolour and rescattering partons. + vector iVal; + vector iGlu; + for (int i = 0; i < size(); ++i) + if (resolved[i].isFromBeam()) { + if ( resolved[i].isValence() ) iVal.push_back(i); + else if ( resolved[i].isCompanion() && resolved[i].companion() > i ) + iGlu.push_back(i); + else if ( resolved[i].id() == 21 + && resolved[i].col() != resolved[i].acol() ) iGlu.push_back(i); + } + + // Pick a valence quark to which gluons are attached. + // Do not resolve quarks in diquark. (More sophisticated??) + int iValSel= iVal[0]; + if (iVal.size() == 2) { + if ( abs(resolved[iValSel].id()) > 10 ) iValSel = iVal[1]; + } else { + double rndmValSel = 3. * rndmPtr->flat(); + if (rndmValSel > 1.) iValSel= iVal[1]; + if (rndmValSel > 2.) iValSel= iVal[2]; + } + + // This valence quark defines initial (anti)colour. + int iBeg = iValSel; + bool hasCol = (resolved[iBeg].col() > 0); + int begCol = (hasCol) ? resolved[iBeg].col() : resolved[iBeg].acol(); + + // Do random stepping through gluon/(sea+companion) list. + vector iGluRndm; + for (int i = 0; i < int(iGlu.size()); ++i) + iGluRndm.push_back( iGlu[i] ); + for (int iOrder = 0; iOrder < int(iGlu.size()); ++iOrder) { + int iRndm = int( double(iGluRndm.size()) * rndmPtr->flat()); + int iGluSel = iGluRndm[iRndm]; + iGluRndm[iRndm] = iGluRndm[iGluRndm.size() - 1]; + iGluRndm.pop_back(); + + // Find matching anticolour/colour to current colour/anticolour. + int iEnd = iGluSel; + int endCol = (hasCol) ? resolved[iEnd].acol() : resolved[iEnd].col(); + // Not gluon but sea+companion pair: go to other. + if (endCol == 0) { + iEnd = resolved[iEnd].companion(); + endCol = (hasCol) ? resolved[iEnd].acol() : resolved[iEnd].col(); + } + + // Collapse this colour-anticolour pair to the lowest one. + if (begCol < endCol) { + if (hasCol) resolved[iEnd].acol(begCol); + else resolved[iEnd].col(begCol); + colFrom.push_back(endCol); + colTo.push_back(begCol); + } else { + if (hasCol) resolved[iBeg].col(endCol); + else resolved[iBeg].acol(endCol); + colFrom.push_back(begCol); + colTo.push_back(endCol); + } + + // Pick up the other colour of the recent gluon and repeat. + iBeg = iEnd; + begCol = (hasCol) ? resolved[iBeg].col() : resolved[iBeg].acol(); + // Not gluon but sea+companion pair: go to other. + if (begCol == 0) { + iBeg = resolved[iBeg].companion(); + begCol = (hasCol) ? resolved[iBeg].col() : resolved[iBeg].acol(); + } + + // At end of gluon/(sea+companion) list. + } + + // Now begin checks, and also finding junction information. + // Loop through remnant partons; isolate all colours and anticolours. + vector colList; + vector acolList; + for (int i = 0; i < size(); ++i) + if ( resolved[i].isFromBeam() ) + if ( resolved[i].col() != resolved[i].acol() ) { + if (resolved[i].col() > 0) colList.push_back( resolved[i].col() ); + if (resolved[i].acol() > 0) acolList.push_back( resolved[i].acol() ); + } + + // Remove all matching colour-anticolour pairs. + bool foundPair = true; + while (foundPair && colList.size() > 0 && acolList.size() > 0) { + foundPair = false; + for (int iCol = 0; iCol < int(colList.size()); ++iCol) { + for (int iAcol = 0; iAcol < int(acolList.size()); ++iAcol) { + if (acolList[iAcol] == colList[iCol]) { + colList[iCol] = colList.back(); + colList.pop_back(); + acolList[iAcol] = acolList.back(); + acolList.pop_back(); + foundPair = true; + break; + } + } if (foundPair) break; + } + } + + // Usually one unmatched pair left to collapse. + if (colList.size() == 1 && acolList.size() == 1) { + int finalFrom = max( colList[0], acolList[0]); + int finalTo = min( colList[0], acolList[0]); + for (int i = 0; i < size(); ++i) + if ( resolved[i].isFromBeam() ) { + if (resolved[i].col() == finalFrom) resolved[i].col(finalTo); + if (resolved[i].acol() == finalFrom) resolved[i].acol(finalTo); + } + colFrom.push_back(finalFrom); + colTo.push_back(finalTo); + + // Store an (anti)junction when three (anti)coloured daughters. + } else if (hasJunctionBeam && colList.size() == 3 + && acolList.size() == 0) { + event.appendJunction( 1, colList[0], colList[1], colList[2]); + junCol[0] = colList[0]; + junCol[1] = colList[1]; + junCol[2] = colList[2]; + } else if (hasJunctionBeam && acolList.size() == 3 + && colList.size() == 0) { + event.appendJunction( 2, acolList[0], acolList[1], acolList[2]); + junCol[0] = acolList[0]; + junCol[1] = acolList[1]; + junCol[2] = acolList[2]; + + // Any other nonvanishing values indicate failure. + } else if (colList.size() > 0 || acolList.size() > 0) { + infoPtr->errorMsg("Error in BeamParticle::remnantColours: " + "leftover unmatched colours"); + return false; + } + + // Store colour assignment of beam particles. + for (int i = nInit; i < size(); ++i) + event[resolved[i].iPos()].cols( resolved[i].col(), resolved[i].acol() ); + + // Done. + return true; +} + + +//-------------------------------------------------------------------------- + +// Pick unrescaled x values for beam remnant sharing. + +double BeamParticle::xRemnant( int i) { + + double x = 0.; + + // Calculation of x of valence quark or diquark, for latter as sum. + if (resolved[i].isValence()) { + + // Resolve diquark into sum of two quarks. + int id1 = resolved[i].id(); + int id2 = 0; + if (abs(id1) > 10) { + id2 = (id1 > 0) ? (id1/100)%10 : -(((-id1)/100)%10); + id1 = (id1 > 0) ? id1/1000 : -((-id1)/1000); + } + + // Loop over (up to) two quarks; add their contributions. + for (int iId = 0; iId < 2; ++iId) { + int idNow = (iId == 0) ? id1 : id2; + if (idNow == 0) break; + double xPart = 0.; + + // Assume form (1-x)^a / sqrt(x). + double xPow = valencePowerMeson; + if (isBaryonBeam) { + if (nValKinds == 3 || nValKinds == 1) + xPow = (3. * rndmPtr->flat() < 2.) + ? valencePowerUinP : valencePowerDinP ; + else if (nValence(idNow) == 2) xPow = valencePowerUinP; + else xPow = valencePowerDinP; + } + do xPart = pow2( rndmPtr->flat() ); + while ( pow(1. - xPart, xPow) < rndmPtr->flat() ); + + // End loop over (up to) two quarks. Possibly enhancement for diquarks. + x += xPart; + } + if (id2 != 0) x *= valenceDiqEnhance; + + // Calculation of x of sea quark, based on companion association. + } else if (resolved[i].isCompanion()) { + + // Find rescaled x value of companion. + double xLeft = 1.; + for (int iInit = 0; iInit < nInit; ++iInit) + if (resolved[iInit].isFromBeam()) xLeft -= resolved[iInit].x(); + double xCompanion = resolved[ resolved[i].companion() ].x(); + xCompanion /= (xLeft + xCompanion); + + // Now use ansatz q(x; x_c) < N/(x +x_c) to pick x. + do x = pow( xCompanion, rndmPtr->flat()) - xCompanion; + while ( pow( (1. - x - xCompanion) / (1. - xCompanion), companionPower) + * (pow2(x) + pow2(xCompanion)) / pow2(x + xCompanion) < rndmPtr->flat() ); + + // Else, rarely, a single gluon remnant, so value does not matter. + } else x = 1.; + return x; + +} + +//-------------------------------------------------------------------------- + +// Print the list of resolved partons in a beam. + +void BeamParticle::list(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA Partons resolved in beam -----------------" + << "-------------------------------------------------------------\n" + << "\n i iPos id x comp xqcomp pTfact " + << "colours p_x p_y p_z e m \n"; + + // Loop over list of removed partons and print it. + double xSum = 0.; + Vec4 pSum; + for (int i = 0; i < size(); ++i) { + ResolvedParton res = resolved[i]; + os << fixed << setprecision(6) << setw(5) << i << setw(6) << res.iPos() + << setw(8) << res.id() << setw(10) << res.x() << setw(6) + << res.companion() << setw(10) << res.xqCompanion() << setw(10) + << res.pTfactor() << setprecision(3) << setw(6) << res.col() + << setw(6) << res.acol() << setw(11) << res.px() << setw(11) + << res.py() << setw(11) << res.pz() << setw(11) << res.e() + << setw(11) << res.m() << "\n"; + + // Also find sum of x and p values. + if (res.companion() != -10) { + xSum += res.x(); + pSum += res.p(); + } + } + + // Print sum and endline. + os << setprecision(6) << " x sum:" << setw(10) << xSum + << setprecision(3) << " p sum:" + << setw(11) << pSum.px() << setw(11) << pSum.py() << setw(11) + << pSum.pz() << setw(11) << pSum.e() + << "\n\n -------- End PYTHIA Partons resolved in beam -----------" + << "---------------------------------------------------------------" + << endl; +} + +//-------------------------------------------------------------------------- + +// Test whether a lepton is to be considered as unresolved. + +bool BeamParticle::isUnresolvedLepton() { + + // Require record to consist of lepton with full energy plus a photon. + if (!isLeptonBeam || resolved.size() > 2 || resolved[1].id() != 22 + || resolved[0].x() < XMINUNRESOLVED) return false; + return true; + +} + +//-------------------------------------------------------------------------- + +// For a diffractive system, decide whether to kick out gluon or quark. + +bool BeamParticle::pickGluon(double mDiff) { + + // Relative weight to pick a quark, assumed falling with energy. + double probPickQuark = pickQuarkNorm / pow( mDiff, pickQuarkPower); + return ( (1. + probPickQuark) * rndmPtr->flat() < 1. ); + +} + +//-------------------------------------------------------------------------- + +// Pick a valence quark at random. (Used for diffractive systems.) + +int BeamParticle::pickValence() { + + // Pick one valence quark at random. + int nTotVal = (isBaryonBeam) ? 3 : 2; + double rnVal = rndmPtr->flat() * nTotVal; + int iVal = (rnVal < 1.) ? 1 : ( (rnVal < 2.) ? 2 : 3 ); + + // This valence in slot 1, the rest thereafter. + idVal1 = 0; + idVal2 = 0; + idVal3 = 0; + int iNow = 0; + for (int i = 0; i < nValKinds; ++i) + for (int j = 0; j < nVal[i]; ++j) { + ++iNow; + if (iNow == iVal) idVal1 = idVal[i]; + else if ( idVal2 == 0) idVal2 = idVal[i]; + else idVal3 = idVal[i]; + } + + // Construct diquark if baryon. + if (idVal3 != 0) idVal2 = flavSelPtr->makeDiquark( idVal2, idVal3); + + // Done. + return idVal1; + +} + +//-------------------------------------------------------------------------- + +// Share lightcone momentum between two remnants in a diffractive system. + +double BeamParticle::zShare( double mDiff, double m1, double m2) { + + // Set up as valence in normal beam so can use xRemnant code. + append(0, idVal1, 0., -3); + append(0, idVal2, 0., -3); + double m2Diff = mDiff*mDiff; + + // Begin to generate z and pT until acceptable solution. + double wtAcc = 0.; + do { + double x1 = xRemnant(0); + double x2 = xRemnant(0); + zRel = x1 / (x1 + x2); + pair gauss2 = rndmPtr->gauss2(); + pxRel = diffPrimKTwidth * gauss2.first; + pyRel = diffPrimKTwidth * gauss2.second; + + // Suppress large invariant masses of remnant system. + double mTS1 = m1*m1 + pxRel*pxRel + pyRel*pyRel; + double mTS2 = m2*m2 + pxRel*pxRel + pyRel*pyRel; + double m2Sys = mTS1 / zRel + mTS2 / (1. - zRel); + wtAcc = (m2Sys < m2Diff) + ? pow( 1. - m2Sys / m2Diff, diffLargeMassSuppress) : 0.; + } while (wtAcc < rndmPtr->flat()); + + // Done. + return zRel; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/BeamRemnants.cxx b/PYTHIA8/pythia8140/src/BeamRemnants.cxx new file mode 100644 index 00000000000..5a29509941c --- /dev/null +++ b/PYTHIA8/pythia8140/src/BeamRemnants.cxx @@ -0,0 +1,1135 @@ +// BeamRemnants.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// BeamRemnants class. + +#include "BeamRemnants.h" + +namespace Pythia8 { + +//========================================================================== + +// The BeamDipole class is purely internal to reconnectColours. + +class BeamDipole { + +public: + + // Constructor. + BeamDipole( int colIn = 0, int iColIn = 0, int iAcolIn = 0) + : col(colIn), iCol(iColIn), iAcol(iAcolIn) {} + + // Members. + int col, iCol, iAcol; + double p1p2; + +}; + +//========================================================================== + +// The BeamRemnants class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// If same (anti)colour appears twice in final state, repair or reject. +const bool BeamRemnants::ALLOWCOLOURTWICE = true; + +// Maximum number of tries to match colours and kinematics in the event. +const int BeamRemnants::NTRYCOLMATCH = 10; +const int BeamRemnants::NTRYKINMATCH = 10; + +// Overall correction step for energy-momentum conservation; only +// becomes relevant in rescattering scenarios when FSR dipole emissions +// and primordial kT is added. Should hopefully not be needed. +const bool BeamRemnants::CORRECTMISMATCH = false; + +//-------------------------------------------------------------------------- + +// Initialization. + +bool BeamRemnants::init( Info* infoPtrIn, Settings& settings, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + PartonSystems* partonSystemsPtrIn) { + + // Save pointers. + infoPtr = infoPtrIn; + rndmPtr = rndmPtrIn; + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + partonSystemsPtr = partonSystemsPtrIn; + + // Width of primordial kT distribution. + doPrimordialKT = settings.flag("BeamRemnants:primordialKT"); + primordialKTsoft = settings.parm("BeamRemnants:primordialKTsoft"); + primordialKThard = settings.parm("BeamRemnants:primordialKThard"); + primordialKTremnant = settings.parm("BeamRemnants:primordialKTremnant"); + halfScaleForKT = settings.parm("BeamRemnants:halfScaleForKT"); + halfMassForKT = settings.parm("BeamRemnants:halfMassForKT"); + + // Handling of rescattering kinematics uncertainties from primodial kT. + allowRescatter = settings.flag("MultipleInteractions:allowRescatter"); + doRescatterRestoreY = settings.flag("BeamRemnants:rescatterRestoreY"); + + // Parameters for colour reconnection scenario, partly borrowed from + // multiple interactions not to introduce too many new ones. + doReconnect = settings.flag("BeamRemnants:reconnectColours"); + reconnectRange = settings.parm("BeamRemnants:reconnectRange"); + pT0Ref = settings.parm("MultipleInteractions:pT0Ref"); + ecmRef = settings.parm("MultipleInteractions:ecmRef"); + ecmPow = settings.parm("MultipleInteractions:ecmPow"); + + // Total and squared CM energy at nominal energy. + eCM = infoPtr->eCM(); + sCM = eCM * eCM; + + // The MI pT0 smoothening scale and its reconnection-strength combination. + pT0 = pT0Ref * pow(eCM / ecmRef, ecmPow); + pT20Rec = pow2(reconnectRange * pT0); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Select the flavours/kinematics/colours of the two beam remnants. +// Notation: iPar = all partons, iSys = matched systems of two beams, +// iRem = additional partons in remnants. + +bool BeamRemnants::add( Event& event) { + + // Update to current CM energy. + eCM = infoPtr->eCM(); + sCM = eCM * eCM; + + // Check that flavour bookkept in event and in beam particles agree. + for (int i = 0; i < beamAPtr->size(); ++i) { + int j = (*beamAPtr)[i].iPos(); + if ((*beamAPtr)[i].id() != event[j].id()) { + infoPtr->errorMsg("Error in BeamRemnants::add: " + "event and beam flavours do not match"); + return false; + } + } + for (int i = 0; i < beamBPtr->size(); ++i) { + int j = (*beamBPtr)[i].iPos(); + if ((*beamBPtr)[i].id() != event[j].id()) { + infoPtr->errorMsg("Error in BeamRemnants::add: " + "event and beam flavours do not match"); + return false; + } + } + + // Number of scattering subsystems. Size of event record before treatment. + nSys = partonSystemsPtr->sizeSys(); + oldSize = event.size(); + + // Add required extra remnant flavour content. + // Start all over if fails (in option where junctions not allowed). + if ( !beamAPtr->remnantFlavours(event) + || !beamBPtr->remnantFlavours(event) ) { + infoPtr->errorMsg("Error in BeamRemnants::add:" + " remnant flavour setup failed"); + return false; + } + + // Do the kinematics of the collision subsystems and two beam remnants. + if (!setKinematics(event)) return false; + + // Allow colour reconnections. + if (doReconnect) reconnectColours(event); + + // Save current modifiable colour configuration for fast restoration. + vector colSave; + vector acolSave; + for (int i = oldSize; i < event.size(); ++i) { + colSave.push_back( event[i].col() ); + acolSave.push_back( event[i].acol() ); + } + event.saveJunctionSize(); + + // Allow several tries to match colours of initiators and remnants. + // Frequent "failures" since shortcutting colours separately on + // the two event sides may give "colour singlet gluons" etc. + bool physical = true; + for (int iTry = 0; iTry < NTRYCOLMATCH; ++iTry) { + physical = true; + + // Reset list of colour "collapses" (transformations). + colFrom.resize(0); + colTo.resize(0); + + // First process each set of beam colours on its own. + if (!beamAPtr->remnantColours(event, colFrom, colTo)) + physical = false; + if (!beamBPtr->remnantColours(event, colFrom, colTo)) + physical = false; + + // Then check that colours and anticolours are matched in whole event. + if ( physical && !checkColours(event) ) physical = false; + + // If no problems then done, else restore and loop. + if (physical) break; + for (int i = oldSize; i < event.size(); ++i) + event[i].cols( colSave[i - oldSize], acolSave[i - oldSize] ); + event.restoreJunctionSize(); + infoPtr->errorMsg("Warning in BeamRemnants::add:" + " colour tracing failed; will try again"); + } + + // If no solution after several tries then failed. + if (!physical) { + infoPtr->errorMsg("Error in BeamRemnants::add:" + " colour tracing failed after several attempts"); + return false; + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Set up trial transverse and longitudinal kinematics for each beam +// separately. Final decisions involve comparing the two beams. + +bool BeamRemnants::setKinematics( Event& event) { + + // References to beams to simplify indexing. + BeamParticle& beamA = *beamAPtr; + BeamParticle& beamB = *beamBPtr; + + // Nothing to do for lepton-lepton scattering with all energy already used. + if ( beamA.isUnresolvedLepton() && beamB.isUnresolvedLepton() ) + return true; + + // Check that has not already used up beams. + if ( (!beamA.isLepton() && beamA.xMax(-1) <= 0.) + || (!beamB.isLepton() && beamB.xMax(-1) <= 0.) ) { + infoPtr->errorMsg("Error in BeamRemnants::setKinematics:" + " no momentum left for beam remnants"); + return false; + } + + // Last beam-status particles. Offset relative to normal beam locations. + int nBeams = 3; + for (int i = 3; i < event.size(); ++i) + if (event[i].statusAbs() < 20) nBeams = i + 1; + int nOffset = nBeams - 3; + + // Reserve space for extra information on the systems and beams. + int nMaxBeam = max( beamA.size(), beamB.size() ); + vector sHatSys(nMaxBeam); + vector kTwidth(nMaxBeam); + vector kTcomp(nMaxBeam); + vector Msys(nSys); + + // Loop over all subsystems. Default values. Find invariant mass. + double kTcompSumA = 0.; + double kTcompSumB = 0.; + for (int iSys = 0; iSys < nSys; ++iSys) { + double kTwidthNow = 0.; + double mHatDamp = 1.; + int iInA = partonSystemsPtr->getInA(iSys); + int iInB = partonSystemsPtr->getInB(iSys); + double sHatNow = (event[iInA].p() + event[iInB].p()).m2Calc(); + + // Allow primordial kT reduction for small-mass and small-pT systems + // (for hardest interaction pT -> renormalization scale so also 2 -> 1). + if (doPrimordialKT) { + double mHat = sqrt(sHatNow); + mHatDamp = mHat / (mHat + halfMassForKT); + double scale = (iSys == 0) ? infoPtr->QRen() : infoPtr->pTMI(iSys); + kTwidthNow = ( (halfScaleForKT * primordialKTsoft + + scale * primordialKThard) / (halfScaleForKT + scale) ) * mHatDamp; + } + + // Store properties of compensation systems and total compensation power. + // Rescattered partons do not compensate, but may be massive. + sHatSys[iSys] = sHatNow; + kTwidth[iSys] = kTwidthNow ; + kTcomp[iSys] = mHatDamp; + if (beamA[iSys].isFromBeam()) kTcompSumA += mHatDamp; + else beamA[iSys].m( event[iInA].m() ); + if (beamB[iSys].isFromBeam()) kTcompSumB += mHatDamp; + else beamB[iSys].m( event[iInB].m() ); + } + + // Primordial kT and compensation power among remnants. + double kTwidthNow = (doPrimordialKT) ? primordialKTremnant : 0.; + for (int iRem = nSys; iRem < nMaxBeam; ++iRem) { + sHatSys[iRem] = 0.; + kTwidth[iRem] = kTwidthNow ; + kTcomp[iRem] = 1.; + } + kTcompSumA += beamA.size() - nSys; + kTcompSumB += beamB.size() - nSys; + + // Allow ten tries to construct kinematics (but normally works first). + bool physical; + double xSum[2], xInvM[2], w2Beam[2], wPosRem, wNegRem, w2Rem; + for (int iTry = 0; iTry < NTRYKINMATCH; ++iTry) { + physical = true; + + // Loop over the two beams. + for (int iBeam = 0; iBeam < 2; ++iBeam) { + BeamParticle& beam = (iBeam == 0) ? beamA : beamB; + int nPar = beam.size(); + + // Generate Gaussian pT for initiator partons inside hadrons. + // Store/restore rescattered parton momenta before primordial kT. + if (beam.isHadron() && doPrimordialKT) { + double pxSum = 0.; + double pySum = 0.; + for (int iPar = 0; iPar < nPar; ++iPar) { + if ( beam[iPar].isFromBeam() ) { + pair gauss2 = rndmPtr->gauss2(); + double px = kTwidth[iPar] * gauss2.first; + double py = kTwidth[iPar] * gauss2.second; + beam[iPar].px(px); + beam[iPar].py(py); + pxSum += px; + pySum += py; + } else { + int iInAB = (iBeam == 0) ? partonSystemsPtr->getInA(iPar) + : partonSystemsPtr->getInB(iPar); + beam[iPar].p( event[iInAB].p() ); + } + } + + // Share recoil between all initiator partons, rescatterers excluded. + double kTcompSum = (iBeam == 0) ? kTcompSumA : kTcompSumB; + for (int iPar = 0; iPar < nPar; ++iPar) + if (beam[iPar].isFromBeam() ) { + beam[iPar].px( beam[iPar].px() - pxSum * kTcomp[iPar] / kTcompSum ); + beam[iPar].py( beam[iPar].py() - pySum * kTcomp[iPar] / kTcompSum ); + } + + // Without primordial kT: still need to store rescattered partons. + } else if (beam.isHadron()) { + for (int iPar = 0; iPar < nPar; ++iPar) + if ( !beam[iPar].isFromBeam() ) { + int iInAB = (iBeam == 0) ? partonSystemsPtr->getInA(iPar) + : partonSystemsPtr->getInB(iPar); + beam[iPar].p( event[iInAB].p() ); + } + } + + // Pick unrescaled x values for remnants. Sum up (unscaled) p+ and p-. + xSum[iBeam] = 0.; + xInvM[iBeam] = 0.; + for (int iRem = nSys; iRem < nPar; ++iRem) { + double xPrel = beam.xRemnant( iRem); + beam[iRem].x(xPrel); + xSum[iBeam] += xPrel; + xInvM[iBeam] += beam[iRem].mT2()/xPrel; + } + + // Squared transverse mass for each beam, using lightcone x. + w2Beam[iBeam] = xSum[iBeam] * xInvM[iBeam]; + + // End separate treatment of the two beams. + } + + // Recalculate kinematics of initiator systems with primordial kT. + wPosRem = eCM; + wNegRem = eCM; + for (int iSys = 0; iSys < nSys; ++iSys) { + int iA = beamA[iSys].iPos(); + int iB = beamB[iSys].iPos(); + double sHat = sHatSys[iSys]; + + // Classify system: rescattering on either or both sides? + bool normalA = beamA[iSys].isFromBeam(); + bool normalB = beamB[iSys].isFromBeam(); + bool normalSys = normalA && normalB; + bool doubleRes = !normalA && !normalB; + + // Check whether final-state system momentum matches initial-state one. + if (allowRescatter && CORRECTMISMATCH) { + Vec4 pInitial = event[iA].p() + event[iB].p(); + Vec4 pFinal; + for (int iMem = 0; iMem < partonSystemsPtr->sizeOut(iSys); ++iMem) { + int iAB = partonSystemsPtr->getOut(iSys, iMem); + if (event[iAB].isFinal()) pFinal += event[iAB].p(); + } + + // Scale down primordial kT from side A if p+ increased. + if (normalA && pFinal.pPos() > pInitial.pPos()) + beamA[iSys].scalePT( pInitial.pPos() / pFinal.pPos() ); + + // Scale down primordial kT from side B if p- increased. + if (normalB && pFinal.pNeg() > pInitial.pNeg()) + beamB[iSys].scalePT( pInitial.pNeg() / pFinal.pNeg() ); + } + + // Rescatter: possible change in sign of lightcone momentum of a + // rescattered parton. If this happens, try to pick + // new primordial kT values + if (allowRescatter + && (event[iA].pPos() / beamA[iSys].pPos() < 0 + || event[iB].pNeg() / beamB[iSys].pNeg() < 0) ) { + infoPtr->errorMsg("Warning in BeamRemnants::setKinematics:" + " change in lightcone momentum sign; retrying kinematics"); + physical = false; + break; + } + + // Begin kinematics of partons after primordial kT has been added. + double sHatTAft = sHat + pow2( beamA[iSys].px() + beamB[iSys].px()) + + pow2( beamA[iSys].py() + beamB[iSys].py()); + double w2A = beamA[iSys].mT2(); + double w2B = beamB[iSys].mT2(); + double w2Diff = sHatTAft - w2A - w2B; + double lambda = pow2(w2Diff) - 4. * w2A * w2B; + + // Too large transverse momenta means that kinematics will not work. + if (lambda <= 0.) { + physical = false; + break; + } + double lamRoot = sqrtpos( lambda ); + + // Mirror solution if the two incoming have reverse rapidity ordering. + if (allowRescatter && doubleRes && (event[iA].pPos() * event[iB].pNeg() + < event[iA].pNeg() * event[iB].pPos()) ) lamRoot = -lamRoot; + + // Two procedures, which agree for normal scattering, separate here. + // First option keeps rapidity (and mass) of system unchanged by + // primordial kT, by modification of rescattered parton. + if (normalSys || doRescatterRestoreY || doubleRes) { + + // Find kinematics of initial system: transverse mass, and + // longitudinal momentum carried by all or rescattered partons. + double sHatTBef = sHat; + double wPosBef, wNegBef, wPosBefRes, wNegBefRes; + // Normal scattering. + if (normalSys) { + wPosBef = beamA[iSys].x() * eCM; + wNegBef = beamB[iSys].x() * eCM; + wPosBefRes = 0.; + wNegBefRes = 0.; + // Rescattering on side A. + } else if (normalB) { + sHatTBef += event[iA].pT2(); + wPosBef = event[iA].pPos(); + wNegBef = event[iA].pNeg() + beamB[iSys].x() * eCM; + wPosBefRes = beamA[iSys].pPos(); + wNegBefRes = beamA[iSys].pNeg(); + // Rescattering on side B. + } else if (normalA) { + sHatTBef += event[iB].pT2(); + wPosBef = beamA[iSys].x() * eCM + event[iB].pPos(); + wNegBef = event[iB].pNeg(); + wPosBefRes = beamB[iSys].pPos(); + wNegBefRes = beamB[iSys].pNeg(); + // Rescattering on both sides. + } else { + sHatTBef += pow2( event[iA].px() + event[iB].px()) + + pow2( event[iA].py() + event[iB].py()); + wPosBef = event[iA].pPos() + event[iB].pPos(); + wNegBef = event[iA].pNeg() + event[iB].pNeg(); + wPosBefRes = beamA[iSys].pPos() + beamB[iSys].pPos(); + wNegBefRes = beamA[iSys].pNeg() + beamB[iSys].pNeg(); + } + + // Rescale outgoing momenta to keep same mass and rapidity of system + // as originally, and solve for kinematics. + double rescale = sqrt(sHatTAft / sHatTBef); + double wPosAft = rescale * wPosBef; + double wNegAft = rescale * wNegBef; + wPosRem -= wPosAft - wPosBefRes; + wNegRem -= wNegAft - wNegBefRes; + double wPosA = 0.5 * (sHatTAft + w2A - w2B + lamRoot) / wNegAft; + double wNegB = 0.5 * (sHatTAft + w2B - w2A + lamRoot) / wPosAft; + + // Store modified beam parton momenta. + beamA[iSys].e( 0.5 * (wPosA + w2A / wPosA) ); + beamA[iSys].pz( 0.5 * (wPosA - w2A / wPosA) ); + beamB[iSys].e( 0.5 * (w2B / wNegB + wNegB) ); + beamB[iSys].pz( 0.5 * (w2B / wNegB - wNegB) ); + + // Second option keeps rescattered parton (and system mass) unchanged + // by primordial kT, by modification of system rapidity. + } else { + + // Rescattering on side A: preserve already scattered parton. + if (normalB) { + double wPosA = beamA[iSys].pPos(); + double wNegB = 0.5 * (w2Diff + lamRoot) / wPosA; + beamB[iSys].e( 0.5 * (w2B / wNegB + wNegB) ); + beamB[iSys].pz( 0.5 * (w2B / wNegB - wNegB) ); + wPosRem -= w2B / wNegB; + wNegRem -= wNegB; + + + // Rescattering on side B: preserve already scattered parton. + } else if (normalA) { + double wNegB = beamB[iSys].pNeg(); + double wPosA = 0.5 * (w2Diff + lamRoot) / wNegB; + beamA[iSys].e( 0.5 * (wPosA + w2A / wPosA) ); + beamA[iSys].pz( 0.5 * (wPosA - w2A / wPosA) ); + wPosRem -= wPosA; + wNegRem -= w2A / wPosA; + + // Primordial kT in double rescattering does change the mass of + // the system without any possible fix in this framework, which + // leads to incorrect boosts. Current choice is therefore always + // to handle it with the first procedure, where mass is retained. + } else { + } + } + + // Construct system rotation and boost caused by primordial kT. + Msys[iSys].reset(); + Msys[iSys].toCMframe( event[iA].p(), event[iB].p() ); + Msys[iSys].fromCMframe( beamA[iSys].p(), beamB[iSys].p() ); + + // Boost rescattered partons in subsequent beam A list. + for (int iSys2 = iSys + 1; iSys2 < nSys; ++iSys2) { + if (!beamA[iSys2].isFromBeam()) { + int iBefResc = event[ beamA[iSys2].iPos() ].mother1(); + for (int iMem = 0; iMem < partonSystemsPtr->sizeOut(iSys); ++iMem) + if (partonSystemsPtr->getOut(iSys, iMem) == iBefResc) { + Vec4 pTemp = event[iBefResc].p(); + pTemp.rotbst( Msys[iSys] ); + beamA[iSys2].p( pTemp ); + } + } + + // Boost rescattered partons in subsequent beam B list. + if (!beamB[iSys2].isFromBeam()) { + int iBefResc = event[ beamB[iSys2].iPos() ].mother1(); + for (int iMem = 0; iMem < partonSystemsPtr->sizeOut(iSys); ++iMem) + if (partonSystemsPtr->getOut(iSys, iMem) == iBefResc) { + Vec4 pTemp = event[iBefResc].p(); + pTemp.rotbst( Msys[iSys] ); + beamB[iSys2].p( pTemp ); + } + } + } + } + + // Check that remaining momentum is enough for remnants. + if (wPosRem < 0. || wNegRem < 0.) physical = false; + w2Rem = wPosRem * wNegRem; + if (sqrtpos(w2Rem) < sqrt(w2Beam[0]) + sqrt(w2Beam[1])) + physical = false; + + // End of loop over ten tries. Do not loop when solution found. + if (physical) break; + } + + // If no solution after ten tries then failed. + if (!physical) { + infoPtr->errorMsg("Error in BeamRemnants::setKinematics:" + " kinematics construction failed"); + return false; + } + + // For successful initiator kinematics process whole systems. + Vec4 pSumOut; + for (int iSys = 0; iSys < nSys; ++iSys) { + + // Copy initiators and their systems and boost them accordingly. + // Update subsystem and beams info on new positions of partons. + // Update daughter info of mothers, i.e. of beams, for hardest interaction. + if (beamA[iSys].isFromBeam()) { + int iA = beamA[iSys].iPos(); + int iAcopy = event.copy(iA, -61); + event[iAcopy].rotbst(Msys[iSys]); + partonSystemsPtr->setInA(iSys, iAcopy); + beamA[iSys].iPos( iAcopy); + if (iSys == 0) { + int mother = event[iAcopy].mother1(); + event[mother].daughter1(iAcopy); + } + } + if (beamB[iSys].isFromBeam()) { + int iB = beamB[iSys].iPos(); + int iBcopy = event.copy(iB, -61); + event[iBcopy].rotbst(Msys[iSys]); + partonSystemsPtr->setInB(iSys, iBcopy); + beamB[iSys].iPos( iBcopy); + if (iSys == 0) { + int mother = event[iBcopy].mother1(); + event[mother].daughter1(iBcopy); + } + } + + for (int iMem = 0; iMem < partonSystemsPtr->sizeOut(iSys); ++iMem) { + int iAB = partonSystemsPtr->getOut(iSys, iMem); + if (event[iAB].isFinal()) { + int iABcopy = event.copy(iAB, 62); + event[iABcopy].rotbst(Msys[iSys]); + partonSystemsPtr->setOut(iSys, iMem, iABcopy); + pSumOut += event[iABcopy].p(); + } + } + + } + + // Colour dipoles spanning systems gives mismatch between FSR recoils + // and primordial kT boosts. + if (allowRescatter && CORRECTMISMATCH) { + + // Find summed pT of beam remnants = - wanted pT of systems. + double pxBeams = 0.; + double pyBeams = 0.; + for (int iRem = nSys; iRem < beamA.size(); ++iRem) { + pxBeams += beamA[iRem].px(); + pyBeams += beamA[iRem].py(); + } + for (int iRem = nSys; iRem < beamB.size(); ++iRem) { + pxBeams += beamB[iRem].px(); + pyBeams += beamB[iRem].py(); + } + + // Boost all final partons in systems transversely, and also their sum. + Vec4 pSumTo( -pxBeams, -pyBeams, pSumOut.pz(), sqrt( pow2(pxBeams) + + pow2(pyBeams) + pow2(pSumOut.pz()) + pSumOut.m2Calc() ) ); + RotBstMatrix Mmismatch; + Mmismatch.bst( pSumOut, pSumTo); + for (int iSys = 0; iSys < nSys; ++iSys) + for (int iMem = 0; iMem < partonSystemsPtr->sizeOut(iSys); ++iMem) { + int iAB = partonSystemsPtr->getOut(iSys, iMem); + if (event[iAB].isFinal()) event[iAB].rotbst(Mmismatch); + } + pSumOut.rotbst(Mmismatch); + + // Reset energy and momentum sum, to be compensated by beam remnants. + wPosRem = eCM - (pSumOut.e() + pSumOut.pz()); + wNegRem = eCM - (pSumOut.e() - pSumOut.pz()); + w2Rem = wPosRem * wNegRem; + if ( wPosRem < 0. || wNegRem < 0. + || sqrtpos(w2Rem) < sqrt(w2Beam[0]) + sqrt(w2Beam[1])) { + infoPtr->errorMsg("Error in BeamRemnants::setKinematics:" + " kinematics construction failed owing to recoil mismatch"); + return false; + } + } + + // Construct x rescaling factors for the two remants. + double lambdaRoot = sqrtpos( pow2(w2Rem - w2Beam[0] - w2Beam[1]) + - 4. * w2Beam[0] * w2Beam[1] ); + double rescaleA = (w2Rem + w2Beam[0] - w2Beam[1] + lambdaRoot) + / (2. * w2Rem * xSum[0]) ; + double rescaleB = (w2Rem + w2Beam[1] - w2Beam[0] + lambdaRoot) + / (2. * w2Rem * xSum[1]) ; + + // Construct energy and pz for remnants in first beam. + for (int iRem = nSys; iRem < beamA.size(); ++iRem) { + double pPos = rescaleA * beamA[iRem].x() * wPosRem; + double pNeg = beamA[iRem].mT2() / pPos; + beamA[iRem].e( 0.5 * (pPos + pNeg) ); + beamA[iRem].pz( 0.5 * (pPos - pNeg) ); + + // Add these partons to the normal event record. + int iNew = event.append( beamA[iRem].id(), 63, 1 + nOffset, 0, 0, 0, + beamA[iRem].col(), beamA[iRem].acol(), beamA[iRem].p(), + beamA[iRem].m() ); + beamA[iRem].iPos( iNew); + } + + // Construct energy and pz for remnants in second beam. + for (int iRem = nSys; iRem < beamB.size(); ++iRem) { + double pNeg = rescaleB * beamB[iRem].x() * wNegRem; + double pPos = beamB[iRem].mT2() / pNeg; + beamB[iRem].e( 0.5 * (pPos + pNeg) ); + beamB[iRem].pz( 0.5 * (pPos - pNeg) ); + + // Add these partons to the normal event record. + int iNew = event.append( beamB[iRem].id(), 63, 2 + nOffset, 0, 0, 0, + beamB[iRem].col(), beamB[iRem].acol(), beamB[iRem].p(), + beamB[iRem].m() ); + beamB[iRem].iPos( iNew); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Allow colour reconnections by mergings of collision subsystems. +// iRec is system that may be reconnected, by moving its gluons to iSys, +// where minimal pT (or equivalently Lambda) is used to pick location. +// Therefore all dipoles in iSys have to be found, and all gluons in iRec. +// Matching q-qbar pairs are treated by analogy with gluons. +// Note: owing to rescatterings some outgoing partons must be skipped. + +bool BeamRemnants::reconnectColours( Event& event) { + + // References to beams to simplify indexing. + BeamParticle& beamA = *beamAPtr; + BeamParticle& beamB = *beamBPtr; + + // Prepare record of which systems should be merged onto another. + // The iSys system must have colour in final state to attach to it. + vector iMerge(nSys); + vector hasColour(nSys); + for (int iSys = 0; iSys < nSys; ++iSys) { + iMerge[iSys] = iSys; + bool hasCol = false; + for (int iMem = 0; iMem < partonSystemsPtr->sizeOut(iSys); ++iMem) { + int iNow = partonSystemsPtr->getOut( iSys, iMem); + if (event[iNow].isFinal() && (event[iNow].col() > 0 + || event[iNow].acol() > 0) ) { + hasCol = true; + break; + } + } + hasColour[iSys] = hasCol; + } + + // Loop over systems to decide which should be reconnected. + for (int iRec = nSys - 1; iRec > 0; --iRec) { + + // Determine reconnection strength from pT scale of system. + double pT2Rec = pow2( infoPtr->pTMI(iRec) ); + double probRec = pT20Rec / (pT20Rec + pT2Rec); + + // Loop over other systems iSys at higher pT scale and + // decide whether to reconnect the iRec gluons onto one of them. + for (int iSys = iRec - 1; iSys >= 0; --iSys) + if (hasColour[iSys] && probRec > rndmPtr->flat()) { + + // The iRec system and all merged with it to be merged with iSys. + iMerge[iRec] = iSys; + for (int iRec2 = iRec + 1; iRec2 < nSys; ++iRec2) + if (iMerge[iRec2] == iRec) iMerge[iRec2] = iSys; + + // Once a system has been merged do not test it anymore. + break; + } + } + + // Loop over systems. Check whether other systems to be merged with it. + for (int iSys = 0; iSys < nSys; ++iSys) { + int nMerge = 0; + for (int iRec = iSys + 1; iRec < nSys; ++iRec) + if (iMerge[iRec] == iSys) ++nMerge; + if (nMerge == 0) continue; + + // Incoming partons not counted if rescattered. + int iInASys = partonSystemsPtr->getInA(iSys); + bool hasInA = (beamA[iSys].isFromBeam()); + int iInBSys = partonSystemsPtr->getInB(iSys); + bool hasInB = (beamB[iSys].isFromBeam()); + + // Begin find dipoles in iSys system. + vector dipoles; + int sizeOut = partonSystemsPtr->sizeOut(iSys); + for (int iMem = 0; iMem < sizeOut; ++iMem) { + + // Find colour dipoles to beam remnant. + int iNow = partonSystemsPtr->getOut( iSys, iMem); + if (!event[iNow].isFinal()) continue; + int col = event[iNow].col(); + if (col > 0) { + if (hasInA && event[iInASys].col() == col) + dipoles.push_back( BeamDipole( col, iNow, iInASys ) ); + else if (hasInB && event[iInBSys].col() == col) + dipoles.push_back( BeamDipole( col, iNow, iInBSys ) ); + + // Find colour dipole between final-state partons. + else for (int iMem2 = 0; iMem2 < sizeOut; ++iMem2) + if (iMem2 != iMem) { + int iNow2 = partonSystemsPtr->getOut( iSys, iMem2); + if (!event[iNow2].isFinal()) continue; + if (event[iNow2].acol() == col) { + dipoles.push_back( BeamDipole( col, iNow, iNow2) ); + break; + } + } + } + + // Find anticolour dipoles to beam remnant. + int acol = event[iNow].acol(); + if (acol > 0) { + if (hasInA && event[iInASys].acol() == acol) + dipoles.push_back( BeamDipole( acol, iInASys, iNow ) ); + else if (hasInB && event[iInBSys].acol() == acol) + dipoles.push_back( BeamDipole( acol, iInBSys, iNow ) ); + } + } + + // Skip mergings if no dipoles found. + if (dipoles.size() == 0) continue; + + // Find dipole sizes. + for (int iDip = 0; iDip < int(dipoles.size()); ++iDip) + dipoles[iDip].p1p2 = event[dipoles[iDip].iCol].p() + * event[dipoles[iDip].iAcol].p(); + + // Loop over systems iRec to be merged with iSys. + for (int iRec = iSys + 1; iRec < nSys; ++iRec) { + if (iMerge[iRec] != iSys) continue; + + // Information on iRec. Vectors for gluons and anything else. + int sizeRec = partonSystemsPtr->sizeOut(iRec); + int iInARec = partonSystemsPtr->getInA(iRec); + int iInBRec = partonSystemsPtr->getInB(iRec); + int nGluRec = 0; + vector iGluRec; + vector pT2GluRec; + int nAnyRec = 0; + vector iAnyRec; + vector freeAnyRec; + + // Copy of gluon positions in descending order. + for (int iMem = 0; iMem < sizeRec; ++iMem) { + int iNow = partonSystemsPtr->getOut( iRec, iMem); + if (!event[iNow].isFinal()) continue; + if (event[iNow].isGluon()) { + ++nGluRec; + iGluRec.push_back( iNow ); + pT2GluRec.push_back( event[iNow].pT2() ); + for (int i = nGluRec - 1; i > 1; --i) { + if (pT2GluRec[i - 1] > pT2GluRec[i]) break; + swap( iGluRec[i - 1], iGluRec[i] ); + swap( pT2GluRec[i - 1], pT2GluRec[i] ); + } + // Copy of anything else, mainly quarks, in no particular order. + } else { + ++nAnyRec; + iAnyRec.push_back( iNow ); + freeAnyRec.push_back( true ); + } + } + + // For each gluon in iRec now find the dipole that gives the smallest + // (pGlu * pI) (pGlu * pJ) / (pI * pJ), i.e. minimal pT (and Lambda). + for (int iGRec = 0; iGRec < nGluRec; ++iGRec) { + int iGlu = iGluRec[iGRec]; + Vec4 pGlu = event[iGlu].p(); + int iDipMin = 0; + double pT2DipMin = sCM; + for (int iDip = 0; iDip < int(dipoles.size()); ++iDip) { + double pT2Dip = (pGlu * event[dipoles[iDip].iCol].p()) + * (pGlu * event[dipoles[iDip].iAcol].p()) / dipoles[iDip].p1p2; + if (pT2Dip < pT2DipMin) { + iDipMin = iDip; + pT2DipMin = pT2Dip; + } + } + + // Attach the gluon to the dipole, i.e. split the dipole in two. + int colGlu = event[iGlu].col(); + int acolGlu = event[iGlu].acol(); + int colDip = dipoles[iDipMin].col; + int iColDip = dipoles[iDipMin].iCol; + int iAcolDip = dipoles[iDipMin].iAcol; + event[iGlu].acol( colDip ); + if (event[iAcolDip].acol() == colDip) + event[iAcolDip].acol( colGlu ); + else event[iAcolDip].col( colGlu ); + dipoles[iDipMin].iAcol = iGlu; + dipoles[iDipMin].p1p2 = event[iColDip].p() * pGlu; + dipoles.push_back( BeamDipole( colGlu, iGlu, iAcolDip ) ); + dipoles.back().p1p2 = pGlu * event[iAcolDip].p(); + + // Remove gluon from old system: reconnect colours. + for (int i = oldSize; i < event.size(); ++i) + if (i != iGlu && i != iAcolDip) { + if (event[i].isFinal()) { + if (event[i].acol() == colGlu) event[i].acol( acolGlu ); + } else { + if (event[i].col() == colGlu) event[i].col( acolGlu ); + } + } + } + + // See if any matching quark-antiquark pairs among the rest. + for (int iQRec = 0; iQRec < nAnyRec; ++iQRec) { + int iQ = iAnyRec[iQRec]; + int idQ = event[iQ].id(); + if (freeAnyRec[iQRec] && idQ > 0 && idQ < 6) + for (int iQbarRec = 0; iQbarRec < nAnyRec; ++iQbarRec) { + int iQbar = iAnyRec[iQbarRec]; + if (freeAnyRec[iQbarRec] && event[iQbar].id() == -idQ) { + + // Check that these can be traced back to same gluon splitting. + // For now also avoid qqbar pairs produced in rescatterings.?? + int iTopQ = event.iTopCopyId(iQ); + int iTopQbar = event.iTopCopyId(iQbar); + int iMother = event[iTopQ].mother1(); + if (event[iTopQbar].mother1() == iMother + && event[iMother].isGluon() && event[iMother].status() != -34 + && event[iMother + 1].status() != -34 ) { + + // Now find the dipole that gives the smallest + // ((pQ + pQbar) * pI) ((pQ + pQbar) * pJ) / (pI * pJ). + Vec4 pGlu = event[iQ].p() + event[iQbar].p(); + int iDipMin = 0; + double pT2DipMin = sCM; + for (int iDip = 0; iDip < int(dipoles.size()); ++iDip) { + double pT2Dip = (pGlu * event[dipoles[iDip].iCol].p()) + * (pGlu * event[dipoles[iDip].iAcol].p()) + / dipoles[iDip].p1p2; + if (pT2Dip < pT2DipMin) { + iDipMin = iDip; + pT2DipMin = pT2Dip; + } + } + + // Attach the q-qbar pair to the dipole, i.e. split the dipole. + int colGlu = event[iQ].col(); + int acolGlu = event[iQbar].acol(); + int colDip = dipoles[iDipMin].col; + int iColDip = dipoles[iDipMin].iCol; + int iAcolDip = dipoles[iDipMin].iAcol; + event[iQbar].acol( colDip ); + if (event[iAcolDip].acol() == colDip) + event[iAcolDip].acol( colGlu ); + else event[iAcolDip].col( colGlu ); + dipoles[iDipMin].iAcol = iQbar; + dipoles[iDipMin].p1p2 = event[iColDip].p() * event[iQbar].p(); + dipoles.push_back( BeamDipole( colGlu, iQ, iAcolDip ) ); + dipoles.back().p1p2 = event[iQ].p() * event[iAcolDip].p(); + + // Remove q-qbar pair from old system: reconnect colours. + freeAnyRec[iQRec] = false; + freeAnyRec[iQbarRec] = false; + for (int i = oldSize; i < event.size(); ++i) + if (i != iQRec && i != iQbarRec && i != iColDip && i != iAcolDip) { + if (event[i].isFinal()) { + if (event[i].acol() == colGlu) event[i].acol( acolGlu ); + } else { + if (event[i].col() == colGlu) event[i].col( acolGlu ); + } + } + + // Done with processing of q-qbar pairs. + } + } + } + } + + // If only two beam gluons left of system, set their colour = anticolour. + // Used by BeamParticle::remnantColours to skip irrelevant gluons. + if ( event[iInARec].isGluon() && !event[iInARec].isRescatteredIncoming() + && event[iInBRec].isGluon() && !event[iInBRec].isRescatteredIncoming() + && event[iInARec].col() == event[iInBRec].acol() + && event[iInARec].acol() == event[iInBRec].col() ) { + event[iInARec].acol( event[iInARec].col() ); + event[iInBRec].acol( event[iInBRec].col() ); + } + + // End of loops over iRec and iSys systems. + } + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Collapse colours and check that they are consistent. + +bool BeamRemnants::checkColours( Event& event) { + + // No colours in lepton beams so no need to do anything. + if (beamAPtr->isLepton() && beamBPtr->isLepton()) return true; + + // Remove ambiguities when one colour collapses two ways. + // Resolve chains where one colour is mapped to another. + for (int iCol = 1; iCol < int(colFrom.size()); ++iCol) + for (int iColRef = 0; iColRef < iCol; ++iColRef) { + if (colFrom[iCol] == colFrom[iColRef]) { + colFrom[iCol] = colTo[iCol]; + colTo[iCol] = colTo[iColRef]; + } + if (colTo[iCol] == colFrom[iColRef]) colTo[iCol] = colTo[iColRef]; + } + + // Transform event record colours from beam remnant colour collapses. + for (int i = oldSize; i < event.size(); ++i) { + int col = event[i].col(); + int acol = event[i].acol(); + for (int iCol = 0; iCol < int(colFrom.size()); ++iCol) { + if (col == colFrom[iCol]) {col = colTo[iCol]; event[i].col(col);} + if (acol == colFrom[iCol]) {acol = colTo[iCol]; event[i].acol(acol);} + } + } + + // Transform junction colours from beam remnant colour collapses. + for (int iJun = 0; iJun < event.sizeJunction(); ++iJun) + for (int leg = 0; leg < 3; ++leg) { + int col = event.colJunction(iJun, leg); + for (int iCol = 0; iCol < int(colFrom.size()); ++iCol) + if (col == colFrom[iCol]) { + col = colTo[iCol]; + event.colJunction(iJun, leg, col); + } + } + + // Arrays for current colours and anticolours, and for singlet gluons. + vector colList; + vector acolList; + vector iSingletGluon; + + // Find current colours and anticolours in the event record. + for (int i = oldSize; i < event.size(); ++i) + if (event[i].isFinal()) { + int id = event[i].id(); + int col = event[i].col(); + int acol = event[i].acol(); + + // Quarks must have colour set, antiquarks anticolour, gluons both. + if ( (id > 0 && id < 9 && (col <= 0 || acol != 0) ) + || (id < 0 && id > -9 && (col != 0 || acol <= 0) ) + || (id == 21 && (col <= 0 || acol <= 0) ) ) { + infoPtr->errorMsg("Error in BeamRemnants::checkColours: " + "q/qbar/g has wrong colour slots set"); + return false; + } + + // Save colours/anticolours, and position of colour singlet gluons. + if ( col > 0) colList.push_back( col ); + if (acol > 0) acolList.push_back( acol ); + if (col > 0 && acol == col) iSingletGluon.push_back(i); + } + + // Run though list of singlet gluons and put them on final-state dipole + // (i,j) that offers smallest (p_g p_i) * (p_g p_j) / (p_i p_j). + for (int iS = 0; iS < int(iSingletGluon.size()); ++iS) { + int iGlu = iSingletGluon[iS]; + int iAcolDip = -1; + double pT2DipMin = sCM; + for (int iC = oldSize; iC < event.size(); ++iC) + if (iC != iGlu && event[iC].isFinal()) { + int colDip = event[iC].col(); + if (colDip > 0 && event[iC].acol() !=colDip) + for (int iA = oldSize; iA < event.size(); ++iA) + if (iA != iGlu && iA != iC && event[iA].isFinal() + && event[iA].acol() == colDip && event[iA].col() !=colDip) { + double pT2Dip = (event[iGlu].p() * event[iC].p()) + * (event[iGlu].p() * event[iA].p()) + / (event[iC].p() * event[iA].p()); + if (pT2Dip < pT2DipMin) { + iAcolDip = iA; + pT2DipMin = pT2Dip; + } + } + } + + // Fail if no dipole. Else insert singlet gluon onto relevant dipole. + if (iAcolDip == -1) return false; + event[iGlu].acol( event[iAcolDip].acol() ); + event[iAcolDip].acol( event[iGlu].col() ); + } + + // Check that not the same colour or anticolour appears twice. + for (int iCol = 0; iCol < int(colList.size()) - 1; ++iCol) { + int col = colList[iCol]; + for (int iCol2 = iCol + 1; iCol2 < int(colList.size()); ++iCol2) + if (colList[iCol2] == col) { + infoPtr->errorMsg("Warning in BeamRemnants::checkColours:" + " colour appears twice"); + if (!ALLOWCOLOURTWICE) return false; + } + } + for (int iAcol = 0; iAcol < int(acolList.size()) - 1; ++iAcol) { + int acol = acolList[iAcol]; + for (int iAcol2 = iAcol + 1; iAcol2 < int(acolList.size()); ++iAcol2) + if (acolList[iAcol2] == acol) { + infoPtr->errorMsg("Warning in BeamRemnants::checkColours:" + " anticolour appears twice"); + if (!ALLOWCOLOURTWICE) return false; + } + } + + // Remove all matching colour-anticolour pairs. + bool foundPair = true; + while (foundPair && colList.size() > 0 && acolList.size() > 0) { + foundPair = false; + for (int iCol = 0; iCol < int(colList.size()); ++iCol) { + for (int iAcol = 0; iAcol < int(acolList.size()); ++iAcol) { + if (acolList[iAcol] == colList[iCol]) { + colList[iCol] = colList.back(); colList.pop_back(); + acolList[iAcol] = acolList.back(); acolList.pop_back(); + foundPair = true; break; + } + } if (foundPair) break; + } + } + + // Check that remaining (anti)colours are accounted for by junctions. + for (int iJun = 0; iJun < event.sizeJunction(); ++iJun) { + int kindJun = event.kindJunction(iJun); + for (int leg = 0; leg < 3; ++leg) { + int colEnd = event.colJunction(iJun, leg); + + // Junction connected to three colours. + if (kindJun == 1) { + bool foundCol = false; + for (int iCol = 0; iCol < int(colList.size()); ++iCol) + if (colList[iCol] == colEnd) { + colList[iCol] = colList.back(); + colList.pop_back(); + foundCol = true; + break; + } + } + + // Junction connected to three anticolours. + else if (kindJun == 2) { + bool foundCol = false; + for (int iAcol = 0; iAcol < int(acolList.size()); ++iAcol) + if (acolList[iAcol] == colEnd) { + acolList[iAcol] = acolList.back(); + acolList.pop_back(); + foundCol = true; + break; + } + } + + // End junction check. More junction cases to come?? + } + } + + + // Repair step - sometimes needed when rescattering allowed. + if (colList.size() > 0 || acolList.size() > 0) + infoPtr->errorMsg("Warning in BeamRemnants::checkColours:" + " need to repair unmatched colours"); + while (colList.size() > 0 && acolList.size() > 0) { + + // Replace one colour and one anticolour index by a new common one. + int colMatch = colList.back(); + int acolMatch = acolList.back(); + int colNew = event.nextColTag(); + colList.pop_back(); + acolList.pop_back(); + for (int i = oldSize; i < event.size(); ++i) + if (event[i].isFinal() && event[i].col() == colMatch) { + event[i].col( colNew); + break; + } + for (int i = oldSize; i < event.size(); ++i) + if (event[i].isFinal() && event[i].acol() == acolMatch) { + event[i].acol( colNew); + break; + } + } + + // Done. + return (colList.size() == 0 && acolList.size() == 0); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/BeamShape.cxx b/PYTHIA8/pythia8140/src/BeamShape.cxx new file mode 100644 index 00000000000..e3f787ed397 --- /dev/null +++ b/PYTHIA8/pythia8140/src/BeamShape.cxx @@ -0,0 +1,151 @@ +// BeamShape.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the BeamShape class. + +#include "BeamShape.h" + +namespace Pythia8 { + +//========================================================================== + +// The BeamShape class. + +//-------------------------------------------------------------------------- + +// Initialize beam parameters. + + void BeamShape::init( Settings& settings, Rndm* rndmPtrIn) { + + // Save pointer. + rndmPtr = rndmPtrIn; + + // Main flags. + allowMomentumSpread = settings.flag("Beams:allowMomentumSpread"); + allowVertexSpread = settings.flag("Beams:allowVertexSpread"); + + // Parameters for beam A momentum spread. + sigmaPxA = settings.parm("Beams:sigmaPxA"); + sigmaPyA = settings.parm("Beams:sigmaPyA"); + sigmaPzA = settings.parm("Beams:sigmaPzA"); + maxDevA = settings.parm("Beams:maxDevA"); + + // Parameters for beam B momentum spread. + sigmaPxB = settings.parm("Beams:sigmaPxB"); + sigmaPyB = settings.parm("Beams:sigmaPyB"); + sigmaPzB = settings.parm("Beams:sigmaPzB"); + maxDevB = settings.parm("Beams:maxDevB"); + + // Parameters for beam vertex spread. + sigmaVertexX = settings.parm("Beams:sigmaVertexX"); + sigmaVertexY = settings.parm("Beams:sigmaVertexY"); + sigmaVertexZ = settings.parm("Beams:sigmaVertexZ"); + maxDevVertex = settings.parm("Beams:maxDevVertex"); + sigmaTime = settings.parm("Beams:sigmaTime"); + maxDevTime = settings.parm("Beams:maxDevTime"); + + // Parameters for beam vertex offset. + offsetX = settings.parm("Beams:offsetVertexX"); + offsetY = settings.parm("Beams:offsetVertexY"); + offsetZ = settings.parm("Beams:offsetVertexZ"); + offsetT = settings.parm("Beams:offsetTime"); + +} + +//-------------------------------------------------------------------------- + +// Set the two beam momentum deviations and the beam vertex. + +void BeamShape::pick() { + + // Reset all values. + deltaPxA = deltaPyA = deltaPzA = deltaPxB = deltaPyB = deltaPzB + = vertexX = vertexY = vertexZ = vertexT = 0.; + + // Set beam A momentum deviation by a three-dimensional Gaussian. + if (allowMomentumSpread) { + double totalDev, gauss; + do { + totalDev = 0.; + if (sigmaPxA > 0.) { + gauss = rndmPtr->gauss(); + deltaPxA = sigmaPxA * gauss; + totalDev += gauss * gauss; + } + if (sigmaPyA > 0.) { + gauss = rndmPtr->gauss(); + deltaPyA = sigmaPyA * gauss; + totalDev += gauss * gauss; + } + if (sigmaPzA > 0.) { + gauss = rndmPtr->gauss(); + deltaPzA = sigmaPzA * gauss; + totalDev += gauss * gauss; + } + } while (totalDev > maxDevA * maxDevA); + + // Set beam B momentum deviation by a three-dimensional Gaussian. + do { + totalDev = 0.; + if (sigmaPxB > 0.) { + gauss = rndmPtr->gauss(); + deltaPxB = sigmaPxB * gauss; + totalDev += gauss * gauss; + } + if (sigmaPyB > 0.) { + gauss = rndmPtr->gauss(); + deltaPyB = sigmaPyB * gauss; + totalDev += gauss * gauss; + } + if (sigmaPzB > 0.) { + gauss = rndmPtr->gauss(); + deltaPzB = sigmaPzB * gauss; + totalDev += gauss * gauss; + } + } while (totalDev > maxDevB * maxDevB); + } + + // Set beam vertex location by a three-dimensional Gaussian. + if (allowVertexSpread) { + double totalDev, gauss; + do { + totalDev = 0.; + if (sigmaVertexX > 0.) { + gauss = rndmPtr->gauss(); + vertexX = sigmaVertexX * gauss; + totalDev += gauss * gauss; + } + if (sigmaVertexY > 0.) { + gauss = rndmPtr->gauss(); + vertexY = sigmaVertexY * gauss; + totalDev += gauss * gauss; + } + if (sigmaVertexZ > 0.) { + gauss = rndmPtr->gauss(); + vertexZ = sigmaVertexZ * gauss; + totalDev += gauss * gauss; + } + } while (totalDev > maxDevVertex * maxDevVertex); + + // Set beam collision time by a Gaussian. + if (sigmaTime > 0.) { + do gauss = rndmPtr->gauss(); + while (abs(gauss) > maxDevTime); + vertexT = sigmaTime * gauss; + } + + // Add offset to beam vertex. + vertexX += offsetX; + vertexY += offsetY; + vertexZ += offsetZ; + vertexT += offsetT; + } + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/BoseEinstein.cxx b/PYTHIA8/pythia8140/src/BoseEinstein.cxx new file mode 100644 index 00000000000..2841c80aa4d --- /dev/null +++ b/PYTHIA8/pythia8140/src/BoseEinstein.cxx @@ -0,0 +1,281 @@ +// BoseEinstein.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the BoseEinsten class. + +#include "BoseEinstein.h" + +namespace Pythia8 { + +//========================================================================== + +// The BoseEinstein class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Enumeration of id codes and table for particle species considered. +const int BoseEinstein::IDHADRON[9] = { 211, -211, 111, 321, -321, + 130, 310, 221, 331 }; +const int BoseEinstein::ITABLE[9] = { 0, 0, 0, 1, 1, 1, 1, 2, 3 }; + +// Distance between table entries, normalized to min( 2*mass, QRef). +const double BoseEinstein::STEPSIZE = 0.05; + +// Skip shift for two extremely close particles, to avoid instabilities. +const double BoseEinstein::Q2MIN = 1e-8; + +// Parameters of energy compensation procedure: maximally allowed +// relative energy error, iterative stepsize, and number of iterations. +const double BoseEinstein::COMPRELERR = 1e-10; +const double BoseEinstein::COMPFACMAX = 1000.; +const int BoseEinstein::NCOMPSTEP = 10; + +//-------------------------------------------------------------------------- + +// Find settings. Precalculate table used to find momentum shifts. + +bool BoseEinstein::init(Info* infoPtrIn, Settings& settings, + ParticleData& particleData) { + + // Save pointer. + infoPtr = infoPtrIn; + + // Main flags. + doPion = settings.flag("BoseEinstein:Pion"); + doKaon = settings.flag("BoseEinstein:Kaon"); + doEta = settings.flag("BoseEinstein:Eta"); + + // Shape of Bose-Einstein enhancement/suppression. + lambda = settings.parm("BoseEinstein:lambda"); + QRef = settings.parm("BoseEinstein:QRef"); + + // Multiples and inverses (= "radii") of distance parameters in Q-space. + QRef2 = 2. * QRef; + QRef3 = 3. * QRef; + R2Ref = 1. / (QRef * QRef); + R2Ref2 = 1. / (QRef2 * QRef2); + R2Ref3 = 1. / (QRef3 * QRef3); + + // Masses of particles with Bose-Einstein implemented. + for (int iSpecies = 0; iSpecies < 9; ++iSpecies) + mHadron[iSpecies] = particleData.m0( IDHADRON[iSpecies] ); + + // Pair pi, K, eta and eta' masses for use in tables. + mPair[0] = 2. * mHadron[0]; + mPair[1] = 2. * mHadron[3]; + mPair[2] = 2. * mHadron[7]; + mPair[3] = 2. * mHadron[8]; + + // Loop over the four required tables. Local variables. + double Qnow, Q2now, centerCorr; + for (int iTab = 0; iTab < 4; ++iTab) { + m2Pair[iTab] = mPair[iTab] * mPair[iTab]; + + // Step size and number of steps in normal table. + deltaQ[iTab] = STEPSIZE * min(mPair[iTab], QRef); + nStep[iTab] = min( 199, 1 + int(3. * QRef / deltaQ[iTab]) ); + maxQ[iTab] = (nStep[iTab] - 0.1) * deltaQ[iTab]; + centerCorr = deltaQ[iTab] * deltaQ[iTab] / 12.; + + // Construct normal table recursively in Q space. + shift[iTab][0] = 0.; + for (int i = 1; i <= nStep[iTab]; ++i) { + Qnow = deltaQ[iTab] * (i - 0.5); + Q2now = Qnow * Qnow; + shift[iTab][i] = shift[iTab][i - 1] + exp(-Q2now * R2Ref) + * deltaQ[iTab] * (Q2now + centerCorr) / sqrt(Q2now + m2Pair[iTab]); + } + + // Step size and number of steps in compensation table. + deltaQ3[iTab] = STEPSIZE * min(mPair[iTab], QRef3); + nStep3[iTab] = min( 199, 1 + int(9. * QRef / deltaQ3[iTab]) ); + maxQ3[iTab] = (nStep3[iTab] - 0.1) * deltaQ3[iTab]; + centerCorr = deltaQ3[iTab] * deltaQ3[iTab] / 12.; + + // Construct compensation table recursively in Q space. + shift3[iTab][0] = 0.; + for (int i = 1; i <= nStep3[iTab]; ++i) { + Qnow = deltaQ3[iTab] * (i - 0.5); + Q2now = Qnow * Qnow; + shift3[iTab][i] = shift3[iTab][i - 1] + exp(-Q2now * R2Ref3) + * deltaQ3[iTab] * (Q2now + centerCorr) / sqrt(Q2now + m2Pair[iTab]); + } + + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Perform Bose-Einstein corrections on an event. + +bool BoseEinstein::shiftEvent( Event& event) { + + // Reset list of identical particles. + hadronBE.resize(0); + + // Loop over all hadron species with BE effects. + nStored[0] = 0; + for (int iSpecies = 0; iSpecies < 9; ++iSpecies) { + nStored[iSpecies + 1] = nStored[iSpecies]; + if (!doPion && iSpecies <= 2) continue; + if (!doKaon && iSpecies >= 3 && iSpecies <= 6) continue; + if (!doEta && iSpecies >= 7) continue; + + // Properties of current hadron species. + int idNow = IDHADRON[ iSpecies ]; + int iTab = ITABLE[ iSpecies ]; + + // Loop through event record to store copies of current species. + for (int i = 0; i < event.size(); ++i) + if ( event[i].id() == idNow && event[i].isFinal() ) + hadronBE.push_back( + BoseEinsteinHadron( idNow, i, event[i].p(), event[i].m() ) ); + nStored[iSpecies + 1] = hadronBE.size(); + + // Loop through pairs of identical particles and find shifts. + for (int i1 = nStored[iSpecies]; i1 < nStored[iSpecies+1] - 1; ++i1) + for (int i2 = i1 + 1; i2 < nStored[iSpecies+1]; ++i2) + shiftPair( i1, i2, iTab); + } + + // Must have at least two pairs to carry out compensation. + if (nStored[9] < 2) return true; + + // Shift momenta and recalculate energies. + double eSumOriginal = 0.; + double eSumShifted = 0.; + double eDiffByComp = 0.; + for (int i = 0; i < nStored[9]; ++i) { + eSumOriginal += hadronBE[i].p.e(); + hadronBE[i].p += hadronBE[i].pShift; + hadronBE[i].p.e( sqrt( hadronBE[i].p.pAbs2() + hadronBE[i].m2 ) ); + eSumShifted += hadronBE[i].p.e(); + eDiffByComp += dot3( hadronBE[i].pComp, hadronBE[i].p) + / hadronBE[i].p.e(); + } + + // Iterate compensation shift until convergence. + int iStep = 0; + while ( abs(eSumShifted - eSumOriginal) > COMPRELERR * eSumOriginal + && abs(eSumShifted - eSumOriginal) < COMPFACMAX * abs(eDiffByComp) + && iStep < NCOMPSTEP ) { + ++iStep; + double compFac = (eSumOriginal - eSumShifted) / eDiffByComp; + eSumShifted = 0.; + eDiffByComp = 0.; + for (int i = 0; i < nStored[9]; ++i) { + hadronBE[i].p += compFac * hadronBE[i].pComp; + hadronBE[i].p.e( sqrt( hadronBE[i].p.pAbs2() + hadronBE[i].m2 ) ); + eSumShifted += hadronBE[i].p.e(); + eDiffByComp += dot3( hadronBE[i].pComp, hadronBE[i].p) + / hadronBE[i].p.e(); + } + } + + // Error if no convergence, and then return without doing BE shift. + // However, not grave enough to kill event, so return true. + if ( abs(eSumShifted - eSumOriginal) > COMPRELERR * eSumOriginal ) { + infoPtr->errorMsg("Warning in BoseEinstein::shiftEvent: " + "no consistent BE shift topology found, so skip BE"); + return true; + } + + // Store new particle copies with shifted momenta. + for (int i = 0; i < nStored[9]; ++i) { + int iNew = event.copy( hadronBE[i].iPos, 99); + event[ iNew ].p( hadronBE[i].p ); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Calculate shift and (unnormalized) compensation for pair. + +void BoseEinstein::shiftPair( int i1, int i2, int iTab) { + + // Calculate old relative momentum. + double Q2old = m2(hadronBE[i1].p, hadronBE[i2].p) - m2Pair[iTab]; + if (Q2old < Q2MIN) return; + double Qold = sqrt(Q2old); + double psFac = sqrt(Q2old + m2Pair[iTab]) / Q2old; + + // Calculate new relative momentum for normal shift. + double Qmove = 0.; + if (Qold < deltaQ[iTab]) Qmove = Qold / 3.; + else if (Qold < maxQ[iTab]) { + double realQbin = Qold / deltaQ[iTab]; + int intQbin = int( realQbin ); + double inter = (pow3(realQbin) - pow3(intQbin)) + / (3 * intQbin * (intQbin + 1) + 1); + Qmove = ( shift[iTab][intQbin] + inter * (shift[iTab][intQbin + 1] + - shift[iTab][intQbin]) ) * psFac; + } + else Qmove = shift[iTab][nStep[iTab]] * psFac; + double Q2new = Q2old * pow( Qold / (Qold + 3. * lambda * Qmove), 2. / 3.); + + // Calculate corresponding three-momentum shift. + double Q2Diff = Q2new - Q2old; + double p2DiffAbs = (hadronBE[i1].p - hadronBE[i2].p).pAbs2(); + double p2AbsDiff = hadronBE[i1].p.pAbs2() - hadronBE[i2].p.pAbs2(); + double eSum = hadronBE[i1].p.e() + hadronBE[i2].p.e(); + double eDiff = hadronBE[i1].p.e() - hadronBE[i2].p.e(); + double sumQ2E = Q2Diff + eSum * eSum; + double rootA = eSum * eDiff * p2AbsDiff - p2DiffAbs * sumQ2E; + double rootB = p2DiffAbs * sumQ2E - p2AbsDiff * p2AbsDiff; + double factor = 0.5 * ( rootA + sqrtpos(rootA * rootA + + Q2Diff * (sumQ2E - eDiff * eDiff) * rootB) ) / rootB; + + // Add shifts to sum. (Energy component dummy.) + Vec4 pDiff = factor * (hadronBE[i1].p - hadronBE[i2].p); + hadronBE[i1].pShift += pDiff; + hadronBE[i2].pShift -= pDiff; + + // Calculate new relative momentum for compensation shift. + double Qmove3 = 0.; + if (Qold < deltaQ3[iTab]) Qmove3 = Qold / 3.; + else if (Qold < maxQ3[iTab]) { + double realQbin = Qold / deltaQ3[iTab]; + int intQbin = int( realQbin ); + double inter = (pow3(realQbin) - pow3(intQbin)) + / (3 * intQbin * (intQbin + 1) + 1); + Qmove3 = ( shift3[iTab][intQbin] + inter * (shift3[iTab][intQbin + 1] + - shift3[iTab][intQbin]) ) * psFac; + } + else Qmove3 = shift3[iTab][nStep3[iTab]] *psFac; + double Q2new3 = Q2old * pow( Qold / (Qold + 3. * lambda * Qmove3), 2. / 3.); + + // Calculate corresponding three-momentum shift. + Q2Diff = Q2new3 - Q2old; + sumQ2E = Q2Diff + eSum * eSum; + rootA = eSum * eDiff * p2AbsDiff - p2DiffAbs * sumQ2E; + rootB = p2DiffAbs * sumQ2E - p2AbsDiff * p2AbsDiff; + factor = 0.5 * ( rootA + sqrtpos(rootA * rootA + + Q2Diff * (sumQ2E - eDiff * eDiff) * rootB) ) / rootB; + + // Extra dampening factor to go from BE_3 to BE_32. + factor *= 1. - exp(-Q2old * R2Ref2); + + // Add shifts to sum. (Energy component dummy.) + pDiff = factor * (hadronBE[i1].p - hadronBE[i2].p); + hadronBE[i1].pComp += pDiff; + hadronBE[i2].pComp -= pDiff; + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/Event.cxx b/PYTHIA8/pythia8140/src/Event.cxx new file mode 100644 index 00000000000..0f424f62896 --- /dev/null +++ b/PYTHIA8/pythia8140/src/Event.cxx @@ -0,0 +1,706 @@ +// Event.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// Particle and Event classes, and some related global functions. + +#include "Event.h" + +namespace Pythia8 { + +//========================================================================== + +// Particle class. +// This class holds info on a particle in general. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Small number to avoid division by zero. +const double Particle::TINY = 1e-20; + +//-------------------------------------------------------------------------- + +// Functions for rapidity and pseudorapidity. + +double Particle::y() const { + double temp = log( ( pSave.e() + abs(pSave.pz()) ) / max( TINY, mT() ) ); + return (pSave.pz() > 0) ? temp : -temp; +} + +double Particle::eta() const { + double temp = log( ( pSave.pAbs() + abs(pSave.pz()) ) / max( TINY, pT() ) ); + return (pSave.pz() > 0) ? temp : -temp; +} + +//-------------------------------------------------------------------------- + +// Particle name, with status but imposed maximum length -> may truncate. + +string Particle::nameWithStatus(int maxLen) const { + + if (pdePtr == 0) return " "; + string temp = (statusSave > 0) ? pdePtr->name(idSave) + : "(" + pdePtr->name(idSave) + ")"; + while (int(temp.length()) > maxLen) { + // Remove from end, excluding closing bracket and charge. + int iRem = temp.find_last_not_of(")+-0"); + temp.erase(iRem, 1); + } + return temp; +} + +//-------------------------------------------------------------------------- + +// Add offsets to mother and daughter pointers (must be non-negative). + +void Particle::offsetHistory( int minMother, int addMother, int minDaughter, + int addDaughter) { + + if (addMother < 0 || addDaughter < 0) return; + if ( mother1Save > minMother ) mother1Save += addMother; + if ( mother2Save > minMother ) mother2Save += addMother; + if (daughter1Save > minDaughter) daughter1Save += addDaughter; + if (daughter2Save > minDaughter) daughter2Save += addDaughter; + +} + +//-------------------------------------------------------------------------- + +// Add offsets to colour and anticolour (must be positive). + +void Particle::offsetCol( int addCol) { + + if (addCol < 0) return; + if ( colSave > 0) colSave += addCol; + if (acolSave > 0) acolSave += addCol; + +} + +//-------------------------------------------------------------------------- + +// Invariant mass of a pair and its square. +// (Not part of class proper, but tightly linked.) + +double m(const Particle& pp1, const Particle& pp2) { + double m2 = pow2(pp1.e() + pp2.e()) - pow2(pp1.px() + pp2.px()) + - pow2(pp1.py() + pp2.py()) - pow2(pp1.pz() + pp2.pz()); + return (m2 > 0. ? sqrt(m2) : 0.); +} + +double m2(const Particle& pp1, const Particle& pp2) { + double m2 = pow2(pp1.e() + pp2.e()) - pow2(pp1.px() + pp2.px()) + - pow2(pp1.py() + pp2.py()) - pow2(pp1.pz() + pp2.pz()); + return m2; +} + +//========================================================================== + +// Event class. +// This class holds info on the complete event record. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Maxmimum number of mothers or daughter indices per line in listing. +const int Event::IPERLINE = 20; + +//-------------------------------------------------------------------------- + +// Copy all information from one event record to another. + +Event& Event::operator=( const Event& oldEvent) { + + // Do not copy if same. + if (this != &oldEvent) { + + // Reset all current info in the event. + clear(); + + // Copy all the particles one by one. + for (int i = 0; i < oldEvent.size(); ++i) append( oldEvent[i] ); + + // Copy all the junctions one by one. + for (int i = 0; i < oldEvent.sizeJunction(); ++i) + appendJunction( oldEvent.getJunction(i) ); + + // Copy all other values. + startColTag = oldEvent.startColTag; + maxColTag = oldEvent.maxColTag; + savedSize = oldEvent.savedSize; + savedJunctionSize = oldEvent.savedJunctionSize; + scaleSave = oldEvent.scaleSave; + scaleSecondSave = oldEvent.scaleSecondSave; + headerList = oldEvent.headerList; + particleDataPtr = oldEvent.particleDataPtr; + + // Done. + } + return *this; + +} + +//-------------------------------------------------------------------------- + +// Add a copy of an existing particle at the end of the event record; +// return index. Three cases, depending on sign of new status code: +// Positive: copy is viewed as daughter, status of original is negated. +// Negative: copy is viewed as mother, status of original is unchanged. +// Zero: the new is a perfect carbon copy (maybe to be changed later). + +int Event::copy(int iCopy, int newStatus) { + + // Simple carbon copy. + entry.push_back(entry[iCopy]); + int iNew = entry.size() - 1; + + // Set up to make new daughter of old. + if (newStatus > 0) { + entry[iCopy].daughters(iNew,iNew); + entry[iCopy].statusNeg(); + entry[iNew].mothers(iCopy, iCopy); + entry[iNew].status(newStatus); + + // Set up to make new mother of old. + } else if (newStatus < 0) { + entry[iCopy].mothers(iNew,iNew); + entry[iNew].daughters(iCopy, iCopy); + entry[iNew].status(newStatus); + } + + // Done. + return iNew; + +} + +//-------------------------------------------------------------------------- + +// Print an event - special cases that rely on the general method. +// Not inline to make them directly callable in (some) debuggers. + +void Event::list() const { + list(false, false, cout); +} + +void Event::list(ostream& os) const { + list(false, false, os); +} + +void Event::list(bool showScaleAndVertex, bool showMothersAndDaughters) +const { + list(showScaleAndVertex, showMothersAndDaughters, cout); +} + +//-------------------------------------------------------------------------- + +// Print an event. + +void Event::list(bool showScaleAndVertex, bool showMothersAndDaughters, + ostream& os) const { + + // Header. + os << "\n -------- PYTHIA Event Listing " << headerList << "----------" + << "------------------------------------------------- \n \n no " + << " id name status mothers daughters colou" + << "rs p_x p_y p_z e m \n"; + if (showScaleAndVertex) + os << " scale " + << " xProd yProd zProd tProd " + << " tau\n"; + + // At high energy switch to scientific format for momenta. + bool useFixed = (entry[0].e() < 1e5); + + // Listing of complete event. + Vec4 pSum; + double chargeSum = 0.; + for (int i = 0; i < int(entry.size()); ++i) { + const Particle& pt = entry[i]; + + // Basic line for a particle, always printed. + os << setw(6) << i << setw(10) << pt.id() << " " << left + << setw(18) << pt.nameWithStatus(18) << right << setw(4) + << pt.status() << setw(6) << pt.mother1() << setw(6) + << pt.mother2() << setw(6) << pt.daughter1() << setw(6) + << pt.daughter2() << setw(6) << pt.col() << setw(6) << pt.acol() + << ( (useFixed) ? fixed : scientific ) << setprecision(3) + << setw(11) << pt.px() << setw(11) << pt.py() << setw(11) + << pt.pz() << setw(11) << pt.e() << setw(11) << pt.m() << "\n"; + + // Optional extra line for scale value and production vertex. + if (showScaleAndVertex) + os << " " << setw(11) << pt.scale() + << " " << scientific + << setprecision(3) << setw(11) << pt.xProd() << setw(11) + << pt.yProd() << setw(11) << pt.zProd() << setw(11) + << pt.tProd() << setw(11) << pt.tau() << "\n"; + + // Optional extra line, giving a complete list of mothers and daughters. + if (showMothersAndDaughters) { + int linefill = 2; + os << " mothers:"; + vector allMothers = motherList(i); + for (int j = 0; j < int(allMothers.size()); ++j) { + os << " " << allMothers[j]; + if (++linefill == IPERLINE) {os << "\n "; linefill = 0;} + } + os << "; daughters:"; + vector allDaughters = daughterList(i); + for (int j = 0; j < int(allDaughters.size()); ++j) { + os << " " << allDaughters[j]; + if (++linefill == IPERLINE) {os << "\n "; linefill = 0;} + } + if (linefill !=0) os << "\n"; + } + + // Statistics on momentum and charge. + if (entry[i].status() > 0) { + pSum += entry[i].p(); + chargeSum += entry[i].charge(); + } + } + + // Line with sum charge, momentum, energy and invariant mass. + os << fixed << setprecision(3) << " " + << "Charge sum:" << setw(7) << chargeSum << " Momentum sum:" + << ( (useFixed) ? fixed : scientific ) << setprecision(3) + << setw(11) << pSum.px() << setw(11) << pSum.py() << setw(11) + << pSum.pz() << setw(11) << pSum.e() << setw(11) << pSum.mCalc() + << "\n"; + + // Listing finished. + os << "\n -------- End PYTHIA Event Listing ----------------------------" + << "-------------------------------------------------------------------" + << endl; +} + +//-------------------------------------------------------------------------- + +// Find complete list of mothers. + +vector Event::motherList(int i) const { + + // Vector of all the mothers; created empty. + vector mothers; + + // Read out the two official mother indices and status code. + int mother1 = entry[i].mother1(); + int mother2 = entry[i].mother2(); + int statusAbs = entry[i].statusAbs(); + + // Special cases in the beginning, where the meaning of zero is unclear. + if (statusAbs == 11 || statusAbs == 12) ; + else if (mother1 == 0 && mother2 == 0) mothers.push_back(0); + + // One mother or a carbon copy + else if (mother2 == 0 || mother2 == mother1) mothers.push_back(mother1); + + // A range of mothers from string fragmentation. + else if ( statusAbs > 80 && statusAbs < 90) + for (int iRange = mother1; iRange <= mother2; ++iRange) + mothers.push_back(iRange); + + // Two separate mothers. + else { + mothers.push_back( min(mother1, mother2) ); + mothers.push_back( max(mother1, mother2) ); + } + + // Done. + return mothers; + +} + +//-------------------------------------------------------------------------- + +// Find complete list of daughters. + +vector Event::daughterList(int i) const { + + // Vector of all the daughters; created empty. + vector daughters; + + // Read out the two official daughter indices. + int daughter1 = entry[i].daughter1(); + int daughter2 = entry[i].daughter2(); + + // Simple cases: no or one daughter. + if (daughter1 == 0 && daughter2 == 0) ; + else if (daughter2 == 0 || daughter2 == daughter1) + daughters.push_back(daughter1); + + // A range of daughters. + else if (daughter2 > daughter1) + for (int iRange = daughter1; iRange <= daughter2; ++iRange) + daughters.push_back(iRange); + + // Two separated daughters. + else { + daughters.push_back(daughter2); + daughters.push_back(daughter1); + } + + // Special case for two incoming beams: attach further + // initiators and remnants that have beam as mother. + if (entry[i].statusAbs() == 12 || entry[i].statusAbs() == 13) + for (int iDau = 3; iDau < size(); ++iDau) + if (entry[iDau].mother1() == i) { + bool isIn = false; + for (int iIn = 0; iIn < int(daughters.size()); ++iIn) + if (iDau == daughters[iIn]) isIn = true; + if (!isIn) daughters.push_back(iDau); + } + + // Done. + return daughters; + +} + +//-------------------------------------------------------------------------- + +// Convert internal Pythia status codes to the HepMC status conventions. + +int Event::statusHepMC(int i) const { + + // Positive codes are final particles. Status -12 are beam particles. + int statusNow = entry[i].status(); + if (statusNow > 0) return 1; + if (statusNow == -12) return 4; + + // Hadrons, muons, taus that decay normally are status 2. + int idNow = entry[i].id(); + if (entry[i].isHadron() || abs(idNow) == 13 || abs(idNow) == 15) { + int iDau = entry[i].daughter1(); + // Particle should not decay into itself (e.g. Bose-Einstein). + if ( entry[iDau].id() != idNow) { + int statusDau = entry[ iDau ].statusAbs(); + if (statusDau > 90 && statusDau < 95) return 2; + } + } + + // Other acceptable negative codes as their positive counterpart. + if (statusNow <= -11 && statusNow >= -200) return -statusNow; + + // Unacceptable codes as 0. + return 0; + +} + +//-------------------------------------------------------------------------- + +// Trace the first and last copy of one and the same particle. + +int Event::iTopCopy( int i) const { + + int iUp = i; + while ( iUp > 0 && entry[iUp].mother2() == entry[iUp].mother1() + && entry[iUp].mother1() > 0) iUp = entry[iUp].mother1(); + return iUp; + +} + +int Event::iBotCopy( int i) const { + + int iDn = i; + while ( iDn > 0 && entry[iDn].daughter2() == entry[iDn].daughter1() + && entry[iDn].daughter1() > 0) iDn = entry[iDn].daughter1(); + return iDn; + +} + +//-------------------------------------------------------------------------- + +// Trace the first and last copy of one and the same particle, +// also through shower branchings, making use of flavour matches. +// Stops tracing when this gives ambiguities. + +int Event::iTopCopyId( int i) const { + + int id = entry[i].id(); + int iUp = i; + for ( ; ; ) { + int mother1 = entry[iUp].mother1(); + int id1 = (mother1 > 0) ? entry[mother1].id() : 0; + int mother2 = entry[iUp].mother2(); + int id2 = (mother2 > 0) ? entry[mother2].id() : 0; + if (mother2 != mother1 && id2 == id1) break; + if (id1 == id) { + iUp = mother1; + continue; + } + if (id2 == id) { + iUp = mother2; + continue; + } + break; + } + return iUp; + +} + +int Event::iBotCopyId( int i) const { + + int id = entry[i].id(); + int iDn = i; + for ( ; ; ) { + int daughter1 = entry[iDn].daughter1(); + int id1 = (daughter1 > 0) ? entry[daughter1].id() : 0; + int daughter2 = entry[iDn].daughter2(); + int id2 = (daughter2 > 0) ? entry[daughter2].id() : 0; + if (daughter2 != daughter1 && id2 == id1) break; + if (id1 == id) { + iDn = daughter1; + continue; + } + if (id2 == id) { + iDn = daughter2; + continue; + } + break; + } + return iDn; + +} + +//-------------------------------------------------------------------------- + +// Find complete list of sisters. + +vector Event::sisterList(int i) const { + + // Vector of all the sisters; created empty. + vector sisters; + if (entry[i].statusAbs() == 11) return sisters; + + // Find mother and all its daughters. + int iMother = entry[i].mother1(); + vector daughters = daughterList(iMother); + + // Copy all daughters, excepting the input particle itself. + for (int j = 0; j < int(daughters.size()); ++j) + if (daughters[j] != i) sisters.push_back( daughters[j] ); + + // Done. + return sisters; + +} + +//-------------------------------------------------------------------------- + +// Find complete list of sisters. Traces up with iTopCopy and +// down with iBotCopy to give sisters at same level of evolution. +// Should this not give any final particles, the search is widened. + +vector Event::sisterListTopBot(int i, bool widenSearch) const { + + // Vector of all the sisters; created empty. + vector sisters; + if (entry[i].statusAbs() == 11) return sisters; + + // Trace up to first copy of current particle. + int iUp = iTopCopy(i); + + // Find mother and all its daughters. + int iMother = entry[iUp].mother1(); + vector daughters = daughterList(iMother); + + // Trace all daughters down, excepting the input particle itself. + for (int jD = 0; jD < int(daughters.size()); ++jD) + if (daughters[jD] != iUp) + sisters.push_back( iBotCopy( daughters[jD] ) ); + + // Prune any non-final particles from list. + int jP = 0; + while (jP < int(sisters.size())) { + if (entry[sisters[jP]].status() > 0) ++jP; + else { + sisters[jP] = sisters.back(); + sisters.pop_back(); + } + } + + // If empty list then restore immediate daughters. + if (sisters.size() == 0 && widenSearch) { + for (int jR = 0; jR < int(daughters.size()); ++jR) + if (daughters[jR] != iUp) + sisters.push_back( iBotCopy( daughters[jR] ) ); + + // Then trace all daughters, not only bottom copy. + for (int jT = 0; jT < int(sisters.size()); ++jT) { + daughters = daughterList( sisters[jT] ); + for (int k = 0; k < int(daughters.size()); ++k) + sisters.push_back( daughters[k] ); + } + + // And then prune any non-final particles from list. + int jN = 0; + while (jN < int(sisters.size())) { + if (entry[sisters[jN]].status() > 0) ++jN; + else { + sisters[jN] = sisters.back(); + sisters.pop_back(); + } + } + } + + // Done. + return sisters; + +} + +//-------------------------------------------------------------------------- + +// Check whether a given particle is an arbitrarily-steps-removed +// mother to another. For the parton -> hadron transition, only +// first-rank hadrons are associated with the respective end quark. + +bool Event::isAncestor(int i, int iAncestor) const { + + // Begin loop to trace upwards from the daughter. + int iUp = i; + for ( ; ; ) { + + // If positive match then done. + if (iUp == iAncestor) return true; + + // If out of range then failed to find match. + if (iUp <= 0 || iUp > size()) return false; + + // If unique mother then keep on moving up the chain. + int mother1 = entry[iUp].mother1(); + int mother2 = entry[iUp].mother2(); + if (mother2 == mother1 || mother2 == 0) {iUp = mother1; continue;} + + // If many mothers, except hadronization, then fail tracing. + int status = entry[iUp].statusAbs(); + if (status < 81 || status > 86) return false; + + // For hadronization step, fail if not first rank, else move up. + if (status == 82) { + iUp = (iUp + 1 < size() && entry[iUp + 1].mother1() == mother1) + ? mother1 : mother2; continue; + } + if (status == 83) { + if (entry[iUp - 1].mother1() == mother1) return false; + iUp = mother1; continue; + } + if (status == 84) { + if (iUp + 1 < size() && entry[iUp + 1].mother1() == mother1) + return false; + iUp = mother1; continue; + } + + // Fail for ministring -> one hadron and for junctions. + return false; + + } + // End of loop. Should never reach beyond here. + return false; + +} + +//-------------------------------------------------------------------------- + +// Erase junction stored in specified slot and move up the ones under. + +void Event::eraseJunction(int i) { + + for (int j = i; j < int(junction.size()) - 1; ++j) + junction[j] = junction[j + 1]; + junction.pop_back(); + +} + +//-------------------------------------------------------------------------- + +// Print the junctions in an event. + +void Event::listJunctions(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA Junction Listing " + << headerList.substr(0,30) << "\n \n no kind col0 col1 col2 " + << "endc0 endc1 endc2 stat0 stat1 stat2\n"; + + // Loop through junctions in event and list them. + for (int i = 0; i < sizeJunction(); ++i) + os << setw(6) << i << setw(6) << kindJunction(i) << setw(6) + << colJunction(i, 0) << setw(6) << colJunction(i, 1) << setw(6) + << colJunction(i, 2) << setw(6) << endColJunction(i, 0) << setw(6) + << endColJunction(i, 1) << setw(6) << endColJunction(i, 2) << setw(6) + << statusJunction(i, 0) << setw(6) << statusJunction(i, 1) << setw(6) + << statusJunction(i, 2) << "\n"; + + // Alternative if no junctions. Listing finished. + if (sizeJunction() == 0) os << " no junctions present \n"; + os << "\n -------- End PYTHIA Junction Listing --------------------" + << "------" << endl; +} + +//-------------------------------------------------------------------------- + +// Operator overloading allows to append one event to an existing one. + +Event& Event::operator+=( const Event& addEvent) { + + // Find offsets. One less since won't copy line 0. + int offsetIdx = entry.size() - 1; + int offsetCol = maxColTag; + + // Add energy to zeroth line and calculate new invariant mass. + entry[0].p( entry[0].p() + addEvent[0].p() ); + entry[0].m( entry[0].mCalc() ); + + // Read out particles from line 1 (not 0) onwards. + Particle temp; + for (int i = 1; i < addEvent.size(); ++i) { + temp = addEvent[i]; + + // Add offset to nonzero mother, daughter and colour indices. + if (temp.mother1() > 0) temp.mother1( temp.mother1() + offsetIdx ); + if (temp.mother2() > 0) temp.mother2( temp.mother2() + offsetIdx ); + if (temp.daughter1() > 0) temp.daughter1( temp.daughter1() + offsetIdx ); + if (temp.daughter2() > 0) temp.daughter2( temp.daughter2() + offsetIdx ); + if (temp.col() > 0) temp.col( temp.col() + offsetCol ); + if (temp.acol() > 0) temp.acol( temp.acol() + offsetCol ); + + // Append particle to summed event. + append( temp ); + } + + // Read out junctions one by one. + Junction tempJ; + int begCol, endCol; + for (int i = 0; i < addEvent.sizeJunction(); ++i) { + tempJ = addEvent.getJunction(i); + + // Add colour offsets to all three legs. + for (int j = 0; j < 3; ++j) { + begCol = tempJ.col(j); + endCol = tempJ.endCol(j); + if (begCol > 0) begCol += offsetCol; + if (endCol > 0) endCol += offsetCol; + tempJ.cols( j, begCol, endCol); + } + + // Append junction to summed event. + appendJunction( tempJ ); + } + + // Set header that indicates character as sum of events. + headerList = "(combination of several events) -------"; + + // Done. + return *this; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/FragmentationFlavZpT.cxx b/PYTHIA8/pythia8140/src/FragmentationFlavZpT.cxx new file mode 100644 index 00000000000..09931e34302 --- /dev/null +++ b/PYTHIA8/pythia8140/src/FragmentationFlavZpT.cxx @@ -0,0 +1,759 @@ +// FragmentationFlavZpT.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// StringFlav, StringZ and StringPT classes. + +#include "FragmentationFlavZpT.h" + +namespace Pythia8 { + +//========================================================================== + +// The StringFlav class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Offset for different meson multiplet id values. +const int StringFlav::mesonMultipletCode[6] + = { 1, 3, 10003, 10001, 20003, 5}; + +// Clebsch-Gordan coefficients for baryon octet and decuplet are +// fixed once and for all, so only weighted sum needs to be edited. +// Order: ud0 + u, ud0 + s, uu1 + u, uu1 + d, ud1 + u, ud1 + s. +const double StringFlav::baryonCGOct[6] + = { 0.75, 0.5, 0., 0.1667, 0.0833, 0.1667}; +const double StringFlav::baryonCGDec[6] + = { 0., 0., 1., 0.3333, 0.6667, 0.3333}; + +//-------------------------------------------------------------------------- + +// Initialize data members of the flavour generation. + +void StringFlav::init(Settings& settings, Rndm* rndmPtrIn) { + + // Save pointer. + rndmPtr = rndmPtrIn; + + // Basic parameters for generation of new flavour. + probQQtoQ = settings.parm("StringFlav:probQQtoQ"); + probStoUD = settings.parm("StringFlav:probStoUD"); + probSQtoQQ = settings.parm("StringFlav:probSQtoQQ"); + probQQ1toQQ0 = settings.parm("StringFlav:probQQ1toQQ0"); + + // Parameters derived from above. + probQandQQ = 1. + probQQtoQ; + probQandS = 2. + probStoUD; + probQandSinQQ = 2. + probSQtoQQ * probStoUD; + probQQ1corr = 3. * probQQ1toQQ0; + probQQ1corrInv = 1. / probQQ1corr; + probQQ1norm = probQQ1corr / (1. + probQQ1corr); + + // Parameters for normal meson production. + for (int i = 0; i < 4; ++i) mesonRate[i][0] = 1.; + mesonRate[0][1] = settings.parm("StringFlav:mesonUDvector"); + mesonRate[1][1] = settings.parm("StringFlav:mesonSvector"); + mesonRate[2][1] = settings.parm("StringFlav:mesonCvector"); + mesonRate[3][1] = settings.parm("StringFlav:mesonBvector"); + + // Parameters for L=1 excited-meson production. + mesonRate[0][2] = settings.parm("StringFlav:mesonUDL1S0J1"); + mesonRate[1][2] = settings.parm("StringFlav:mesonSL1S0J1"); + mesonRate[2][2] = settings.parm("StringFlav:mesonCL1S0J1"); + mesonRate[3][2] = settings.parm("StringFlav:mesonBL1S0J1"); + mesonRate[0][3] = settings.parm("StringFlav:mesonUDL1S1J0"); + mesonRate[1][3] = settings.parm("StringFlav:mesonSL1S1J0"); + mesonRate[2][3] = settings.parm("StringFlav:mesonCL1S1J0"); + mesonRate[3][3] = settings.parm("StringFlav:mesonBL1S1J0"); + mesonRate[0][4] = settings.parm("StringFlav:mesonUDL1S1J1"); + mesonRate[1][4] = settings.parm("StringFlav:mesonSL1S1J1"); + mesonRate[2][4] = settings.parm("StringFlav:mesonCL1S1J1"); + mesonRate[3][4] = settings.parm("StringFlav:mesonBL1S1J1"); + mesonRate[0][5] = settings.parm("StringFlav:mesonUDL1S1J2"); + mesonRate[1][5] = settings.parm("StringFlav:mesonSL1S1J2"); + mesonRate[2][5] = settings.parm("StringFlav:mesonCL1S1J2"); + mesonRate[3][5] = settings.parm("StringFlav:mesonBL1S1J2"); + + // Store sum over multiplets for Monte Carlo generation. + for (int i = 0; i < 4; ++i) mesonRateSum[i] + = mesonRate[i][0] + mesonRate[i][1] + mesonRate[i][2] + + mesonRate[i][3] + mesonRate[i][4] + mesonRate[i][5]; + + // Parameters for uubar - ddbar - ssbar meson mixing. + for (int spin = 0; spin < 6; ++spin) { + double theta; + if (spin == 0) theta = settings.parm("StringFlav:thetaPS"); + else if (spin == 1) theta = settings.parm("StringFlav:thetaV"); + else if (spin == 2) theta = settings.parm("StringFlav:thetaL1S0J1"); + else if (spin == 3) theta = settings.parm("StringFlav:thetaL1S1J0"); + else if (spin == 4) theta = settings.parm("StringFlav:thetaL1S1J1"); + else theta = settings.parm("StringFlav:thetaL1S1J2"); + double alpha = (spin == 0) ? 90. - (theta + 54.7) : theta + 54.7; + alpha *= M_PI / 180.; + // Fill in (flavour, spin)-dependent probability of producing + // the lightest or the lightest two mesons of the nonet. + mesonMix1[0][spin] = 0.5; + mesonMix2[0][spin] = 0.5 * (1. + pow2(sin(alpha))); + mesonMix1[1][spin] = 0.; + mesonMix2[1][spin] = pow2(cos(alpha)); + } + + // Additional suppression of eta and etaPrime. + etaSup = settings.parm("StringFlav:etaSup"); + etaPrimeSup = settings.parm("StringFlav:etaPrimeSup"); + + // Sum of baryon octet and decuplet weights. + decupletSup = settings.parm("StringFlav:decupletSup"); + for (int i = 0; i < 6; ++i) baryonCGSum[i] + = baryonCGOct[i] + decupletSup * baryonCGDec[i]; + + // Maximum SU(6) weight for ud0, ud1, uu1 types. + baryonCGMax[0] = max( baryonCGSum[0], baryonCGSum[1]); + baryonCGMax[1] = baryonCGMax[0]; + baryonCGMax[2] = max( baryonCGSum[2], baryonCGSum[3]); + baryonCGMax[3] = baryonCGMax[2]; + baryonCGMax[4] = max( baryonCGSum[4], baryonCGSum[5]); + baryonCGMax[5] = baryonCGMax[4]; + + // Popcorn baryon parameters. + popcornRate = settings.parm("StringFlav:popcornRate"); + popcornSpair = settings.parm("StringFlav:popcornSpair"); + popcornSmeson = settings.parm("StringFlav:popcornSmeson"); + + // Suppression of leading (= first-rank) baryons. + suppressLeadingB = settings.flag("StringFlav:suppressLeadingB"); + lightLeadingBSup = settings.parm("StringFlav:lightLeadingBSup"); + heavyLeadingBSup = settings.parm("StringFlav:heavyLeadingBSup"); + + // Begin calculation of derived parameters for baryon production. + + // Enumerate distinguishable diquark types (in diquark first is popcorn q). + enum Diquark {ud0, ud1, uu1, us0, su0, us1, su1, ss1}; + + // Maximum SU(6) weight by diquark type. + double barCGMax[8]; + barCGMax[ud0] = baryonCGMax[0]; + barCGMax[ud1] = baryonCGMax[4]; + barCGMax[uu1] = baryonCGMax[2]; + barCGMax[us0] = baryonCGMax[0]; + barCGMax[su0] = baryonCGMax[0]; + barCGMax[us1] = baryonCGMax[4]; + barCGMax[su1] = baryonCGMax[4]; + barCGMax[ss1] = baryonCGMax[2]; + + // Diquark SU(6) survival = Sum_quark (quark tunnel weight) * SU(6). + double dMB[8]; + dMB[ud0] = 2. * baryonCGSum[0] + probStoUD * baryonCGSum[1]; + dMB[ud1] = 2. * baryonCGSum[4] + probStoUD * baryonCGSum[5]; + dMB[uu1] = baryonCGSum[2] + (1. + probStoUD) * baryonCGSum[3]; + dMB[us0] = (1. + probStoUD) * baryonCGSum[0] + baryonCGSum[1]; + dMB[su0] = dMB[us0]; + dMB[us1] = (1. + probStoUD) * baryonCGSum[4] + baryonCGSum[5]; + dMB[su1] = dMB[us1]; + dMB[ss1] = probStoUD * baryonCGSum[2] + 2. * baryonCGSum[3]; + for (int i = 1; i < 8; ++i) dMB[i] = dMB[i] / dMB[0]; + + // Tunneling factors for diquark production; only half a pair = sqrt. + double probStoUDroot = sqrt(probStoUD); + double probSQtoQQroot = sqrt(probSQtoQQ); + double probQQ1toQQ0root = sqrt(probQQ1toQQ0); + double qBB[8]; + qBB[ud1] = probQQ1toQQ0root; + qBB[uu1] = probQQ1toQQ0root; + qBB[us0] = probSQtoQQroot; + qBB[su0] = probStoUDroot * probSQtoQQroot; + qBB[us1] = probQQ1toQQ0root * qBB[us0]; + qBB[su1] = probQQ1toQQ0root * qBB[su0]; + qBB[ss1] = probStoUDroot * pow2(probSQtoQQroot) * probQQ1toQQ0root; + + // spin * (vertex factor) * (half-tunneling factor above). + double qBM[8]; + qBM[ud1] = 3. * qBB[ud1]; + qBM[uu1] = 6. * qBB[uu1]; + qBM[us0] = probStoUD * qBB[us0]; + qBM[su0] = qBB[su0]; + qBM[us1] = probStoUD * 3. * qBB[us1]; + qBM[su1] = 3. * qBB[su1]; + qBM[ss1] = probStoUD * 6. * qBB[ss1]; + + // Combine above two into total diquark weight for q -> B Bbar. + for (int i = 1; i < 8; ++i) qBB[i] = qBB[i] * qBM[i]; + + // Suppression from having strange popcorn meson. + qBM[us0] *= popcornSmeson; + qBM[us1] *= popcornSmeson; + qBM[ss1] *= popcornSmeson; + + // Suppression for a heavy quark of a diquark to fit into a baryon + // on the other side of popcorn meson: (0) s/u for q -> B M; + // (1) s/u for rank 0 diquark su -> M B; (2) ditto for s -> c/b. + double uNorm = 1. + qBM[ud1] + qBM[uu1] + qBM[us0] + qBM[us1]; + scbBM[0] = (2. * (qBM[su0] + qBM[su1]) + qBM[ss1]) / uNorm; + scbBM[1] = scbBM[0] * popcornSpair * qBM[su0] / qBM[us0]; + scbBM[2] = (1. + qBM[ud1]) * (2. + qBM[us0]) / uNorm; + + // Include maximum of Clebsch-Gordan coefficients. + for (int i = 1; i < 8; ++i) dMB[i] *= qBM[i]; + for (int i = 1; i < 8; ++i) qBM[i] *= barCGMax[i] / barCGMax[0]; + for (int i = 1; i < 8; ++i) qBB[i] *= barCGMax[i] / barCGMax[0]; + + // Popcorn fraction for normal diquark production. + double qNorm = uNorm * popcornRate / 3.; + double sNorm = scbBM[0] * popcornSpair; + popFrac = qNorm * (1. + qBM[ud1] + qBM[uu1] + qBM[us0] + qBM[us1] + + sNorm * (qBM[su0] + qBM[su1] + 0.5 * qBM[ss1])) / (1. + qBB[ud1] + + qBB[uu1] + 2. * (qBB[us0] + qBB[us1]) + 0.5 * qBB[ss1]); + + // Popcorn fraction for rank 0 diquarks, depending on number of s quarks. + popS[0] = qNorm * qBM[ud1] / qBB[ud1]; + popS[1] = qNorm * 0.5 * (qBM[us1] / qBB[us1] + + sNorm * qBM[su1] / qBB[su1]); + popS[2] = qNorm * sNorm * qBM[ss1] / qBB[ss1]; + + // Recombine diquark weights to flavour and spin ratios. Second index: + // 0 = s/u popcorn quark ratio. + // 1, 2 = s/u ratio for vertex quark if popcorn quark is u/d or s. + // 3 = q/q' vertex quark ratio if popcorn quark is light and = q. + // 4, 5, 6 = (spin 1)/(spin 0) ratio for su, us and ud. + + // Case 0: q -> B B. + dWT[0][0] = (2. * (qBB[su0] + qBB[su1]) + qBB[ss1]) + / (1. + qBB[ud1] + qBB[uu1] + qBB[us0] + qBB[us1]); + dWT[0][1] = 2. * (qBB[us0] + qBB[us1]) / (1. + qBB[ud1] + qBB[uu1]); + dWT[0][2] = qBB[ss1] / (qBB[su0] + qBB[su1]); + dWT[0][3] = qBB[uu1] / (1. + qBB[ud1] + qBB[uu1]); + dWT[0][4] = qBB[su1] / qBB[su0]; + dWT[0][5] = qBB[us1] / qBB[us0]; + dWT[0][6] = qBB[ud1]; + + // Case 1: q -> B M B. + dWT[1][0] = (2. * (qBM[su0] + qBM[su1]) + qBM[ss1]) + / (1. + qBM[ud1] + qBM[uu1] + qBM[us0] + qBM[us1]); + dWT[1][1] = 2. * (qBM[us0] + qBM[us1]) / (1. + qBM[ud1] + qBM[uu1]); + dWT[1][2] = qBM[ss1] / (qBM[su0] + qBM[su1]); + dWT[1][3] = qBM[uu1] / (1. + qBM[ud1] + qBM[uu1]); + dWT[1][4] = qBM[su1] / qBM[su0]; + dWT[1][5] = qBM[us1] / qBM[us0]; + dWT[1][6] = qBM[ud1]; + + // Case 2: qq -> M B; diquark inside chain. + dWT[2][0] = (2. * (dMB[su0] + dMB[su1]) + dMB[ss1]) + / (1. + dMB[ud1] + dMB[uu1] + dMB[us0] + dMB[us1]); + dWT[2][1] = 2. * (dMB[us0] + dMB[us1]) / (1. + dMB[ud1] + dMB[uu1]); + dWT[2][2] = dMB[ss1] / (dMB[su0] + dMB[su1]); + dWT[2][3] = dMB[uu1] / (1. + dMB[ud1] + dMB[uu1]); + dWT[2][4] = dMB[su1] / dMB[su0]; + dWT[2][5] = dMB[us1] / dMB[us0]; + dWT[2][6] = dMB[ud1]; + +} + +//-------------------------------------------------------------------------- + +// Pick a new flavour (including diquarks) given an incoming one. + +FlavContainer StringFlav::pick(FlavContainer& flavOld) { + + // Initial values for new flavour. + FlavContainer flavNew; + flavNew.rank = flavOld.rank + 1; + + // For original diquark assign popcorn quark and whether popcorn meson. + int idOld = abs(flavOld.id); + if (flavOld.rank == 0 && idOld > 1000) assignPopQ(flavOld); + + // Diquark exists, to be forced into baryon now. + bool doOldBaryon = (idOld > 1000 && flavOld.nPop == 0); + // Diquark exists, but do meson now. + bool doPopcornMeson = flavOld.nPop > 0; + // Newly created diquark gives baryon now, antibaryon later. + bool doNewBaryon = false; + + // Choose whether to generate a new meson or a new baryon. + if (!doOldBaryon && !doPopcornMeson && probQandQQ * rndmPtr->flat() > 1.) { + doNewBaryon = true; + if ((1. + popFrac) * rndmPtr->flat() > 1.) flavNew.nPop = 1; + } + + // Optional suppression of first-rank baryon. + if (flavOld.rank == 0 && doNewBaryon && suppressLeadingB) { + double leadingBSup = (idOld < 4) ? lightLeadingBSup : heavyLeadingBSup; + if (rndmPtr->flat() > leadingBSup) { + doNewBaryon = false; + flavNew.nPop = 0; + } + } + + // Single quark for new meson or for baryon where diquark already exists. + if (!doPopcornMeson && !doNewBaryon) { + flavNew.id = pickLightQ(); + if ( (flavOld.id > 0 && flavOld.id < 9) || flavOld.id < -1000 ) + flavNew.id = -flavNew.id; + + // Done for simple-quark case. + return flavNew; + } + + // Case: 0 = q -> B B, 1 = q -> B M B, 2 = qq -> M B. + int iCase = flavNew.nPop; + if (flavOld.nPop == 1) iCase = 2; + + // Flavour of popcorn quark (= q shared between B and Bbar). + if (doNewBaryon) { + double sPopWT = dWT[iCase][0]; + if (iCase == 1) sPopWT *= scbBM[0] * popcornSpair; + double rndmFlav = (2. + sPopWT) * rndmPtr->flat(); + flavNew.idPop = 1; + if (rndmFlav > 1.) flavNew.idPop = 2; + if (rndmFlav > 2.) flavNew.idPop = 3; + } else flavNew.idPop = flavOld.idPop; + + // Flavour of vertex quark. + double sVtxWT = dWT[iCase][1]; + if (flavNew.idPop >= 3) sVtxWT = dWT[iCase][2]; + if (flavNew.idPop > 3) sVtxWT *= 0.5 * (1. + 1./dWT[iCase][4]); + double rndmFlav = (2. + sVtxWT) * rndmPtr->flat(); + flavNew.idVtx = 1; + if (rndmFlav > 1.) flavNew.idVtx = 2; + if (rndmFlav > 2.) flavNew.idVtx = 3; + + // Special case for light flavours, possibly identical. + if (flavNew.idPop < 3 && flavNew.idVtx < 3) { + flavNew.idVtx = flavNew.idPop; + if (rndmPtr->flat() > dWT[iCase][3]) flavNew.idVtx = 3 - flavNew.idPop; + } + + // Pick 2 * spin + 1. + int spin = 3; + if (flavNew.idVtx != flavNew.idPop) { + double spinWT = dWT[iCase][6]; + if (flavNew.idVtx == 3) spinWT = dWT[iCase][5]; + if (flavNew.idPop >= 3) spinWT = dWT[iCase][4]; + if ((1. + spinWT) * rndmPtr->flat() < 1.) spin = 1; + } + + // Form outgoing diquark. Done. + flavNew.id = 1000 * max(flavNew.idVtx, flavNew.idPop) + + 100 * min(flavNew.idVtx, flavNew.idPop) + spin; + if ( (flavOld.id < 0 && flavOld.id > -9) || flavOld.id > 1000 ) + flavNew.id = -flavNew.id; + return flavNew; + +} + +//-------------------------------------------------------------------------- + +// Combine two flavours (including diquarks) to produce a hadron. +// The weighting of the combination may fail, giving output 0. + +int StringFlav::combine(FlavContainer& flav1, FlavContainer& flav2) { + + // Recognize largest and smallest flavour. + int id1Abs = abs(flav1.id); + int id2Abs = abs(flav2.id); + int idMax = max(id1Abs, id2Abs); + int idMin = min(id1Abs, id2Abs); + + // Construct a meson. + if (idMax < 9 || idMin > 1000) { + + // Popcorn meson: use only vertex quarks. + if (idMin > 1000) { + id1Abs = flav1.idVtx; + id2Abs = flav2.idVtx; + idMax = max(id1Abs, id2Abs); + idMin = min(id1Abs, id2Abs); + } + + // Pick spin state and preliminary code. + int flav = (idMax < 3) ? 0 : idMax - 2; + double rndmSpin = mesonRateSum[flav] * rndmPtr->flat(); + int spin = -1; + do rndmSpin -= mesonRate[flav][++spin]; + while (rndmSpin > 0.); + int idMeson = 100 * idMax + 10 * idMin + mesonMultipletCode[spin]; + + // For nondiagonal mesons distinguish particle/antiparticle. + if (idMax != idMin) { + int sign = (idMax%2 == 0) ? 1 : -1; + if ( (idMax == id1Abs && flav1.id < 0) + || (idMax == id2Abs && flav2.id < 0) ) sign = -sign; + idMeson *= sign; + + // For light diagonal mesons include uubar - ddbar - ssbar mixing. + } else if (flav < 2) { + double rMix = rndmPtr->flat(); + if (rMix < mesonMix1[flav][spin]) idMeson = 110; + else if (rMix < mesonMix2[flav][spin]) idMeson = 220; + else idMeson = 330; + idMeson += mesonMultipletCode[spin]; + + // Additional suppression of eta and eta' may give failure. + if (idMeson == 221 && etaSup < rndmPtr->flat()) return 0; + if (idMeson == 331 && etaPrimeSup < rndmPtr->flat()) return 0; + } + + // Finished for mesons. + return idMeson; + } + + // SU(6) factors for baryon production may give failure. + int idQQ1 = idMax / 1000; + int idQQ2 = (idMax / 100) % 10; + int spinQQ = idMax % 10; + int spinFlav = spinQQ - 1; + if (spinFlav == 2 && idQQ1 != idQQ2) spinFlav = 4; + if (idMin != idQQ1 && idMin != idQQ2) spinFlav++; + if (baryonCGSum[spinFlav] < rndmPtr->flat() * baryonCGMax[spinFlav]) + return 0; + + // Order quarks to form baryon. Pick spin. + int idOrd1 = max( idMin, max( idQQ1, idQQ2) ); + int idOrd3 = min( idMin, min( idQQ1, idQQ2) ); + int idOrd2 = idMin + idQQ1 + idQQ2 - idOrd1 - idOrd3; + int spinBar = (baryonCGSum[spinFlav] * rndmPtr->flat() + < baryonCGOct[spinFlav]) ? 2 : 4; + + // Distinguish Lambda- and Sigma-like. + bool LambdaLike = false; + if (spinBar == 2 && idOrd1 > idOrd2 && idOrd2 > idOrd3) { + LambdaLike = (spinQQ == 1); + if (idOrd1 != idMin && spinQQ == 1) LambdaLike = (rndmPtr->flat() < 0.25); + else if (idOrd1 != idMin) LambdaLike = (rndmPtr->flat() < 0.75); + } + + // Form baryon code and return with sign. + int idBaryon = (LambdaLike) + ? 1000 * idOrd1 + 100 * idOrd3 + 10 * idOrd2 + spinBar + : 1000 * idOrd1 + 100 * idOrd2 + 10 * idOrd3 + spinBar; + return (flav1.id > 0) ? idBaryon : -idBaryon; + +} + +//-------------------------------------------------------------------------- + +// Assign popcorn quark inside an original (= rank 0) diquark. + +void StringFlav::assignPopQ(FlavContainer& flav) { + + // Safety check that intended to do something. + int idAbs = abs(flav.id); + if (flav.rank > 0 || idAbs < 1000) return; + + // Make choice of popcorn quark. + int id1 = (idAbs/1000)%10; + int id2 = (idAbs/100)%10; + double pop2WT = 1.; + if (id1 == 3) pop2WT = scbBM[1]; + else if (id1 > 3) pop2WT = scbBM[2]; + if (id2 == 3) pop2WT /= scbBM[1]; + else if (id2 > 3) pop2WT /= scbBM[2]; + // Agrees with Patrik code, but opposite to intention?? + flav.idPop = ((1. + pop2WT) * rndmPtr->flat() > 1.) ? id2 : id1; + flav.idVtx = id1 + id2 - flav.idPop; + + // Also determine if to produce popcorn meson. + flav.nPop = 0; + double popWT = popS[0]; + if (id1 == 3) popWT = popS[1]; + if (id2 == 3) popWT = popS[2]; + if (idAbs%10 == 1) popWT *= sqrt(probQQ1toQQ0); + if ((1. + popWT) * rndmPtr->flat() > 1.) flav.nPop = 1; + +} + +//-------------------------------------------------------------------------- + +// Combine two quarks to produce a diquark. +// Normally according to production composition, but nonvanishing idHad +// means diquark from known hadron content, so use SU(6) wave fucntion. + +int StringFlav::makeDiquark(int id1, int id2, int idHad) { + + // Initial values. + int idMin = min( abs(id1), abs(id2)); + int idMax = max( abs(id1), abs(id2)); + int spin = 1; + + // Select spin of diquark formed from two valence quarks in proton. + // (More hadron cases??) + if (abs(idHad) == 2212) { + if (idMin == 1 && idMax == 2 && rndmPtr->flat() < 0.75) spin = 0; + + // Else select spin of diquark according to production composition. + } else { + if (idMin != idMax && rndmPtr->flat() > probQQ1norm) spin = 0; + } + + // Combined diquark code. + int idNewAbs = 1000 * idMax + 100 * idMin + 2 * spin + 1; + return (id1 > 0) ? idNewAbs : -idNewAbs; + +} + +//========================================================================== + +// The StringZ class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// When a or c are close to special cases, default to these. +const double StringZ::CFROMUNITY = 0.01; +const double StringZ::AFROMZERO = 0.02; +const double StringZ::AFROMC = 0.01; + +// Do not take exponent of too large or small number. +const double StringZ::EXPMAX = 50.; + +//-------------------------------------------------------------------------- + +// Initialize data members of the string z selection. + +void StringZ::init(Settings& settings, ParticleData& particleData, + Rndm* rndmPtrIn) { + + // Save pointer. + rndmPtr = rndmPtrIn; + + // c and b quark masses. + mc2 = pow2( particleData.m0(4)); + mb2 = pow2( particleData.m0(5)); + + // Paramaters of Lund/Bowler symmetric fragmentation function. + aLund = settings.parm("StringZ:aLund"); + bLund = settings.parm("StringZ:bLund"); + aExtraDiquark = settings.parm("StringZ:aExtraDiquark"); + rFactC = settings.parm("StringZ:rFactC"); + rFactB = settings.parm("StringZ:rFactB"); + rFactH = settings.parm("StringZ:rFactH"); + + // Flags and parameters of Peterson/SLAC fragmentation function. + usePetersonC = settings.flag("StringZ:usePetersonC"); + usePetersonB = settings.flag("StringZ:usePetersonB"); + usePetersonH = settings.flag("StringZ:usePetersonH"); + epsilonC = settings.parm("StringZ:epsilonC"); + epsilonB = settings.parm("StringZ:epsilonB"); + epsilonH = settings.parm("StringZ:epsilonH"); + +} + +//-------------------------------------------------------------------------- + +// Generate the fraction z that the next hadron will take, +// using either Lund/Bowler or, for heavy, Peterson/SLAC functions. +// Note: for a heavy new coloured particle we assume pT negligible. + +double StringZ::zFrag( int idOld, int idNew, double mT2) { + + // Find if old or new flavours correspond to diquarks. + int idOldAbs = abs(idOld); + int idNewAbs = abs(idNew); + bool isOldDiquark = (idOldAbs > 1000 && idOldAbs < 10000); + bool isNewDiquark = (idNewAbs > 1000 && idNewAbs < 10000); + + // Find heaviest quark in fragmenting parton/diquark. + int idFrag = idOldAbs; + if (isOldDiquark) idFrag = max( idOldAbs / 1000, (idOldAbs / 100) % 10); + + // Use Peterson where explicitly requested for heavy flavours. + if (idFrag == 4 && usePetersonC) return zPeterson( epsilonC); + if (idFrag == 5 && usePetersonB) return zPeterson( epsilonB); + if (idFrag > 5 && usePetersonH) { + double epsilon = epsilonH * mb2 / mT2; + return zPeterson( epsilon); + } + + // Shape parameters of Lund symmetric fragmentation function. + double aShape = aLund; + if (isOldDiquark) aShape += aExtraDiquark; + double bShape = bLund * mT2; + double cShape = 1.; + if (isOldDiquark) cShape -= aExtraDiquark; + if (isNewDiquark) cShape += aExtraDiquark; + if (idFrag == 4) cShape += rFactC * bLund * mc2; + if (idFrag == 5) cShape += rFactB * bLund * mb2; + if (idFrag > 5) cShape += rFactH * bLund * mT2; + return zLund( aShape, bShape, cShape); + +} + +//-------------------------------------------------------------------------- + +// Generate a random z according to the Lund/Bowler symmetric +// fragmentation function f(z) = (1 -z)^a * exp(-b/z) / z^c. +// Normalized so that f(z_max) = 1 it can also be written as +// f(z) = exp( a * ln( (1 - z) / (1 - z_max) ) + b * (1/z_max - 1/z) +// + c * ln(z_max/z) ). + +double StringZ::zLund( double a, double b, double c) { + + // Special cases for c = 1, a = 0 and a = c. + bool cIsUnity = (abs( c - 1.) < CFROMUNITY); + bool aIsZero = (a < AFROMZERO); + bool aIsC = (abs(a - c) < AFROMC); + + // Determine position of maximum. + double zMax; + if (aIsZero) zMax = (c > b) ? b / c : 1.; + else if (aIsC) zMax = b / (b + c); + else { zMax = 0.5 * (b + c - sqrt( pow2(b - c) + 4. * a * b)) / (c - a); + if (zMax > 0.9999 && b > 100.) zMax = min(zMax, 1. - a / b); } + + // Subdivide z range if distribution very peaked near either endpoint. + bool peakedNearZero = (zMax < 0.1); + bool peakedNearUnity = (zMax > 0.85 && b > 1.); + + // Find integral of trial function everywhere bigger than f. + // (Dummy start values.) + double fIntLow = 1.; + double fIntHigh = 1.; + double fInt = 2.; + double zDiv = 0.5; + double zDivC = 0.5; + // When z_max is small use that f(z) + // < 1 for z < z_div = 2.75 * z_max, + // < (z_div/z)^c for z > z_div (=> logarithm for c = 1, else power). + if (peakedNearZero) { + zDiv = 2.75 * zMax; + fIntLow = zDiv; + if (cIsUnity) fIntHigh = -zDiv * log(zDiv); + else { zDivC = pow( zDiv, 1. - c); + fIntHigh = zDiv * (1. - 1./zDivC) / (c - 1.);} + fInt = fIntLow + fIntHigh; + // When z_max large use that f(z) + // < exp( b * (z - z_div) ) for z < z_div with z_div messy expression, + // < 1 for z > z_div. + // To simplify expressions the integral is extended to z = -infinity. + } else if (peakedNearUnity) { + double rcb = sqrt(4. + pow2(c / b)); + zDiv = rcb - 1./zMax - (c / b) * log( zMax * 0.5 * (rcb + c / b) ); + if (!aIsZero) zDiv += (a/b) * log(1. - zMax); + zDiv = min( zMax, max(0., zDiv)); + fIntLow = 1. / b; + fIntHigh = 1. - zDiv; + fInt = fIntLow + fIntHigh; + } + + // Choice of z, preweighted for peaks at low or high z. (Dummy start values.) + double z = 0.5; + double fPrel = 1.; + double fVal = 1.; + do { + // Choice of z flat good enough for distribution peaked in the middle; + // if not this z can be reused as a random number in general. + z = rndmPtr->flat(); + fPrel = 1.; + // When z_max small use flat below z_div and 1/z^c above z_div. + if (peakedNearZero) { + if (fInt * rndmPtr->flat() < fIntLow) z = zDiv * z; + else if (cIsUnity) {z = pow( zDiv, z); fPrel = zDiv / z;} + else { z = pow( zDivC + (1. - zDivC) * z, 1. / (1. - c) ); + fPrel = pow( zDiv / z, c); } + // When z_max large use exp( b * (z -z_div) ) below z_div and flat above it. + } else if (peakedNearUnity) { + if (fInt * rndmPtr->flat() < fIntLow) { + z = zDiv + log(z) / b; + fPrel = exp( b * (z - zDiv) ); + } else z = zDiv + (1. - zDiv) * z; + } + + // Evaluate actual f(z) (if in physical range) and correct. + if (z > 0 && z < 1) { + double fExp = b * (1. / zMax - 1. / z)+ c * log(zMax / z); + if (!aIsZero) fExp += a * log( (1. - z) / (1. - zMax) ); + fVal = exp( max( -EXPMAX, min( EXPMAX, fExp) ) ) ; + } else fVal = 0.; + } while (fVal < rndmPtr->flat() * fPrel); + + // Done. + return z; + +} + +//-------------------------------------------------------------------------- + +// Generate a random z according to the Peterson/SLAC formula +// f(z) = 1 / ( z * (1 - 1/z - epsilon/(1-z))^2 ) +// = z * (1-z)^2 / ((1-z)^2 + epsilon * z)^2. + +double StringZ::zPeterson( double epsilon) { + + double z, fVal; + + // For large epsilon pick z flat and reject, + // knowing that 4 * epsilon * f(z) < 1 everywhere. + if (epsilon > 0.01) { + do { + z = rndmPtr->flat(); + fVal = 4. * epsilon * z * pow2(1. - z) + / pow2( pow2(1. - z) + epsilon * z); + } while (fVal < rndmPtr->flat()); + return z; + } + + // Else split range, using that 4 * epsilon * f(z) + // < 4 * epsilon / (1 - z)^2 for 0 < z < 1 - 2 * sqrt(epsilon) + // < 1 for 1 - 2 * sqrt(epsilon) < z < 1 + double epsRoot = sqrt(epsilon); + double epsComb = 0.5 / epsRoot - 1.; + double fIntLow = 4. * epsilon * epsComb; + double fInt = fIntLow + 2. * epsRoot; + do { + if (rndmPtr->flat() * fInt < fIntLow) { + z = 1. - 1. / (1. + rndmPtr->flat() * epsComb); + fVal = z * pow2( pow2(1. - z) / (pow2(1. - z) + epsilon * z) ); + } else { + z = 1. - 2. * epsRoot * rndmPtr->flat(); + fVal = 4. * epsilon * z * pow2(1. - z) + / pow2( pow2(1. - z) + epsilon * z); + } + } while (fVal < rndmPtr->flat()); + return z; + +} + +//========================================================================== + +// The StringPT class. + +//-------------------------------------------------------------------------- + +// Initialize data members of the string pT selection. + +void StringPT::init(Settings& settings, Rndm* rndmPtrIn) { + + // Save pointer. + rndmPtr = rndmPtrIn; + + // Parameters of the pT width and enhancement. + sigmaQ = settings.parm("StringPT:sigma") / sqrt(2.); + enhancedFraction = settings.parm("StringPT:enhancedFraction"); + enhancedWidth = settings.parm("StringPT:enhancedWidth"); + +} + +//-------------------------------------------------------------------------- + +// Generate Gaussian pT such that = = sigma^2 = width^2/2, +// but with small fraction multiplied up to a broader spectrum. + +pair StringPT::pxy() { + + double sigma = sigmaQ; + if (rndmPtr->flat() < enhancedFraction) sigma *= enhancedWidth; + pair gauss2 = rndmPtr->gauss2(); + return pair(sigma * gauss2.first, sigma * gauss2.second); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/FragmentationSystems.cxx b/PYTHIA8/pythia8140/src/FragmentationSystems.cxx new file mode 100644 index 00000000000..f4d7a352821 --- /dev/null +++ b/PYTHIA8/pythia8140/src/FragmentationSystems.cxx @@ -0,0 +1,491 @@ +// FragmentationSystems.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// ColConfig, StringRegion and StringSystem classes. + +#include "FragmentationSystems.h" + +namespace Pythia8 { + +//========================================================================== + +// The ColConfig class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// A typical u/d constituent mass. +const double ColConfig::CONSTITUENTMASS = 0.325; + +//-------------------------------------------------------------------------- + +// Initialize and save pointers. + +void ColConfig::init(Info* infoPtrIn, Settings& settings, + StringFlav* flavSelPtrIn) { + + // Save pointers. + infoPtr = infoPtrIn; + flavSelPtr = flavSelPtrIn; + + // Joining of nearby partons along the string. + mJoin = settings.parm("FragmentationSystems:mJoin"); + + // For consistency ensure that mJoin is bigger than in StringRegion. + mJoin = max( mJoin, 2. * StringRegion::MJOIN); + + // Simplification of q q q junction topology to quark - diquark one. + mJoinJunction = settings.parm("FragmentationSystems:mJoinJunction"); + mStringMin = settings.parm("HadronLevel:mStringMin"); + +} + +//-------------------------------------------------------------------------- + +// Insert a new colour singlet system in ascending mass order. +// Calculate its properties. Join nearby partons. + +bool ColConfig::insert( vector& iPartonIn, Event& event) { + + // Find momentum and invariant mass of system, minus endpoint masses. + Vec4 pSumIn; + double mSumIn = 0.; + bool hasJunctionIn = false; + for (int i = 0; i < int(iPartonIn.size()); ++i) { + if (iPartonIn[i] < 0) { + hasJunctionIn = true; + continue; + } + pSumIn += event[ iPartonIn[i] ].p(); + if (!event[ iPartonIn[i] ].isGluon()) + mSumIn += event[ iPartonIn[i] ].constituentMass(); + } + double massIn = pSumIn.mCalc(); + double massExcessIn = massIn - mSumIn; + + // Check that momenta do not contain not-a-number. + if (abs(massExcessIn) >= 0.); + else { + infoPtr->errorMsg("Error in ColConfig::insert: " + "not-a-number system mass"); + return false; + } + + // Identify closed gluon loop. Assign "endpoint" masses as light quarks. + bool isClosedIn = (iPartonIn[0] >= 0 && event[ iPartonIn[0] ].isGluon()); + if (isClosedIn) massExcessIn -= 2. * CONSTITUENTMASS; + + // For junction topology: join two nearby legs into a diquark. + if (hasJunctionIn && joinJunction( iPartonIn, event, massExcessIn)) + hasJunctionIn = false; + + // Loop while > 2 partons left and hope of finding joining pair. + bool hasJoined = true; + while (hasJoined && iPartonIn.size() > 2) { + + // Look for the pair of neighbour partons (along string) with + // the smallest invariant mass (subtracting quark masses). + int iJoinMin = -1; + double mJoinMin = 2. * mJoin; + int nSize = iPartonIn.size(); + int nPair = (isClosedIn) ? nSize : nSize - 1; + for (int i = 0; i < nPair; ++i) { + // Keep three legs of junction separate. + if (iPartonIn[i] < 0 || iPartonIn[(i + 1)%nSize] < 0) continue; + Particle& parton1 = event[ iPartonIn[i] ]; + Particle& parton2 = event[ iPartonIn[(i + 1)%nSize] ]; + Vec4 pSumNow; + pSumNow += (parton1.isGluon()) ? 0.5 * parton1.p() : parton1.p(); + pSumNow += (parton2.isGluon()) ? 0.5 * parton2.p() : parton2.p(); + double mJoinNow = pSumNow.mCalc(); + if (!parton1.isGluon()) mJoinNow -= parton1.m(); + if (!parton2.isGluon()) mJoinNow -= parton2.m(); + if (mJoinNow < mJoinMin) { iJoinMin = i; mJoinMin = mJoinNow; } + } + + // If sufficiently nearby then join into one new parton. + // Note: error sensitivity to mJoin indicates unstable precedure?? + hasJoined = false; + if (mJoinMin < mJoin) { + int iJoin1 = iPartonIn[iJoinMin]; + int iJoin2 = iPartonIn[(iJoinMin + 1)%nSize]; + int idNew = (event[iJoin1].isGluon()) ? event[iJoin2].id() + : event[iJoin1].id(); + int colNew = event[iJoin1].col(); + int acolNew = event[iJoin2].acol(); + if (colNew == acolNew) { + colNew = event[iJoin2].col(); + acolNew = event[iJoin1].acol(); + } + Vec4 pNew = event[iJoin1].p() + event[iJoin2].p(); + + // Append joined parton to event record. + int iNew = event.append( idNew, 73, min(iJoin1, iJoin2), + max(iJoin1, iJoin2), 0, 0, colNew, acolNew, pNew, pNew.mCalc() ); + + // Mark joined partons and reduce remaining system. + event[iJoin1].statusNeg(); + event[iJoin2].statusNeg(); + event[iJoin1].daughter1(iNew); + event[iJoin2].daughter1(iNew); + if (iJoinMin == nSize - 1) iPartonIn[0] = iNew; + else { + iPartonIn[iJoinMin] = iNew; + for (int i = iJoinMin + 1; i < nSize - 1; ++i) + iPartonIn[i] = iPartonIn[i + 1]; + } + iPartonIn.pop_back(); + + // If joined,then loopback to look for more. + hasJoined = true; + } + } + + // Store new colour singlet system at the end. + singlets.push_back( ColSinglet(iPartonIn, pSumIn, massIn, + massExcessIn, hasJunctionIn, isClosedIn) ); + + // Now move around, so that smallest mass excesses come first. + int iInsert = singlets.size() - 1; + for (int iSub = singlets.size() - 2; iSub >= 0; --iSub) { + if (massExcessIn > singlets[iSub].massExcess) break; + singlets[iSub + 1] = singlets[iSub]; + iInsert = iSub; + } + if (iInsert < int(singlets.size()) - 1) singlets[iInsert] = + ColSinglet(iPartonIn, pSumIn, massIn, massExcessIn, + hasJunctionIn, isClosedIn); + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Join two legs of junction to a diquark for small invariant masses. +// Note: for junction system, iPartonIn points to structure +// (-code0) g...g.q0 (-code1) g...g.q1 (-code2) g...g.q2 + +bool ColConfig::joinJunction( vector& iPartonIn, Event& event, + double massExcessIn) { + + // Find four-momentum and endpoint quarks and masses on the three legs. + Vec4 pLeg[3]; + double mLeg[3]; + int idAbsLeg[3]; + int leg = -1; + for (int i = 0; i < int(iPartonIn.size()); ++ i) { + if (iPartonIn[i] < 0) ++leg; + else { + pLeg[leg] += event[ iPartonIn[i] ].p(); + mLeg[leg] = event[ iPartonIn[i] ].m(); + idAbsLeg[leg] = event[ iPartonIn[i] ].idAbs(); + } + } + + // Calculate invariant mass of three pairs, minus endpoint masses. + double m01 = (pLeg[0] + pLeg[1]).mCalc() - mLeg[0] - mLeg[1]; + double m02 = (pLeg[0] + pLeg[2]).mCalc() - mLeg[0] - mLeg[2]; + double m12 = (pLeg[1] + pLeg[2]).mCalc() - mLeg[1] - mLeg[2]; + + // Find lowest-mass pair not involving diquark. + double mMin = mJoinJunction + 1.; + int legA = -1; + int legB = -1; + if (m01 < mMin && idAbsLeg[0] < 9 && idAbsLeg[1] < 9) { + mMin = m01; + legA = 0; + legB = 1; + } + if (m02 < mMin && idAbsLeg[0] < 9 && idAbsLeg[2] < 9) { + mMin = m02; + legA = 0; + legB = 2; + } + if (m12 < mMin && idAbsLeg[1] < 9 && idAbsLeg[2] < 9) { + mMin = m12; + legA = 1; + legB = 2; + } + int legC = 3 - legA - legB; + + // Nothing to do if no two legs have small invariant mass, and + // system as a whole is above MiniStringFragmentation threshold. + if (mMin > mJoinJunction && massExcessIn > mStringMin) return false; + + // Construct separate index arrays for the three legs. + vector iLegA, iLegB, iLegC; + leg = -1; + for (int i = 0; i < int(iPartonIn.size()); ++ i) { + if (iPartonIn[i] < 0) ++leg; + else if( leg == legA) iLegA.push_back( iPartonIn[i] ); + else if( leg == legB) iLegB.push_back( iPartonIn[i] ); + else if( leg == legC) iLegC.push_back( iPartonIn[i] ); + } + + // First step: successively combine any gluons on the two legs. + // (Presumably overkill; not likely to be (m)any extra gluons.) + // (Do as successive binary joinings, so only need two mothers.) + for (leg = 0; leg < 2; ++leg) { + vector& iLegNow = (leg == 0) ? iLegA : iLegB; + int sizeNow = iLegNow.size(); + for (int i = sizeNow - 2; i >= 0; --i) { + int iQ = iLegNow.back(); + int iG = iLegNow[i]; + int colNew = (event[iQ].id() > 0) ? event[iG].col() : 0; + int acolNew = (event[iQ].id() < 0) ? event[iG].acol() : 0; + Vec4 pNew = event[iQ].p() + event[iG].p(); + int iNew = event.append( event[iQ].id(), 74, min(iQ, iG), + max(iQ, iG), 0, 0, colNew, acolNew, pNew, pNew.mCalc() ); + + // Mark joined partons and update iLeg end. + event[iQ].statusNeg(); + event[iG].statusNeg(); + event[iQ].daughter1(iNew); + event[iG].daughter1(iNew); + iLegNow.back() = iNew; + } + } + + // Second step: combine two quarks into a diquark. + int iQA = iLegA.back(); + int iQB = iLegB.back(); + int idQA = event[iQA].id(); + int idQB = event[iQB].id(); + int idNew = flavSelPtr->makeDiquark( idQA, idQB ); + // Diquark colour is opposite to parton closest to junction on third leg. + int colNew = (idNew > 0) ? 0 : event[ iLegC[0] ].acol(); + int acolNew = (idNew > 0) ? event[ iLegC[0] ].col() : 0; + Vec4 pNew = pLeg[legA] + pLeg[legB]; + int iNew = event.append( idNew, 74, min(iQA, iQB), max( iQA, iQB), + 0, 0, colNew, acolNew, pNew, pNew.mCalc() ); + + // Mark joined partons and reduce remaining system. + event[iQA].statusNeg(); + event[iQB].statusNeg(); + event[iQA].daughter1(iNew); + event[iQB].daughter1(iNew); + iPartonIn.resize(0); + iPartonIn.push_back( iNew); + for (int i = 0; i < int(iLegC.size()) ; ++i) + iPartonIn.push_back( iLegC[i]); + + // Remove junction from event record list, identifying by colour. + int iJun = -1; + for (int i = 0; i < event.sizeJunction(); ++i) + for (int j = 0; j < 3; ++ j) + if ( event.colJunction(i,j) == max(colNew, acolNew) ) iJun = i; + if (iJun >= 0) event.eraseJunction(iJun); + + // Done, having eliminated junction. + return true; + +} + +//-------------------------------------------------------------------------- + +// Collect all partons of singlet to be consecutively ordered. + +void ColConfig::collect(int iSub, Event& event) { + + // Partons may already have been collected, e.g. at ministring collapse. + if (singlets[iSub].isCollected) return; + singlets[iSub].isCollected = true; + + // Check if partons already "by chance" happen to be ordered. + bool inOrder = true; + for (int i = 0; i < singlets[iSub].size() - 1; ++i) { + int iFirst = singlets[iSub].iParton[i]; + if (iFirst < 0) continue; + int iSecond = singlets[iSub].iParton[i + 1]; + if (iSecond < 0) iSecond = singlets[iSub].iParton[i + 2]; + if (iSecond != iFirst + 1) { inOrder = false; break;} + } + if (inOrder) return; + + // Copy down system. Update current partons. + for (int i = 0; i < singlets[iSub].size(); ++i) { + int iOld = singlets[iSub].iParton[i]; + if (iOld < 0) continue; + int iNew = event.copy(iOld, 71); + singlets[iSub].iParton[i] = iNew; + } + + // Done. +} + +//-------------------------------------------------------------------------- + +// List all currently identified singlets. + +void ColConfig::list(ostream& os) const { + + // Header. Loop over all individual singlets. + os << "\n -------- Colour Singlet Systems Listing -------------------\n"; + for (int iSub = 0; iSub < int(singlets.size()); ++iSub) { + + // List all partons belonging to each singlet. + os << " singlet " << iSub << " contains " ; + for (int i = 0; i < singlets[iSub].size(); ++i) + os << singlets[iSub].iParton[i] << " "; + os << "\n"; + + // Done. + } +} + +//========================================================================== + +// The StringRegion class. + +// Currently a number of simplifications, in particular ?? +// 1) No popcorn baryon production. +// 2) Simplified treatment of pT in stepping and joining. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// If a string region is smaller thsan this it is assumed empty. +const double StringRegion::MJOIN = 0.1; + +// Avoid division by zero. +const double StringRegion::TINY = 1e-20; + +//-------------------------------------------------------------------------- + +// Set up four-vectors for longitudinal and transverse directions. + +void StringRegion::setUp(Vec4 p1, Vec4 p2, bool isMassless) { + + // Simple case: the two incoming four-vectors guaranteed massless. + if (isMassless) { + + // Calculate w2, minimum value. Lightcone directions = input. + w2 = 2. * (p1 * p2); + if (w2 < MJOIN*MJOIN) {isSetUp = true; isEmpty = true; return;} + pPos = p1; + pNeg = p2; + + // Else allow possibility of masses for incoming partons (also gluons!). + } else { + + // Generic four-momentum combinations. + double m1Sq = p1 * p1; + double m2Sq = p2 * p2; + double p1p2 = p1 * p2; + w2 = m1Sq + 2. * p1p2 + m2Sq; + double rootSq = pow2(p1p2) - m1Sq * m2Sq; + + // If crazy kinematics (should not happen!) modify energies. + if (w2 <= 0. || rootSq <= 0.) { + if (m1Sq < 0.) m1Sq = 0.; + p1.e( sqrt(m1Sq + p1.pAbs2()) ); + if (m2Sq < 0.) m2Sq = 0.; + p2.e( sqrt(m2Sq + p2.pAbs2()) ); + p1p2 = p1 * p2; + w2 = m1Sq + 2. * p1p2 + m2Sq; + rootSq = pow2(p1p2) - m1Sq * m2Sq; + } + + // If still small invariant mass then empty region (e.g. in gg system). + if (w2 < MJOIN*MJOIN) {isSetUp = true; isEmpty = true; return;} + + // Find two lightconelike longitudinal four-vector directions. + double root = sqrt( max(TINY, rootSq) ); + double k1 = 0.5 * ( (m2Sq + p1p2) / root - 1.); + double k2 = 0.5 * ( (m1Sq + p1p2) / root - 1.); + pPos = (1. + k1) * p1 - k2 * p2; + pNeg = (1. + k2) * p2 - k1 * p1; + } + + // Find two spacelike transverse four-vector directions. + // Begin by picking two sensible trial directions. + Vec4 eDiff = pPos / pPos.e() - pNeg / pNeg.e(); + double eDx = pow2( eDiff.px() ); + double eDy = pow2( eDiff.py() ); + double eDz = pow2( eDiff.pz() ); + if (eDx < min(eDy, eDz)) { + eX = Vec4( 1., 0., 0., 0.); + eY = (eDy < eDz) ? Vec4( 0., 1., 0., 0.) : Vec4( 0., 0., 1., 0.); + } else if (eDy < eDz) { + eX = Vec4( 0., 1., 0., 0.); + eY = (eDx < eDz) ? Vec4( 1., 0., 0., 0.) : Vec4( 0., 0., 1., 0.); + } else { + eX = Vec4( 0., 0., 1., 0.); + eY = (eDx < eDy) ? Vec4( 1., 0., 0., 0.) : Vec4( 0., 1., 0., 0.); + } + + // Then construct orthogonal linear combinations. + double pPosNeg = pPos * pNeg; + double kXPos = eX * pPos / pPosNeg; + double kXNeg = eX * pNeg / pPosNeg; + double kXX = 1. / sqrt( 1. + 2. * kXPos * kXNeg * pPosNeg ); + double kYPos = eY * pPos / pPosNeg; + double kYNeg = eY * pNeg / pPosNeg; + double kYX = kXX * (kXPos * kYNeg + kXNeg * kYPos) * pPosNeg; + double kYY = 1. / sqrt(1. + 2. * kYPos * kYNeg * pPosNeg - pow2(kYX)); + eX = kXX * (eX - kXNeg * pPos - kXPos * pNeg); + eY = kYY * (eY - kYNeg * pPos - kYPos * pNeg - kYX * eX); + + // Done. + isSetUp = true; + isEmpty = false; + +} + +//-------------------------------------------------------------------------- + +// Project a four-momentum onto (x+, x-, px, py). + +void StringRegion::project(Vec4 pIn) { + + // Perform projections by four-vector multiplication. + xPosProj = 2. * (pIn * pNeg) / w2; + xNegProj = 2. * (pIn * pPos) / w2; + pxProj = - (pIn * eX); + pyProj = - (pIn * eY); + +} + +//========================================================================== + +// The StringSystem class. + +//-------------------------------------------------------------------------- + +// Set up system from parton list. + +void StringSystem::setUp(vector& iSys, Event& event) { + + // Figure out how big the system is. (Closed gluon loops?) + sizePartons = iSys.size(); + sizeStrings = sizePartons - 1; + sizeRegions = (sizeStrings * (sizeStrings + 1)) / 2; + indxReg = 2 * sizeStrings + 1; + iMax = sizeStrings - 1; + + // Reserve space for the required number of regions. + system.clear(); + system.resize(sizeRegions); + + // Set up the lowest-lying regions. + for (int i = 0; i < sizeStrings; ++i) { + Vec4 p1 = event[ iSys[i] ].p(); + if ( event[ iSys[i] ].isGluon() ) p1 *= 0.5; + Vec4 p2 = event[ iSys[i+1] ].p(); + if ( event[ iSys[i+1] ].isGluon() ) p2 *= 0.5; + system[ iReg(i, iMax - i) ].setUp( p1, p2, false); + } + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/HadronLevel.cxx b/PYTHIA8/pythia8140/src/HadronLevel.cxx new file mode 100644 index 00000000000..4f4358386de --- /dev/null +++ b/PYTHIA8/pythia8140/src/HadronLevel.cxx @@ -0,0 +1,919 @@ +// HadronLevel.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the HadronLevel class. + +#include "HadronLevel.h" + +namespace Pythia8 { + +//========================================================================== + +// The HadronLevel class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// For breaking J-J string, pick a Gamma by taking a step with fictitious mass. +const double HadronLevel::JJSTRINGM2MAX = 25.; +const double HadronLevel::JJSTRINGM2FRAC = 0.1; + +// Iterate junction rest frame boost until convergence or too many tries. +const double HadronLevel::CONVJNREST = 1e-5; +const int HadronLevel::NTRYJNREST = 20; + +// Typical average transvere primary hadron mass . +const double HadronLevel::MTHAD = 0.9; + +//-------------------------------------------------------------------------- + +// Find settings. Initialize HadronLevel classes as required. + +bool HadronLevel::init(Info* infoPtrIn, Settings& settings, + ParticleData& particleData, Rndm* rndmPtrIn, TimeShower* timesDecPtr, + DecayHandler* decayHandlePtr, vector handledParticles) { + + // Save pointers. + infoPtr = infoPtrIn; + rndmPtr = rndmPtrIn; + + // Main flags. + doHadronize = settings.flag("HadronLevel:Hadronize"); + doDecay = settings.flag("HadronLevel:Decay"); + doBoseEinstein = settings.flag("HadronLevel:BoseEinstein"); + + // Boundary mass between string and ministring handling. + mStringMin = settings.parm("HadronLevel:mStringMin"); + + // For junction processing. + eNormJunction = settings.parm("StringFragmentation:eNormJunction"); + + // Particles that should decay or not before Bose-Einstein stage. + widthSepBE = settings.parm("BoseEinstein:widthSep"); + + // Initialize string and ministring fragmentation. + stringFrag.init(infoPtr, settings, &particleData, rndmPtr, &flavSel, &pTSel, + &zSel); + ministringFrag.init(infoPtr, settings, &particleData, rndmPtr, &flavSel); + + // Initialize particle decays. + decays.init(infoPtr, settings, &particleData, rndmPtr, timesDecPtr, &flavSel, + decayHandlePtr, handledParticles); + + // Initialize BoseEinstein. + boseEinstein.init(infoPtr, settings, particleData); + + // Initialize auxiliary administrative classes. + colConfig.init(infoPtr, settings, &flavSel); + + // Initialize auxiliary fragmentation classes. + flavSel.init(settings, rndmPtr); + pTSel.init(settings, rndmPtr); + zSel.init(settings, particleData, rndmPtr); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Hadronize and decay the next parton-level. + +bool HadronLevel::next( Event& event) { + + // Colour-octet onia states must be decayed to singlet + gluon. + if (!decayOctetOnia(event)) return false; + + // Possibility of hadronization inside decay, but then no BE second time. + bool moreToDo; + bool doBoseEinsteinNow = doBoseEinstein; + do { + moreToDo = false; + + // First part: string fragmentation. + if (doHadronize) { + + // Find the complete colour singlet configuration of the event. + if (!findSinglets( event)) return false; + + // Process all colour singlet (sub)system + for (int iSub = 0; iSub < colConfig.size(); ++iSub) { + + // Collect sequentially all partons in a colour singlet subsystem. + colConfig.collect(iSub, event); + + // String fragmentation of each colour singlet (sub)system. + if ( colConfig[iSub].massExcess > mStringMin ) { + if (!stringFrag.fragment( iSub, colConfig, event)) return false; + + // Low-mass string treated separately. Tell if diffractive system. + } else { + bool isDiff = infoPtr->isDiffractiveA() + || infoPtr->isDiffractiveB(); + if (!ministringFrag.fragment( iSub, colConfig, event, isDiff)) + return false; + } + } + } + + // Second part: sequential decays of short-lived particles (incl. K0). + if (doDecay) { + + // Loop through all entries to find those that should decay. + int iDec = 0; + do { + Particle& decayer = event[iDec]; + if ( decayer.isFinal() && decayer.canDecay() && decayer.mayDecay() + && (decayer.mWidth() > widthSepBE || decayer.idAbs() == 311) ) { + decays.decay( iDec, event); + if (decays.moreToDo()) moreToDo = true; + } + } while (++iDec < event.size()); + } + + // Third part: include Bose-Einstein effects among current particles. + if (doBoseEinsteinNow) { + if (!boseEinstein.shiftEvent(event)) return false; + doBoseEinsteinNow = false; + } + + // Fourth part: sequential decays also of long-lived particles. + if (doDecay) { + + // Loop through all entries to find those that should decay. + int iDec = 0; + do { + Particle& decayer = event[iDec]; + if ( decayer.isFinal() && decayer.canDecay() && decayer.mayDecay() ) { + decays.decay( iDec, event); + if (decays.moreToDo()) moreToDo = true; + } + } while (++iDec < event.size()); + } + + // Normally done first time around, but sometimes not (e.g. Upsilon). + } while (moreToDo); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Allow more decays if on/off switches changed. +// Note: does not do sequential hadronization, e.g. for Upsilon. + +bool HadronLevel::moreDecays( Event& event) { + + // Colour-octet onia states must be decayed to singlet + gluon. + if (!decayOctetOnia(event)) return false; + + // Loop through all entries to find those that should decay. + int iDec = 0; + do { + if ( event[iDec].isFinal() && event[iDec].canDecay() + && event[iDec].mayDecay() ) decays.decay( iDec, event); + } while (++iDec < event.size()); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Decay colour-octet onium states. + +bool HadronLevel::decayOctetOnia(Event& event) { + + // Onium states to be decayed. + int idOnium[6] = { 9900443, 9900441, 9910441, + 9900553, 9900551, 9910551 }; + + // Loop over particles and identify onia. + for (int iDec = 0; iDec < event.size(); ++iDec) + if (event[iDec].isFinal()) { + int id = event[iDec].id(); + bool isOnium = false; + for (int j = 0; j < 6; ++j) if (id == idOnium[j]) isOnium = true; + + // Decay any onia encountered. + if (isOnium) { + if (!decays.decay( iDec, event)) return false; + + // Set colour flow by hand: gluon inherits octet-onium state. + int iGlu = event.size() - 1; + event[iGlu].cols( event[iDec].col(), event[iDec].acol() ); + } + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Trace colour flow in the event to form colour singlet subsystems. + +bool HadronLevel::findSinglets(Event& event) { + + // Find a list of final partons and of all colour ends and gluons. + iColEnd.resize(0); + iAcolEnd.resize(0); + iColAndAcol.resize(0); + for (int i = 0; i < event.size(); ++i) if (event[i].isFinal()) { + if (event[i].col() > 0 && event[i].acol() > 0) iColAndAcol.push_back(i); + else if (event[i].col() > 0) iColEnd.push_back(i); + else if (event[i].acol() > 0) iAcolEnd.push_back(i); + } + + // Begin arrange the partons into separate colour singlets. + colConfig.clear(); + iPartonJun.resize(0); + iPartonAntiJun.resize(0); + + // Junctions: loop over them, and identify kind. + for (int iJun = 0; iJun < event.sizeJunction(); ++iJun) + if (event.remainsJunction(iJun)) { + event.remainsJunction(iJun, false); + int kindJun = event.kindJunction(iJun); + iParton.resize(0); + + // First kind: three (anti)colours out from junction. + if (kindJun == 1 || kindJun == 2) { + for (int iCol = 0; iCol < 3; ++iCol) { + int indxCol = event.colJunction(iJun, iCol); + iParton.push_back( -(10 + 10 * iJun + iCol) ); + if (kindJun == 1 && !traceFromAcol(indxCol, event, iJun, iCol)) + return false; + if (kindJun == 2 && !traceFromCol(indxCol, event, iJun, iCol)) + return false; + } + } + + // Keep in memory a junction hooked up with an antijunction, + // else store found single-junction system. + int nNeg = 0; + for (int i = 0; i < int(iParton.size()); ++i) if (iParton[i] < 0) + ++nNeg; + if (nNeg > 3 && kindJun == 1) { + for (int i = 0; i < int(iParton.size()); ++i) + iPartonJun.push_back(iParton[i]); + } else if (nNeg > 3 && kindJun == 2) { + for (int i = 0; i < int(iParton.size()); ++i) + iPartonAntiJun.push_back(iParton[i]); + } else { + // A junction may be eliminated by insert if two quarks are nearby. + int nJunOld = event.sizeJunction(); + if (!colConfig.insert(iParton, event)) return false; + if (event.sizeJunction() < nJunOld) --iJun; + } + } + + // Split junction-antijunction system into two, and store those. + // (Only one system in extreme cases, and then second empty.) + if (iPartonJun.size() > 0 && iPartonAntiJun.size() > 0) { + if (!splitJunctionPair(event)) return false; + if (!colConfig.insert(iPartonJun, event)) return false; + if (iPartonAntiJun.size() > 0) + if (!colConfig.insert(iPartonAntiJun, event)) return false; + // Error if only one of junction and antijuction left here. + } else if (iPartonJun.size() > 0 || iPartonAntiJun.size() > 0) { + infoPtr->errorMsg("Error in HadronLevel::findSinglets: " + "unmatched (anti)junction"); + return false; + } + + // Open strings: pick up each colour end and trace to its anticolor end. + for (int iEnd = 0; iEnd < int(iColEnd.size()); ++iEnd) { + iParton.resize(0); + iParton.push_back( iColEnd[iEnd] ); + int indxCol = event[ iColEnd[iEnd] ].col(); + if (!traceFromCol(indxCol, event)) return false; + + // Store found open string system. Analyze its properties. + if (!colConfig.insert(iParton, event)) return false; + } + + // Closed strings : begin at any gluon and trace until back at it. + while (iColAndAcol.size() > 0) { + iParton.resize(0); + iParton.push_back( iColAndAcol[0] ); + int indxCol = event[ iColAndAcol[0] ].col(); + int indxAcol = event[ iColAndAcol[0] ].acol(); + iColAndAcol[0] = iColAndAcol.back(); + iColAndAcol.pop_back(); + if (!traceInLoop(indxCol, indxAcol, event)) return false; + + // Store found closed string system. Analyze its properties. + if (!colConfig.insert(iParton, event)) return false; + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Trace a colour line, from a colour to an anticolour. + +bool HadronLevel::traceFromCol(int indxCol, Event& event, int iJun, + int iCol) { + + // Junction kind, if any. + int kindJun = (iJun >= 0) ? event.kindJunction(iJun) : 0; + + // Begin to look for a matching anticolour. + int loop = 0; + int loopMax = iColAndAcol.size() + 2; + bool hasFound = false; + do { + ++loop; + hasFound= false; + + // First check list of matching anticolour ends. + for (int i = 0; i < int(iAcolEnd.size()); ++i) + if (event[ iAcolEnd[i] ].acol() == indxCol) { + iParton.push_back( iAcolEnd[i] ); + indxCol = 0; + iAcolEnd[i] = iAcolEnd.back(); + iAcolEnd.pop_back(); + hasFound = true; + break; + } + + // Then check list of intermediate gluons. + if (!hasFound) + for (int i = 0; i < int(iColAndAcol.size()); ++i) + if (event[ iColAndAcol[i] ].acol() == indxCol) { + iParton.push_back( iColAndAcol[i] ); + + // Update to new colour. Remove gluon. + indxCol = event[ iColAndAcol[i] ].col(); + if (kindJun > 0) event.endColJunction(iJun, iCol, indxCol); + iColAndAcol[i] = iColAndAcol.back(); + iColAndAcol.pop_back(); + hasFound = true; + break; + } + + // In a pinch, check list of end colours on other (anti)junction. + if (!hasFound && kindJun == 2 && event.sizeJunction() > 1) + for (int iAntiJun = 0; iAntiJun < event.sizeJunction(); ++iAntiJun) + if (iAntiJun != iJun && event.kindJunction(iAntiJun) == 1) + for (int iColAnti = 0; iColAnti < 3; ++iColAnti) + if (event.endColJunction(iAntiJun, iColAnti) == indxCol) { + iParton.push_back( -(10 + 10 * iAntiJun + iColAnti) ); + indxCol = 0; + hasFound = true; + break; + } + + // Keep on tracing via gluons until reached end of leg. + } while (hasFound && indxCol > 0 && loop < loopMax); + + // Something went wrong in colour tracing. + if (!hasFound || loop == loopMax) { + infoPtr->errorMsg("Error in HadronLevel::traceFromCol: " + "colour tracing failed"); + return false; + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Trace a colour line, from an anticolour to a colour. + +bool HadronLevel::traceFromAcol(int indxCol, Event& event, int iJun, + int iCol) { + + // Junction kind, if any. + int kindJun = (iJun >= 0) ? event.kindJunction(iJun) : 0; + + // Begin to look for a matching colour. + int loop = 0; + int loopMax = iColAndAcol.size() + 2; + bool hasFound = false; + do { + ++loop; + hasFound= false; + + // First check list of matching colour ends. + for (int i = 0; i < int(iColEnd.size()); ++i) + if (event[ iColEnd[i] ].col() == indxCol) { + iParton.push_back( iColEnd[i] ); + indxCol = 0; + iColEnd[i] = iColEnd.back(); + iColEnd.pop_back(); + hasFound = true; + break; + } + + // Then check list of intermediate gluons. + if (!hasFound) + for (int i = 0; i < int(iColAndAcol.size()); ++i) + if (event[ iColAndAcol[i] ].col() == indxCol) { + iParton.push_back( iColAndAcol[i] ); + + // Update to new colour. Remove gluon. + indxCol = event[ iColAndAcol[i] ].acol(); + if (kindJun > 0) event.endColJunction(iJun, iCol, indxCol); + iColAndAcol[i] = iColAndAcol.back(); + iColAndAcol.pop_back(); + hasFound = true; + break; + } + + // In a pinch, check list of colours on other (anti)junction. + if (!hasFound && kindJun == 1 && event.sizeJunction() > 1) + for (int iAntiJun = 0; iAntiJun < event.sizeJunction(); ++iAntiJun) + if (iAntiJun != iJun && event.kindJunction(iAntiJun) == 2) + for (int iColAnti = 0; iColAnti < 3; ++iColAnti) + if (event.endColJunction(iAntiJun, iColAnti) == indxCol) { + iParton.push_back( -(10 + 10 * iAntiJun + iColAnti) ); + indxCol = 0; + hasFound = true; + break; + } + + // Keep on tracing via gluons until reached end of leg. + } while (hasFound && indxCol > 0 && loop < loopMax); + + // Something went wrong in colour tracing. + if (!hasFound || loop == loopMax) { + infoPtr->errorMsg("Error in HadronLevel::traceFromAcol: " + "colour tracing failed"); + return false; + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Trace a colour loop, from a colour back to the anticolour of the same. + +bool HadronLevel::traceInLoop(int indxCol, int indxAcol, Event& event) { + + // Move around until back where begun. + int loop = 0; + int loopMax = iColAndAcol.size() + 2; + bool hasFound = false; + do { + ++loop; + hasFound= false; + + // Check list of gluons. + for (int i = 0; i < int(iColAndAcol.size()); ++i) + if (event[ iColAndAcol[i] ].acol() == indxCol) { + iParton.push_back( iColAndAcol[i] ); + indxCol = event[ iColAndAcol[i] ].col(); + iColAndAcol[i] = iColAndAcol.back(); + iColAndAcol.pop_back(); + hasFound = true; + break; + } + } while (hasFound && indxCol != indxAcol && loop < loopMax); + + // Something went wrong in colour tracing. + if (!hasFound || loop == loopMax) { + infoPtr->errorMsg("Error in HadronLevel::traceInLoop: " + "colour tracing failed"); + return false; + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Split junction-antijunction system into two, or simplify other way. + +bool HadronLevel::splitJunctionPair(Event& event) { + + // Construct separate index arrays for the three junction legs. + int identJun = (-iPartonJun[0])/10; + iJunLegA.resize(0); + iJunLegB.resize(0); + iJunLegC.resize(0); + int leg = -1; + for (int i = 0; i < int(iPartonJun.size()); ++ i) { + if ( (-iPartonJun[i])/10 == identJun) ++leg; + if (leg == 0) iJunLegA.push_back( iPartonJun[i] ); + else if (leg == 1) iJunLegB.push_back( iPartonJun[i] ); + else iJunLegC.push_back( iPartonJun[i] ); + } + + // Construct separate index arrays for the three antijunction legs. + int identAnti = (-iPartonAntiJun[0])/10; + iAntiLegA.resize(0); + iAntiLegB.resize(0); + iAntiLegC.resize(0); + leg = -1; + for (int i = 0; i < int(iPartonAntiJun.size()); ++ i) { + if ( (-iPartonAntiJun[i])/10 == identAnti) ++leg; + if (leg == 0) iAntiLegA.push_back( iPartonAntiJun[i] ); + else if (leg == 1) iAntiLegB.push_back( iPartonAntiJun[i] ); + else iAntiLegC.push_back( iPartonAntiJun[i] ); + } + + // Find interjunction legs, i.e. between junction and antijunction. + int nMatch = 0; + int legJun[3], legAnti[3], nGluLeg[3]; + if (iJunLegA.back() < 0) { legJun[nMatch] = 0; + legAnti[nMatch] = (-iJunLegA.back())%10; ++nMatch;} + if (iJunLegB.back() < 0) { legJun[nMatch] = 1; + legAnti[nMatch] = (-iJunLegB.back())%10; ++nMatch;} + if (iJunLegC.back() < 0) { legJun[nMatch] = 2; + legAnti[nMatch] = (-iJunLegC.back())%10; ++nMatch;} + + // Loop over interjunction legs. + for (int iMatch = 0; iMatch < nMatch; ++iMatch) { + vector& iJunLeg = (legJun[iMatch] == 0) ? iJunLegA + : ( (legJun[iMatch] == 1) ? iJunLegB : iJunLegC ); + vector& iAntiLeg = (legAnti[iMatch] == 0) ? iAntiLegA + : ( (legAnti[iMatch] == 1) ? iAntiLegB : iAntiLegC ); + + // Find number of gluons on each. Do nothing for now if none. + nGluLeg[iMatch] = iJunLeg.size() + iAntiLeg.size() - 4; + if (nGluLeg[iMatch] == 0) continue; + + // Else pick up the gluons on the interjunction leg in order. + iGluLeg.resize(0); + for (int i = 1; i < int(iJunLeg.size()) - 1; ++i) + iGluLeg.push_back( iJunLeg[i] ); + for (int i = int(iAntiLeg.size()) - 2; i > 0; --i) + iGluLeg.push_back( iAntiLeg[i] ); + + // Remove those gluons from the junction/antijunction leg lists. + iJunLeg.resize(1); + iAntiLeg.resize(1); + + // Pick a new quark at random; for simplicity no diquarks. + int idQ = flavSel.pickLightQ(); + int colQ, acolQ; + + // If one gluon on leg, split it into a collinear q-qbar pair. + if (iGluLeg.size() == 1) { + + // Store the new q qbar pair, sharing gluon colour and momentum. + colQ = event[ iGluLeg[0] ].col(); + acolQ = event[ iGluLeg[0] ].acol(); + Vec4 pQ = 0.5 * event[ iGluLeg[0] ].p(); + double mQ = 0.5 * event[ iGluLeg[0] ].m(); + int iQ = event.append( idQ, 75, iGluLeg[0], 0, 0, 0, colQ, 0, pQ, mQ ); + int iQbar = event.append( -idQ, 75, iGluLeg[0], 0, 0, 0, 0, acolQ, + pQ, mQ ); + + // Mark split gluon and update junction and antijunction legs. + event[ iGluLeg[0] ].statusNeg(); + event[ iGluLeg[0] ].daughters( iQ, iQbar); + iJunLeg.push_back(iQ); + iAntiLeg.push_back(iQbar); + + // If several gluons on the string, decide which g-g region to split up. + } else { + + // Evaluate mass-squared for all adjacent gluon pairs. + m2Pair.resize(0); + double m2Sum = 0.; + for (int i = 0; i < int(iGluLeg.size()) - 1; ++i) { + double m2Now = 0.5 * event[ iGluLeg[i] ].p() + * event[ iGluLeg[i + 1] ].p(); + m2Pair.push_back(m2Now); + m2Sum += m2Now; + } + + // Pick breakup region with probability proportional to mass-squared. + double m2Reg = m2Sum * rndmPtr->flat(); + int iReg = -1; + do m2Reg -= m2Pair[++iReg]; + while (m2Reg > 0. && iReg < int(iGluLeg.size()) - 1); + m2Reg = m2Pair[iReg]; + + // Pick breaking point of string in chosen region (symmetrically). + double m2Temp = min( JJSTRINGM2MAX, JJSTRINGM2FRAC * m2Reg); + double xPos = 0.5; + double xNeg = 0.5; + do { + double zTemp = zSel.zFrag( idQ, 0, m2Temp); + xPos = 1. - zTemp; + xNeg = m2Temp / (zTemp * m2Reg); + } while (xNeg > 1.); + if (rndmPtr->flat() > 0.5) swap(xPos, xNeg); + + // Pick up two "mother" gluons of breakup. Mark them decayed. + Particle& gJun = event[ iGluLeg[iReg] ]; + Particle& gAnti = event[ iGluLeg[iReg + 1] ]; + gJun.statusNeg(); + gAnti.statusNeg(); + int dau1 = event.size(); + gJun.daughters(dau1, dau1 + 3); + gAnti.daughters(dau1, dau1 + 3); + int mother1 = min( iGluLeg[iReg], iGluLeg[iReg + 1]); + int mother2 = max( iGluLeg[iReg], iGluLeg[iReg + 1]); + + // Can keep one of old colours but need one new so unambiguous. + colQ = gJun.acol(); + acolQ = event.nextColTag(); + + // Store copied gluons with reduced momenta. + int iGjun = event.append( 21, 75, mother1, mother2, 0, 0, + gJun.col(), gJun.acol(), (1. - 0.5 * xPos) * gJun.p(), + (1. - 0.5 * xPos) * gJun.m()); + int iGanti = event.append( 21, 75, mother1, mother2, 0, 0, + acolQ, gAnti.acol(), (1. - 0.5 * xNeg) * gAnti.p(), + (1. - 0.5 * xNeg) * gAnti.m()); + + // Store the new q qbar pair with remaining momenta. + int iQ = event.append( idQ, 75, mother1, mother2, 0, 0, + colQ, 0, 0.5 * xNeg * gAnti.p(), 0.5 * xNeg * gAnti.m() ); + int iQbar = event.append( -idQ, 75, mother1, mother2, 0, 0, + 0, acolQ, 0.5 * xPos * gJun.p(), 0.5 * xPos * gJun.m() ); + + // Update junction and antijunction legs with gluons and quarks. + for (int i = 0; i < iReg; ++i) + iJunLeg.push_back( iGluLeg[i] ); + iJunLeg.push_back(iGjun); + iJunLeg.push_back(iQ); + for (int i = int(iGluLeg.size()) - 1; i > iReg + 1; --i) + iAntiLeg.push_back( iGluLeg[i] ); + iAntiLeg.push_back(iGanti); + iAntiLeg.push_back(iQbar); + } + + // Update end colours for both g -> q qbar and g g -> g g q qbar. + event.endColJunction(identJun - 1, legJun[iMatch], colQ); + event.endColJunction(identAnti - 1, legAnti[iMatch], acolQ); + } + + // Update list of interjunction legs after splittings above. + int iMatchUp = 0; + while (iMatchUp < nMatch) { + if (nGluLeg[iMatchUp] > 0) { + for (int i = iMatchUp; i < nMatch - 1; ++i) { + legJun[i] = legJun[i + 1]; + legAnti[i] = legAnti[i + 1]; + nGluLeg[i] = nGluLeg[i + 1]; + } --nMatch; + } else ++iMatchUp; + } + + // Should not ever have three empty interjunction legs. + if (nMatch == 3) { + infoPtr->errorMsg("Error in HadronLevel::splitJunctionPair: " + "three empty junction-junction legs"); + return false; + } + + // If two legs are empty, then collapse system to a single string. + if (nMatch == 2) { + int legJunLeft = 3 - legJun[0] - legJun[1]; + int legAntiLeft = 3 - legAnti[0] - legAnti[1]; + vector& iJunLeg = (legJunLeft == 0) ? iJunLegA + : ( (legJunLeft == 1) ? iJunLegB : iJunLegC ); + vector& iAntiLeg = (legAntiLeft == 0) ? iAntiLegA + : ( (legAntiLeft == 1) ? iAntiLegB : iAntiLegC ); + iPartonJun.resize(0); + for (int i = int(iJunLeg.size()) - 1; i > 0; --i) + iPartonJun.push_back( iJunLeg[i] ); + for (int i = 1; i < int(iAntiLeg.size()); ++i) + iPartonJun.push_back( iAntiLeg[i] ); + + // Match up the colours where the strings are joined. + int iColJoin = iJunLeg[1]; + int iAcolJoin = iAntiLeg[1]; + event[iAcolJoin].acol( event[iColJoin].col() ); + + // Other string system empty. Remove junctions from their list. Done. + iPartonAntiJun.resize(0); + event.eraseJunction( max(identJun, identAnti) - 1); + event.eraseJunction( min(identJun, identAnti) - 1); + return true; + } + + // If one leg is empty then, depending on string length, either + // (a) annihilate junction and antijunction into two simple strings, or + // (b) split the empty leg by borrowing energy from nearby legs. + if (nMatch == 1) { + + // Identify the two external legs of either junction. + vector& iJunLeg0 = (legJun[0] == 0) ? iJunLegB : iJunLegA; + vector& iJunLeg1 = (legJun[0] == 2) ? iJunLegB : iJunLegC; + vector& iAntiLeg0 = (legAnti[0] == 0) ? iAntiLegB : iAntiLegA; + vector& iAntiLeg1 = (legAnti[0] == 2) ? iAntiLegB : iAntiLegC; + + // Simplified procedure: mainly study first parton on each leg. + Vec4 pJunLeg0 = event[ iJunLeg0[1] ].p(); + Vec4 pJunLeg1 = event[ iJunLeg1[1] ].p(); + Vec4 pAntiLeg0 = event[ iAntiLeg0[1] ].p(); + Vec4 pAntiLeg1 = event[ iAntiLeg1[1] ].p(); + + // Starting frame hopefully intermediate to two junction directions. + Vec4 pStart = pJunLeg0 / pJunLeg0.e() + pJunLeg1 / pJunLeg1.e() + + pAntiLeg0 / pAntiLeg0.e() + pAntiLeg1 / pAntiLeg1.e(); + + // Loop over iteration to junction/antijunction rest frames (JRF/ARF). + RotBstMatrix MtoJRF, MtoARF; + Vec4 pInJRF[3], pInARF[3]; + for (int iJun = 0; iJun < 2; ++iJun) { + int offset = (iJun == 0) ? 0 : 2; + + // Iterate from system rest frame towards the junction rest frame. + RotBstMatrix MtoRF, Mstep; + MtoRF.bstback(pStart); + Vec4 pInRF[4]; + int iter = 0; + do { + ++iter; + + // Find rest-frame momenta on the three sides of the junction. + // Only consider first parton on each leg, for simplicity. + pInRF[0 + offset] = pJunLeg0; + pInRF[1 + offset] = pJunLeg1; + pInRF[2 - offset] = pAntiLeg0; + pInRF[3 - offset] = pAntiLeg1; + for (int i = 0; i < 4; ++i) pInRF[i].rotbst(MtoRF); + + // For third side add both legs beyond other junction, weighted. + double wt2 = 1. - exp( -pInRF[2].e() / eNormJunction); + double wt3 = 1. - exp( -pInRF[3].e() / eNormJunction); + pInRF[2] = wt2 * pInRF[2] + wt3 * pInRF[3]; + + // Find new junction rest frame from the set of momenta. + Mstep = stringFrag.junctionRestFrame( pInRF[0], pInRF[1], pInRF[2]); + MtoRF.rotbst( Mstep ); + } while (iter < 3 || (Mstep.deviation() > CONVJNREST + && iter < NTRYJNREST) ); + + // Store final boost and rest-frame (weighted) momenta. + if (iJun == 0) { + MtoJRF = MtoRF; + for (int i = 0; i < 3; ++i) pInJRF[i] = pInRF[i]; + } else { + MtoARF = MtoRF; + for (int i = 0; i < 3; ++i) pInARF[i] = pInRF[i]; + } + } + + // Opposite operations: boost from JRF/ARF to original system. + RotBstMatrix MfromJRF = MtoJRF; + MfromJRF.invert(); + RotBstMatrix MfromARF = MtoARF; + MfromARF.invert(); + + // Velocity vectors of junctions and momentum of legs in lab frame. + Vec4 vJun(0., 0., 0., 1.); + vJun.rotbst(MfromJRF); + Vec4 vAnti(0., 0., 0., 1.); + vAnti.rotbst(MfromARF); + Vec4 pLabJ[3], pLabA[3]; + for (int i = 0; i < 3; ++i) { + pLabJ[i] = pInJRF[i]; + pLabJ[i].rotbst(MfromJRF); + pLabA[i] = pInARF[i]; + pLabA[i].rotbst(MfromARF); + } + + // Calculate Lambda-measure length of three possible topologies. + double vJvA = vJun * vAnti; + double vJvAe2y = vJvA + sqrt(vJvA*vJvA - 1.); + double LambdaJA = (2. * pInJRF[0].e()) * (2. * pInJRF[1].e()) + * (2. * pInARF[0].e()) * (2. * pInARF[1].e()) * vJvAe2y; + double Lambda00 = (2. * pLabJ[0] * pLabA[0]) + * (2. * pLabJ[1] * pLabA[1]); + double Lambda01 = (2. * pLabJ[0] * pLabA[1]) + * (2. * pLabJ[1] * pLabA[0]); + + // Case when either topology without junctions is the shorter one. + if (LambdaJA > min( Lambda00, Lambda01)) { + vector& iAntiMatch0 = (Lambda00 < Lambda01) + ? iAntiLeg0 : iAntiLeg1; + vector& iAntiMatch1 = (Lambda00 < Lambda01) + ? iAntiLeg1 : iAntiLeg0; + + // Define two quark-antiquark strings. + iPartonJun.resize(0); + for (int i = int(iJunLeg0.size()) - 1; i > 0; --i) + iPartonJun.push_back( iJunLeg0[i] ); + for (int i = 1; i < int(iAntiMatch0.size()); ++i) + iPartonJun.push_back( iAntiMatch0[i] ); + iPartonAntiJun.resize(0); + for (int i = int(iJunLeg1.size()) - 1; i > 0; --i) + iPartonAntiJun.push_back( iJunLeg1[i] ); + for (int i = 1; i < int(iAntiMatch1.size()); ++i) + iPartonAntiJun.push_back( iAntiMatch1[i] ); + + // Match up the colours where the strings are joined. + int iColJoin = iJunLeg0[1]; + int iAcolJoin = iAntiMatch0[1]; + event[iAcolJoin].acol( event[iColJoin].col() ); + iColJoin = iJunLeg1[1]; + iAcolJoin = iAntiMatch1[1]; + event[iAcolJoin].acol( event[iColJoin].col() ); + + // Remove junctions from their list. Done. + event.eraseJunction( max(identJun, identAnti) - 1); + event.eraseJunction( min(identJun, identAnti) - 1); + return true; + } + + // Case where junction and antijunction to be separated. + // Shuffle (p+/p-) momentum of order between systems, + // times 2/3 for 120 degree in JRF, times 1/2 for two legs, + // but not more than half of what nearest parton carries. + double eShift = MTHAD / (3. * sqrt(vJvAe2y)); + double fracJ0 = min(0.5, eShift / pInJRF[0].e()); + double fracJ1 = min(0.5, eShift / pInJRF[0].e()); + Vec4 pFromJun = fracJ0 * pJunLeg0 + fracJ1 * pJunLeg1; + double fracA0 = min(0.5, eShift / pInARF[0].e()); + double fracA1 = min(0.5, eShift / pInARF[0].e()); + Vec4 pFromAnti = fracA0 * pAntiLeg0 + fracA1 * pAntiLeg1; + + // Copy partons with scaled-down momenta and update legs. + int iNew = event.copy(iJunLeg0[1], 76); + event[iNew].rescale5(1. - fracJ0); + iJunLeg0[1] = iNew; + iNew = event.copy(iJunLeg1[1], 76); + event[iNew].rescale5(1. - fracJ1); + iJunLeg1[1] = iNew; + iNew = event.copy(iAntiLeg0[1], 76); + event[iNew].rescale5(1. - fracA0); + iAntiLeg0[1] = iNew; + iNew = event.copy(iAntiLeg1[1], 76); + event[iNew].rescale5(1. - fracA1); + iAntiLeg1[1] = iNew; + + // Pick a new quark at random; for simplicity no diquarks. + int idQ = flavSel.pickLightQ(); + + // Update junction colours for new quark and antiquark. + int colQ = event.nextColTag(); + int acolQ = event.nextColTag(); + event.endColJunction(identJun - 1, legJun[0], colQ); + event.endColJunction(identAnti - 1, legAnti[0], acolQ); + + // Store new quark and antiquark with momentum from other junction. + int mother1 = min(iJunLeg0[1], iJunLeg1[1]); + int mother2 = max(iJunLeg0[1], iJunLeg1[1]); + int iNewJ = event.append( idQ, 76, mother1, mother2, 0, 0, + colQ, 0, pFromAnti, pFromAnti.mCalc() ); + mother1 = min(iAntiLeg0[1], iAntiLeg1[1]); + mother2 = max(iAntiLeg0[1], iAntiLeg1[1]); + int iNewA = event.append( -idQ, 76, mother1, mother2, 0, 0, + 0, acolQ, pFromJun, pFromJun.mCalc() ); + + // Bookkeep new quark and antiquark on third legs. + if (legJun[0] == 0) iJunLegA[1] = iNewJ; + else if (legJun[0] == 1) iJunLegB[1] = iNewJ; + else iJunLegC[1] = iNewJ; + if (legAnti[0] == 0) iAntiLegA[1] = iNewA; + else if (legAnti[0] == 1) iAntiLegB[1] = iNewA; + else iAntiLegC[1] = iNewA; + + // Done with splitting junction from antijunction. + } + + // Put together new junction parton list. + iPartonJun.resize(0); + for (int i = 0; i < int(iJunLegA.size()); ++i) + iPartonJun.push_back( iJunLegA[i] ); + for (int i = 0; i < int(iJunLegB.size()); ++i) + iPartonJun.push_back( iJunLegB[i] ); + for (int i = 0; i < int(iJunLegC.size()); ++i) + iPartonJun.push_back( iJunLegC[i] ); + + // Put together new antijunction parton list. + iPartonAntiJun.resize(0); + for (int i = 0; i < int(iAntiLegA.size()); ++i) + iPartonAntiJun.push_back( iAntiLegA[i] ); + for (int i = 0; i < int(iAntiLegB.size()); ++i) + iPartonAntiJun.push_back( iAntiLegB[i] ); + for (int i = 0; i < int(iAntiLegC.size()); ++i) + iPartonAntiJun.push_back( iAntiLegC[i] ); + + // Now the two junction systems are separated and can be stored. + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/Info.cxx b/PYTHIA8/pythia8140/src/Info.cxx new file mode 100644 index 00000000000..4269a7ce4b8 --- /dev/null +++ b/PYTHIA8/pythia8140/src/Info.cxx @@ -0,0 +1,187 @@ +// Info.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the Info class. + +#include "Info.h" + +namespace Pythia8 { + +//========================================================================== + +// Info class. +// This class contains a mixed bag of information on the event generation +// activity, especially on the current subprocess properties. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of times the same error message will be repeated at most. +const int Info::TIMESTOPRINT = 1; + +//-------------------------------------------------------------------------- + +// List (almost) all information currently set. + +void Info::list(ostream& os) const { + + // Header and beam info. + os << "\n -------- PYTHIA Info Listing ------------------------" + << "---------------- \n \n" + << scientific << setprecision(3) + << " Beam A: id = " << setw(6) << idASave << ", pz = " << setw(10) + << pzASave << ", e = " << setw(10) << eASave << ", m = " << setw(10) + << mASave << ".\n" + << " Beam B: id = " << setw(6) << idBSave << ", pz = " << setw(10) + << pzBSave << ", e = " << setw(10) << eBSave << ", m = " << setw(10) + << mBSave << ".\n\n"; + + // Done if no subprocess has been defined. + if (codeSave == 0 && nFinalSave == 0) { + os << " No process has been set; something must have gone wrong! \n" + << "\n -------- End PYTHIA Info Listing --------------------" + << "----------------" << endl; + return; + } + + // Colliding parton info. + if (isRes) + os << " In 1: id = " << setw(4) << id1Save << ", x = " << setw(10) + << x1Save << ", pdf = " << setw(10) << pdf1Save << " at Q2 = " + << setw(10) << Q2FacSave << ".\n" + << " In 2: id = " << setw(4) << id2Save << ", x = " << setw(10) + << x2Save << ", pdf = " << setw(10) << pdf2Save << " at same Q2.\n\n"; + + // Process name and code. + os << ((isRes && !hasSubSave) ? " Subprocess " : " Process ") << nameSave + << " with code " << codeSave << " is 2 -> " << nFinalSave << ".\n"; + + // Subprocess name and code for minimum bias processes. + if (hasSubSave) + os << " Subprocess " << nameSubSave << " with code " << codeSubSave + << " is 2 -> " << nFinalSubSave << ".\n"; + + // Process-type-specific kinematics information. + if (isRes && nFinalSave == 1) + os << " It has sHat = " << setw(10) << sH << ".\n"; + else if ( isRes && nFinalSave == 2) + os << " It has sHat = " << setw(10) << sH << ", tHat = " + << setw(10) << tH << ", uHat = " << setw(10) << uH << ",\n" + << " pTHat = " << setw(10) << pTH << ", m3Hat = " + << setw(10) << m3H << ", m4Hat = " << setw(10) << m4H << ",\n" + << " thetaHat = " << setw(10) << thetaH << ", phiHat = " + << setw(10) << phiH << ".\n"; + else if ( nFinalSave == 2) + os << " It has s = " << setw(10) << sH << ", t = " << setw(10) + << tH << ", u = " << setw(10) << uH << ",\n" + << " pT = " << setw(10) << pTH << ", m3 = " << setw(10) + << m3H << ", m4 = " << setw(10) << m4H << ",\n" + << " theta = " << setw(10) << thetaH << ", phi = " << setw(10) + << phiH << ".\n"; + else if ( isRes && nFinalSave == 3) + os << " It has sHat = " << setw(10) << sH << ", = " + << setw(10) << pTH << ".\n"; + + // Couplings. + if (isRes) os << " alphaEM = " << setw(10) << alphaEMSave + << ", alphaS = " << setw(10) << alphaSSave << " at Q2 = " + << setw(10) << Q2RenSave << ".\n"; + + // Impact parameter. + if (bIsSet) os << "\n Impact parameter b =" << setw(10) << bMISave + << " gives enhancement factor = " << setw(10) << enhanceMISave + << ".\n"; + + // Multiple interactions and shower evolution. + if (evolIsSet) os << " Max pT scale for MI = " << setw(10) << pTmaxMISave + << ", ISR = " << setw(10) << pTmaxISRSave << ", FSR = " << setw(10) + << pTmaxISRSave << ".\n Number of MI = " << setw(5) << nMISave + << ", ISR = " << setw(5) << nISRSave << ", FSRproc = " << setw(5) + << nFSRinProcSave << ", FSRreson = " << setw(5) << nFSRinResSave + << ".\n"; + + // Listing finished. + os << "\n -------- End PYTHIA Info Listing --------------------" + << "----------------" << endl; + +} + +//-------------------------------------------------------------------------- + +// Print a message the first few times. Insert in database. + + void Info::errorMsg(string messageIn, string extraIn, bool showAlways, + ostream& os) { + + // Recover number of times message occured. Also inserts new string. + int times = messages[messageIn]; + ++messages[messageIn]; + + // Print message the first few times. + if (times < TIMESTOPRINT || showAlways) os << " PYTHIA " + << messageIn << " " << extraIn << endl; + +} + +//-------------------------------------------------------------------------- + +// Provide total number of errors/aborts/warnings experienced to date. + +int Info::errorTotalNumber() { + + int nTot = 0; + for ( map::iterator messageEntry = messages.begin(); + messageEntry != messages.end(); ++messageEntry) + nTot += messageEntry->second; + return nTot; + +} + +//-------------------------------------------------------------------------- + +// Print statistics on errors/aborts/warnings. + +void Info::errorStatistics(ostream& os) { + + // Header. + os << "\n *------- PYTHIA Error and Warning Messages Statistics " + << "----------------------------------------------------------* \n" + << " | " + << " | \n" + << " | times message " + << " | \n" + << " | " + << " | \n"; + + // Loop over all messages + map::iterator messageEntry = messages.begin(); + if (messageEntry == messages.end()) + os << " | 0 no errors or warnings to report " + << " | \n"; + while (messageEntry != messages.end()) { + // Message printout. + string temp = messageEntry->first; + int len = temp.length(); + temp.insert( len, max(0, 102 - len), ' '); + os << " | " << setw(6) << messageEntry->second << " " + << temp << " | \n"; + ++messageEntry; + } + + // Done. + os << " | " + << " | \n" + << " *------- End PYTHIA Error and Warning Messages Statistics" + << " ------------------------------------------------------* " + << endl; + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/LesHouches.cxx b/PYTHIA8/pythia8140/src/LesHouches.cxx new file mode 100644 index 00000000000..15c64e39fab --- /dev/null +++ b/PYTHIA8/pythia8140/src/LesHouches.cxx @@ -0,0 +1,529 @@ +// LesHouches.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the LHAup and +// LHAupLHEF classes. + +#include "LesHouches.h" + +// Access time information. +#include + +namespace Pythia8 { + +//========================================================================== + +// LHAup class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// LHA convention with cross section in pb may require conversion from mb. +const double LHAup::CONVERTMB2PB = 1e9; + +//-------------------------------------------------------------------------- + +// Print the initialization info; to check it worked. + +void LHAup::listInit(ostream& os) { + + // Header. + os << "\n -------- LHA initialization information ------------ \n"; + + // Beam info. + os << fixed << setprecision(3) + << "\n beam kind energy pdfgrp pdfset \n" + << " A " << setw(6) << idBeamASave + << setw(12) << eBeamASave + << setw(8) << pdfGroupBeamASave + << setw(8) << pdfSetBeamASave << "\n" + << " B " << setw(6) << idBeamBSave + << setw(12) << eBeamBSave + << setw(8) << pdfGroupBeamBSave + << setw(8) << pdfSetBeamBSave << "\n"; + + // Event weighting strategy. + os << "\n Event weighting strategy = " << setw(2) + << strategySave << "\n" ; + + // Process list. + os << scientific << setprecision(4) + << "\n Processes, with strategy-dependent cross section info \n" + << " number xsec (pb) xerr (pb) xmax (pb) \n" ; + for (int ip = 0; ip < int(processes.size()); ++ip) { + os << setw(8) << processes[ip].idProc + << setw(15) << processes[ip].xSecProc + << setw(15) << processes[ip].xErrProc + << setw(15) << processes[ip].xMaxProc << "\n"; + } + + // Finished. + os << "\n -------- End LHA initialization information -------- \n"; + +} + +//-------------------------------------------------------------------------- + +// Print the event info; to check it worked. + +void LHAup::listEvent(ostream& os) { + + // Header. + os << "\n -------- LHA event information and listing -------------" + << "--------------------------------------------------------- \n"; + + // Basic event info. + os << scientific << setprecision(4) + << "\n process = " << setw(8) << idProc + << " weight = " << setw(12) << weightProc + << " scale = " << setw(12) << scaleProc << " (GeV) \n" + << " " + << " alpha_em = " << setw(12) << alphaQEDProc + << " alpha_strong = " << setw(12) << alphaQCDProc << "\n"; + + // Particle list + os << fixed << setprecision(3) + << "\n Participating Particles \n" + << " no id stat mothers colours p_x " + << "p_y p_z e m tau spin \n" ; + for (int ip = 1; ip < int(particles.size()); ++ip) { + os << setw(6) << ip + << setw(10) << particles[ip].idPart + << setw(5) << particles[ip].statusPart + << setw(6) << particles[ip].mother1Part + << setw(6) << particles[ip].mother2Part + << setw(6) << particles[ip].col1Part + << setw(6) << particles[ip].col2Part + << setw(11) << particles[ip].pxPart + << setw(11) << particles[ip].pyPart + << setw(11) << particles[ip].pzPart + << setw(11) << particles[ip].ePart + << setw(11) << particles[ip].mPart + << setw(8) << particles[ip].tauPart + << setw(8) << particles[ip].spinPart << "\n"; + } + + // PDF info - optional. + if (pdfIsSetSave) os << "\n pdf: id1 =" << setw(5) << id1Save + << " id2 =" << setw(5) << id2Save + << " x1 =" << scientific << setw(10) << x1Save + << " x2 =" << setw(10) << x2Save + << " scalePDF =" << setw(10) << scalePDFSave + << " xpdf1 =" << setw(10) << xpdf1Save + << " xpdf2 =" << setw(10) << xpdf2Save << "\n"; + + // Finished. + os << "\n -------- End LHA event information and listing ---------" + << "--------------------------------------------------------- \n"; + +} + +//-------------------------------------------------------------------------- + +// Open and write header to a Les Houches Event File. + +bool LHAup::openLHEF(string fileNameIn) { + + // Open file for writing. Reset it to be empty. + fileName = fileNameIn; + const char* cstring = fileName.c_str(); + osLHEF.open(cstring, ios::out | ios::trunc); + if (!osLHEF) { + infoPtr->errorMsg("Error in LHAup::openLHEF:" + " could not open file", fileName); + return false; + } + + // Read out current date and time. + time_t t = time(0); + strftime(dateNow,12,"%d %b %Y",localtime(&t)); + strftime(timeNow,9,"%H:%M:%S",localtime(&t)); + + // Write header. + osLHEF << "\n" + << "" << endl; + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Write initialization information to a Les Houches Event File. + +bool LHAup::initLHEF() { + + // Write information on beams. + osLHEF << "\n" << scientific << setprecision(6) + << " " << idBeamASave << " " << idBeamBSave + << " " << eBeamASave << " " << eBeamBSave + << " " << pdfGroupBeamASave << " " << pdfGroupBeamBSave + << " " << pdfSetBeamASave << " " << pdfSetBeamBSave + << " " << strategySave << " " << processes.size() << "\n"; + + // Write information on all the subprocesses. + for (int ip = 0; ip < int(processes.size()); ++ip) + osLHEF << " " << setw(13) << processes[ip].xSecProc + << " " << setw(13) << processes[ip].xErrProc + << " " << setw(13) << processes[ip].xMaxProc + << " " << setw(6) << processes[ip].idProc << "\n"; + + // Done. + osLHEF << "" << endl; + return true; + +} + +//-------------------------------------------------------------------------- + +// Write event information to a Les Houches Event File. + +bool LHAup::eventLHEF() { + + // Write information on process as such. + osLHEF << "\n" << scientific << setprecision(6) + << " " << setw(5) << particles.size() - 1 + << " " << setw(5) << idProc + << " " << setw(13) << weightProc + << " " << setw(13) << scaleProc + << " " << setw(13) << alphaQEDProc + << " " << setw(13) << alphaQCDProc << "\n"; + + // Write information on the particles, excluding zeroth. + for (int ip = 1; ip < int(particles.size()); ++ip) { + osLHEF << " " << setw(8) << particles[ip].idPart + << " " << setw(5) << particles[ip].statusPart + << " " << setw(5) << particles[ip].mother1Part + << " " << setw(5) << particles[ip].mother2Part + << " " << setw(5) << particles[ip].col1Part + << " " << setw(5) << particles[ip].col2Part << setprecision(10) + << " " << setw(17) << particles[ip].pxPart + << " " << setw(17) << particles[ip].pyPart + << " " << setw(17) << particles[ip].pzPart + << " " << setw(17) << particles[ip].ePart + << " " << setw(17) << particles[ip].mPart << setprecision(6); + if (particles[ip].tauPart == 0.) osLHEF << " 0."; + else osLHEF << " " << setw(13) << particles[ip].tauPart; + if (particles[ip].spinPart == 9.) osLHEF << " 9."; + else osLHEF << " " << setw(13) << particles[ip].spinPart; + osLHEF << "\n"; + } + + // Optionally write information on PDF values at hard interaction. + if (pdfIsSetSave) osLHEF << "#pdf" + << " " << setw(4) << id1Save + << " " << setw(4) << id2Save + << " " << setw(13) << x1Save + << " " << setw(13) << x2Save + << " " << setw(13) << scalePDFSave + << " " << setw(13) << xpdf1Save + << " " << setw(13) << xpdf2Save << "\n"; + + // Done. + osLHEF << "" << endl; + return true; + +} + +//-------------------------------------------------------------------------- + +// Write end of a Les Houches Event File and close it. + +bool LHAup::closeLHEF(bool updateInit) { + + // Write an end to the file. + osLHEF << "" << endl; + osLHEF.close(); + + // Optionally update the cross section information. + if (updateInit) { + const char* cstring = fileName.c_str(); + osLHEF.open(cstring, ios::in | ios::out); + + // Rewrite header; identically with what openLHEF did. + osLHEF << "\n" + << "" << endl; + + // Redo initialization information. + initLHEF(); + osLHEF.close(); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Read in initialization information from a Les Houches Event File. + +bool LHAup::setInitLHEF(ifstream& is) { + + // Check that first line is consistent with proper LHEF file. + string line; + if (!getline(is, line)) return false; + if (line.find("> tag; + if (!getfirst) return false; + } + } while (tag != "" && tag != "> idbmupA >> idbmupB >> ebmupA >> ebmupB >> pdfgupA + >> pdfgupB >> pdfsupA >> pdfsupB >> idwtup >> nprup; + if (!getbms) return false; + setBeamA(idbmupA, ebmupA, pdfgupA, pdfsupA); + setBeamB(idbmupB, ebmupB, pdfgupB, pdfsupB); + setStrategy(idwtup); + + // Read in process info, one process at a time, and store it. + double xsecup, xerrup, xmaxup; + int lprup; + for (int ip = 0; ip < nprup; ++ip) { + if (!getline(is, line)) return false; + istringstream getpro(line); + getpro >> xsecup >> xerrup >> xmaxup >> lprup ; + if (!getpro) return false; + addProcess(lprup, xsecup, xerrup, xmaxup); + } + + // Reading worked. + return true; + +} + +//-------------------------------------------------------------------------- + +// Read in event information from a Les Houches Event File, +// into a staging area where it can be reused by setOldEventLHEF. + +bool LHAup::setNewEventLHEF(ifstream& is) { + + // Loop over lines until an > tag; + if (!getfirst) return false; + } + } while (tag != "" && tag != "> nupSave >> idprupSave >> xwgtupSave >> scalupSave + >> aqedupSave >> aqcdupSave; + if (!getpro) return false; + + // Reset particlesSave vector, add slot-0 empty particle. + particlesSave.clear(); + particlesSave.push_back( LHAParticle() ); + + // Read in particle info one by one, and store it. + // Note unusual C++ loop range, to better reflect LHA/Fortran standard. + // (Recall that process(...) above added empty particle at index 0.) + int idup, istup, mothup1, mothup2, icolup1, icolup2; + double pup1, pup2, pup3, pup4, pup5, vtimup, spinup; + for (int ip = 1; ip <= nupSave; ++ip) { + if (!getline(is, line)) return false; + istringstream getall(line); + getall >> idup >> istup >> mothup1 >> mothup2 >> icolup1 >> icolup2 + >> pup1 >> pup2 >> pup3 >> pup4 >> pup5 >> vtimup >> spinup; + if (!getall) return false; + particlesSave.push_back( LHAParticle( idup, istup, mothup1, mothup2, + icolup1, icolup2, pup1, pup2, pup3, pup4, pup5, vtimup, spinup) ); + } + + // Continue parsing till . Extract pdf info if present. + getPDFSave = false; + do { + if (!getline(is, line)) return false; + istringstream getpdf(line); + getpdf >> tag; + if (!getpdf) return false; + if (tag == "#pdf") { + getpdf >> id1InSave >> id2InSave >> x1InSave >> x2InSave + >> scalePDFInSave >> xpdf1InSave >> xpdf2InSave; + if (!getpdf) return false; + getPDFSave = true; + } + } while (tag != "" && tag != "idA(); + int idbmupB = infoPtr->idB(); + double ebmupA = infoPtr->eA(); + double ebmupB = infoPtr->eB(); + int pdfgupA = 0; + int pdfgupB = 0; + int pdfsupA = 0; + int pdfsupB = 0; + setBeamA(idbmupA, ebmupA, pdfgupA, pdfsupA); + setBeamB(idbmupB, ebmupB, pdfgupB, pdfsupB); + + // Currently only one allowed strategy. + int idwtup = 3; + setStrategy(idwtup); + + // Only one process with dummy information. (Can overwrite at the end.) + int lprup = 9999; + double xsecup = 1.; + double xerrup = 0.; + double xmaxup = 1.; + addProcess(lprup, xsecup, xerrup, xmaxup); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Read in event information from PYTHIA 8. + +bool LHAupFromPYTHIA8::setEvent( int ) { + + // Read process information from Info class, and store it. + // Note: renormalization scale here, factorization further down. + int idprup = infoPtr->code(); + // For now always convert to process 9999. + idprup = 9999; + double xwgtup = infoPtr->weight(); + double scalup = infoPtr->QRen(); + double aqedup = infoPtr->alphaEM(); + double aqcdup = infoPtr->alphaS(); + setProcess(idprup, xwgtup, scalup, aqedup, aqcdup); + + // Read in particle info one by one, excluding zero and beams, and store it. + // Note unusual C++ loop range, to better reflect LHA/Fortran standard. + int nup = processPtr->size() - 3; + int idup, statusup, istup, mothup1, mothup2, icolup1, icolup2; + double pup1, pup2, pup3, pup4, pup5, vtimup, spinup; + for (int ip = 1; ip <= nup; ++ip) { + Particle& particle = (*processPtr)[ip + 2]; + idup = particle.id(); + // Convert from PYTHIA8 to LHA status codes. + statusup = particle.status(); + if (ip < 3) istup = -1; + else if (statusup < 0) istup = 2; + else istup = 1; + mothup1 = max(0, particle.mother1() - 2); + mothup2 = max(0, particle.mother2() - 2); + icolup1 = particle.col(); + icolup2 = particle.acol(); + pup1 = particle.px(); + pup2 = particle.py(); + pup3 = particle.pz(); + pup4 = particle.e(); + pup5 = particle.m(); + vtimup = particle.tau(); + spinup = 9.; + addParticle(idup, istup, mothup1, mothup2, icolup1, icolup2, + pup1, pup2, pup3, pup4, pup5, vtimup, spinup) ; + } + + // Also extract pdf information from Info class, and store it. + int id1up = infoPtr->id1(); + int id2up = infoPtr->id2(); + double x1up = infoPtr->x1(); + double x2up = infoPtr->x2(); + double scalePDFup = infoPtr->QFac(); + double xpdf1up = infoPtr->pdf1(); + double xpdf2up = infoPtr->pdf2(); + setPdf(id1up, id2up, x1up, x2up, scalePDFup, xpdf1up, xpdf2up, true); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Update cross-section information at the end of the run. + +bool LHAupFromPYTHIA8::updateSigma() { + + // Read out information from PYTHIA 8 and send it in to LHA. + double sigGen = CONVERTMB2PB * infoPtr->sigmaGen(); + double sigErr = CONVERTMB2PB * infoPtr->sigmaErr(); + setXSec(0, sigGen); + setXErr(0, sigErr); + + // Done. + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/MiniStringFragmentation.cxx b/PYTHIA8/pythia8140/src/MiniStringFragmentation.cxx new file mode 100644 index 00000000000..77880cb509b --- /dev/null +++ b/PYTHIA8/pythia8140/src/MiniStringFragmentation.cxx @@ -0,0 +1,320 @@ +// MiniStringFragmentation.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the . +// MiniStringFragmentation class + +#include "MiniStringFragmentation.h" + +namespace Pythia8 { + +//========================================================================== + +// The MiniStringFragmentation class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Since diffractive by definition is > 1 particle, try hard. +const int MiniStringFragmentation::NTRYDIFFRACTIVE = 200; + +// After one-body fragmentation failed, try two-body once more. +const int MiniStringFragmentation::NTRYLASTRESORT = 100; + +// To avoid division by zero one must have sigma > 0. +const double MiniStringFragmentation::SIGMAMIN = 0.01; + +// Loop try to combine available endquarks to valid hadron. +const int MiniStringFragmentation::NTRYFLAV = 10; + +//-------------------------------------------------------------------------- + +// Initialize and save pointers. + +void MiniStringFragmentation::init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + StringFlav* flavSelPtrIn) { + + // Save pointers. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + flavSelPtr = flavSelPtrIn; + + // Initialize the MiniStringFragmentation class proper. + nTryMass = settings.mode("MiniStringFragmentation:nTry"); + sigma = settings.parm("StringPT:sigma"); + sigma2Had = 2. * pow2( max( SIGMAMIN, sigma) ); + + // Initialize the b parameter of the z spectrum, used when joining jets. + bLund = settings.parm("StringZ:bLund"); + +} + +//-------------------------------------------------------------------------- + +// Do the fragmentation: driver routine. + +bool MiniStringFragmentation::fragment(int iSub, ColConfig& colConfig, + Event& event, bool isDiff) { + + // Read in info on system to be treated. + iParton = colConfig[iSub].iParton; + flav1 = FlavContainer( event[ iParton.front() ].id() ); + flav2 = FlavContainer( event[ iParton.back() ].id() ); + pSum = colConfig[iSub].pSum; + mSum = colConfig[iSub].mass; + m2Sum = mSum*mSum; + isClosed = colConfig[iSub].isClosed; + + // Do not want diffractive systems to easily collapse to one particle. + int nTryFirst = (isDiff) ? NTRYDIFFRACTIVE : nTryMass; + + // First try to produce two particles from the system. + if (ministring2two( nTryFirst, event)) return true; + + // If this fails, then form one hadron and shuffle momentum. + if (ministring2one( iSub, colConfig, event)) return true; + + // If also this fails, then try harder to produce two particles. + if (ministring2two( NTRYLASTRESORT, event)) return true; + + // Else complete failure. + infoPtr->errorMsg("Error in MiniStringFragmentation::fragment: " + "no 1- or 2-body state found above mass threshold"); + return false; + +} + +//-------------------------------------------------------------------------- + + // Attempt to produce two particles from the ministring. + +bool MiniStringFragmentation::ministring2two( int nTry, Event& event) { + + // Properties of the produced hadrons. + int idHad1 = 0; + int idHad2 = 0; + double mHad1 = 0.; + double mHad2 = 0.; + double mHadSum = 0.; + + // Allow a few attempts to find a particle pair with low enough masses. + for (int iTry = 0; iTry < nTry; ++iTry) { + + // For closed gluon loop need to pick an initial flavour. + if (isClosed) do { + int idStart = flavSelPtr->pickLightQ(); + FlavContainer flavStart(idStart, 1); + flavStart = flavSelPtr->pick( flavStart); + flav1 = flavSelPtr->pick( flavStart); + flav2.anti(flav1); + } while (flav1.id == 0 || flav1.nPop > 0); + + // Create a new q qbar flavour to form two hadrons. + // Start from a diquark, if any. + do { + FlavContainer flav3 = + (abs(flav1.id) > 8 || (abs(flav2.id) < 9 && rndmPtr->flat() < 0.5) ) + ? flavSelPtr->pick( flav1) : flavSelPtr->pick( flav2).anti(); + idHad1 = flavSelPtr->combine( flav1, flav3); + idHad2 = flavSelPtr->combine( flav2, flav3.anti()); + } while (idHad1 == 0 || idHad2 == 0); + + // Check whether the mass sum fits inside the available phase space. + mHad1 = particleDataPtr->mass(idHad1); + mHad2 = particleDataPtr->mass(idHad2); + mHadSum = mHad1 + mHad2; + if (mHadSum < mSum) break; + } + if (mHadSum >= mSum) return false; + + // Define an effective two-parton string, by splitting intermediate + // gluon momenta in proportion to their closeness to either endpoint. + Vec4 pSum1 = event[ iParton.front() ].p(); + Vec4 pSum2 = event[ iParton.back() ].p(); + if (iParton.size() > 2) { + Vec4 pEnd1 = pSum1; + Vec4 pEnd2 = pSum2; + Vec4 pEndSum = pEnd1 + pEnd2; + for (int i = 1; i < int(iParton.size()) - 1 ; ++i) { + Vec4 pNow = event[ iParton[i] ].p(); + double ratio = (pEnd2 * pNow) / (pEndSum * pNow); + pSum1 += ratio * pNow; + pSum2 += (1. - ratio) * pNow; + } + } + + // Set up a string region based on the two effective endpoints. + StringRegion region; + region.setUp( pSum1, pSum2); + + // Generate an isotropic decay in the ministring rest frame, + // suppressed at large pT by a fragmentation pT Gaussian. + double pAbs2 = 0.25 * ( pow2(m2Sum - mHad1*mHad1 - mHad2*mHad2) + - pow2(2. * mHad1 * mHad2) ) / m2Sum; + double pT2 = 0.; + do { + double cosTheta = rndmPtr->flat(); + if (sigma < SIGMAMIN) cosTheta = 1.; + pT2 = (1. - pow2(cosTheta)) * pAbs2; + } while ( exp( -pT2 / sigma2Had) < rndmPtr->flat() ); + + // Construct the forward-backward asymmetry of the two particles. + double mT21 = mHad1*mHad1 + pT2; + double mT22 = mHad2*mHad2 + pT2; + double lambda = sqrtpos( pow2(m2Sum - mT21 - mT22) - 4. * mT21 * mT22 ); + double probReverse = 1. / (1. + exp( min( 50., bLund * lambda) ) ); + + // Construct kinematics, as viewed in the transverse rest frame. + double xpz1 = 0.5 * lambda/ m2Sum; + if (probReverse > rndmPtr->flat()) xpz1 = -xpz1; + double xmDiff = (mT21 - mT22) / m2Sum; + double xe1 = 0.5 * (1. + xmDiff); + double xe2 = 0.5 * (1. - xmDiff ); + + // Distribute pT isotropically in angle. + double phi = 2. * M_PI * rndmPtr->flat(); + double pT = sqrt(pT2); + double px = pT * cos(phi); + double py = pT * sin(phi); + + // Translate this into kinematics in the string frame. + Vec4 pHad1 = region.pHad( xe1 + xpz1, xe1 - xpz1, px, py); + Vec4 pHad2 = region.pHad( xe2 - xpz1, xe2 + xpz1, -px, -py); + + // Add produced particles to the event record. + int iFirst = event.append( idHad1, 82, iParton.front(), iParton.back(), + 0, 0, 0, 0, pHad1, mHad1); + int iLast = event.append( idHad2, 82, iParton.front(), iParton.back(), + 0, 0, 0, 0, pHad2, mHad2); + + // Set decay vertex when this is displaced. + if (event[iParton.front()].hasVertex()) { + Vec4 vDec = event[iParton.front()].vDec(); + event[iFirst].vProd( vDec ); + event[iLast].vProd( vDec ); + } + + // Set lifetime of hadrons. + event[iFirst].tau( event[iFirst].tau0() * rndmPtr->exp() ); + event[iLast].tau( event[iLast].tau0() * rndmPtr->exp() ); + + // Mark original partons as hadronized and set their daughter range. + for (int i = 0; i < int(iParton.size()); ++i) { + event[ iParton[i] ].statusNeg(); + event[ iParton[i] ].daughters(iFirst, iLast); + } + + // Successfully done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Attempt to produce one particle from a ministring. +// Current algorithm: find the system with largest invariant mass +// relative to the existing one, and boost that system appropriately. +// Try more sophisticated alternatives later?? (Z0 mass shifted??) +// Also, if problems, attempt several times to obtain closer mass match?? + +bool MiniStringFragmentation::ministring2one( int iSub, + ColConfig& colConfig, Event& event) { + + // Cannot handle qq + qbarqbar system. + if (abs(flav1.id) > 100 && abs(flav2.id) > 100) return false; + + // For closed gluon loop need to pick an initial flavour. + if (isClosed) do { + int idStart = flavSelPtr->pickLightQ(); + FlavContainer flavStart(idStart, 1); + flav1 = flavSelPtr->pick( flavStart); + flav2 = flav1.anti(); + } while (abs(flav1.id) > 100); + + // Select hadron flavour from available quark flavours. + int idHad = 0; + for (int iTryFlav = 0; iTryFlav < NTRYFLAV; ++iTryFlav) { + idHad = flavSelPtr->combine( flav1, flav2); + if (idHad != 0) break; + } + if (idHad == 0) return false; + + // Find mass. + double mHad = particleDataPtr->mass(idHad); + + // Find the untreated parton system which combines to the largest + // squared mass above mimimum required. + int iMax = -1; + double deltaM2 = mHad*mHad - mSum*mSum; + double delta2Max = 0.; + for (int iRec = iSub + 1; iRec < colConfig.size(); ++iRec) { + double delta2Rec = 2. * (pSum * colConfig[iRec].pSum) - deltaM2 + - 2. * mHad * colConfig[iRec].mass; + if (delta2Rec > delta2Max) { iMax = iRec; delta2Max = delta2Rec;} + } + if (iMax == -1) return false; + + // Construct kinematics of the hadron and recoiling system. + Vec4& pRec = colConfig[iMax].pSum; + double mRec = colConfig[iMax].mass; + double vecProd = pSum * pRec; + double coefOld = mSum*mSum + vecProd; + double coefNew = mHad*mHad + vecProd; + double coefRec = mRec*mRec + vecProd; + double coefSum = coefOld + coefNew; + double sHat = coefOld + coefRec; + double root = sqrtpos( (pow2(coefSum) - 4. * sHat * mHad*mHad) + / (pow2(vecProd) - pow2(mSum * mRec)) ); + double k2 = 0.5 * (coefOld * root - coefSum) / sHat; + double k1 = (coefRec * k2 + 0.5 * deltaM2) / coefOld; + Vec4 pHad = (1. + k1) * pSum - k2 * pRec; + Vec4 pRecNew = (1. + k2) * pRec - k1 * pSum; + + // Add the produced particle to the event record. + int iHad = event.append( idHad, 81, iParton.front(), iParton.back(), + 0, 0, 0, 0, pHad, mHad); + + // Set decay vertex when this is displaced. + if (event[iParton.front()].hasVertex()) { + Vec4 vDec = event[iParton.front()].vDec(); + event[iHad].vProd( vDec ); + } + + // Set lifetime of hadron. + event[iHad].tau( event[iHad].tau0() * rndmPtr->exp() ); + + // Mark original partons as hadronized and set their daughter range. + for (int i = 0; i < int(iParton.size()); ++i) { + event[ iParton[i] ].statusNeg(); + event[ iParton[i] ].daughters(iHad, iHad); + } + + // Copy down recoiling system, with boosted momentum. Update current partons. + RotBstMatrix M; + M.bst(pRec, pRecNew); + for (int i = 0; i < colConfig[iMax].size(); ++i) { + int iOld = colConfig[iMax].iParton[i]; + // Do not touch negative iOld = beginning of new junction leg. + if (iOld >= 0) { + int iNew = event.copy(iOld, 72); + event[iNew].rotbst(M); + colConfig[iMax].iParton[i] = iNew; + } + } + colConfig[iMax].pSum = pRecNew; + colConfig[iMax].isCollected = true; + + // Successfully done. + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/MultipleInteractions.cxx b/PYTHIA8/pythia8140/src/MultipleInteractions.cxx new file mode 100644 index 00000000000..f9a52d59d52 --- /dev/null +++ b/PYTHIA8/pythia8140/src/MultipleInteractions.cxx @@ -0,0 +1,2095 @@ +// MultipleInteractions.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// SigmaMultiple and MultipleInteractions classes. + +#include "MultipleInteractions.h" + +// Internal headers for special processes. +#include "SigmaQCD.h" +#include "SigmaEW.h" +#include "SigmaOnia.h" + +namespace Pythia8 { + +//========================================================================== + +// The SigmaMultiple class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// The sum of outgoing masses must not be too close to the cm energy. +const double SigmaMultiple::MASSMARGIN = 0.1; + +// Fraction of time not the dominant "gluon t-channel" process is picked. +const double SigmaMultiple::OTHERFRAC = 0.2; + +//-------------------------------------------------------------------------- + +// Initialize the generation process for given beams. + + bool SigmaMultiple::init(int inState, int processLevel, Info* infoPtr, + Settings* settingsPtr, ParticleData* particleDataPtr, Rndm* rndmPtrIn, + BeamParticle* beamAPtr, BeamParticle* beamBPtr, CoupSM* coupSMPtr) { + + // Store input pointer for future use. + rndmPtr = rndmPtrIn; + + // Reset vector sizes (necessary in case of re-initialization). + if (sigmaT.size() > 0) { + for (int i = 0; i < int(sigmaT.size()); ++i) delete sigmaT[i]; + sigmaT.resize(0); + } + if (sigmaU.size() > 0) { + for (int i = 0; i < int(sigmaU.size()); ++i) delete sigmaU[i]; + sigmaU.resize(0); + } + + // Always store mimimal set of processes:QCD 2 -> 2 t-channel. + + // Gluon-gluon instate. + if (inState == 0) { + sigmaT.push_back( new Sigma2gg2gg() ); + sigmaU.push_back( new Sigma2gg2gg() ); + + // Quark-gluon instate. + } else if (inState == 1) { + sigmaT.push_back( new Sigma2qg2qg() ); + sigmaU.push_back( new Sigma2qg2qg() ); + + // Quark-(anti)quark instate. + } else { + sigmaT.push_back( new Sigma2qq2qq() ); + sigmaU.push_back( new Sigma2qq2qq() ); + } + + // Normally store QCD processes to new flavour. + if (processLevel > 0) { + if (inState == 0) { + sigmaT.push_back( new Sigma2gg2qqbar() ); + sigmaU.push_back( new Sigma2gg2qqbar() ); + sigmaT.push_back( new Sigma2gg2QQbar(4, 121) ); + sigmaU.push_back( new Sigma2gg2QQbar(4, 121) ); + sigmaT.push_back( new Sigma2gg2QQbar(5, 123) ); + sigmaU.push_back( new Sigma2gg2QQbar(5, 123) ); + } else if (inState == 2) { + sigmaT.push_back( new Sigma2qqbar2gg() ); + sigmaU.push_back( new Sigma2qqbar2gg() ); + sigmaT.push_back( new Sigma2qqbar2qqbarNew() ); + sigmaU.push_back( new Sigma2qqbar2qqbarNew() ); + sigmaT.push_back( new Sigma2qqbar2QQbar(4, 122) ); + sigmaU.push_back( new Sigma2qqbar2QQbar(4, 122) ); + sigmaT.push_back( new Sigma2qqbar2QQbar(5, 124) ); + sigmaU.push_back( new Sigma2qqbar2QQbar(5, 124) ); + } + } + + // Optionally store electroweak processes, mainly photon production. + if (processLevel > 1) { + if (inState == 0) { + sigmaT.push_back( new Sigma2gg2ggamma() ); + sigmaU.push_back( new Sigma2gg2ggamma() ); + sigmaT.push_back( new Sigma2gg2gammagamma() ); + sigmaU.push_back( new Sigma2gg2gammagamma() ); + } else if (inState == 1) { + sigmaT.push_back( new Sigma2qg2qgamma() ); + sigmaU.push_back( new Sigma2qg2qgamma() ); + } else if (inState == 2) { + sigmaT.push_back( new Sigma2qqbar2ggamma() ); + sigmaU.push_back( new Sigma2qqbar2ggamma() ); + sigmaT.push_back( new Sigma2ffbar2gammagamma() ); + sigmaU.push_back( new Sigma2ffbar2gammagamma() ); + sigmaT.push_back( new Sigma2ffbar2ffbarsgm() ); + sigmaU.push_back( new Sigma2ffbar2ffbarsgm() ); + } + if (inState >= 2) { + sigmaT.push_back( new Sigma2ff2fftgmZ() ); + sigmaU.push_back( new Sigma2ff2fftgmZ() ); + sigmaT.push_back( new Sigma2ff2fftW() ); + sigmaU.push_back( new Sigma2ff2fftW() ); + } + } + + // Optionally store charmonium and bottomonium production. + if (processLevel > 2) { + if (inState == 0) { + sigmaT.push_back( new Sigma2gg2QQbar3S11g(4, 401) ); + sigmaU.push_back( new Sigma2gg2QQbar3S11g(4, 401) ); + sigmaT.push_back( new Sigma2gg2QQbar3PJ1g(4, 0, 402) ); + sigmaU.push_back( new Sigma2gg2QQbar3PJ1g(4, 0, 402) ); + sigmaT.push_back( new Sigma2gg2QQbar3PJ1g(4, 1, 403) ); + sigmaU.push_back( new Sigma2gg2QQbar3PJ1g(4, 1, 403) ); + sigmaT.push_back( new Sigma2gg2QQbar3PJ1g(4, 2, 404) ); + sigmaU.push_back( new Sigma2gg2QQbar3PJ1g(4, 2, 404) ); + sigmaT.push_back( new Sigma2gg2QQbarX8g(4, 0, 411) ); + sigmaU.push_back( new Sigma2gg2QQbarX8g(4, 0, 411) ); + sigmaT.push_back( new Sigma2gg2QQbarX8g(4, 1, 412) ); + sigmaU.push_back( new Sigma2gg2QQbarX8g(4, 1, 412) ); + sigmaT.push_back( new Sigma2gg2QQbarX8g(4, 2, 413) ); + sigmaU.push_back( new Sigma2gg2QQbarX8g(4, 2, 413) ); + sigmaT.push_back( new Sigma2gg2QQbar3S11g(5, 501) ); + sigmaU.push_back( new Sigma2gg2QQbar3S11g(5, 501) ); + sigmaT.push_back( new Sigma2gg2QQbar3PJ1g(5, 0, 502) ); + sigmaU.push_back( new Sigma2gg2QQbar3PJ1g(5, 0, 502) ); + sigmaT.push_back( new Sigma2gg2QQbar3PJ1g(5, 1, 503) ); + sigmaU.push_back( new Sigma2gg2QQbar3PJ1g(5, 1, 503) ); + sigmaT.push_back( new Sigma2gg2QQbar3PJ1g(5, 2, 504) ); + sigmaU.push_back( new Sigma2gg2QQbar3PJ1g(5, 2, 504) ); + sigmaT.push_back( new Sigma2gg2QQbarX8g(5, 0, 511) ); + sigmaU.push_back( new Sigma2gg2QQbarX8g(5, 0, 511) ); + sigmaT.push_back( new Sigma2gg2QQbarX8g(5, 1, 512) ); + sigmaU.push_back( new Sigma2gg2QQbarX8g(5, 1, 512) ); + sigmaT.push_back( new Sigma2gg2QQbarX8g(5, 2, 513) ); + sigmaU.push_back( new Sigma2gg2QQbarX8g(5, 2, 513) ); + } else if (inState == 1) { + sigmaT.push_back( new Sigma2qg2QQbar3PJ1q(4, 0, 405) ); + sigmaU.push_back( new Sigma2qg2QQbar3PJ1q(4, 0, 405) ); + sigmaT.push_back( new Sigma2qg2QQbar3PJ1q(4, 1, 406) ); + sigmaU.push_back( new Sigma2qg2QQbar3PJ1q(4, 1, 406) ); + sigmaT.push_back( new Sigma2qg2QQbar3PJ1q(4, 2, 407) ); + sigmaU.push_back( new Sigma2qg2QQbar3PJ1q(4, 2, 407) ); + sigmaT.push_back( new Sigma2qg2QQbarX8q(4, 0, 414) ); + sigmaU.push_back( new Sigma2qg2QQbarX8q(4, 0, 414) ); + sigmaT.push_back( new Sigma2qg2QQbarX8q(4, 1, 415) ); + sigmaU.push_back( new Sigma2qg2QQbarX8q(4, 1, 415) ); + sigmaT.push_back( new Sigma2qg2QQbarX8q(4, 2, 416) ); + sigmaU.push_back( new Sigma2qg2QQbarX8q(4, 2, 416) ); + sigmaT.push_back( new Sigma2qg2QQbar3PJ1q(5, 0, 505) ); + sigmaU.push_back( new Sigma2qg2QQbar3PJ1q(5, 0, 505) ); + sigmaT.push_back( new Sigma2qg2QQbar3PJ1q(5, 1, 506) ); + sigmaU.push_back( new Sigma2qg2QQbar3PJ1q(5, 1, 506) ); + sigmaT.push_back( new Sigma2qg2QQbar3PJ1q(5, 2, 507) ); + sigmaU.push_back( new Sigma2qg2QQbar3PJ1q(5, 2, 507) ); + sigmaT.push_back( new Sigma2qg2QQbarX8q(5, 0, 514) ); + sigmaU.push_back( new Sigma2qg2QQbarX8q(5, 0, 514) ); + sigmaT.push_back( new Sigma2qg2QQbarX8q(5, 1, 515) ); + sigmaU.push_back( new Sigma2qg2QQbarX8q(5, 1, 515) ); + sigmaT.push_back( new Sigma2qg2QQbarX8q(5, 2, 516) ); + sigmaU.push_back( new Sigma2qg2QQbarX8q(5, 2, 516) ); + } else if (inState == 2) { + sigmaT.push_back( new Sigma2qqbar2QQbar3PJ1g(4, 0, 408) ); + sigmaU.push_back( new Sigma2qqbar2QQbar3PJ1g(4, 0, 408) ); + sigmaT.push_back( new Sigma2qqbar2QQbar3PJ1g(4, 1, 409) ); + sigmaU.push_back( new Sigma2qqbar2QQbar3PJ1g(4, 1, 409) ); + sigmaT.push_back( new Sigma2qqbar2QQbar3PJ1g(4, 2, 410) ); + sigmaU.push_back( new Sigma2qqbar2QQbar3PJ1g(4, 2, 410) ); + sigmaT.push_back( new Sigma2qqbar2QQbarX8g(4, 0, 417) ); + sigmaU.push_back( new Sigma2qqbar2QQbarX8g(4, 0, 417) ); + sigmaT.push_back( new Sigma2qqbar2QQbarX8g(4, 1, 418) ); + sigmaU.push_back( new Sigma2qqbar2QQbarX8g(4, 1, 418) ); + sigmaT.push_back( new Sigma2qqbar2QQbarX8g(4, 2, 419) ); + sigmaU.push_back( new Sigma2qqbar2QQbarX8g(4, 2, 419) ); + sigmaT.push_back( new Sigma2qqbar2QQbar3PJ1g(5, 0, 508) ); + sigmaU.push_back( new Sigma2qqbar2QQbar3PJ1g(5, 0, 508) ); + sigmaT.push_back( new Sigma2qqbar2QQbar3PJ1g(5, 1, 509) ); + sigmaU.push_back( new Sigma2qqbar2QQbar3PJ1g(5, 1, 509) ); + sigmaT.push_back( new Sigma2qqbar2QQbar3PJ1g(5, 2, 510) ); + sigmaU.push_back( new Sigma2qqbar2QQbar3PJ1g(5, 2, 510) ); + sigmaT.push_back( new Sigma2qqbar2QQbarX8g(5, 0, 517) ); + sigmaU.push_back( new Sigma2qqbar2QQbarX8g(5, 0, 517) ); + sigmaT.push_back( new Sigma2qqbar2QQbarX8g(5, 1, 518) ); + sigmaU.push_back( new Sigma2qqbar2QQbarX8g(5, 1, 518) ); + sigmaT.push_back( new Sigma2qqbar2QQbarX8g(5, 2, 519) ); + sigmaU.push_back( new Sigma2qqbar2QQbarX8g(5, 2, 519) ); + } + } + + // Resize arrays to match sizes above. + nChan = sigmaT.size(); + needMasses.resize(nChan); + m3Fix.resize(nChan); + m4Fix.resize(nChan); + sHatMin.resize(nChan); + sigmaTval.resize(nChan); + sigmaUval.resize(nChan); + + // Initialize the processes. + for (int i = 0; i < nChan; ++i) { + sigmaT[i]->init( infoPtr, settingsPtr, particleDataPtr, rndmPtr, + beamAPtr, beamBPtr, coupSMPtr); + sigmaT[i]->initProc(); + sigmaU[i]->init( infoPtr, settingsPtr, particleDataPtr, rndmPtr, + beamAPtr, beamBPtr, coupSMPtr); + sigmaU[i]->initProc(); + + // Prepare for massive kinematics (but fixed masses!) where required. + needMasses[i] = false; + int id3Mass = sigmaT[i]->id3Mass(); + int id4Mass = sigmaT[i]->id4Mass(); + m3Fix[i] = 0.; + m4Fix[i] = 0.; + if (id3Mass > 0 || id4Mass > 0) { + needMasses[i] = true; + m3Fix[i] = particleDataPtr->m0(id3Mass); + m4Fix[i] = particleDataPtr->m0(id4Mass); + } + sHatMin[i] = pow2( m3Fix[i] + m4Fix[i] + MASSMARGIN); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Calculate cross section summed over possibilities. + +double SigmaMultiple::sigma( int id1, int id2, double x1, double x2, + double sHat, double tHat, double uHat, double alpS, double alpEM, + bool restore, bool pickOtherIn) { + + // Choose either the dominant process (in slot 0) or the rest of them. + if (restore) pickOther = pickOtherIn; + else pickOther = (rndmPtr->flat() < OTHERFRAC); + + // Iterate over all subprocesses. + sigmaTsum = 0.; + sigmaUsum = 0.; + for (int i = 0; i < nChan; ++i) { + sigmaTval[i] = 0.; + sigmaUval[i] = 0.; + + // Skip the not chosen processes. + if (i == 0 && pickOther) continue; + if (i > 0 && !pickOther) continue; + + // t-channel-sampling contribution. + if (sHat > sHatMin[i]) { + sigmaT[i]->set2KinMI( x1, x2, sHat, tHat, uHat, + alpS, alpEM, needMasses[i], m3Fix[i], m4Fix[i]); + sigmaTval[i] = sigmaT[i]->sigmaHatWrap(id1, id2); + sigmaT[i]->pickInState(id1, id2); + // Correction factor for tHat rescaling in massive kinematics. + if (needMasses[i]) sigmaTval[i] *= sigmaT[i]->sHBetaMI() / sHat; + sigmaTsum += sigmaTval[i]; + } + + // u-channel-sampling contribution. + if (sHat > sHatMin[i]) { + sigmaU[i]->set2KinMI( x1, x2, sHat, uHat, tHat, + alpS, alpEM, needMasses[i], m3Fix[i], m4Fix[i]); + sigmaUval[i] = sigmaU[i]->sigmaHatWrap( id1, id2); + sigmaU[i]->pickInState(id1, id2); + // Correction factor for tHat rescaling in massive kinematics. + if (needMasses[i]) sigmaUval[i] *= sigmaU[i]->sHBetaMI() / sHat; + sigmaUsum += sigmaUval[i]; + } + + // Average of t- and u-channel sampling; corrected for not selected channels. + } + double sigmaAvg = 0.5 * (sigmaTsum + sigmaUsum); + if (pickOther) sigmaAvg /= OTHERFRAC; + if (!pickOther) sigmaAvg /= (1. - OTHERFRAC); + return sigmaAvg; + +} + +//-------------------------------------------------------------------------- + +// Return one subprocess, picked according to relative cross sections. + +SigmaProcess* SigmaMultiple::sigmaSel() { + + // Decide between t- and u-channel-sampled kinematics. + pickedU = (rndmPtr->flat() * (sigmaTsum + sigmaUsum) < sigmaUsum); + + // Pick one of t-channel-sampled processes. + if (!pickedU) { + double sigmaRndm = sigmaTsum * rndmPtr->flat(); + int iPick = -1; + do sigmaRndm -= sigmaTval[++iPick]; + while (sigmaRndm > 0.); + return sigmaT[iPick]; + + // Pick one of u-channel-sampled processes. + } else { + double sigmaRndm = sigmaUsum * rndmPtr->flat(); + int iPick = -1; + do sigmaRndm -= sigmaUval[++iPick]; + while (sigmaRndm > 0.); + return sigmaU[iPick]; + } + +} + +//========================================================================== + +// The MultipleInteractions class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Factorization scale pT2 by default, but could be shifted to pT2 + pT02. +// (A priori possible, but problems for flavour threshold interpretation.) +const bool MultipleInteractions::SHIFTFACSCALE = false; + +// Pick one parton to represent rescattering cross section to speed up. +const bool MultipleInteractions::PREPICKRESCATTER = true; + +// Naive upper estimate of cross section too pessimistic, so reduce by this. +const double MultipleInteractions::SIGMAFUDGE = 0.7; + +// The r value above, picked to allow a flatter correct/trial cross section. +const double MultipleInteractions::RPT20 = 0.25; + +// Reduce pT0 by factor pT0STEP if sigmaInt < SIGMASTEP * sigmaND. +const double MultipleInteractions::PT0STEP = 0.9; +const double MultipleInteractions::SIGMASTEP = 1.1; + +// Stop if pT0 or pTmin fall below this, or alpha_s blows up. +const double MultipleInteractions::PT0MIN = 0.2; + +// Refuse too low expPow in impact parameter profile. +const double MultipleInteractions::EXPPOWMIN = 0.4; + +// Define low-b region by interaction rate above given number. +const double MultipleInteractions::PROBATLOWB = 0.6; + +// Basic step size for b integration; sometimes modified. +const double MultipleInteractions::BSTEP = 0.01; + +// Stop b integration when integrand dropped enough. +const double MultipleInteractions::BMAX = 1e-8; + +// Do not allow too large argument to exp function. +const double MultipleInteractions::EXPMAX = 50.; + +// Convergence criterion for k iteration. +const double MultipleInteractions::KCONVERGE = 1e-7; + +// Conversion of GeV^{-2} to mb for cross section. +const double MultipleInteractions::CONVERT2MB = 0.389380; + +// Stay away from division by zero in Jacobian for tHat -> pT2. +const double MultipleInteractions::ROOTMIN = 0.01; + +// No need to reinitialize parameters if energy close to previous. +const double MultipleInteractions::ECMDEV = 0.01; + +//-------------------------------------------------------------------------- + +// Initialize the generation process for given beams. + +bool MultipleInteractions::init( bool doMIinit, int diffractiveModeIn, + Info* infoPtrIn, Settings& settings, ParticleData* particleDataPtr, + Rndm* rndmPtrIn, BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + CoupSM* coupSMPtrIn, PartonSystems* partonSystemsPtrIn, + SigmaTotal* sigmaTotPtrIn, ostream& os) { + + // Store input pointers for future use. Done if no initialization. + diffractiveMode = diffractiveModeIn; + infoPtr = infoPtrIn; + rndmPtr = rndmPtrIn; + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + coupSMPtr = coupSMPtrIn; + partonSystemsPtr = partonSystemsPtrIn; + sigmaTotPtr = sigmaTotPtrIn; + if (!doMIinit) return false; + + // If both beams are baryons then softer PDF's than for mesons/Pomerons. + hasBaryonBeams = ( beamAPtr->isBaryon() && beamBPtr->isBaryon() ); + + // Matching in pT of hard interaction to further interactions. + pTmaxMatch = settings.mode("MultipleInteractions:pTmaxMatch"); + + // Parameters of alphaStrong generation. + alphaSvalue = settings.parm("MultipleInteractions:alphaSvalue"); + alphaSorder = settings.mode("MultipleInteractions:alphaSorder"); + + // Parameters of alphaEM generation. + alphaEMorder = settings.mode("MultipleInteractions:alphaEMorder"); + + // Parameters of cross section generation. + Kfactor = settings.parm("MultipleInteractions:Kfactor"); + + // Regularization of QCD evolution for pT -> 0. + pT0Ref = settings.parm("MultipleInteractions:pT0Ref"); + ecmRef = settings.parm("MultipleInteractions:ecmRef"); + ecmPow = settings.parm("MultipleInteractions:ecmPow"); + pTmin = settings.parm("MultipleInteractions:pTmin"); + + // Impact parameter profile. + bProfile = settings.mode("MultipleInteractions:bProfile"); + coreRadius = settings.parm("MultipleInteractions:coreRadius"); + coreFraction = settings.parm("MultipleInteractions:coreFraction"); + expPow = settings.parm("MultipleInteractions:expPow"); + expPow = max(EXPPOWMIN, expPow); + + // Process sets to include in machinery. + processLevel = settings.mode("MultipleInteractions:processLevel"); + + // Parameters of rescattering description. + allowRescatter = settings.flag("MultipleInteractions:allowRescatter"); + allowDoubleRes = settings.flag("MultipleInteractions:allowDoubleRescatter"); + rescatterMode = settings.mode("MultipleInteractions:rescatterMode"); + ySepResc = settings.parm("MultipleInteractions:ySepRescatter"); + deltaYResc = settings.parm("MultipleInteractions:deltaYRescatter"); + + // Various other parameters. + nQuarkIn = settings.mode("MultipleInteractions:nQuarkIn"); + nSample = settings.mode("MultipleInteractions:nSample"); + + // Optional dampening at small pT's when large multiplicities. + enhanceScreening = settings.mode("MultipleInteractions:enhanceScreening"); + + // Parameters for diffractive systems. + sigmaPomP = settings.parm("Diffraction:sigmaPomP"); + mMinPertDiff = settings.parm("Diffraction:mMinPert"); + + // Some common combinations for double Gaussian, as shorthand. + if (bProfile == 2) { + fracA = pow2(1. - coreFraction); + fracB = 2. * coreFraction * (1. - coreFraction); + fracC = pow2(coreFraction); + radius2B = 0.5 * (1. + pow2(coreRadius)); + radius2C = pow2(coreRadius); + + // Some common combinations for exp(b^pow), as shorthand. + } else if (bProfile == 3) { + hasLowPow = (expPow < 2.); + expRev = 2. / expPow - 1.; + } + + // Initialize alpha_strong generation. + alphaS.init( alphaSvalue, alphaSorder); + double Lambda3 = alphaS.Lambda3(); + + // Initialize alphaEM generation. + alphaEM.init( alphaEMorder, &settings); + + // Attach matrix-element calculation objects. + sigma2gg.init( 0, processLevel, infoPtr, &settings, particleDataPtr, + rndmPtr, beamAPtr, beamBPtr, coupSMPtr); + sigma2qg.init( 1, processLevel, infoPtr, &settings, particleDataPtr, + rndmPtr, beamAPtr, beamBPtr, coupSMPtr); + sigma2qqbarSame.init( 2, processLevel, infoPtr, &settings, particleDataPtr, + rndmPtr, beamAPtr, beamBPtr, coupSMPtr); + sigma2qq.init( 3, processLevel, infoPtr, &settings, particleDataPtr, + rndmPtr, beamAPtr, beamBPtr, coupSMPtr); + + // Calculate invariant mass of system. + eCM = infoPtr->eCM(); + sCM = eCM * eCM; + mMaxPertDiff = eCM; + eCMsave = eCM; + + // Get the total inelastic and nondiffractive cross section. + if (!sigmaTotPtr->hasSigmaTot()) return false; + bool isNonDiff = (diffractiveMode == 0); + sigmaND = (isNonDiff) ? sigmaTotPtr->sigmaND() : sigmaPomP; + double sigmaMaxViol = 0.; + + // Output initialization info - first part. + os << "\n *------- PYTHIA Multiple Interactions Initialization --" + << "----------* \n" + << " | " + << " | \n"; + if (isNonDiff) + os << " | sigmaNonDiffractive = " << fixed + << setprecision(2) << setw(7) << sigmaND << " mb | \n"; + else if (diffractiveMode == 1) + os << " | diffraction XB with sigmaNorm = " << fixed + << setprecision(2) << setw(7) << sigmaND << " mb | \n"; + else if (diffractiveMode == 2) + os << " | diffraction AX with sigmaNorm = " << fixed + << setprecision(2) << setw(7) << sigmaND << " mb | \n"; + os << " | " + << " | \n"; + + // For diffraction need to cover range of diffractive masses. + nStep = (diffractiveMode == 0) ? 1 : 5; + eStepSize = (nStep < 2) ? 1. + : log(mMaxPertDiff / mMinPertDiff) / (nStep - 1.); + for (int iStep = 0; iStep < nStep; ++iStep) { + + // Update and output current diffractive mass + if (nStep > 1) { + eCM = mMinPertDiff * pow( mMaxPertDiff / mMinPertDiff, + iStep / (nStep - 1.) ); + sCM = eCM * eCM; + os << " | diffractive mass = " << scientific + << setprecision(3) << setw(9) << eCM + << " GeV | \n"; + } + + // Set current pT0 scale. + pT0 = pT0Ref * pow(eCM / ecmRef, ecmPow); + + // The pT0 value may need to be decreased, if sigmaInt < sigmaND. + double pT4dSigmaMaxBeg = 0.; + for ( ; ; ) { + + // Derived pT kinematics combinations. + pT20 = pT0*pT0; + pT2min = pTmin*pTmin; + pTmax = 0.5*eCM; + pT2max = pTmax*pTmax; + pT20R = RPT20 * pT20; + pT20minR = pT2min + pT20R; + pT20maxR = pT2max + pT20R; + pT20min0maxR = pT20minR * pT20maxR; + pT2maxmin = pT2max - pT2min; + + // Provide upper estimate of interaction rate d(Prob)/d(pT2). + upperEnvelope(); + + // Integrate the parton-parton interaction cross section. + pT4dSigmaMaxBeg = pT4dSigmaMax; + jetCrossSection(); + + // Sufficiently big SigmaInt or reduce pT0; maybe also pTmin. + if (sigmaInt > SIGMASTEP * sigmaND) break; + os << fixed << setprecision(2) << " | pT0 = " << setw(5) << pT0 + << " gives sigmaInteraction = " << setw(7) << sigmaInt + << " mb: rejected | \n"; + if (pTmin > pT0) pTmin *= PT0STEP; + pT0 *= PT0STEP; + + // Give up if pT0 and pTmin fall too low. + if ( max(pT0, pTmin) < max(PT0MIN, Lambda3) ) { + infoPtr->errorMsg("Error in MultipleInteractions::init:" + " failed to find acceptable pT0 and pTmin"); + infoPtr->setTooLowPTmin(true); + return false; + } + } + + // Output for accepted pT0. + os << fixed << setprecision(2) << " | pT0 = " << setw(5) << pT0 + << " gives sigmaInteraction = "<< setw(7) << sigmaInt + << " mb: accepted | \n"; + + // Calculate factor relating matter overlap and interaction rate. + overlapInit(); + + // Maximum violation relative to first estimate. + sigmaMaxViol = max( sigmaMaxViol, pT4dSigmaMax / pT4dSigmaMaxBeg); + + // Save values calculated. + if (nStep > 1) { + pT0Save[iStep] = pT0; + pT4dSigmaMaxSave[iStep] = pT4dSigmaMax; + pT4dProbMaxSave[iStep] = pT4dProbMax; + sigmaIntSave[iStep] = sigmaInt; + for (int j = 0; j <= 100; ++j) sudExpPTSave[iStep][j] = sudExpPT[j]; + zeroIntCorrSave[iStep] = zeroIntCorr; + normOverlapSave[iStep] = normOverlap; + kNowSave[iStep] = kNow; + bAvgSave[iStep] = bAvg; + bDivSave[iStep] = bDiv; + probLowBSave[iStep] = probLowB; + fracAhighSave[iStep] = fracAhigh; + fracBhighSave[iStep] = fracBhigh; + fracChighSave[iStep] = fracBhigh; + fracABChighSave[iStep] = fracABChigh; + cDivSave[iStep] = cDiv; + cMaxSave[iStep] = cMax; + } + + // End of loop over diffractive masses. + } + os << " | " + << " | \n" + << " *------- End PYTHIA Multiple Interactions Initialization" + << " --------* " << endl; + + // Amount of violation from upperEnvelope to jetCrossSection. + if (sigmaMaxViol > 1.) { + ostringstream osWarn; + osWarn << "by factor " << fixed << setprecision(3) << sigmaMaxViol; + infoPtr->errorMsg("Warning in MultipleInteractions::init:" + " maximum increased", osWarn.str()); + } + + // Reset statistics. + SigmaMultiple* dSigma; + for (int i = 0; i < 4; ++i) { + if (i == 0) dSigma = &sigma2gg; + else if (i == 1) dSigma = &sigma2qg; + else if (i == 2) dSigma = &sigma2qqbarSame; + else dSigma = &sigma2qq; + int nProc = dSigma->nProc(); + for (int iProc = 0; iProc < nProc; ++iProc) + nGen[ dSigma->codeProc(iProc) ] = 0; + } + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Reset impact parameter choice and update the CM energy. +// For diffraction also interpolate parameters to current CM energy. + +void MultipleInteractions::reset( ) { + + // Reset impact parameter choice. + bIsSet = false; + bSetInFirst = false; + + // Update CM energy. Done if not diffraction and not new energy. + eCM = infoPtr->eCM(); + sCM = eCM * eCM; + if (nStep == 1 || abs( eCM / eCMsave - 1.) < ECMDEV) return; + + // Current interpolation point. + eCMsave = eCM; + eStepSave = log(eCM / mMinPertDiff) / eStepSize; + iStepFrom = max( 0, min( nStep - 2, int( eStepSave) ) ); + iStepTo = iStepFrom + 1; + eStepTo = max( 0., min( 1., eStepSave - iStepFrom) ); + eStepFrom = 1. - eStepTo; + + // Update pT0 and combinations derived from it. + pT0 = eStepFrom * pT0Save[iStepFrom] + + eStepTo * pT0Save[iStepTo]; + pT20 = pT0*pT0; + pT2min = pTmin*pTmin; + pTmax = 0.5*eCM; + pT2max = pTmax*pTmax; + pT20R = RPT20 * pT20; + pT20minR = pT2min + pT20R; + pT20maxR = pT2max + pT20R; + pT20min0maxR = pT20minR * pT20maxR; + pT2maxmin = pT2max - pT2min; + + // Update other parameters used in pT choice. + pT4dSigmaMax = eStepFrom * pT4dSigmaMaxSave[iStepFrom] + + eStepTo * pT4dSigmaMaxSave[iStepTo]; + pT4dProbMax = eStepFrom * pT4dProbMaxSave[iStepFrom] + + eStepTo * pT4dProbMaxSave[iStepTo]; + sigmaInt = eStepFrom * sigmaIntSave[iStepFrom] + + eStepTo * sigmaIntSave[iStepTo]; + for (int j = 0; j <= 100; ++j) + sudExpPT[j] = eStepFrom * sudExpPTSave[iStepFrom][j] + + eStepTo * sudExpPTSave[iStepTo][j]; + + // Update parameters related to the impact-parameter picture. + zeroIntCorr = eStepFrom * zeroIntCorrSave[iStepFrom] + + eStepTo * zeroIntCorrSave[iStepTo]; + normOverlap = eStepFrom * normOverlapSave[iStepFrom] + + eStepTo * normOverlapSave[iStepTo]; + kNow = eStepFrom * kNowSave[iStepFrom] + + eStepTo * kNowSave[iStepTo]; + bAvg = eStepFrom * bAvgSave[iStepFrom] + + eStepTo * bAvgSave[iStepTo]; + bDiv = eStepFrom * bDivSave[iStepFrom] + + eStepTo * bDivSave[iStepTo]; + probLowB = eStepFrom * probLowBSave[iStepFrom] + + eStepTo * probLowBSave[iStepTo]; + fracAhigh = eStepFrom * fracAhighSave[iStepFrom] + + eStepTo * fracAhighSave[iStepTo]; + fracBhigh = eStepFrom * fracBhighSave[iStepFrom] + + eStepTo * fracBhighSave[iStepTo]; + fracChigh = eStepFrom * fracChighSave[iStepFrom] + + eStepTo * fracChighSave[iStepTo]; + fracABChigh = eStepFrom * fracABChighSave[iStepFrom] + + eStepTo * fracABChighSave[iStepTo]; + cDiv = eStepFrom * cDivSave[iStepFrom] + + eStepTo * cDivSave[iStepTo]; + cMax = eStepFrom * cMaxSave[iStepFrom] + + eStepTo * cMaxSave[iStepTo]; + +} + +//-------------------------------------------------------------------------- + +// Select first = hardest pT in minbias process. +// Requires separate treatment at low and high b values + +void MultipleInteractions::pTfirst() { + + // Pick impact parameter and thereby interaction rate enhancement. + overlapFirst(); + bSetInFirst = true; + double WTacc; + + // At low b values evolve downwards with Sudakov. + if (isAtLowB) { + pT2 = pT2max; + do { + + // Pick a pT using a quick-and-dirty cross section estimate. + pT2 = fastPT2(pT2); + + // If fallen below lower cutoff then need to restart at top. + if (pT2 < pT2min) { + pT2 = pT2max; + WTacc = 0.; + + // Else pick complete kinematics and evaluate cross-section correction. + } else WTacc = sigmaPT2scatter(true) / dSigmaApprox; + + // Loop until acceptable pT and acceptable kinematics. + } while (WTacc < rndmPtr->flat() || !dSigmaDtSel->final2KinMI()); + + // At high b values make preliminary pT choice without Sudakov factor. + } else { + do { + pT2 = pT20min0maxR / (pT20minR + rndmPtr->flat() * pT2maxmin) - pT20R; + + // Evaluate upper estimate of cross section for this pT2 choice. + dSigmaApprox = pT4dSigmaMax / pow2(pT2 + pT20R); + + // Pick complete kinematics and evaluate cross-section correction. + WTacc = sigmaPT2scatter(true) / dSigmaApprox; + + // Evaluate and include Sudakov factor. + WTacc *= sudakov( pT2, enhanceB); + + // Loop until acceptable pT and acceptable kinematics. + } while (WTacc < rndmPtr->flat() || !dSigmaDtSel->final2KinMI()); + } + +} + +//-------------------------------------------------------------------------- + +// Set up kinematics for first = hardest pT in minbias process. + +void MultipleInteractions::setupFirstSys( Event& process) { + + // Last beam-status particles. Offset relative to normal beam locations. + int sizeProc = process.size(); + int nBeams = 3; + for (int i = 3; i < sizeProc; ++i) + if (process[i].statusAbs() < 20) nBeams = i + 1; + int nOffset = nBeams - 3; + + // Remove any partons of previous failed interactions. + if (sizeProc > nBeams) { + process.popBack( sizeProc - nBeams); + process.initColTag(); + } + + // Entries 3 and 4, now to be added, come from 1 and 2. + process[1 + nOffset].daughter1(3 + nOffset); + process[2 + nOffset].daughter1(4 + nOffset); + + // Negate beam status, if not already done. (Case with offset beams.) + process[1 + nOffset].statusNeg(); + process[2 + nOffset].statusNeg(); + + // Loop over four partons and offset info relative to subprocess itself. + int colOffset = process.lastColTag(); + for (int i = 1; i <= 4; ++i) { + Particle parton = dSigmaDtSel->getParton(i); + if (i <= 2 ) parton.mothers( i + nOffset, 0); + else parton.mothers( 3 + nOffset, 4 + nOffset); + if (i <= 2 ) parton.daughters( 5 + nOffset, 6 + nOffset); + else parton.daughters( 0, 0); + int col = parton.col(); + if (col > 0) parton.col( col + colOffset); + int acol = parton.acol(); + if (acol > 0) parton.acol( acol + colOffset); + + // Put the partons into the event record. + process.append(parton); + } + + // Set scale from which to begin evolution. + process.scale( sqrt(pT2Fac) ); + + // Info on subprocess - specific to mimimum-bias events. + string nameSub = dSigmaDtSel->name(); + int codeSub = dSigmaDtSel->code(); + int nFinalSub = dSigmaDtSel->nFinal(); + double pTMI = dSigmaDtSel->pTMIFin(); + infoPtr->setSubType( nameSub, codeSub, nFinalSub); + infoPtr->setTypeMI( codeSub, pTMI); + + // Further standard info on process. + infoPtr->setPDFalpha( id1, id2, xPDF1now, xPDF2now, pT2Fac, alpEM, alpS, + pT2Ren); + double m3 = dSigmaDtSel->m(3); + double m4 = dSigmaDtSel->m(4); + double theta = dSigmaDtSel->thetaMI(); + double phi = dSigmaDtSel->phiMI(); + infoPtr->setKin( x1, x2, sHat, tHat, uHat, sqrt(pT2), m3, m4, theta, phi); + +} + +//-------------------------------------------------------------------------- + +// Find whether to limit maximum scale of emissions. + +bool MultipleInteractions::limitPTmax( Event& event) { + + // User-set cases. + if (pTmaxMatch == 1) return true; + if (pTmaxMatch == 2) return false; + + // Look if only quarks (u, d, s, c, b), gluons and photons in final state. + bool onlyQGP = true; + for (int i = 5; i < event.size(); ++i) + if (event[i].status() != -21) { + int idAbs = event[i].idAbs(); + if (idAbs > 5 && idAbs != 21 && idAbs != 22) onlyQGP = false; + } + return (onlyQGP); + +} + +//-------------------------------------------------------------------------- + +// Select next pT in downwards evolution. + +double MultipleInteractions::pTnext( double pTbegAll, double pTendAll, + Event& event) { + + // Initial values. + bool pickRescatter, acceptKin; + double dSigmaScatter, dSigmaRescatter, WTacc; + double pT2end = pow2( max(pTmin, pTendAll) ); + pT2 = pow2(pTbegAll); + + // Find the set of already scattered partons on the two sides. + if (allowRescatter) findScatteredPartons( event); + + // Pick a pT2 using a quick-and-dirty cross section estimate. + do { + do { + pT2 = fastPT2(pT2); + if (pT2 < pT2end) return 0.; + + // Initial values: no rescattering. + i1Sel = 0; + i2Sel = 0; + dSigmaSum = 0.; + pickRescatter = false; + + // Pick complete kinematics and evaluate interaction cross-section. + dSigmaScatter = sigmaPT2scatter(false); + + // Also cross section from rescattering if allowed. + dSigmaRescatter = (allowRescatter) ? sigmaPT2rescatter( event) : 0.; + + // Normalize to dSigmaApprox, which was set in fastPT2 above. + WTacc = (dSigmaScatter + dSigmaRescatter) / dSigmaApprox; + if (WTacc > 1.) infoPtr->errorMsg("Warning in MultipleInteractions::" + "pTnext: weight above unity"); + + // Idea suggested by Gosta Gustafson: increased screening in events + // with large activity can be simulated by pT0_eff = sqrt(n) * pT0. + if (enhanceScreening > 0) { + int nSysNow = infoPtr->nMI() + 1; + if (enhanceScreening == 2) nSysNow += infoPtr->nISR(); + double WTscreen = pow2( (pT2 + pT20) / (pT2 + nSysNow * pT20) ); + WTacc *= WTscreen; + } + + // Decide whether to keep the event based on weight. + } while (WTacc < rndmPtr->flat()); + + // When rescattering possible: new interaction or rescattering? + if (allowRescatter) { + pickRescatter = (i1Sel > 0 || i2Sel > 0); + + // Restore kinematics for selected scattering/rescattering. + id1 = id1Sel; + id2 = id2Sel; + x1 = x1Sel; + x2 = x2Sel; + sHat = sHatSel; + tHat = tHatSel; + uHat = uHatSel; + sigma2Sel->sigma( id1, id2, x1, x2, sHat, tHat, uHat, alpS, alpEM, + true, pickOtherSel); + } + + // Pick one of the possible channels summed above. + dSigmaDtSel = sigma2Sel->sigmaSel(); + if (sigma2Sel->swapTU()) swap( tHat, uHat); + + // Decide to keep event based on kinematics (normally always OK). + // Rescattering: need to provide incoming four-vectors and masses. + if (pickRescatter) { + Vec4 p1Res = (i1Sel == 0) ? 0.5 * eCM * x1Sel * Vec4( 0., 0., 1., 1.) + : event[i1Sel].p(); + Vec4 p2Res = (i2Sel == 0) ? 0.5 * eCM * x2Sel * Vec4( 0., 0., -1., 1.) + : event[i2Sel].p(); + double m1Res = (i1Sel == 0) ? 0. : event[i1Sel].m(); + double m2Res = (i2Sel == 0) ? 0. : event[i2Sel].m(); + acceptKin = dSigmaDtSel->final2KinMI( i1Sel, i2Sel, p1Res, p2Res, + m1Res, m2Res); + // New interaction: already stored values enough. + } else acceptKin = dSigmaDtSel->final2KinMI(); + } while (!acceptKin); + + // Done. + return sqrt(pT2); + +} + +//-------------------------------------------------------------------------- + +// Set up the kinematics of the 2 -> 2 scattering process, +// and store the scattering in the event record. + +void MultipleInteractions::scatter( Event& event) { + + // Last beam-status particles. Offset relative to normal beam locations. + int sizeProc = event.size(); + int nBeams = 3; + for (int i = 3; i < sizeProc; ++i) + if (event[i].statusAbs() < 20) nBeams = i + 1; + int nOffset = nBeams - 3; + + // Loop over four partons and offset info relative to subprocess itself. + int motherOffset = event.size(); + int colOffset = event.lastColTag(); + for (int i = 1; i <= 4; ++i) { + Particle parton = dSigmaDtSel->getParton(i); + if (i <= 2 ) parton.mothers( i + nOffset, 0); + else parton.mothers( motherOffset, motherOffset + 1); + if (i <= 2 ) parton.daughters( motherOffset + 2, motherOffset + 3); + else parton.daughters( 0, 0); + int col = parton.col(); + if (col > 0) parton.col( col + colOffset); + int acol = parton.acol(); + if (acol > 0) parton.acol( acol + colOffset); + + // Put the partons into the event record. + event.append(parton); + } + + // Store participating partons as a new set in list of all systems. + int iSys = partonSystemsPtr->addSys(); + partonSystemsPtr->setInA(iSys, motherOffset); + partonSystemsPtr->setInB(iSys, motherOffset + 1); + partonSystemsPtr->addOut(iSys, motherOffset + 2); + partonSystemsPtr->addOut(iSys, motherOffset + 3); + partonSystemsPtr->setSHat(iSys, sHat); + + // Tag double rescattering graphs that annihilate one initial colour. + bool annihil1 = false; + bool annihil2 = false; + if (i1Sel > 0 && i2Sel > 0) { + if (event[motherOffset].col() == event[motherOffset + 1].acol() + && event[motherOffset].col() > 0) annihil1 = true; + if (event[motherOffset].acol() == event[motherOffset + 1].col() + && event[motherOffset].acol() > 0) annihil2 = true; + } + + // Beam remnant A: add scattered partons to list. + BeamParticle& beamA = *beamAPtr; + int iA = beamA.append( motherOffset, id1, x1); + + // Find whether incoming partons are valence or sea, so prepared for ISR. + if (i1Sel == 0) { + beamA.xfISR( iA, id1, x1, pT2); + beamA.pickValSeaComp(); + + // Remove rescattered parton from final state and change history. + // Propagate existing colour labels throught graph. + } else { + beamA[iA].companion(-10); + event[i1Sel].statusNeg(); + event[i1Sel].daughters( motherOffset, motherOffset); + event[motherOffset].mothers( i1Sel, i1Sel); + int colOld = event[i1Sel].col(); + if (colOld > 0) { + int colNew = event[motherOffset].col(); + for (int i = motherOffset; i < motherOffset + 4; ++i) { + if (event[i].col() == colNew) event[i].col( colOld); + if (event[i].acol() == colNew) event[i].acol( colOld); + } + } + int acolOld = event[i1Sel].acol(); + if (acolOld > 0) { + int acolNew = event[motherOffset].acol(); + for (int i = motherOffset; i < motherOffset + 4; ++i) { + if (event[i].col() == acolNew) event[i].col( acolOld); + if (event[i].acol() == acolNew) event[i].acol( acolOld); + } + } + } + + // Beam remnant B: add scattered partons to list. + BeamParticle& beamB = *beamBPtr; + int iB = beamB.append( motherOffset + 1, id2, x2); + + // Find whether incoming partons are valence or sea, so prepared for ISR. + if (i2Sel == 0) { + beamB.xfISR( iB, id2, x2, pT2); + beamB.pickValSeaComp(); + + // Remove rescattered parton from final state and change history. + // Propagate existing colour labels throught graph. + } else { + beamB[iB].companion(-10); + event[i2Sel].statusNeg(); + event[i2Sel].daughters( motherOffset + 1, motherOffset + 1); + event[motherOffset + 1].mothers( i2Sel, i2Sel); + int colOld = event[i2Sel].col(); + if (colOld > 0) { + int colNew = event[motherOffset + 1].col(); + for (int i = motherOffset; i < motherOffset + 4; ++i) { + if (event[i].col() == colNew) event[i].col( colOld); + if (event[i].acol() == colNew) event[i].acol( colOld); + } + } + int acolOld = event[i2Sel].acol(); + if (acolOld > 0) { + int acolNew = event[motherOffset + 1].acol(); + for (int i = motherOffset; i < motherOffset + 4; ++i) { + if (event[i].col() == acolNew) event[i].col( acolOld); + if (event[i].acol() == acolNew) event[i].acol( acolOld); + } + } + } + + // Annihilating colour in double rescattering requires relabelling + // of one colour into the other in the whole preceding event. + if (annihil1 || annihil2) { + int colLeft = (annihil1) ? event[motherOffset].col() + : event[motherOffset].acol(); + int mother1 = event[motherOffset].mother1(); + int mother2 = event[motherOffset + 1].mother1(); + int colLost = (annihil1) + ? event[mother1].col() + event[mother2].acol() - colLeft + : event[mother1].acol() + event[mother2].col() - colLeft; + for (int i = 0; i < motherOffset; ++i) { + if (event[i].col() == colLost) event[i].col( colLeft ); + if (event[i].acol() == colLost) event[i].acol( colLeft ); + } + } + + // Store info on subprocess code and rescattered partons. + int codeMI = dSigmaDtSel->code(); + double pTMI = dSigmaDtSel->pTMIFin(); + infoPtr->setTypeMI( codeMI, pTMI, i1Sel, i2Sel); + + // Done. +} + +//-------------------------------------------------------------------------- + +// Determine constant in d(Prob)/d(pT2) < const / (pT2 + r * pT20)^2. + +void MultipleInteractions::upperEnvelope() { + + // Initially determine constant in jet cross section upper estimate + // d(sigma_approx)/d(pT2) < const / (pT2 + r * pT20)^2. + pT4dSigmaMax = 0.; + + // Loop thorough allowed pT range logarithmically evenly. + for (int iPT = 0; iPT < 100; ++iPT) { + double pT = pTmin * pow( pTmax/pTmin, 0.01 * (iPT + 0.5) ); + pT2 = pT*pT; + pT2shift = pT2 + pT20; + pT2Ren = pT2shift; + pT2Fac = (SHIFTFACSCALE) ? pT2shift : pT2; + xT = 2. * pT / eCM; + + // Evaluate parton density sums at x1 = x2 = xT. + double xPDF1sumMax = (9./4.) * beamAPtr->xf(21, xT, pT2Fac); + for (int id = 1; id <= nQuarkIn; ++id) + xPDF1sumMax += beamAPtr->xf( id, xT, pT2Fac) + + beamAPtr->xf(-id, xT, pT2Fac); + double xPDF2sumMax = (9./4.) * beamBPtr->xf(21, xT, pT2Fac); + for (int id = 1; id <= nQuarkIn; ++id) + xPDF2sumMax += beamBPtr->xf( id, xT, pT2Fac) + + beamBPtr->xf(-id, xT, pT2Fac); + + // Evaluate alpha_strong and _EM, matrix element and phase space volume. + alpS = alphaS.alphaS(pT2Ren); + alpEM = alphaEM.alphaEM(pT2Ren); + double dSigmaPartonApprox = CONVERT2MB * Kfactor * 0.5 * M_PI + * pow2(alpS / pT2shift); + double yMax = log(1./xT + sqrt(1./(xT*xT) - 1.)); + double volumePhSp = pow2(2. * yMax); + + // Final comparison to determine upper estimate. + double dSigmaApproxNow = SIGMAFUDGE * xPDF1sumMax * xPDF2sumMax + * dSigmaPartonApprox * volumePhSp; + double pT4dSigmaNow = pow2(pT2 + pT20R) * dSigmaApproxNow; + if ( pT4dSigmaNow > pT4dSigmaMax) pT4dSigmaMax = pT4dSigmaNow; + } + + // Get wanted constant by dividing by the nondiffractive cross section. + pT4dProbMax = pT4dSigmaMax / sigmaND; + +} + +//-------------------------------------------------------------------------- + +// Integrate the parton-parton interaction cross section, +// using stratified Monte Carlo sampling. +// Store result in pT bins for use as Sudakov form factors. + +void MultipleInteractions::jetCrossSection() { + + // Common factor from bin size in dpT2 / (pT2 + r * pT20)^2 and statistics. + double sigmaFactor = (1. / pT20minR - 1. / pT20maxR) / (100. * nSample); + + // Loop through allowed pT range evenly in dpT2 / (pT2 + r * pT20)^2. + sigmaInt = 0.; + double dSigmaMax = 0.; + sudExpPT[100] = 0.; + for (int iPT = 99; iPT >= 0; --iPT) { + double sigmaSum = 0.; + + // In each pT bin sample a number of random pT values. + for (int iSample = 0; iSample < nSample; ++iSample) { + double mappedPT2 = 1. - 0.01 * (iPT + rndmPtr->flat()); + pT2 = pT20min0maxR / (pT20minR + mappedPT2 * pT2maxmin) - pT20R; + + // Evaluate cross section dSigma/dpT2 in phase space point. + double dSigma = sigmaPT2scatter(true); + + // Multiply by (pT2 + r * pT20)^2 to compensate for pT sampling. Sum. + dSigma *= pow2(pT2 + pT20R); + sigmaSum += dSigma; + if (dSigma > dSigmaMax) dSigmaMax = dSigma; + } + + // Store total cross section and exponent of Sudakov. + sigmaSum *= sigmaFactor; + sigmaInt += sigmaSum; + sudExpPT[iPT] = sudExpPT[iPT + 1] + sigmaSum / sigmaND; + + // End of loop over pT values. + } + + // Update upper estimate of differential cross section. Done. + if (dSigmaMax > pT4dSigmaMax) { + pT4dSigmaMax = dSigmaMax; + pT4dProbMax = dSigmaMax / sigmaND; + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate "Sudakov form factor" for not having a harder interaction +// at the selected b value, given the pT scale of the event. + +double MultipleInteractions::sudakov(double pT2sud, double enhance) { + + // Find bin the pT2 scale falls in. + double xBin = (pT2sud - pT2min) * pT20maxR + / (pT2maxmin * (pT2sud + pT20R)); + xBin = max(1e-6, min(100. - 1e-6, 100. * xBin) ); + int iBin = int(xBin); + + // Interpolate inside bin. Optionally include enhancement factor. + double sudExp = sudExpPT[iBin] + (xBin - iBin) + * (sudExpPT[iBin + 1] - sudExpPT[iBin]); + return exp( -enhance * sudExp); + +} + +//-------------------------------------------------------------------------- + +// Pick a trial next pT, based on a simple upper estimate of the +// d(sigma)/d(pT2) spectrum. + +double MultipleInteractions::fastPT2( double pT2beg) { + + // Use d(Prob)/d(pT2) < pT4dProbMax / (pT2 + r * pT20)^2. + double pT20begR = pT2beg + pT20R; + double pT4dProbMaxNow = pT4dProbMax * enhanceB; + double pT2try = pT4dProbMaxNow * pT20begR + / (pT4dProbMaxNow - pT20begR * log(rndmPtr->flat())) - pT20R; + + // Save cross section associated with ansatz above. Done. + dSigmaApprox = pT4dSigmaMax / pow2(pT2try + pT20R); + return pT2try; + +} + +//-------------------------------------------------------------------------- + +// Calculate the actual cross section to decide whether fast choice is OK. +// Select flavours and kinematics for interaction at given pT. +// Slightly different treatment for first interaction and subsequent ones. + +double MultipleInteractions::sigmaPT2scatter(bool isFirst) { + + // Derive recormalization and factorization scales, amd alpha_strong/em. + pT2shift = pT2 + pT20; + pT2Ren = pT2shift; + pT2Fac = (SHIFTFACSCALE) ? pT2shift : pT2; + alpS = alphaS.alphaS(pT2Ren); + alpEM = alphaEM.alphaEM(pT2Ren); + + // Derive rapidity limits from chosen pT2. + xT = 2. * sqrt(pT2) / eCM; + if (xT >= 1.) return 0.; + xT2 = xT*xT; + double yMax = log(1./xT + sqrt(1./xT2 - 1.)); + + // Select rapidities y3 and y4 of the two produced partons. + double y3 = yMax * (2. * rndmPtr->flat() - 1.); + double y4 = yMax * (2. * rndmPtr->flat() - 1.); + y = 0.5 * (y3 + y4); + + // Reject some events at large rapidities to improve efficiency. + // (Works for baryons, not pions or Pomerons if they have hard PDF's.) + double WTy = (hasBaryonBeams) + ? (1. - pow2(y3/yMax)) * (1. - pow2(y4/yMax)) : 1.; + if (WTy < rndmPtr->flat()) return 0.; + + // Failure if x1 or x2 exceed what is left in respective beam. + x1 = 0.5 * xT * (exp(y3) + exp(y4)); + x2 = 0.5 * xT * (exp(-y3) + exp(-y4)); + if (isFirst) { + if (x1 > 1. || x2 > 1.) return 0.; + } else { + if (x1 > beamAPtr->xMax() || x2 > beamBPtr->xMax()) return 0.; + } + tau = x1 * x2; + + // Begin evaluate parton densities at actual x1 and x2. + double xPDF1[21]; + double xPDF1sum = 0.; + double xPDF2[21]; + double xPDF2sum = 0.; + + // For first interaction use normal densities. + if (isFirst) { + for (int id = -nQuarkIn; id <= nQuarkIn; ++id) { + if (id == 0) xPDF1[10] = (9./4.) * beamAPtr->xf(21, x1, pT2Fac); + else xPDF1[id+10] = beamAPtr->xf(id, x1, pT2Fac); + xPDF1sum += xPDF1[id+10]; + } + for (int id = -nQuarkIn; id <= nQuarkIn; ++id) { + if (id == 0) xPDF2[10] = (9./4.) * beamBPtr->xf(21, x2, pT2Fac); + else xPDF2[id+10] = beamBPtr->xf(id, x2, pT2Fac); + xPDF2sum += xPDF2[id+10]; + } + + // For subsequent interactions use rescaled densities. + } else { + for (int id = -nQuarkIn; id <= nQuarkIn; ++id) { + if (id == 0) xPDF1[10] = (9./4.) * beamAPtr->xfMI(21, x1, pT2Fac); + else xPDF1[id+10] = beamAPtr->xfMI(id, x1, pT2Fac); + xPDF1sum += xPDF1[id+10]; + } + for (int id = -nQuarkIn; id <= nQuarkIn; ++id) { + if (id == 0) xPDF2[10] = (9./4.) * beamBPtr->xfMI(21, x2, pT2Fac); + else xPDF2[id+10] = beamBPtr->xfMI(id, x2, pT2Fac); + xPDF2sum += xPDF2[id+10]; + } + } + + // Select incoming flavours according to actual PDF's. + id1 = -nQuarkIn - 1; + double temp = xPDF1sum * rndmPtr->flat(); + do { xPDF1now = xPDF1[(++id1) + 10]; temp -= xPDF1now; } + while (temp > 0. && id1 < nQuarkIn); + if (id1 == 0) id1 = 21; + id2 = -nQuarkIn-1; + temp = xPDF2sum * rndmPtr->flat(); + do { xPDF2now = xPDF2[(++id2) + 10]; temp -= xPDF2now;} + while (temp > 0. && id2 < nQuarkIn); + if (id2 == 0) id2 = 21; + + // Assign pointers to processes relevant for incoming flavour choice: + // g + g, q + g, q + qbar (same flavour), q + q(bar) (the rest). + // Factor 4./9. per incoming gluon to compensate for preweighting. + SigmaMultiple* sigma2Tmp; + double gluFac = 1.; + if (id1 == 21 && id2 == 21) { + sigma2Tmp = &sigma2gg; + gluFac = 16. / 81.; + } else if (id1 == 21 || id2 == 21) { + sigma2Tmp = &sigma2qg; + gluFac = 4. / 9.; + } else if (id1 == -id2) sigma2Tmp = &sigma2qqbarSame; + else sigma2Tmp = &sigma2qq; + + // Prepare to generate differential cross sections. + sHat = tau * sCM; + double root = sqrtpos(1. - xT2 / tau); + tHat = -0.5 * sHat * (1. - root); + uHat = -0.5 * sHat * (1. + root); + + // Evaluate cross sections, include possibility of K factor. + // Use kinematics for two symmetrical configurations (tHat <-> uHat). + // (Not necessary, but makes for better MC efficiency.) + double dSigmaPartonCorr = Kfactor * gluFac + * sigma2Tmp->sigma( id1, id2, x1, x2, sHat, tHat, uHat, alpS, alpEM); + + // Combine cross section, pdf's and phase space integral. + double volumePhSp = pow2(2. * yMax) / WTy; + double dSigmaScat = dSigmaPartonCorr * xPDF1sum * xPDF2sum * volumePhSp; + + // Dampen cross section at small pT values; part of formalism. + // Use pT2 corrected for massive kinematics at this step.?? + // double pT2massive = dSigmaDtSel->pT2MI(); + double pT2massive = pT2; + dSigmaScat *= pow2( pT2massive / (pT2massive + pT20) ); + + // Sum up total contribution for all scatterings and rescatterings. + dSigmaSum += dSigmaScat; + + // Save values for comparison with rescattering processes. + i1Sel = 0; + i2Sel = 0; + id1Sel = id1; + id2Sel = id2; + x1Sel = x1; + x2Sel = x2; + sHatSel = sHat; + tHatSel = tHat; + uHatSel = uHat; + sigma2Sel = sigma2Tmp; + pickOtherSel = sigma2Tmp->pickedOther(); + + // For first interaction: pick one of the possible channels summed above. + if (isFirst) { + dSigmaDtSel = sigma2Tmp->sigmaSel(); + if (sigma2Tmp->swapTU()) swap( tHat, uHat); + } + + // Done. + return dSigmaScat; +} + +//-------------------------------------------------------------------------- + +// Find the partons that are allowed to rescatter. + +void MultipleInteractions::findScatteredPartons( Event& event) { + + // Reset arrays. + scatteredA.resize(0); + scatteredB.resize(0); + double yTmp, probA, probB; + + // Loop though the event record and catch "final" partons. + for (int i = 0; i < event.size(); ++i) + if (event[i].isFinal() && (event[i].idAbs() <= nQuarkIn + || event[i].id() == 21)) { + yTmp = event[i].y(); + + // Different strategies to determine which partons may rescatter. + switch(rescatterMode) { + + // Case 0: step function at origin + case 0: + if ( yTmp > 0.) scatteredA.push_back( i); + if (-yTmp > 0.) scatteredB.push_back( i); + break; + + // Case 1: step function as ySepResc. + case 1: + if ( yTmp > ySepResc) scatteredA.push_back( i); + if (-yTmp > ySepResc) scatteredB.push_back( i); + break; + + // Case 2: linear rise from ySep - deltaY to ySep + deltaY. + case 2: + probA = 0.5 * (1. + ( yTmp - ySepResc) / deltaYResc); + if (probA > rndmPtr->flat()) scatteredA.push_back( i); + probB = 0.5 * (1. + (-yTmp - ySepResc) / deltaYResc); + if (probB > rndmPtr->flat()) scatteredB.push_back( i); + break; + + // Case 3: rise like (1/2) * ( 1 + tanh((y - ySep) / deltaY) ). + // Use that (1/2) (1 + tanh(x)) = 1 / (1 + exp(-2x)). + case 3: + probA = 1. / (1. + exp(-2. * ( yTmp - ySepResc) / deltaYResc)); + if (probA > rndmPtr->flat()) scatteredA.push_back( i); + probB = 1. / (1. + exp(-2. * (-yTmp - ySepResc) / deltaYResc)); + if (probB > rndmPtr->flat()) scatteredB.push_back( i); + break; + + // Case 4 and undefined values: all partons can rescatter. + default: + scatteredA.push_back( i); + scatteredB.push_back( i); + break; + + // End of loop over partons. Done. + } + } + +} + +//-------------------------------------------------------------------------- + +// Rescattering contribution summed over all already scattered partons. +// Calculate the actual cross section to decide whether fast choice is OK. +// Select flavours and kinematics for interaction at given pT. + +double MultipleInteractions::sigmaPT2rescatter( Event& event) { + + // Derive xT scale from chosen pT2. + xT = 2. * sqrt(pT2) / eCM; + if (xT >= 1.) return 0.; + xT2 = xT*xT; + + // Pointer to cross section and total rescatter contribution. + SigmaMultiple* sigma2Tmp; + double dSigmaResc = 0.; + + // Normally save time by picking one random scattered parton from side A. + int nScatA = scatteredA.size(); + int iScatA = -1; + if (PREPICKRESCATTER && nScatA > 0) iScatA = min( nScatA - 1, + int( rndmPtr->flat() * double(nScatA) ) ); + + // Loop over all already scattered partons from side A. + for (int iScat = 0; iScat < nScatA; ++iScat) { + if (PREPICKRESCATTER && iScat != iScatA) continue; + int iA = scatteredA[iScat]; + int id1Tmp = event[iA].id(); + + // Calculate maximum possible sHat and check whether big enough. + double x1Tmp = event[iA].pPos() / eCM; + double sHatMax = x1Tmp * beamBPtr->xMax() * sCM; + if (sHatMax < 4. * pT2) continue; + + // Select rapidity separation between two produced partons. + double dyMax = log( sqrt(0.25 * sHatMax / pT2) + * (1. + sqrtpos(1. - 4. * pT2 / sHatMax)) ); + double dy = dyMax * (2. * rndmPtr->flat() - 1.); + + // Reconstruct kinematical variables, especially x2. + // Incoming c/b masses handled better if tau != x1 * x2. + double m2Tmp = event[iA].m2(); + double sHatTmp = m2Tmp + 4. * pT2 * pow2(cosh(dy)); + double x2Tmp = (sHatTmp - m2Tmp) /(x1Tmp * sCM); + double tauTmp = sHatTmp / sCM; + double root = sqrtpos(1. - xT2 / tauTmp); + double tHatTmp = -0.5 * sHatTmp * (1. - root); + double uHatTmp = -0.5 * sHatTmp * (1. + root); + + // Begin evaluate parton densities at actual x2. + double xPDF2[21]; + double xPDF2sum = 0.; + + // Use rescaled densities, with preweighting 9/4 for gluons. + for (int id = -nQuarkIn; id <= nQuarkIn; ++id) { + if (id == 0) xPDF2[10] = (9./4.) * beamBPtr->xfMI(21, x2Tmp, pT2Fac); + else xPDF2[id+10] = beamBPtr->xfMI(id, x2Tmp, pT2Fac); + xPDF2sum += xPDF2[id+10]; + } + + // Select incoming flavour according to actual PDF's. + int id2Tmp = -nQuarkIn - 1; + double temp = xPDF2sum * rndmPtr->flat(); + do { xPDF2now = xPDF2[(++id2Tmp) + 10]; temp -= xPDF2now;} + while (temp > 0. && id2Tmp < nQuarkIn); + if (id2Tmp == 0) id2Tmp = 21; + + // Assign pointers to processes relevant for incoming flavour choice: + // g + g, q + g, q + qbar (same flavour), q + q(bar) (the rest). + // Factor 4./9. for incoming gluon 2 to compensate for preweighting. + if (id1Tmp == 21 && id2Tmp == 21) sigma2Tmp = &sigma2gg; + else if (id1Tmp == 21 || id2Tmp == 21) sigma2Tmp = &sigma2qg; + else if (id1Tmp == -id2Tmp) sigma2Tmp = &sigma2qqbarSame; + else sigma2Tmp = &sigma2qq; + double gluFac = (id2Tmp == 21) ? 4. / 9. : 1.; + + // Evaluate cross sections, include possibility of K factor. + // Use kinematics for two symmetrical configurations (tHat <-> uHat). + // (Not necessary, but makes for better MC efficiency.) + double dSigmaPartonCorr = Kfactor * gluFac + * sigma2Tmp->sigma( id1Tmp, id2Tmp, x1Tmp, x2Tmp, sHatTmp, tHatTmp, + uHatTmp, alpS, alpEM); + + // Combine cross section, pdf's and phase space integral. + double volumePhSp = 4. *dyMax; + double dSigmaCorr = dSigmaPartonCorr * xPDF2sum * volumePhSp; + + // Dampen cross section at small pT values; part of formalism. + // Use pT2 corrected for massive kinematics at this step. + //?? double pT2massive = dSigmaDtSel->pT2MI(); + double pT2massive = pT2; + dSigmaCorr *= pow2( pT2massive / (pT2massive + pT20) ); + + // Compensate for prepicked rescattering if appropriate. + if (PREPICKRESCATTER) dSigmaCorr *= nScatA; + + // Sum up total contribution for all scatterings or rescattering only. + dSigmaSum += dSigmaCorr; + dSigmaResc += dSigmaCorr; + + // Determine whether current rescattering should be selected. + if (dSigmaCorr > rndmPtr->flat() * dSigmaSum) { + i1Sel = iA; + i2Sel = 0; + id1Sel = id1Tmp; + id2Sel = id2Tmp; + x1Sel = x1Tmp; + x2Sel = x2Tmp; + sHatSel = sHatTmp; + tHatSel = tHatTmp; + uHatSel = uHatTmp; + sigma2Sel = sigma2Tmp; + pickOtherSel = sigma2Tmp->pickedOther(); + } + } + + // Normally save time by picking one random scattered parton from side B. + int nScatB = scatteredB.size(); + int iScatB = -1; + if (PREPICKRESCATTER && nScatB > 0) iScatB = min( nScatB - 1, + int( rndmPtr->flat() * double(nScatB) ) ); + + // Loop over all already scattered partons from side B. + for (int iScat = 0; iScat < nScatB; ++iScat) { + if (PREPICKRESCATTER && iScat != iScatB) continue; + int iB = scatteredB[iScat]; + int id2Tmp = event[iB].id(); + + // Calculate maximum possible sHat and check whether big enough. + double x2Tmp = event[iB].pNeg() / eCM; + double sHatMax = beamAPtr->xMax() * x2Tmp * sCM; + if (sHatMax < 4. * pT2) continue; + + // Select rapidity separation between two produced partons. + double dyMax = log( sqrt(0.25 * sHatMax / pT2) + * (1. + sqrtpos(1. - 4. * pT2 / sHatMax)) ); + double dy = dyMax * (2. * rndmPtr->flat() - 1.); + + // Reconstruct kinematical variables, especially x1. + // Incoming c/b masses handled better if tau != x1 * x2. + double m2Tmp = event[iB].m2(); + double sHatTmp = m2Tmp + 4. * pT2 * pow2(cosh(dy)); + double x1Tmp = (sHatTmp - m2Tmp) /(x2Tmp * sCM); + double tauTmp = sHatTmp / sCM; + double root = sqrtpos(1. - xT2 / tauTmp); + double tHatTmp = -0.5 * sHatTmp * (1. - root); + double uHatTmp = -0.5 * sHatTmp * (1. + root); + + // Begin evaluate parton densities at actual x1. + double xPDF1[21]; + double xPDF1sum = 0.; + + // Use rescaled densities, with preweighting 9/4 for gluons. + for (int id = -nQuarkIn; id <= nQuarkIn; ++id) { + if (id == 0) xPDF1[10] = (9./4.) * beamAPtr->xfMI(21, x1Tmp, pT2Fac); + else xPDF1[id+10] = beamAPtr->xfMI(id, x1Tmp, pT2Fac); + xPDF1sum += xPDF1[id+10]; + } + + // Select incoming flavour according to actual PDF's. + int id1Tmp = -nQuarkIn - 1; + double temp = xPDF1sum * rndmPtr->flat(); + do { xPDF1now = xPDF1[(++id1Tmp) + 10]; temp -= xPDF1now;} + while (temp > 0. && id1Tmp < nQuarkIn); + if (id1Tmp == 0) id1Tmp = 21; + + // Assign pointers to processes relevant for incoming flavour choice: + // g + g, q + g, q + qbar (same flavour), q + q(bar) (the rest). + // Factor 4./9. for incoming gluon 2 to compensate for preweighting. + if (id1Tmp == 21 && id2Tmp == 21) sigma2Tmp = &sigma2gg; + else if (id1Tmp == 21 || id2Tmp == 21) sigma2Tmp = &sigma2qg; + else if (id1Tmp == -id2Tmp) sigma2Tmp = &sigma2qqbarSame; + else sigma2Tmp = &sigma2qq; + double gluFac = (id1Tmp == 21) ? 4. / 9. : 1.; + + // Evaluate cross sections, include possibility of K factor. + // Use kinematics for two symmetrical configurations (tHat <-> uHat). + // (Not necessary, but makes for better MC efficiency.) + double dSigmaPartonCorr = Kfactor * gluFac + * sigma2Tmp->sigma( id1Tmp, id2Tmp, x1Tmp, x2Tmp, sHatTmp, tHatTmp, + uHatTmp, alpS, alpEM); + + // Combine cross section, pdf's and phase space integral. + double volumePhSp = 4. *dyMax; + double dSigmaCorr = dSigmaPartonCorr * xPDF1sum * volumePhSp; + + // Dampen cross section at small pT values; part of formalism. + // Use pT2 corrected for massive kinematics at this step. + //?? double pT2massive = dSigmaDtSel->pT2MI(); + double pT2massive = pT2; + dSigmaCorr *= pow2( pT2massive / (pT2massive + pT20) ); + + // Compensate for prepicked rescattering if appropriate. + if (PREPICKRESCATTER) dSigmaCorr *= nScatB; + + // Sum up total contribution for all scatterings or rescattering only. + dSigmaSum += dSigmaCorr; + dSigmaResc += dSigmaCorr; + + // Determine whether current rescattering should be selected. + if (dSigmaCorr > rndmPtr->flat() * dSigmaSum) { + i1Sel = 0; + i2Sel = iB; + id1Sel = id1Tmp; + id2Sel = id2Tmp; + x1Sel = x1Tmp; + x2Sel = x2Tmp; + sHatSel = sHatTmp; + tHatSel = tHatTmp; + uHatSel = uHatTmp; + sigma2Sel = sigma2Tmp; + pickOtherSel = sigma2Tmp->pickedOther(); + } + } + + // Double rescatter: loop over already scattered partons from both sides. + // As before, allow to use only one parton per side to speed up. + if (allowDoubleRes) { + for (int iScat1 = 0; iScat1 < nScatA; ++iScat1) { + if (PREPICKRESCATTER && iScat1 != iScatA) continue; + int iA = scatteredA[iScat1]; + int id1Tmp = event[iA].id(); + for (int iScat2 = 0; iScat2 < nScatB; ++iScat2) { + if (PREPICKRESCATTER && iScat2 != iScatB) continue; + int iB = scatteredB[iScat2]; + int id2Tmp = event[iB].id(); + + // Calculate current sHat and check whether big enough. + double sHatTmp = (event[iA].p() + event[iB].p()).m2Calc(); + if (sHatTmp < 4. * pT2) continue; + + // Reconstruct other kinematical variables. (x values not needed.) + double x1Tmp = event[iA].pPos() / eCM; + double x2Tmp = event[iB].pNeg() / eCM; + double tauTmp = sHatTmp / sCM; + double root = sqrtpos(1. - xT2 / tauTmp); + double tHatTmp = -0.5 * sHatTmp * (1. - root); + double uHatTmp = -0.5 * sHatTmp * (1. + root); + + // Assign pointers to processes relevant for incoming flavour choice: + // g + g, q + g, q + qbar (same flavour), q + q(bar) (the rest). + if (id1Tmp == 21 && id2Tmp == 21) sigma2Tmp = &sigma2gg; + else if (id1Tmp == 21 || id2Tmp == 21) sigma2Tmp = &sigma2qg; + else if (id1Tmp == -id2Tmp) sigma2Tmp = &sigma2qqbarSame; + else sigma2Tmp = &sigma2qq; + + // Evaluate cross sections, include possibility of K factor. + // Use kinematics for two symmetrical configurations (tHat <-> uHat). + // (Not necessary, but makes for better MC efficiency.) + double dSigmaPartonCorr = Kfactor + * sigma2Tmp->sigma( id1Tmp, id2Tmp, x1Tmp, x2Tmp, sHatTmp, tHatTmp, + uHatTmp, alpS, alpEM); + + // Combine cross section and Jacobian tHat -> pT2 (with safety minvalue). + double dSigmaCorr = dSigmaPartonCorr / max(ROOTMIN, root); + + // Dampen cross section at small pT values; part of formalism. + // Use pT2 corrected for massive kinematics at this step. + //?? double pT2massive = dSigmaDtSel->pT2MI(); + double pT2massive = pT2; + dSigmaCorr *= pow2( pT2massive / (pT2massive + pT20) ); + + // Compensate for prepicked rescattering if appropriate. + if (PREPICKRESCATTER) dSigmaCorr *= nScatA * nScatB; + + // Sum up total contribution for all scatterings or rescattering only. + dSigmaSum += dSigmaCorr; + dSigmaResc += dSigmaCorr; + + // Determine whether current rescattering should be selected. + if (dSigmaCorr > rndmPtr->flat() * dSigmaSum) { + i1Sel = iA; + i2Sel = iB; + id1Sel = id1Tmp; + id2Sel = id2Tmp; + x1Sel = x1Tmp; + x2Sel = x2Tmp; + sHatSel = sHatTmp; + tHatSel = tHatTmp; + uHatSel = uHatTmp; + sigma2Sel = sigma2Tmp; + pickOtherSel = sigma2Tmp->pickedOther(); + } + } + } + } + + // Done. + return dSigmaResc; +} + + +//-------------------------------------------------------------------------- + +// Calculate factor relating matter overlap and interaction rate, +// i.e. k in = k * overlap(b) (neglecting +// n_int = 0 corrections and energy-momentum conservation effects). + +void MultipleInteractions::overlapInit() { + + // Initial values for iteration. Step size of b integration. + nAvg = sigmaInt / sigmaND; + kNow = 0.5; + int stepDir = 1; + double deltaB = BSTEP; + if (bProfile == 2) deltaB *= min( 0.5, 2.5 * coreRadius); + if (bProfile == 3) deltaB *= max(1., pow(2. / expPow, 1. / expPow)); + + // Further variables, with dummy initial values. + double nNow = 0.; + double kLow = 0.; + double nLow = 0.; + double kHigh = 0.; + double nHigh = 0.; + double overlapNow = 0.; + double probNow = 0.; + double overlapInt = 0.5; + double probInt = 0.; + double probOverlapInt = 0.; + double bProbInt = 0.; + normPi = 1. / (2. * M_PI); + + // Subdivision into low-b and high-b region by interaction rate. + bool pastBDiv = false; + double overlapHighB = 0.; + + // First close k into an interval by binary steps, + // then find k by successive interpolation. + do { + if (stepDir == 1) kNow *= 2.; + else if (stepDir == -1) kNow *= 0.5; + else kNow = kLow + (nAvg - nLow) * (kHigh - kLow) / (nHigh - nLow); + + // Overlap trivial if no impact parameter dependence. + if (bProfile <= 0 || bProfile > 3) { + probInt = 0.5 * M_PI * (1. - exp(-kNow)); + probOverlapInt = probInt / M_PI; + bProbInt = probInt; + + // Else integrate overlap over impact parameter. + } else { + + // Reset integrals. + overlapInt = (bProfile == 3) ? 0. : 0.5; + probInt = 0.; + probOverlapInt = 0.; + bProbInt = 0.; + pastBDiv = false; + overlapHighB = 0.; + + // Step in b space. + double b = -0.5 * deltaB; + double bArea = 0.; + do { + b += deltaB; + bArea = 2. * M_PI * b * deltaB; + + // Evaluate overlap at current b value. + if (bProfile == 1) { + overlapNow = normPi * exp( -b*b); + } else if (bProfile == 2) { + overlapNow = normPi * ( fracA * exp( -min(EXPMAX, b*b)) + + fracB * exp( -min(EXPMAX, b*b / radius2B)) / radius2B + + fracC * exp( -min(EXPMAX, b*b / radius2C)) / radius2C ); + } else { + overlapNow = normPi * exp( -pow( b, expPow)); + overlapInt += bArea * overlapNow; + } + if (pastBDiv) overlapHighB += bArea * overlapNow; + + // Calculate interaction probability and integrate. + probNow = 1. - exp( -min(EXPMAX, M_PI * kNow * overlapNow)); + probInt += bArea * probNow; + probOverlapInt += bArea * overlapNow * probNow; + bProbInt += b * bArea * probNow; + + // Check when interaction probability has dropped sufficiently. + if (!pastBDiv && probNow < PROBATLOWB) { + bDiv = b + 0.5 * deltaB; + pastBDiv = true; + } + + // Continue out in b until overlap too small. + } while (b < 1. || b * probNow > BMAX); + } + + // Ratio of b-integrated k * overlap / (1 - exp( - k * overlap)). + nNow = M_PI * kNow * overlapInt / probInt; + + // Replace lower or upper limit of k. + if (nNow < nAvg) { + kLow = kNow; + nLow = nNow; + if (stepDir == -1) stepDir = 0; + } else { + kHigh = kNow; + nHigh = nNow; + if (stepDir == 1) stepDir = -1; + } + + // Continue iteration until convergence. + } while (abs(nNow - nAvg) > KCONVERGE * nAvg); + + // Save relevant final numbers for overlap values. + double avgOverlap = probOverlapInt / probInt; + zeroIntCorr = probOverlapInt / overlapInt; + normOverlap = normPi * zeroIntCorr / avgOverlap; + bAvg = bProbInt / probInt; + + // Relative rates for preselection of low-b and high-b region. + // Other useful combinations for subsequent selection. + if (bProfile > 0 && bProfile <= 3) { + probLowB = M_PI * bDiv*bDiv; + double probHighB = M_PI * kNow * overlapHighB; + if (bProfile == 1) probHighB = M_PI * kNow * 0.5 * exp( -bDiv*bDiv); + else if (bProfile == 2) { + fracAhigh = fracA * exp( -bDiv*bDiv); + fracBhigh = fracB * exp( -bDiv*bDiv / radius2B); + fracChigh = fracC * exp( -bDiv*bDiv / radius2C); + fracABChigh = fracAhigh + fracBhigh + fracChigh; + probHighB = M_PI * kNow * 0.5 * fracABChigh; + } else { + cDiv = pow( bDiv, expPow); + cMax = max(2. * expRev, cDiv); + } + probLowB /= (probLowB + probHighB); + } + +} + +//-------------------------------------------------------------------------- + +// Pick impact parameter and interaction rate enhancement beforehand, +// i.e. before even the hardest interaction for minimum-bias events. + +void MultipleInteractions::overlapFirst() { + + // Trivial values if no impact parameter dependence. + if (bProfile <= 0 || bProfile > 3) { + bNow = bAvg; + enhanceB = zeroIntCorr; + bIsSet = true; + isAtLowB = true; + return; + } + + // Preliminary choice between and inside low-b and high-b regions. + double overlapNow = 0.; + double probAccept = 0.; + do { + + // Treatment in low-b region: pick b flat in area. + if (rndmPtr->flat() < probLowB) { + isAtLowB = true; + bNow = bDiv * sqrt(rndmPtr->flat()); + + // Evaluate overlap and from that acceptance probability. + if (bProfile == 1) overlapNow = normPi * exp( -bNow*bNow); + else if (bProfile == 2) overlapNow = normPi * + ( fracA * exp( -bNow*bNow) + + fracB * exp( -bNow*bNow / radius2B) / radius2B + + fracC * exp( -bNow*bNow / radius2C) / radius2C ); + else overlapNow = normPi * exp( -pow( bNow, expPow)); + probAccept = 1. - exp( -min(EXPMAX, M_PI * kNow * overlapNow)); + + // Treatment in high-b region: pick b according to overlap. + } else { + isAtLowB = false; + + // For simple and double Gaussian pick b according to exp(-b^2 / r^2). + if (bProfile == 1) { + bNow = sqrt(bDiv*bDiv - log(rndmPtr->flat())); + overlapNow = normPi * exp( -min(EXPMAX, bNow*bNow)); + } else if (bProfile == 2) { + double pickFrac = rndmPtr->flat() * fracABChigh; + if (pickFrac < fracAhigh) bNow = sqrt(bDiv*bDiv - log(rndmPtr->flat())); + else if (pickFrac < fracAhigh + fracBhigh) + bNow = sqrt(bDiv*bDiv - radius2B * log(rndmPtr->flat())); + else bNow = sqrt(bDiv*bDiv - radius2C * log(rndmPtr->flat())); + overlapNow = normPi * ( fracA * exp( -min(EXPMAX, bNow*bNow)) + + fracB * exp( -min(EXPMAX, bNow*bNow / radius2B)) / radius2B + + fracC * exp( -min(EXPMAX, bNow*bNow / radius2C)) / radius2C ); + + // For exp( - b^expPow) transform to variable c = b^expPow so that + // f(b) = b * exp( - b^expPow) -> f(c) = c^r * exp(-c) with r = expRev. + // case hasLowPow: expPow < 2 <=> r > 0: preselect according to + // f(c) < N exp(-c/2) and then accept with N' * c^r * exp(-c/2). + } else if (hasLowPow) { + double cNow, acceptC; + do { + cNow = cDiv - 2. * log(rndmPtr->flat()); + acceptC = pow(cNow / cMax, expRev) * exp( -0.5 * (cNow - cMax)); + } while (acceptC < rndmPtr->flat()); + bNow = pow( cNow, 1. / expPow); + overlapNow = normPi * exp( -cNow); + + // case !hasLowPow: expPow >= 2 <=> - 1 < r < 0: preselect according to + // f(c) < N exp(-c) and then accept with N' * c^r. + } else { + double cNow, acceptC; + do { + cNow = cDiv - log(rndmPtr->flat()); + acceptC = pow(cNow / cDiv, expRev); + } while (acceptC < rndmPtr->flat()); + bNow = pow( cNow, 1. / expPow); + overlapNow = normPi * exp( -cNow); + } + double temp = M_PI * kNow *overlapNow; + probAccept = (1. - exp( -min(EXPMAX, temp))) / temp; + } + + // Confirm choice of b value. Derive enhancement factor. + } while (probAccept < rndmPtr->flat()); + enhanceB = (normOverlap / normPi) * overlapNow ; + + // Done. + bIsSet = true; + +} + +//-------------------------------------------------------------------------- + +// Pick impact parameter and interaction rate enhancement afterwards, +// i.e. after a hard interaction is known but before rest of MI treatment. + +void MultipleInteractions::overlapNext(double pTscale) { + + // Default, valid for bProfile = 0. Also initial Sudakov. + enhanceB = zeroIntCorr; + if (bProfile <= 0 || bProfile > 3) return; + double pT2scale = pTscale*pTscale; + + // Begin loop over pT-dependent rejection of b value. + do { + + // Flat enhancement distribution for simple Gaussian. + if (bProfile == 1) { + double expb2 = rndmPtr->flat(); + enhanceB = normOverlap * expb2; + bNow = sqrt( -log(expb2)); + + // For double Gaussian go the way via b, according to each Gaussian. + } else if (bProfile == 2) { + double bType = rndmPtr->flat(); + double b2 = -log( rndmPtr->flat() ); + if (bType < fracA) ; + else if (bType < fracA + fracB) b2 *= radius2B; + else b2 *= radius2C; + enhanceB = normOverlap * ( fracA * exp( -min(EXPMAX, b2)) + + fracB * exp( -min(EXPMAX, b2 / radius2B)) / radius2B + + fracC * exp( -min(EXPMAX, b2 / radius2C)) / radius2C ); + bNow = sqrt(b2); + + // For exp( - b^expPow) transform to variable c = b^expPow so that + // f(b) = b * exp( - b^expPow) -> f(c) = c^r * exp(-c) with r = expRev. + // case hasLowPow: expPow < 2 <=> r > 0: + // f(c) < r^r exp(-r) for c < 2r, < (2r)^r exp(-r-c/2) for c > 2r. + } else if (hasLowPow) { + double cNow, acceptC; + double probLowC = expRev / (expRev + pow(2., expRev) * exp( - expRev)); + do { + if (rndmPtr->flat() < probLowC) { + cNow = 2. * expRev * rndmPtr->flat(); + acceptC = pow( cNow / expRev, expRev) * exp(expRev - cNow); + } else { + cNow = 2. * (expRev - log( rndmPtr->flat() )); + acceptC = pow(0.5 * cNow / expRev, expRev) * exp(expRev - 0.5 * cNow); + } + } while (acceptC < rndmPtr->flat()); + enhanceB = normOverlap *exp(-cNow); + bNow = pow( cNow, 1. / expPow); + + // case !hasLowPow: expPow >= 2 <=> - 1 < r < 0: + // f(c) < c^r for c < 1, f(c) < exp(-c) for c > 1. + } else { + double cNow, acceptC; + double probLowC = expPow / (2. * exp(-1.) + expPow); + do { + if (rndmPtr->flat() < probLowC) { + cNow = pow( rndmPtr->flat(), 0.5 * expPow); + acceptC = exp(-cNow); + } else { + cNow = 1. - log( rndmPtr->flat() ); + acceptC = pow( cNow, expRev); + } + } while (acceptC < rndmPtr->flat()); + enhanceB = normOverlap * exp(-cNow); + bNow = pow( cNow, 1. / expPow); + } + + // Evaluate "Sudakov form factor" for not having a harder interaction. + } while (sudakov(pT2scale, enhanceB) < rndmPtr->flat()); + + // Done. + bIsSet = true; +} + +//-------------------------------------------------------------------------- + +// Printe statistics on number of multiple-interactions processes. + +void MultipleInteractions::statistics(bool resetStat, ostream& os) { + + // Header. + os << "\n *------- PYTHIA Multiple Interactions Statistics --------" + << "---*\n" + << " | " + << " |\n" + << " | Note: excludes hardest subprocess if already listed above " + << " |\n" + << " | " + << " |\n" + << " | Subprocess Code | Times" + << " |\n" + << " | | " + << " |\n" + << " |------------------------------------------------------------" + << "-|\n" + << " | | " + << " |\n"; + + // Loop over existing processes. Sum of all subprocesses. + int numberSum = 0; + for ( map::iterator iter = nGen.begin(); iter != nGen.end(); + ++iter) { + int code = iter -> first; + int number = iter->second; + numberSum += number; + + // Find process name that matches code. + string name = " "; + bool foundName = false; + SigmaMultiple* dSigma; + for (int i = 0; i < 4; ++i) { + if (i == 0) dSigma = &sigma2gg; + else if (i == 1) dSigma = &sigma2qg; + else if (i == 2) dSigma = &sigma2qqbarSame; + else dSigma = &sigma2qq; + int nProc = dSigma->nProc(); + for (int iProc = 0; iProc < nProc; ++iProc) + if (dSigma->codeProc(iProc) == code) { + name = dSigma->nameProc(iProc); + foundName = true; + } + if (foundName) break; + } + + // Print individual process info. + os << " | " << left << setw(40) << name << right << setw(5) << code + << " | " << setw(11) << number << " |\n"; + } + + // Print summed process info. + os << " | " + << " |\n" + << " | " << left << setw(45) << "sum" << right << " | " << setw(11) + << numberSum << " |\n"; + + // Listing finished. + os << " | | " + << " |\n" + << " *------- End PYTHIA Multiple Interactions Statistics -------" + << "-*" << endl; + + // Optionally reset statistics contants. + if (resetStat) for ( map::iterator iter = nGen.begin(); + iter != nGen.end(); ++iter) iter->second = 0; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/ParticleData.cxx b/PYTHIA8/pythia8140/src/ParticleData.cxx new file mode 100644 index 00000000000..849cac66863 --- /dev/null +++ b/PYTHIA8/pythia8140/src/ParticleData.cxx @@ -0,0 +1,2055 @@ +// ParticleData.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// DecayChannel, ParticleDataEntry and ParticleData classes. + +#include "ParticleData.h" +#include "StandardModel.h" + +// Allow string and character manipulation. +#include + +namespace Pythia8 { + +//========================================================================== + +// DecayChannel class. +// This class holds info on a single decay channel. + +//-------------------------------------------------------------------------- + +// Check whether id1 occurs anywhere in product list. + +bool DecayChannel::contains(int id1) const { + + bool found1 = false; + for (int i = 0; i < nProd; ++i) if (prod[i] == id1) found1 = true; + return found1; + +} + +//-------------------------------------------------------------------------- + +// Check whether id1 and id2 occur anywhere in product list. +// iF ID1 == ID2 then two copies of this particle must be present. + +bool DecayChannel::contains(int id1, int id2) const { + + bool found1 = false; + bool found2 = false; + for (int i = 0; i < nProd; ++i) { + if (!found1 && prod[i] == id1) {found1 = true; continue;} + if (!found2 && prod[i] == id2) {found2 = true; continue;} + } + return found1 && found2; + +} + +//-------------------------------------------------------------------------- + +// Check whether id1, id2 and id3 occur anywhere in product list. +// iF ID1 == ID2 then two copies of this particle must be present, etc. + +bool DecayChannel::contains(int id1, int id2, int id3) const { + + bool found1 = false; + bool found2 = false; + bool found3 = false; + for (int i = 0; i < nProd; ++i) { + if (!found1 && prod[i] == id1) {found1 = true; continue;} + if (!found2 && prod[i] == id2) {found2 = true; continue;} + if (!found3 && prod[i] == id3) {found3 = true; continue;} + } + return found1 && found2 && found3; + +} + +//========================================================================== + +// ParticleDataEntry class. +// This class holds info on a single particle species. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// A particle is invisible if it has neither strong nor electric charge, +// and is not made up of constituents that have it. Only relevant for +// long-lived particles. This list may need to be extended. +const int ParticleDataEntry::INVISIBLENUMBER = 38; +const int ParticleDataEntry::INVISIBLETABLE[38] = { 12, 14, 16, 18, 23, 25, + 32, 33, 35, 36, 39, 41, 1000012, 1000014, 1000016, 1000018, 1000022, + 1000023, 1000025, 1000035, 1000045, 1000039, 2000012, 2000014, 2000016, + 2000018, 4900012, 4900014, 4900016, 4900021, 4900022, 4900101, 5000039, + 5100039, 9900012, 9900014, 9900016, 9900023}; + +// Particles with a read-in tau0 (in mm/c) below this mayDecay by default. +const double ParticleDataEntry::MAXTAU0FORDECAY = 1000.; + +// Particles with a read-in m0 above this isResonance by default. +const double ParticleDataEntry::MINMASSRESONANCE = 20.; + +// Narrow states are assigned nominal mass. +const double ParticleDataEntry::NARROWMASS = 1e-6; + +// Constituent quark masses (d, u, s, c, b). +const double ParticleDataEntry::CONSTITUENTMASSTABLE[6] + = {0., 0.325, 0.325, 0.50, 1.60, 5.00}; + +//-------------------------------------------------------------------------- + +// Destructor: delete any ResonanceWidths object. + +ParticleDataEntry::~ParticleDataEntry() { + if (resonancePtr != 0) delete resonancePtr; +} + +//-------------------------------------------------------------------------- + +// Set initial default values for some quantities. + +void ParticleDataEntry::setDefaults() { + + // A particle is a resonance if it is heavy enough. + isResonanceSave = (m0Save > MINMASSRESONANCE); + + // A particle may decay if it is shortlived enough. + mayDecaySave = (tau0Save < MAXTAU0FORDECAY); + + // A particle by default has no external decays. + doExternalDecaySave = false; + + // A particle is invisible if in current table of such. + isVisibleSave = true; + for (int i = 0; i < INVISIBLENUMBER; ++i) + if (idSave == INVISIBLETABLE[i]) isVisibleSave = false; + + // Normally a resonance should not have width forced to fixed value. + doForceWidthSave = false; + + // Set up constituent masses. + setConstituentMass(); + + // No Breit-Wigner mass selection before initialized. + modeBWnow = 0; + +} + +//-------------------------------------------------------------------------- + +// Find out if a particle is a hadron. +// Only covers normal hadrons, not e.g. R-hadrons. + +bool ParticleDataEntry::isHadron() const { + + if (idSave <= 100 || (idSave >= 1000000 && idSave <= 9000000) + || idSave >= 9900000) return false; + if (idSave == 130 || idSave == 310) return true; + if (idSave%10 == 0 || (idSave/10)%10 == 0 || (idSave/100)%10 == 0) + return false; + return true; + +} + +//-------------------------------------------------------------------------- + +// Find out if a particle is a meson. +// Only covers normal hadrons, not e.g. R-hadrons. + +bool ParticleDataEntry::isMeson() const { + + if (idSave <= 100 || (idSave >= 1000000 && idSave <= 9000000) + || idSave >= 9900000) return false; + if (idSave == 130 || idSave == 310) return true; + if (idSave%10 == 0 || (idSave/10)%10 == 0 || (idSave/100)%10 == 0 + || (idSave/1000)%10 != 0) return false; + return true; + +} + +//-------------------------------------------------------------------------- + +// Find out if a particle is a baryon. +// Only covers normal hadrons, not e.g. R-hadrons. + +bool ParticleDataEntry::isBaryon() const { + + if (idSave <= 1000 || (idSave >= 1000000 && idSave <= 9000000) + || idSave >= 9900000) return false; + if (idSave%10 == 0 || (idSave/10)%10 == 0 || (idSave/100)%10 == 0 + || (idSave/1000)%10 == 0) return false; + return true; + + +} + +//-------------------------------------------------------------------------- + +// Extract the heaviest (= largest id) quark in a hadron. + +int ParticleDataEntry::heaviestQuark(int idIn) const { + + if (!isHadron()) return 0; + int hQ = 0; + + // Meson. + if ( (idSave/1000)%10 == 0 ) { + hQ = (idSave/100)%10; + if (idSave == 130) hQ = 3; + if (hQ%2 == 1) hQ = -hQ; + + // Baryon. + } else hQ = (idSave/1000)%10; + + // Done. + return (idIn > 0) ? hQ : -hQ; + +} + +//-------------------------------------------------------------------------- + +// Calculate three times baryon number, i.e. net quark - antiquark number. + +int ParticleDataEntry::baryonNumberType(int idIn) const { + + // Quarks. + if (isQuark()) return (idIn > 0) ? 1 : -1; + + // Diquarks + if (isDiquark()) return (idIn > 0) ? 2 : -2; + + // Baryons. + if (isBaryon()) return (idIn > 0) ? 3 : -3; + + // Done. + return 0; + +} + +//-------------------------------------------------------------------------- + +// Prepare the Breit-Wigner mass selection by precalculating +// frequently-used expressions. + +void ParticleDataEntry::initBWmass() { + + // Find Breit-Wigner mode for current particle. + modeBWnow = particleDataPtr->modeBreitWigner; + if ( mWidthSave < NARROWMASS || (mMaxSave > mMinSave + && mMaxSave - mMinSave < NARROWMASS) ) modeBWnow = 0; + if (modeBWnow == 0) return; + + // Find atan expressions to be used in random mass selection. + if (modeBWnow < 3) { + atanLow = atan( 2. * (mMinSave - m0Save) / mWidthSave ); + double atanHigh = (mMaxSave > mMinSave) + ? atan( 2. * (mMaxSave - m0Save) / mWidthSave ) : 0.5 * M_PI; + atanDif = atanHigh - atanLow; + } else { + atanLow = atan( (pow2(mMinSave) - pow2(m0Save)) + / (m0Save * mWidthSave) ); + double atanHigh = (mMaxSave > mMinSave) + ? atan( (pow2(mMaxSave) - pow2(m0Save)) / (m0Save * mWidthSave) ) + : 0.5 * M_PI; + atanDif = atanHigh - atanLow; + } + + // Done if no threshold factor. + if (modeBWnow%2 == 1) return; + + // Find average mass threshold for threshold-factor correction. + double bRatSum = 0.; + double mThrSum = 0; + for (int i = 0; i < int(channels.size()); ++i) + if (channels[i].onMode() >= 0) { + bRatSum += channels[i].bRatio(); + double mChannelSum = 0.; + for (int j = 0; j < channels[i].multiplicity(); ++j) + mChannelSum += particleDataPtr->m0( channels[i].product(j) ); + mThrSum += channels[i].bRatio() * mChannelSum; + } + mThr = (bRatSum == 0.) ? 0. : mThrSum / bRatSum; + + // Switch off Breit-Wigner if very close to threshold. + if (mThr + NARROWMASS > m0Save) { + ostringstream osWarn; + osWarn << "for id = " << idSave; + particleDataPtr->infoPtr->errorMsg("Warning in ParticleDataEntry::" + "initBWmass: switching off width", osWarn.str(), true); + modeBWnow = 0; + } + +} + +//-------------------------------------------------------------------------- + +// Function to give mass of a particle, either at the nominal value +// or picked according to a (linear or quadratic) Breit-Wigner. + +double ParticleDataEntry::mass() { + + // Nominal value. + if (modeBWnow == 0) return m0Save; + double mNow, m2Now; + + // Mass according to a Breit-Wigner linear in m. + if (modeBWnow == 1) { + mNow = m0Save + 0.5 * mWidthSave + * tan( atanLow + atanDif * particleDataPtr->rndmPtr->flat() ); + + // Ditto, but make Gamma proportional to sqrt(m^2 - m_threshold^2). + } else if (modeBWnow == 2) { + double mWidthNow, fixBW, runBW; + double m0ThrS = m0Save*m0Save - mThr*mThr; + do { + mNow = m0Save + 0.5 * mWidthSave + * tan( atanLow + atanDif * particleDataPtr->rndmPtr->flat() ); + mWidthNow = mWidthSave * sqrtpos( (mNow*mNow - mThr*mThr) / m0ThrS ); + fixBW = mWidthSave / (pow2(mNow - m0Save) + pow2(0.5 * mWidthSave)); + runBW = mWidthNow / (pow2(mNow - m0Save) + pow2(0.5 * mWidthNow)); + } while (runBW < particleDataPtr->rndmPtr->flat() + * particleDataPtr->maxEnhanceBW * fixBW); + + // Mass according to a Breit-Wigner quadratic in m. + } else if (modeBWnow == 3) { + m2Now = m0Save*m0Save + m0Save * mWidthSave + * tan( atanLow + atanDif * particleDataPtr->rndmPtr->flat() ); + mNow = sqrtpos( m2Now); + + // Ditto, but m_0 Gamma_0 -> m Gamma(m) with threshold factor as above. + } else { + double mwNow, fixBW, runBW; + double m2Ref = m0Save * m0Save; + double mwRef = m0Save * mWidthSave; + double m2Thr = mThr * mThr; + do { + m2Now = m2Ref + mwRef * tan( atanLow + atanDif + * particleDataPtr->rndmPtr->flat() ); + mNow = sqrtpos( m2Now); + mwNow = mNow * mWidthSave + * sqrtpos( (m2Now - m2Thr) / (m2Ref - m2Thr) ); + fixBW = mwRef / (pow2(m2Now - m2Ref) + pow2(mwRef)); + runBW = mwNow / (pow2(m2Now - m2Ref) + pow2(mwNow)); + } while (runBW < particleDataPtr->rndmPtr->flat() + * particleDataPtr->maxEnhanceBW * fixBW); + } + + // Done. + return mNow; +} + +//-------------------------------------------------------------------------- + +// Function to calculate running mass at given mass scale. + +double ParticleDataEntry::mRun(double mHat) { + + // Except for six quarks return nominal mass. + if (idSave > 6) return m0Save; + double mQRun = particleDataPtr->mQRun[idSave]; + double Lam5 = particleDataPtr->Lambda5Run; + + // For d, u, s quarks start running at 2 GeV (RPP 2006 p. 505). + if (idSave < 4) return mQRun * pow ( log(2. / Lam5) + / log(max(2., mHat) / Lam5), 12./23.); + + // For c, b and t quarks start running at respective mass. + return mQRun * pow ( log(mQRun / Lam5) + / log(max(mQRun, mHat) / Lam5), 12./23.); + +} + +//-------------------------------------------------------------------------- + +// Rescale all branching ratios to assure normalization to unity. + +void ParticleDataEntry::rescaleBR(double newSumBR) { + + // Sum up branching ratios. Find rescaling factor. Rescale. + double oldSumBR = 0.; + for ( int i = 0; i < int(channels.size()); ++ i) + oldSumBR += channels[i].bRatio(); + double rescaleFactor = newSumBR / oldSumBR; + for ( int i = 0; i < int(channels.size()); ++ i) + channels[i].rescaleBR(rescaleFactor); + +} + +//-------------------------------------------------------------------------- + +// Prepare to pick a decay channel. + +bool ParticleDataEntry::preparePick(int idSgn, double mHat, int idInFlav) { + + // Reset sum of allowed widths/branching ratios. + currentBRSum = 0.; + + // For resonances the widths are calculated dynamically. + if (resonancePtr != 0) { + resonancePtr->widthStore(idSgn, mHat, idInFlav); + for (int i = 0; i < int(channels.size()); ++i) + currentBRSum += channels[i].currentBR(); + + // Else use normal fixed branching ratios. + } else { + int onMode; + double currentBRNow; + for (int i = 0; i < int(channels.size()); ++i) { + onMode = channels[i].onMode(); + currentBRNow = 0.; + if ( idSgn > 0 && (onMode == 1 || onMode == 2) ) + currentBRNow = channels[i].bRatio(); + else if ( idSgn < 0 && (onMode == 1 || onMode == 3) ) + currentBRNow = channels[i].bRatio(); + channels[i].currentBR(currentBRNow); + currentBRSum += currentBRNow; + } + } + + // Failure if no channels found with positive branching ratios. + return (currentBRSum > 0.); + +} + +//-------------------------------------------------------------------------- + +// Pick a decay channel according to branching ratios from preparePick. + +DecayChannel& ParticleDataEntry::pickChannel() { + + // Find channel in table. + int size = channels.size(); + double rndmBR = currentBRSum * particleDataPtr->rndmPtr->flat(); + int i = -1; + do rndmBR -= channels[++i].currentBR(); + while (rndmBR > 0. && i < size); + + // Emergency if no channel found. Done. + if (i == size) i = 0; + return channels[i]; + +} + +//-------------------------------------------------------------------------- + +// Access methods stored in ResonanceWidths. Could have been +// inline in .h, except for problems with forward declarations. + +void ParticleDataEntry::setResonancePtr( + ResonanceWidths* resonancePtrIn) { + if (resonancePtr == resonancePtrIn) return; + if (resonancePtr != 0) delete resonancePtr; + resonancePtr = resonancePtrIn; +} + +void ParticleDataEntry::resInit(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, CoupSM* coupSMPtrIn) { + if (resonancePtr != 0) resonancePtr->init(infoPtrIn, settingsPtrIn, + particleDataPtrIn, coupSMPtrIn); +} + +double ParticleDataEntry::resWidth(int idSgn, double mHat, int idIn, + bool openOnly, bool setBR) { + return (resonancePtr != 0) ? resonancePtr->width( idSgn, mHat, + idIn, openOnly, setBR) : 0.; +} + +double ParticleDataEntry::resWidthOpen(int idSgn, double mHat, int idIn) { + return (resonancePtr != 0) ? resonancePtr->widthOpen( idSgn, mHat, idIn) + : 0.; +} + +double ParticleDataEntry::resWidthStore(int idSgn, double mHat, int idIn) { + return (resonancePtr != 0) ? resonancePtr->widthStore( idSgn, mHat, idIn) + : 0.; +} + +double ParticleDataEntry::resOpenFrac(int idSgn) { + return (resonancePtr != 0) ? resonancePtr->openFrac(idSgn) : 1.; +} + +double ParticleDataEntry::resWidthRescaleFactor() { + return (resonancePtr != 0) ? resonancePtr->widthRescaleFactor() : 1.; +} + +double ParticleDataEntry::resWidthChan(double mHat, int idAbs1, + int idAbs2) { + return (resonancePtr != 0) ? resonancePtr->widthChan( mHat, idAbs1, + idAbs2) : 0.; +} + +//-------------------------------------------------------------------------- + +// Constituent masses for (d, u, s, c, b) quarks and diquarks. +// Hardcoded in CONSTITUENTMASSTABLE so that they are not overwritten +// by mistake, and separated from the "normal" masses. +// Called both by setDefaults and setM0 so kept as separate method. + +void ParticleDataEntry::setConstituentMass() { + + // Equate with the normal masses as default guess. + constituentMassSave = m0Save; + + // Quark masses trivial. + if (idSave < 6) constituentMassSave = CONSTITUENTMASSTABLE[idSave]; + + // Diquarks as simple sum of constituent quarks. + if (idSave > 1000 && idSave < 10000 && (idSave/10)%10 == 0) { + int id1 = idSave/1000; + int id2 = (idSave/100)%10; + if (id1 <6 && id2 < 6) constituentMassSave + = CONSTITUENTMASSTABLE[id1] + CONSTITUENTMASSTABLE[id2]; + } + +} + +//-------------------------------------------------------------------------- + +// Convert string to lowercase for case-insensitive comparisons. + +string ParticleDataEntry::toLower(const string& nameConv) { + + string temp(nameConv); + for (int i = 0; i < int(temp.length()); ++i) + temp[i] = std::tolower(temp[i]); + return temp; + +} + +//========================================================================== + +// ParticleData class. +// This class holds a map of all ParticleDataEntries, +// each entry containing info on a particle species. + +//-------------------------------------------------------------------------- + +// Get data to be distributed among particles during setp. + +void ParticleData::initCommon() { + + // Mass generation: fixed mass or linear/quadratic Breit-Wigner. + modeBreitWigner = settingsPtr->mode("ParticleData:modeBreitWigner"); + + // Maximum tail enhancement when adding threshold factor to Breit-Wigner. + maxEnhanceBW = settingsPtr->parm("ParticleData:maxEnhanceBW"); + + // Find initial MSbar masses for five light flavours. + mQRun[1] = settingsPtr->parm("ParticleData:mdRun"); + mQRun[2] = settingsPtr->parm("ParticleData:muRun"); + mQRun[3] = settingsPtr->parm("ParticleData:msRun"); + mQRun[4] = settingsPtr->parm("ParticleData:mcRun"); + mQRun[5] = settingsPtr->parm("ParticleData:mbRun"); + mQRun[6] = settingsPtr->parm("ParticleData:mtRun"); + + // Find Lambda5 value to use in running of MSbar masses. + double alphaSvalue = settingsPtr->parm("ParticleData:alphaSvalueMRun"); + AlphaStrong alphaS; + alphaS.init( alphaSvalue, 1); + Lambda5Run = alphaS.Lambda5(); + +} + +//-------------------------------------------------------------------------- + +// Initialize pointer for particles to the full database, the Breit-Wigners +// of normal hadrons and the ResonanceWidths of resonances. For the latter +// the order of initialization is essential to get secondary widths right. + +void ParticleData::initWidths( vector resonancePtrs) { + + // Pointer to database and Breit-Wigner mass initialization for each + // particle. + ResonanceWidths* resonancePtr = 0; + for (map::iterator pdtEntry = pdt.begin(); + pdtEntry != pdt.end(); ++pdtEntry) { + ParticleDataEntry& pdtNow = pdtEntry->second; + pdtNow.initPtr( this); + pdtNow.initBWmass(); + + // Remove any existing resonances. + resonancePtr = pdtNow.getResonancePtr(); + if (resonancePtr != 0) pdtNow.setResonancePtr(0); + } + + // Begin set up new resonance objects. + // Z0, W+- and top are almost always needed. + resonancePtr = new ResonanceGmZ(23); + setResonancePtr( 23, resonancePtr); + resonancePtr = new ResonanceW(24); + setResonancePtr( 24, resonancePtr); + resonancePtr = new ResonanceTop(6); + setResonancePtr( 6, resonancePtr); + + // Higgs in SM. + if (!settingsPtr->flag("Higgs:useBSM")) { + resonancePtr = new ResonanceH(0, 25); + setResonancePtr( 25, resonancePtr); + + // Higgses in BSM. + } else { + resonancePtr = new ResonanceH(1, 25); + setResonancePtr( 25, resonancePtr); + resonancePtr = new ResonanceH(2, 35); + setResonancePtr( 35, resonancePtr); + resonancePtr = new ResonanceH(3, 36); + setResonancePtr( 36, resonancePtr); + resonancePtr = new ResonanceHchg(37); + setResonancePtr( 37, resonancePtr); + } + + // A fourth generation: b', t', tau', nu'_tau. + resonancePtr = new ResonanceFour(7); + setResonancePtr( 7, resonancePtr); + resonancePtr = new ResonanceFour(8); + setResonancePtr( 8, resonancePtr); + resonancePtr = new ResonanceFour(17); + setResonancePtr( 17, resonancePtr); + resonancePtr = new ResonanceFour(18); + setResonancePtr( 18, resonancePtr); + + // New gauge bosons: Z', W', R. + resonancePtr = new ResonanceZprime(32); + setResonancePtr( 32, resonancePtr); + resonancePtr = new ResonanceWprime(34); + setResonancePtr( 34, resonancePtr); + resonancePtr = new ResonanceRhorizontal(41); + setResonancePtr( 41, resonancePtr); + + // A leptoquark. + resonancePtr = new ResonanceLeptoquark(42); + setResonancePtr( 42, resonancePtr); + + // Excited quarks and leptons. + for (int i = 1; i < 7; ++i) { + resonancePtr = new ResonanceExcited(4000000 + i); + setResonancePtr( 4000000 + i, resonancePtr); + } + for (int i = 11; i < 17; ++i) { + resonancePtr = new ResonanceExcited(4000000 + i); + setResonancePtr( 4000000 + i, resonancePtr); + } + + // An excited graviton/gluon in extra-dimensional scenarios. + resonancePtr = new ResonanceGraviton(5100039); + setResonancePtr( 5100039, resonancePtr); + resonancePtr = new ResonanceKKgluon(5100021); + setResonancePtr( 5100021, resonancePtr); + + // A left-right-symmetric scenario with new righthanded neutrinos, + // righthanded gauge bosons and doubly charged Higgses. + resonancePtr = new ResonanceNuRight(9900012); + setResonancePtr( 9900012, resonancePtr); + resonancePtr = new ResonanceNuRight(9900014); + setResonancePtr( 9900014, resonancePtr); + resonancePtr = new ResonanceNuRight(9900016); + setResonancePtr( 9900016, resonancePtr); + resonancePtr = new ResonanceZRight(9900023); + setResonancePtr( 9900023, resonancePtr); + resonancePtr = new ResonanceWRight(9900024); + setResonancePtr( 9900024, resonancePtr); + resonancePtr = new ResonanceHchgchgLeft(9900041); + setResonancePtr( 9900041, resonancePtr); + resonancePtr = new ResonanceHchgchgRight(9900042); + setResonancePtr( 9900042, resonancePtr); + + // Attach user-defined external resonances and do basic initialization. + for (int i = 0; i < int(resonancePtrs.size()); ++i) { + int idNow = resonancePtrs[i]->id(); + resonancePtrs[i]->initBasic(idNow); + setResonancePtr( idNow, resonancePtrs[i]); + } + + // Set up lists to order resonances in ascending mass. + vector idOrdered; + vector m0Ordered; + + // Put Z0 and W+- first, since known to be SM and often off-shell. + idOrdered.push_back(23); + m0Ordered.push_back(m0(23)); + idOrdered.push_back(24); + m0Ordered.push_back(m0(24)); + + // Loop through particle table to find resonances. + for (map::iterator pdtEntry = pdt.begin(); + pdtEntry != pdt.end(); ++pdtEntry) { + ParticleDataEntry& pdtNow = pdtEntry->second; + int idNow = pdtNow.id(); + + // Set up a simple default object for uninitialized resonances. + if (pdtNow.isResonance() && pdtNow.getResonancePtr() == 0) { + resonancePtr = new ResonanceGeneric(idNow); + setResonancePtr( idNow, resonancePtr); + } + + // Insert resonances in ascending mass, to respect decay hierarchies. + if (pdtNow.getResonancePtr() != 0 && idNow != 23 && idNow != 24) { + double m0Now = pdtNow.m0(); + idOrdered.push_back(idNow); + m0Ordered.push_back(m0Now); + for (int i = int(idOrdered.size()) - 2; i > 1; --i) { + if (m0Ordered[i] < m0Now) break; + swap( idOrdered[i], idOrdered[i + 1]); + swap( m0Ordered[i], m0Ordered[i + 1]); + } + } + } + + // Initialize the resonances in ascending mass order. + for (int i = 0; i < int(idOrdered.size()); ++i) resInit( idOrdered[i]); + +} + +//-------------------------------------------------------------------------- + +// Read in database from specific XML file (which may refer to others). + +bool ParticleData::readXML(string inFile, bool reset) { + + // Normally reset whole database before beginning. + if (reset) {pdt.clear(); isInit = false;} + + // List of files to be checked. + vector files; + files.push_back(inFile); + + // Loop over files. Open them for read. + for (int i = 0; i < int(files.size()); ++i) { + const char* cstring = files[i].c_str(); + ifstream is(cstring); + + // Check that instream is OK. + if (!is.good()) { + infoPtr->errorMsg("Error in ParticleData::readXML:" + " did not find file", files[i]); + return false; + } + + // Read in one line at a time. + particlePtr = 0; + string line; + while ( getline(is, line) ) { + + // Get first word of a line. + istringstream getfirst(line); + string word1; + getfirst >> word1; + + // Check for occurence of a particle. Add any continuation lines. + if (word1 == "") == string::npos) { + string addLine; + getline(is, addLine); + line += addLine; + } + + // Read in particle properties. + int idTmp = intAttributeValue( line, "id"); + string nameTmp = attributeValue( line, "name"); + string antiNameTmp = attributeValue( line, "antiName"); + if (antiNameTmp == "") antiNameTmp = "void"; + int spinTypeTmp = intAttributeValue( line, "spinType"); + int chargeTypeTmp = intAttributeValue( line, "chargeType"); + int colTypeTmp = intAttributeValue( line, "colType"); + double m0Tmp = doubleAttributeValue( line, "m0"); + double mWidthTmp = doubleAttributeValue( line, "mWidth"); + double mMinTmp = doubleAttributeValue( line, "mMin"); + double mMaxTmp = doubleAttributeValue( line, "mMax"); + double tau0Tmp = doubleAttributeValue( line, "tau0"); + + // Erase if particle already exists. + if (isParticle(idTmp)) pdt.erase(idTmp); + + // Store new particle. Save pointer, to be used for decay channels. + addParticle( idTmp, nameTmp, antiNameTmp, spinTypeTmp, chargeTypeTmp, + colTypeTmp, m0Tmp, mWidthTmp, mMinTmp, mMaxTmp, tau0Tmp); + particlePtr = particleDataEntryPtr(idTmp); + + // Check for occurence of a decay channel. Add any continuation lines. + } else if (word1 == "") == string::npos) { + string addLine; + getline(is, addLine); + line += addLine; + } + + // Read in channel properties - products so far only as a string. + int onMode = intAttributeValue( line, "onMode"); + double bRatio = doubleAttributeValue( line, "bRatio"); + int meMode = intAttributeValue( line, "meMode"); + string products = attributeValue( line, "products"); + + // Read in decay products from stream. Must have at least one. + istringstream prodStream(products); + int prod0 = 0; int prod1 = 0; int prod2 = 0; int prod3 = 0; + int prod4 = 0; int prod5 = 0; int prod6 = 0; int prod7 = 0; + prodStream >> prod0 >> prod1 >> prod2 >> prod3 >> prod4 >> prod5 + >> prod6 >> prod7; + if (prod0 == 0) { + infoPtr->errorMsg("Error in ParticleData::readXML:" + " incomplete decay channel", line); + return false; + } + + // Store new channel (if particle already known). + if (particlePtr == 0) { + infoPtr->errorMsg("Error in ParticleData::readXML:" + " orphan decay channel", line); + return false; + } + particlePtr->addChannel(onMode, bRatio, meMode, prod0, prod1, + prod2, prod3, prod4, prod5, prod6, prod7); + + // Check for occurence of a file also to be read. + } else if (word1 == "errorMsg("Warning in ParticleData::readXML:" + " skip unrecognized file name", line); + } else files.push_back(file); + } + + // End of loop over lines in input file and loop over files. + }; + }; + + // All particle data at this stage defines baseline original. + if (reset) for (map::iterator pdtEntry + = pdt.begin(); pdtEntry != pdt.end(); ++pdtEntry) { + particlePtr = &pdtEntry->second; + particlePtr->setHasChanged(false); + } + + // Done. + isInit = true; + return true; + +} + +//-------------------------------------------------------------------------- + +// Print out complete database in numerical order as an XML file. + +void ParticleData::listXML(string outFile) { + + // Convert file name to ofstream. + const char* cstring = outFile.c_str(); + ofstream os(cstring); + + // Iterate through the particle data table. + for (map::iterator pdtEntry + = pdt.begin(); pdtEntry != pdt.end(); ++pdtEntry) { + particlePtr = &pdtEntry->second; + + // Print particle properties. + os << "id() << "\"" + << " name=\"" << particlePtr->name() << "\""; + if (particlePtr->hasAnti()) + os << " antiName=\"" << particlePtr->name(-1) << "\""; + os << " spinType=\"" << particlePtr->spinType() << "\"" + << " chargeType=\"" << particlePtr->chargeType() << "\"" + << " colType=\"" << particlePtr->colType() << "\"\n"; + // Pick format for mass and width based on mass value. + double m0Now = particlePtr->m0(); + if (m0Now == 0 || (m0Now > 0.1 && m0Now < 1000.)) + os << fixed << setprecision(5); + else os << scientific << setprecision(3); + os << " m0=\"" << m0Now << "\""; + if (particlePtr->mWidth() > 0.) + os << " mWidth=\"" << particlePtr->mWidth() << "\"" + << " mMin=\"" << particlePtr->mMin() << "\"" + << " mMax=\"" << particlePtr->mMax() << "\""; + if (particlePtr->tau0() > 0.) os << scientific << setprecision(5) + << " tau0=\"" << particlePtr->tau0() << "\""; + os << ">\n"; + + // Loop through the decay channel table for each particle. + if (particlePtr->sizeChannels() > 0) { + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + const DecayChannel& channel = particlePtr->channel(i); + int mult = channel.multiplicity(); + + // Print decay channel properties. + os << " 0) + os << " meMode=\"" << channel.meMode() << "\""; + os << " products=\""; + for (int j = 0; j < mult; ++j) { + os << channel.product(j); + if (j < mult - 1) os << " "; + } + + // Finish off line and loop over allowed decay channels. + os << "\"/>\n"; + } + } + + // Finish off existing particle. + os << "\n\n"; + + } + +} + +//-------------------------------------------------------------------------- + +// Read in database from specific free format file. + +bool ParticleData::readFF(string inFile, bool reset) { + + // Normally reset whole database before beginning. + if (reset) {pdt.clear(); isInit = false;} + + // Open file for read and check that instream is OK. + const char* cstring = inFile.c_str(); + ifstream is(cstring); + if (!is.good()) { + infoPtr->errorMsg("Error in ParticleData::readFF:" + " did not find file", inFile); + return false; + } + + // Read in one line at a time. + particlePtr = 0; + string line; + bool readParticle = false; + while ( getline(is, line) ) { + + // Empty lines begins new particle. + if (line.find_first_not_of(" \n\t\v\b\r\f\a") == string::npos) { + readParticle = true; + continue; + } + + // Prepare to use standard read from line. + istringstream readLine(line); + + // Read in a line with particle information. + if (readParticle) { + + // Properties to be read. + int idTmp; + string nameTmp, antiNameTmp; + int spinTypeTmp, chargeTypeTmp, colTypeTmp; + double m0Tmp, mWidthTmp, mMinTmp, mMaxTmp, tau0Tmp; + string mayTmp; + + // Do the reading. + readLine >> idTmp >> nameTmp >> antiNameTmp >> spinTypeTmp + >> chargeTypeTmp >> colTypeTmp >> m0Tmp >> mWidthTmp + >> mMinTmp >> mMaxTmp >> tau0Tmp; + + // Error printout if something went wrong. + if (!readLine) { + infoPtr->errorMsg("Error in ParticleData::readFF:" + " incomplete particle", line); + return false; + } + + // Erase if particle already exists. + if (isParticle(idTmp)) pdt.erase(idTmp); + + // Store new particle. Save pointer, to be used for decay channels. + addParticle( idTmp, nameTmp, antiNameTmp, spinTypeTmp, chargeTypeTmp, + colTypeTmp, m0Tmp, mWidthTmp, mMinTmp, mMaxTmp, tau0Tmp); + particlePtr = particleDataEntryPtr(idTmp); + readParticle = false; + + // Read in a line with decay channel information. + } else { + + // Properties to be read. + int onMode = 0; + double bRatio = 0.; + int meMode = 0; + int prod0 = 0; int prod1 = 0; int prod2 = 0; int prod3 = 0; + int prod4 = 0; int prod5 = 0; int prod6 = 0; int prod7 = 0; + + // Read in data from stream. Need at least one decay product. + readLine >> onMode >> bRatio >> meMode >> prod0; + if (!readLine) { + infoPtr->errorMsg("Error in ParticleData::readFF:" + " incomplete decay channel", line); + return false; + } + readLine >> prod1 >> prod2 >> prod3 >> prod4 >> prod5 + >> prod6 >> prod7; + + // Store new channel. + if (particlePtr == 0) { + infoPtr->errorMsg("Error in ParticleData::readFF:" + " orphan decay channel", line); + return false; + } + particlePtr->addChannel(onMode, bRatio, meMode, prod0, prod1, + prod2, prod3, prod4, prod5, prod6, prod7); + + } + + // End of while loop over lines in the file. + } + + + // Done. + isInit = true; + return true; + +} + +//-------------------------------------------------------------------------- + +// Print out complete database in numerical order as a free format file. + +void ParticleData::listFF(string outFile) { + + // Convert file name to ofstream. + const char* cstring = outFile.c_str(); + ofstream os(cstring); + + // Iterate through the particle data table. + for (map::iterator pdtEntry + = pdt.begin(); pdtEntry != pdt.end(); ++pdtEntry) { + particlePtr = &pdtEntry->second; + + // Pick format for mass and width based on mass value. + double m0Now = particlePtr->m0(); + if (m0Now == 0 || (m0Now > 0.1 && m0Now < 1000.)) + os << fixed << setprecision(5); + else os << scientific << setprecision(3); + + // Print particle properties. + os << "\n" << setw(8) << particlePtr->id() << " " + << left << setw(16) << particlePtr->name() << " " + << setw(16) << particlePtr->name(-1) << " " + << right << setw(2) << particlePtr->spinType() << " " + << setw(2) << particlePtr->chargeType() << " " + << setw(2) << particlePtr->colType() << " " + << setw(10) << particlePtr->m0() << " " + << setw(10) << particlePtr->mWidth() << " " + << setw(10) << particlePtr->mMin() << " " + << setw(10) << particlePtr->mMax() << " " + << scientific << setprecision(5) + << setw(12) << particlePtr->tau0() << "\n"; + + // Loop through the decay channel table for each particle. + if (particlePtr->sizeChannels() > 0) { + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + const DecayChannel& channel = particlePtr->channel(i); + os << " " << setw(6) << channel.onMode() + << " " << fixed << setprecision(7) << setw(10) + << channel.bRatio() << " " + << setw(3) << channel.meMode() << " "; + for (int j = 0; j < channel.multiplicity(); ++j) + os << setw(8) << channel.product(j) << " "; + os << "\n"; + } + } + + } + +} + +//-------------------------------------------------------------------------- + +// Read in updates from a character string, like a line of a file. +// Is used by readString (and readFile) in Pythia. + + bool ParticleData::readString(string lineIn, bool warn, ostream& os) { + + // If empty line then done. + if (lineIn.find_first_not_of(" \n\t\v\b\r\f\a") == string::npos) return true; + + // Take copy that will be modified. + string line = lineIn; + + // If first character is not a digit then taken to be a comment. + int firstChar = line.find_first_not_of(" \n\t\v\b\r\f\a"); + if (!isdigit(line[firstChar])) return true; + + // Replace colons and equal signs by blanks to make parsing simpler. + for ( int j = 0; j < int(line.size()); ++ j) + if (line[j] == ':' || line[j] == '=') line[j] = ' '; + + // Get particle id and property name. + int idTmp; + string property; + istringstream getWord(line); + getWord >> idTmp >> property; + property = toLower(property); + + // Check that valid particle. + if ( (!isParticle(idTmp) && property != "all" && property != "new") + || idTmp <= 0) { + if (warn) os << "\n Warning: input particle not found in Particle" + << " Data Table; skip:\n " << lineIn << "\n"; + return false; + } + + // Identify particle property and read + set its value, case by case. + if (property == "name") { + string nameTmp; + getWord >> nameTmp; + pdt[idTmp].setName(nameTmp); + return true; + } + if (property == "antiname") { + string antiNameTmp; + getWord >> antiNameTmp; + pdt[idTmp].setAntiName(antiNameTmp); + return true; + } + if (property == "names") { + string nameTmp, antiNameTmp; + getWord >> nameTmp >> antiNameTmp; + pdt[idTmp].setNames(nameTmp, antiNameTmp); + return true; + } + if (property == "spintype") { + int spinTypeTmp; + getWord >> spinTypeTmp; + pdt[idTmp].setSpinType(spinTypeTmp); + return true; + } + if (property == "chargetype") { + int chargeTypeTmp; + getWord >> chargeTypeTmp; + pdt[idTmp].setChargeType(chargeTypeTmp); + return true; + } + if (property == "coltype") { + int colTypeTmp; + getWord >> colTypeTmp; + pdt[idTmp].setColType(colTypeTmp); + return true; + } + if (property == "m0") { + double m0Tmp; + getWord >> m0Tmp; + pdt[idTmp].setM0(m0Tmp); + return true; + } + if (property == "mwidth") { + double mWidthTmp; + getWord >> mWidthTmp; + pdt[idTmp].setMWidth(mWidthTmp); + return true; + } + if (property == "mmin") { + double mMinTmp; + getWord >> mMinTmp; + pdt[idTmp].setMMin(mMinTmp); + return true; + } + if (property == "mmax") { + double mMaxTmp; + getWord >> mMaxTmp; + pdt[idTmp].setMMax(mMaxTmp); + return true; + } + if (property == "tau0") { + double tau0Tmp; + getWord >> tau0Tmp; + pdt[idTmp].setTau0(tau0Tmp); + return true; + } + if (property == "isresonance") { + string isresTmp; + getWord >> isresTmp; + bool isResonanceTmp = boolString(isresTmp); + pdt[idTmp].setIsResonance(isResonanceTmp); + return true; + } + if (property == "maydecay") { + string mayTmp; + getWord >> mayTmp; + bool mayDecayTmp = boolString(mayTmp); + pdt[idTmp].setMayDecay(mayDecayTmp); + return true; + } + if (property == "doexternaldecay") { + string extdecTmp; + getWord >> extdecTmp; + bool doExternalDecayTmp = boolString(extdecTmp); + pdt[idTmp].setDoExternalDecay(doExternalDecayTmp); + return true; + } + if (property == "isvisible") { + string isvisTmp; + getWord >> isvisTmp; + bool isVisibleTmp = boolString(isvisTmp); + pdt[idTmp].setIsVisible(isVisibleTmp); + return true; + } + if (property == "doforcewidth") { + string doforceTmp; + getWord >> doforceTmp; + bool doForceWidthTmp = boolString(doforceTmp); + pdt[idTmp].setDoForceWidth(doForceWidthTmp); + return true; + } + + // Addition or complete replacement of a particle. + if (property == "all" || property == "new") { + + // Default values for properties to be read. + string nameTmp = "void"; + string antiNameTmp = "void"; + int spinTypeTmp = 0; + int chargeTypeTmp = 0; + int colTypeTmp = 0; + double m0Tmp = 0.; + double mWidthTmp = 0.; + double mMinTmp = 0.; + double mMaxTmp = 0.; + double tau0Tmp = 0.; + + // Read in data from stream. + getWord >> nameTmp >> antiNameTmp >> spinTypeTmp >> chargeTypeTmp + >> colTypeTmp >> m0Tmp >> mWidthTmp >> mMinTmp >> mMaxTmp + >> tau0Tmp; + + // To keep existing decay channels, only overwrite particle data. + if (property == "all" && isParticle(idTmp)) { + setAll( idTmp, nameTmp, antiNameTmp, spinTypeTmp, chargeTypeTmp, + colTypeTmp, m0Tmp, mWidthTmp, mMinTmp, mMaxTmp, tau0Tmp); + + // Else start over completely from scratch. + } else { + if (isParticle(idTmp)) pdt.erase(idTmp); + addParticle( idTmp, nameTmp, antiNameTmp, spinTypeTmp, chargeTypeTmp, + colTypeTmp, m0Tmp, mWidthTmp, mMinTmp, mMaxTmp, tau0Tmp); + } + return true; + } + + // Set onMode of all decay channels in one go. + if (property == "onmode") { + int onMode = 0; + string onModeIn; + getWord >> onModeIn; + // For onMode allow the optional possibility of Bool input. + if (isdigit(onModeIn[0])) { + istringstream getOnMode(onModeIn); + getOnMode >> onMode; + } else onMode = (boolString(onModeIn)) ? 1 : 0; + for (int i = 0; i < pdt[idTmp].sizeChannels(); ++i) + pdt[idTmp].channel(i).onMode(onMode); + return true; + } + + // Selective search for matching decay channels. + int matchKind = 0; + if (property == "offifany" || property == "onifany" || + property == "onposifany" || property == "onnegifany") matchKind = 1; + if (property == "offifall" || property == "onifall" || + property == "onposifall" || property == "onnegifall") matchKind = 2; + if (property == "offifmatch" || property == "onifmatch" || + property == "onposifmatch" || property == "onnegifmatch") matchKind = 3; + if (matchKind > 0) { + int onMode = 0; + if (property == "onifany" || property == "onifall" + || property == "onifmatch") onMode = 1; + if (property == "onposifany" || property == "onposifall" + || property == "onposifmatch") onMode = 2; + if (property == "onnegifany" || property == "onnegifall" + || property == "onnegifmatch") onMode = 3; + + // Read in particles to match. + vector idToMatch; + int idRead; + for ( ; ; ) { + getWord >> idRead; + if (!getWord) break; + idToMatch.push_back(abs(idRead)); + } + int nToMatch = idToMatch.size(); + + // Loop over all decay channels. + for (int i = 0; i < pdt[idTmp].sizeChannels(); ++i) { + int multi = pdt[idTmp].channel(i).multiplicity(); + + // Look for any match at all. + if (matchKind == 1) { + bool foundMatch = false; + for (int j = 0; j < multi; ++j) { + int idNow = abs(pdt[idTmp].channel(i).product(j)); + for (int k = 0; k < nToMatch; ++k) + if (idNow == idToMatch[k]) {foundMatch = true; break;} + if (foundMatch) break; + } + if (foundMatch) pdt[idTmp].channel(i).onMode(onMode); + + // Look for match of all products provided. + } else { + int nUnmatched = nToMatch; + if (multi < nToMatch); + else if (multi > nToMatch && matchKind == 3); + else { + vector idUnmatched; + for (int k = 0; k < nToMatch; ++k) + idUnmatched.push_back(idToMatch[k]); + for (int j = 0; j < multi; ++j) { + int idNow = abs(pdt[idTmp].channel(i).product(j)); + for (int k = 0; k < nUnmatched; ++k) + if (idNow == idUnmatched[k]) { + idUnmatched[k] = idUnmatched[--nUnmatched]; + break; + } + if (nUnmatched == 0) break; + } + } + if (nUnmatched == 0) pdt[idTmp].channel(i).onMode(onMode); + } + } + return true; + } + + // Rescale all branching ratios by common factor. + if (property == "rescalebr") { + double factor; + getWord >> factor; + pdt[idTmp].rescaleBR(factor); + return true; + } + + // Reset decay table in preparation for new input. + if (property == "onechannel") pdt[idTmp].clearChannels(); + + // Add or change a decay channel: get channel number and new property. + if (property == "addchannel" || property == "onechannel" + || isdigit(property[0])) { + int channel; + if (property == "addchannel" || property == "onechannel") { + pdt[idTmp].addChannel(); + channel = pdt[idTmp].sizeChannels() - 1; + property = "all"; + } else{ + istringstream getChannel(property); + getChannel >> channel; + getWord >> property; + property = toLower(property); + } + + // Check that channel exists. + if (channel < 0 || channel >= pdt[idTmp].sizeChannels()) return false; + + // Find decay channel property and value, case by case. + // At same time also do case where all should be replaced. + if (property == "onmode" || property == "all") { + int onMode = 0; + string onModeIn; + getWord >> onModeIn; + // For onMode allow the optional possibility of Bool input. + if (isdigit(onModeIn[0])) { + istringstream getOnMode(onModeIn); + getOnMode >> onMode; + } else onMode = (boolString(onModeIn)) ? 1 : 0; + pdt[idTmp].channel(channel).onMode(onMode); + if (property == "onmode") return true; + } + if (property == "bratio" || property == "all") { + double bRatio; + getWord >> bRatio; + pdt[idTmp].channel(channel).bRatio(bRatio); + if (property == "bratio") return true; + } + if (property == "memode" || property == "all") { + int meMode; + getWord >> meMode; + pdt[idTmp].channel(channel).meMode(meMode); + if (property == "memode") return true; + } + + // Scan for products until end of line. + if (property == "products" || property == "all") { + int nProd = 0; + for (int iProd = 0; iProd < 8; ++iProd) { + int idProd; + getWord >> idProd; + if (!getWord) break; + pdt[idTmp].channel(channel).product(iProd, idProd); + ++nProd; + } + for (int iProd = nProd; iProd < 8; ++iProd) + pdt[idTmp].channel(channel).product(iProd, 0); + pdt[idTmp].channel(channel).multiplicity(nProd); + return true; + } + + // Rescale an existing branching ratio. + if (property == "rescalebr") { + double factor; + getWord >> factor; + pdt[idTmp].channel(channel).rescaleBR(factor); + return true; + } + } + + // Return false if failed to recognize property. + if (warn) os << "\n Warning: input property not found in Particle" + << " Data Table; skip:\n " << lineIn << "\n"; + return false; + +} + +//-------------------------------------------------------------------------- + +// Print out complete or changed table of database in numerical order. + +void ParticleData::list(bool changedOnly, bool changedRes, ostream& os) { + + // Table header; output for bool as off/on. + if (!changedOnly) { + os << "\n -------- PYTHIA Particle Data Table (complete) --------" + << "------------------------------------------------------------" + << "--------------\n \n"; + + } else { + os << "\n -------- PYTHIA Particle Data Table (changed only) ----" + << "------------------------------------------------------------" + << "--------------\n \n"; + } + os << " id name antiName spn chg col m0" + << " mWidth mMin mMax tau0 res dec ext " + << "vis wid\n no onMode bRatio meMode products \n"; + + // Iterate through the particle data table. Option to skip unchanged. + int nList = 0; + for (map::iterator pdtEntry + = pdt.begin(); pdtEntry != pdt.end(); ++pdtEntry) { + particlePtr = &pdtEntry->second; + if ( !changedOnly || particlePtr->hasChanged() || + ( changedRes && particlePtr->getResonancePtr() != 0 ) ) { + + // Pick format for mass and width based on mass value. + double m0Now = particlePtr->m0(); + if (m0Now == 0 || (m0Now > 0.1 && m0Now < 1000.)) + os << fixed << setprecision(5); + else os << scientific << setprecision(3); + + // Print particle properties. + ++nList; + string antiNameTmp = particlePtr->name(-1); + if (antiNameTmp == "void") antiNameTmp = " "; + os << "\n" << setw(8) << particlePtr->id() << " " + << left << setw(16) << particlePtr->name() << " " + << setw(16) << antiNameTmp << " " + << right << setw(2) << particlePtr->spinType() << " " + << setw(2) << particlePtr->chargeType() << " " + << setw(2) << particlePtr->colType() << " " + << setw(10) << particlePtr->m0() << " " + << setw(10) << particlePtr->mWidth() << " " + << setw(10) << particlePtr->mMin() << " " + << setw(10) << particlePtr->mMax() << " " + << scientific << setprecision(5) + << setw(12) << particlePtr->tau0() << " " << setw(2) + << particlePtr->isResonance() << " " << setw(2) + << (particlePtr->mayDecay() && particlePtr->canDecay()) + << " " << setw(2) << particlePtr->doExternalDecay() << " " + << setw(2) << particlePtr->isVisible()<< " " + << setw(2) << particlePtr->doForceWidth() << "\n"; + + // Loop through the decay channel table for each particle. + if (particlePtr->sizeChannels() > 0) { + for (int i = 0; i < int(particlePtr->sizeChannels()); ++i) { + const DecayChannel& channel = particlePtr->channel(i); + os << " " << setprecision(7) + << setw(5) << i + << setw(6) << channel.onMode() + << fixed<< setw(12) << channel.bRatio() + << setw(5) << channel.meMode() << " "; + for (int j = 0; j < channel.multiplicity(); ++j) + os << setw(8) << channel.product(j) << " "; + os << "\n"; + } + } + } + + } + + // End of loop over database contents. + if (changedOnly && nList == 0) os << "\n no particle data has been " + << "changed from its default value \n"; + os << "\n -------- End PYTHIA Particle Data Table -----------------" + << "--------------------------------------------------------------" + << "----------\n" << endl; + +} + +//-------------------------------------------------------------------------- + +// Print out partial table of database in input order. + +void ParticleData::list(vector idList, ostream& os) { + + // Table header; output for bool as off/on. + os << "\n -------- PYTHIA Particle Data Table (partial) ---------" + << "------------------------------------------------------------" + << "--------------\n \n"; + os << " id name antiName spn chg col m0" + << " mWidth mMin mMax tau0 res dec ext " + << "vis wid\n no onMode bRatio meMode products \n"; + + // Iterate through the given list of input particles. + for (int i = 0; i < int(idList.size()); ++i) { + particlePtr = particleDataEntryPtr(idList[i]); + + // Pick format for mass and width based on mass value. + double m0Now = particlePtr->m0(); + if (m0Now == 0 || (m0Now > 0.1 && m0Now < 1000.)) + os << fixed << setprecision(5); + else os << scientific << setprecision(3); + + // Print particle properties. + string antiNameTmp = particlePtr->name(-1); + if (antiNameTmp == "void") antiNameTmp = " "; + os << "\n" << setw(8) << particlePtr->id() << " " + << left << setw(16) << particlePtr->name() << " " + << setw(16) << antiNameTmp << " " + << right << setw(2) << particlePtr->spinType() << " " + << setw(2) << particlePtr->chargeType() << " " + << setw(2) << particlePtr->colType() << " " + << setw(10) << particlePtr->m0() << " " + << setw(10) << particlePtr->mWidth() << " " + << setw(10) << particlePtr->mMin() << " " + << setw(10) << particlePtr->mMax() << " " + << scientific << setprecision(5) + << setw(12) << particlePtr->tau0() << " " << setw(2) + << particlePtr->isResonance() << " " << setw(2) + << (particlePtr->mayDecay() && particlePtr->canDecay()) + << " " << setw(2) << particlePtr->doExternalDecay() << " " + << setw(2) << particlePtr->isVisible() << " " + << setw(2) << particlePtr->doForceWidth() << "\n"; + + // Loop through the decay channel table for each particle. + if (particlePtr->sizeChannels() > 0) { + for (int j = 0; j < int(particlePtr->sizeChannels()); ++j) { + const DecayChannel& channel = particlePtr->channel(j); + os << " " << setprecision(7) + << setw(5) << j + << setw(6) << channel.onMode() + << fixed<< setw(12) << channel.bRatio() + << setw(5) << channel.meMode() << " "; + for (int k = 0; k < channel.multiplicity(); ++k) + os << setw(8) << channel.product(k) << " "; + os << "\n"; + } + } + + } + + // End of loop over database contents. + os << "\n -------- End PYTHIA Particle Data Table -----------------" + << "--------------------------------------------------------------" + << "----------\n" << endl; + +} + +//-------------------------------------------------------------------------- + +// Check that table makes sense: e.g. consistent names and mass ranges, +// that branching ratios sum to unity, that charge is conserved and +// that phase space is open in each channel. +// verbosity = 0: mimimal amount of checks, e.g. that no channels open. +// = 1: further warning if individual channels closed +// (except for resonances). +// = 2: also print branching-ratio-averaged threshold mass. +// = 11, 12: as 1, 2, but include resonances in detailed checks. + +void ParticleData::checkTable(int verbosity, ostream& os) { + + // Header. + os << "\n -------- PYTHIA Check of Particle Data Table ------------" + <<"------\n\n"; + int nErr = 0; + + // Loop through all particles. + for (map::iterator pdtEntry + = pdt.begin(); pdtEntry != pdt.end(); ++pdtEntry) { + particlePtr = &pdtEntry->second; + + // Extract some particle properties. Set some flags. + int idNow = particlePtr->id(); + bool hasAntiNow = particlePtr->hasAnti(); + int spinTypeNow = particlePtr->spinType(); + int chargeTypeNow = particlePtr->chargeType(); + int baryonTypeNow = particlePtr->baryonNumberType(); + double m0Now = particlePtr->m0(); + double mMinNow = particlePtr->mMin(); + double mMaxNow = particlePtr->mMax(); + double mWidthNow = particlePtr->mWidth(); + double tau0Now = particlePtr->tau0(); + bool isResonanceNow = particlePtr->isResonance(); + bool hasPrinted = false; + bool studyCloser = verbosity > 10 || !isResonanceNow; + + // Check that particle name consistent with charge information. + string particleName = particlePtr->name(1); + if (particleName.size() > 16) { + os << " Warning: particle " << idNow << " has name " << particleName + << " of length " << particleName.size() << "\n"; + hasPrinted = true; + ++nErr; + } + int nPos = 0; + int nNeg = 0; + for (int i = 0; i < int(particleName.size()); ++i) { + if (particleName[i] == '+') ++nPos; + if (particleName[i] == '-') ++nNeg; + } + if ( (nPos > 0 && nNeg > 0) || ( nPos + nNeg > 0 + && 3 * (nPos - nNeg) != chargeTypeNow )) { + os << " Warning: particle " << idNow << " has name " << particleName + << " inconsistent with charge type " << chargeTypeNow << "\n"; + hasPrinted = true; + ++nErr; + } + + // Check that antiparticle name consistent with charge information. + if (hasAntiNow) { + particleName = particlePtr->name(-1); + if (particleName.size() > 16) { + os << " Warning: particle " << idNow << " has name " << particleName + << " of length " << particleName.size() << "\n"; + hasPrinted = true; + ++nErr; + } + nPos = 0; + nNeg = 0; + for (int i = 0; i < int(particleName.size()); ++i) { + if (particleName[i] == '+') ++nPos; + if (particleName[i] == '-') ++nNeg; + } + if ( (nPos > 0 && nNeg > 0) || ( nPos + nNeg > 0 + && 3 * (nPos - nNeg) != -chargeTypeNow )) { + os << " Warning: particle " << -idNow << " has name " + << particleName << " inconsistent with charge type " + << -chargeTypeNow << "\n"; + hasPrinted = true; + ++nErr; + } + } + + // Check that mass, mass range and width are consistent. + if (particlePtr->useBreitWigner()) { + if (mMinNow > m0Now) { + os << " Error: particle " << idNow << " has mMin " + << fixed << setprecision(5) << mMinNow + << " larger than m0 " << m0Now << "\n"; + hasPrinted = true; + ++nErr; + } + if (mMaxNow > mMinNow && mMaxNow < m0Now) { + os << " Error: particle " << idNow << " has mMax " + << fixed << setprecision(5) << mMaxNow + << " smaller than m0 " << m0Now << "\n"; + hasPrinted = true; + ++nErr; + } + if (mMaxNow > mMinNow && mMaxNow - mMinNow < mWidthNow) { + os << " Warning: particle " << idNow << " has mMax - mMin " + << fixed << setprecision(5) << mMaxNow - mMinNow + << " smaller than mWidth " << mWidthNow << "\n"; + hasPrinted = true; + ++nErr; + } + } + + // Check that particle does not both have width and lifetime. + if (mWidthNow > 0. && tau0Now > 0.) { + os << " Warning: particle " << idNow << " has both nonvanishing width " + << scientific << setprecision(5) << mWidthNow << " and lifetime " + << tau0Now << "\n"; + hasPrinted = true; + ++nErr; + } + + // Begin study decay channels. + if (particlePtr->sizeChannels() > 0) { + + // Loop through all decay channels. + double bRatioSum = 0.; + double bRatioPos = 0.; + double bRatioNeg = 0.; + bool hasPosBR = false; + bool hasNegBR = false; + double threshMass = 0.; + bool openChannel = false; + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + + // Extract channel properties. + int onMode = particlePtr->channel(i).onMode(); + double bRatio = particlePtr->channel(i).bRatio(); + int meMode = particlePtr->channel(i).meMode(); + int mult = particlePtr->channel(i).multiplicity(); + int prod[8]; + for (int j = 0; j < 8; ++j) + prod[j] = particlePtr->channel(i).product(j); + + // Sum branching ratios. Include off-channels. + if (onMode == 0 || onMode == 1) bRatioSum += bRatio; + else if (onMode == 2) {bRatioPos += bRatio; hasPosBR = true;} + else if (onMode == 3) {bRatioNeg += bRatio; hasNegBR = true;} + + // Error printout when unknown decay product code. + for (int j = 0; j < 8; ++j) { + if ( prod[j] != 0 && !isParticle(prod[j]) ) { + os << " Error: unknown decay product for " << idNow + << " -> " << prod[j] << "\n"; + hasPrinted = true; + ++nErr; + continue; + } + } + + // Error printout when no decay products or 0 interspersed. + int nLast = 0; + for (int j = 0; j < 8; ++j) + if (prod[j] != 0) nLast = j + 1; + if (mult == 0 || mult != nLast) { + os << " Error: corrupted decay product list for " + << particlePtr->id() << " -> "; + for (int j = 0; j < 8; ++j) os << prod[j] << " "; + os << "\n"; + hasPrinted = true; + ++nErr; + continue; + } + + // Check charge conservation and open phase space in decay channel. + int chargeTypeSum = -chargeTypeNow; + int baryonTypeSum = -baryonTypeNow; + double avgFinalMass = 0.; + double minFinalMass = 0.; + bool canHandle = true; + for (int j = 0; j < mult; ++j) { + chargeTypeSum += chargeType( prod[j] ); + baryonTypeSum += baryonNumberType( prod[j] ); + avgFinalMass += m0( prod[j] ); + minFinalMass += m0Min( prod[j] ); + if (prod[j] == 81 || prod[j] == 82 || prod[j] == 83) + canHandle = false; + } + threshMass += bRatio * avgFinalMass; + + // Error printout when charge or baryon number not conserved. + if (chargeTypeSum != 0 && canHandle) { + os << " Error: 3*charge changed by " << chargeTypeSum + << " in " << idNow << " -> "; + for (int j = 0; j < mult; ++j) os << prod[j] << " "; + os << "\n"; + hasPrinted = true; + ++nErr; + continue; + } + if ( baryonTypeSum != 0 && canHandle && particlePtr->isHadron() ) { + os << " Error: 3*baryon number changed by " << baryonTypeSum + << " in " << idNow << " -> "; + for (int j = 0; j < mult; ++j) os << prod[j] << " "; + os << "\n"; + hasPrinted = true; + ++nErr; + continue; + } + + // Begin check that some matrix elements are used correctly. + bool correctME = true; + + // Check matrix element mode 0: recommended not into partons. + if (meMode == 0 && !isResonanceNow) { + bool hasPartons = false; + for (int j = 0; j < mult; ++j) { + int idAbs = abs(prod[j]); + if ( idAbs < 10 || idAbs == 21 || idAbs == 81 || idAbs == 82 + || idAbs == 83 || (idAbs > 1000 && idAbs < 10000 + && (idAbs/10)%10 == 0) ) hasPartons = true; + } + if (hasPartons) correctME = false; + } + + // Check matrix element mode 1: rho/omega -> pi+ pi- pi0. + bool useME1 = ( mult == 3 && spinTypeNow == 3 && idNow > 100 + && idNow < 1000 && particlePtr->channel(i).contains(211, -211, 111) ); + if ( meMode == 1 && !useME1 ) correctME = false; + if ( meMode != 1 && useME1 ) correctME = false; + + // Check matrix element mode 2: polarization in V -> PS + PS. + bool useME2 = ( mult == 2 && spinTypeNow == 3 && idNow > 100 + && idNow < 1000 && spinType(prod[0]) == 1 + && spinType(prod[1]) == 1 ); + if ( meMode == 2 && !useME2 ) correctME = false; + if ( meMode != 2 && useME2 ) correctME = false; + + // Check matrix element mode 11, 12 and 13: Dalitz decay with + // one or more particles in addition to the lepton pair, + // or double Dalitz decay. + bool useME11 = ( mult == 3 && !isResonanceNow + && (prod[1] == 11 || prod[1] == 13 || prod[1] == 15) + && prod[2] == -prod[1] ); + bool useME12 = ( mult > 3 && !isResonanceNow + && (prod[mult - 2] == 11 || prod[mult - 2] == 13 + || prod[mult - 2] == 15) && prod[mult - 1] == -prod[mult - 2] ); + bool useME13 = ( mult == 4 && !isResonanceNow + && (prod[0] == 11 || prod[0] == 13) && prod[1] == -prod[0] + && (prod[2] == 11 || prod[2] == 13) && prod[3] == -prod[2] ); + if (useME13) useME12 = false; + if ( meMode == 11 && !useME11 ) correctME = false; + if ( meMode != 11 && useME11 ) correctME = false; + if ( meMode == 12 && !useME12 ) correctME = false; + if ( meMode != 12 && useME12 ) correctME = false; + if ( meMode == 13 && !useME13 ) correctME = false; + if ( meMode != 13 && useME13 ) correctME = false; + + // Check matrix element mode 21: tau -> nu_tau hadrons. + bool useME21 = (idNow == 15 && mult > 2 && prod[0] == 16 + && abs(prod[1]) > 100); + if ( meMode == 21 && !useME21 ) correctME = false; + if ( meMode != 21 && useME21 ) correctME = false; + + // Check matrix element mode 22, but only for semileptonic decay. + // For a -> b c d require types u = 2, ubar = -2, d = 1, dbar = -1. + if ( isLepton(prod[0]) && isLepton(prod[1]) ) { + bool useME22 = false; + int typeA = 0; + int typeB = 0; + int typeC = 0; + if (particlePtr->isLepton()) { + typeA = (idNow > 0) ? 1 + (idNow-1)%2 : -1 - (1-idNow)%2; + } else if (particlePtr->isHadron()) { + int hQ = particlePtr->heaviestQuark(); + // Special case: for B_c either bbar or c decays. + if (idNow == 541 && heaviestQuark(prod[2]) == -5) hQ = 4; + typeA = (hQ > 0) ? 1 + (hQ-1)%2 : -1 - (1-hQ)%2; + } + typeB = (prod[0] > 0) ? 1 + (prod[0]-1)%2 : -1 - (1-prod[0])%2; + typeC = (prod[1] > 0) ? 1 + (prod[1]-1)%2 : -1 - (1-prod[1])%2; + // Special cases. + if ( (idNow == 130 || idNow == 310) && typeC * typeA < 0) + typeA = -typeA; + if (mult == 3 && idNow == 2112 && prod[2] == 2212) + typeA = 3 - typeA; + if (mult == 3 && idNow == 3222 && prod[2] == 3122) + typeA = 3 - typeA; + if (mult > 2 && typeC == typeA && typeB * typeC < 0 + && (typeB + typeC)%2 != 0) useME22 = true; + if ( meMode == 22 && !useME22 ) correctME = false; + if ( meMode != 22 && useME22 ) correctME = false; + } + + // Check for matrix element mode 31. + if (meMode == 31) { + int nGamma = 0; + for (int j = 0; j < mult; ++j) if (prod[j] == 22) ++nGamma; + if (nGamma != 1) correctME = false; + } + + // Check for unknown mode, or resonance-only mode. + if ( !isResonanceNow && (meMode < 0 || (meMode > 2 && meMode <= 10) + || (meMode > 13 && meMode <= 20) || (meMode > 23 && meMode <= 30) + || (meMode > 31 && meMode <= 41) || meMode == 51 || meMode == 61 + || meMode == 71 || (meMode > 80 && meMode <= 90) + || (!particlePtr->isOctetHadron() && meMode > 92) ) ) + correctME = false; + + // Print if incorrect matrix element mode. + if ( !correctME ) { + os << " Warning: meMode " << meMode << " used for " + << idNow << " -> "; + for (int j = 0; j < mult; ++j) os << prod[j] << " "; + os << "\n"; + hasPrinted = true; + ++nErr; + } + + // Warning printout when no phase space for decay. + if ( studyCloser && verbosity > 0 && canHandle && onMode > 0 + && particlePtr->m0Min() - minFinalMass < 0. ) { + if (particlePtr->m0Max() - minFinalMass < 0.) + os << " Error: decay never possible for "; + else os << " Warning: decay sometimes not possible for "; + os << idNow << " -> "; + for (int j = 0; j < mult; ++j) os << prod[j] << " "; + os << "\n"; + hasPrinted = true; + ++nErr; + } + + // End loop over decay channels. + if (onMode > 0 && bRatio > 0.) openChannel = true; + } + + // Optional printout of threshold. + if (verbosity%10 > 1 && particlePtr->useBreitWigner()) { + threshMass /= bRatioSum; + os << " Info: particle " << idNow << fixed << setprecision(5) + << " has average mass threshold " << threshMass + << " while mMin is " << mMinNow << "\n"; + hasPrinted = true; + } + + // Error printout when no acceptable decay channels found. + if (studyCloser && !openChannel) { + os << " Error: no acceptable decay channel found for particle " + << idNow << "\n"; + hasPrinted = true; + ++nErr; + } + + // Warning printout when branching ratios do not sum to unity. + if (studyCloser && (!hasAntiNow || (!hasPosBR && !hasNegBR)) + && abs(bRatioSum + bRatioPos - 1.) > 1e-8) { + os << " Warning: particle " << idNow << fixed << setprecision(8) + << " has branching ratio sum " << bRatioSum << "\n"; + hasPrinted = true; + ++nErr; + } else if (studyCloser && hasAntiNow + && (abs(bRatioSum + bRatioPos - 1.) > 1e-8 + || abs(bRatioSum + bRatioNeg - 1.) > 1e-8)) { + os << " Warning: particle " << idNow << fixed << setprecision(8) + << " has branching ratio sum " << bRatioSum + bRatioPos + << " while its antiparticle has " << bRatioSum + bRatioNeg + << "\n"; + hasPrinted = true; + ++nErr; + } + + // End study of decay channels and loop over particles. + } + if (hasPrinted) os << "\n"; + } + + // Final output. Done. + os << " Total number of errors and warnings is " << nErr << "\n"; + os << "\n -------- End PYTHIA Check of Particle Data Table --------" + << "------\n" << endl; + +} + +//-------------------------------------------------------------------------- + +// Return the id of the sequentially next particle stored in table. + +int ParticleData::nextId(int idIn) { + + // Return 0 for negative or unknown codes. Return first for 0. + if (idIn < 0 || (idIn > 0 && !isParticle(idIn))) return 0; + if (idIn == 0) return pdt.begin()->first; + + // Find pointer to current particle and step up. Return 0 if impossible. + map::const_iterator pdtIn = pdt.find(idIn); + if (pdtIn == pdt.end()) return 0; + return (++pdtIn)->first; + +} + +//-------------------------------------------------------------------------- + +// Fractional width associated with open channels of one or two resonances. + +double ParticleData::resOpenFrac(int id1In, int id2In, int id3In) { + + // Default value. + double answer = 1.; + + // First resonance. + if (isParticle(id1In)) answer = pdt[abs(id1In)].resOpenFrac(id1In); + + // Possibly second resonance. + if (isParticle(id2In)) answer *= pdt[abs(id2In)].resOpenFrac(id2In); + + // Possibly third resonance. + if (isParticle(id3In)) answer *= pdt[abs(id2In)].resOpenFrac(id3In); + + // Done. + return answer; + +} + +//-------------------------------------------------------------------------- + +// Convert string to lowercase for case-insensitive comparisons. + +string ParticleData::toLower(const string& nameConv) { + + string temp(nameConv); + for (int i = 0; i < int(temp.length()); ++i) + temp[i] = std::tolower(temp[i]); + return temp; + +} + +//-------------------------------------------------------------------------- + +// Allow several alternative inputs for true/false. + +bool ParticleData::boolString(string tag) { + + string tagLow = toLower(tag); + return ( tagLow == "true" || tagLow == "1" || tagLow == "on" + || tagLow == "yes" || tagLow == "ok" ); + +} + +//-------------------------------------------------------------------------- + +// Extract XML value string following XML attribute. + +string ParticleData::attributeValue(string line, string attribute) { + + if (line.find(attribute) == string::npos) return ""; + int iBegAttri = line.find(attribute); + int iBegQuote = line.find("\"", iBegAttri + 1); + int iEndQuote = line.find("\"", iBegQuote + 1); + return line.substr(iBegQuote + 1, iEndQuote - iBegQuote - 1); + +} + +//-------------------------------------------------------------------------- + +// Extract XML bool value following XML attribute. + +bool ParticleData::boolAttributeValue(string line, string attribute) { + + string valString = attributeValue(line, attribute); + if (valString == "") return false; + return boolString(valString); + +} + +//-------------------------------------------------------------------------- + +// Extract XML int value following XML attribute. + +int ParticleData::intAttributeValue(string line, string attribute) { + string valString = attributeValue(line, attribute); + if (valString == "") return 0; + istringstream valStream(valString); + int intVal; + valStream >> intVal; + return intVal; + +} + +//-------------------------------------------------------------------------- + +// Extract XML double value following XML attribute. + +double ParticleData::doubleAttributeValue(string line, string attribute) { + string valString = attributeValue(line, attribute); + if (valString == "") return 0.; + istringstream valStream(valString); + double doubleVal; + valStream >> doubleVal; + return doubleVal; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/ParticleDecays.cxx b/PYTHIA8/pythia8140/src/ParticleDecays.cxx new file mode 100644 index 00000000000..0fcec2f396c --- /dev/null +++ b/PYTHIA8/pythia8140/src/ParticleDecays.cxx @@ -0,0 +1,1248 @@ +// ParticleDecays.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// ParticleDecays class. + +#include "ParticleDecays.h" + +namespace Pythia8 { + +//========================================================================== + +// The ParticleDecays class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of times one tries to let decay happen (for 2 nested loops). +const int ParticleDecays::NTRYDECAY = 10; + +// Number of times one tries to pick valid hadronic content in decay. +const int ParticleDecays::NTRYPICK = 100; + +// Number of times one tries to pick decay topology. +const int ParticleDecays::NTRYMEWT = 1000; + +// Maximal loop count in Dalitz decay treatment. +const int ParticleDecays::NTRYDALITZ = 1000; + +// Minimal Dalitz pair mass this factor above threshold. +const double ParticleDecays::MSAFEDALITZ = 1.000001; + +// These numbers are hardwired empirical parameters, +// intended to speed up the M-generator. +const double ParticleDecays::WTCORRECTION[11] = { 1., 1., 1., + 2., 5., 15., 60., 250., 1250., 7000., 50000. }; + +//-------------------------------------------------------------------------- + +// Initialize and save pointers. + +void ParticleDecays::init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, TimeShower* timesDecPtrIn, + StringFlav* flavSelPtrIn, DecayHandler* decayHandlePtrIn, + vector handledParticles) { + + // Save pointers to error messages handling and flavour generation. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + flavSelPtr = flavSelPtrIn; + + // Save pointer to timelike shower, as needed in some few decays. + timesDecPtr = timesDecPtrIn; + + // Save pointer for external handling of some decays. + decayHandlePtr = decayHandlePtrIn; + + // Set which particles should be handled externally. + if (decayHandlePtr != 0) + for (int i = 0; i < int(handledParticles.size()); ++i) + particleDataPtr->doExternalDecay(handledParticles[i], true); + + // Safety margin in mass to avoid troubles. + mSafety = settings.parm("ParticleDecays:mSafety"); + + // Lifetime and vertex rules for determining whether decay allowed. + limitTau0 = settings.flag("ParticleDecays:limitTau0"); + tau0Max = settings.parm("ParticleDecays:tau0Max"); + limitTau = settings.flag("ParticleDecays:limitTau"); + tauMax = settings.parm("ParticleDecays:tauMax"); + limitRadius = settings.flag("ParticleDecays:limitRadius"); + rMax = settings.parm("ParticleDecays:rMax"); + limitCylinder = settings.flag("ParticleDecays:limitCylinder"); + xyMax = settings.parm("ParticleDecays:xyMax"); + zMax = settings.parm("ParticleDecays:zMax"); + limitDecay = limitTau0 || limitTau || limitRadius || limitCylinder; + + // B-Bbar mixing parameters. + mixB = settings.flag("ParticleDecays:mixB"); + xBdMix = settings.parm("ParticleDecays:xBdMix"); + xBsMix = settings.parm("ParticleDecays:xBsMix"); + + // Suppression of extra-hadron momenta in semileptonic decays. + sigmaSoft = settings.parm("ParticleDecays:sigmaSoft"); + + // Selection of multiplicity and colours in "phase space" model. + multIncrease = settings.parm("ParticleDecays:multIncrease"); + multRefMass = settings.parm("ParticleDecays:multRefMass"); + multGoffset = settings.parm("ParticleDecays:multGoffset"); + colRearrange = settings.parm("ParticleDecays:colRearrange"); + + // Minimum energy in system (+ m_q) from StringFragmentation. + stopMass = settings.parm("StringFragmentation:stopMass"); + + // Parameters for Dalitz decay virtual gamma mass spectrum. + sRhoDal = pow2(particleDataPtr->m0(113)); + wRhoDal = pow2(particleDataPtr->mWidth(113)); + + // Allow showers in decays to qqbar/gg/ggg/gammagg. + doFSRinDecays = settings.flag("ParticleDecays:FSRinDecays"); + +} + +//-------------------------------------------------------------------------- + +// Decay a particle; main method. + +bool ParticleDecays::decay( int iDec, Event& event) { + + // Check whether a decay is allowed, given the upcoming decay vertex. + Particle& decayer = event[iDec]; + hasPartons = false; + keepPartons = false; + if (limitDecay && !checkVertex(decayer)) return true; + + // Fill the decaying particle in slot 0 of arrays. + idDec = decayer.id(); + iProd.resize(0); + idProd.resize(0); + mProd.resize(0); + iProd.push_back( iDec ); + idProd.push_back( idDec ); + mProd.push_back( decayer.m() ); + + // Check for oscillations B0 <-> B0bar or B_s0 <-> B_s0bar. + bool hasOscillated = (abs(idDec) == 511 || abs(idDec) == 531) + ? oscillateB(decayer) : false; + if (hasOscillated) {idDec = - idDec; idProd[0] = idDec;} + + // Particle data for decaying particle. + decDataPtr = &decayer.particleDataEntry(); + + // Optionally send on to external decay program. + bool doneExternally = false; + if (decDataPtr->doExternalDecay()) { + pProd.resize(0); + pProd.push_back(decayer.p()); + doneExternally = decayHandlePtr->decay(idProd, mProd, pProd, + iDec, event); + + // If it worked, then store the decay products in the event record. + if (doneExternally) { + mult = idProd.size() - 1; + int status = (hasOscillated) ? 94 : 93; + for (int i = 1; i <= mult; ++i) { + int iPos = event.append( idProd[i], status, iDec, 0, 0, 0, + 0, 0, pProd[i], mProd[i]); + iProd.push_back( iPos); + } + + // Also mark mother decayed and store daughters. + event[iDec].statusNeg(); + event[iDec].daughters( iProd[1], iProd[mult]); + } + } + + // Now begin normal internal decay treatment. + if (!doneExternally) { + + // Allow up to ten tries to pick a channel. + if (!decDataPtr->preparePick(idDec)) return false; + bool foundChannel = false; + bool hasStored = false; + for (int iTryChannel = 0; iTryChannel < NTRYDECAY; ++iTryChannel) { + + // Remove previous failed channel. + if (hasStored) event.popBack(mult); + hasStored = false; + + // Pick new channel. Read out basics. + DecayChannel& channel = decDataPtr->pickChannel(); + meMode = channel.meMode(); + keepPartons = (meMode > 90 && meMode <= 100); + mult = channel.multiplicity(); + + // Allow up to ten tries for each channel (e.g with different masses). + bool foundMode = false; + for (int iTryMode = 0; iTryMode < NTRYDECAY; ++iTryMode) { + idProd.resize(1); + mProd.resize(1); + scale = 0.; + + // Extract and store the decay products in local arrays. + hasPartons = false; + for (int i = 0; i < mult; ++i) { + int idNow = channel.product(i); + int idAbs = abs(idNow); + if ( idAbs < 10 || idAbs == 21 || idAbs == 81 || idAbs == 82 + || idAbs == 83 || (idAbs > 1000 && idAbs < 10000 + && (idAbs/10)%10 == 0) ) hasPartons = true; + if (idDec < 0 && particleDataPtr->hasAnti(idNow)) idNow = -idNow; + double mNow = particleDataPtr->mass(idNow); + idProd.push_back( idNow); + mProd.push_back( mNow); + } + + // Decays into partons usually translate into hadrons. + if (hasPartons && !keepPartons && !pickHadrons()) continue; + + // Need to set colour flow if explicit decay to partons. + cols.resize(0); + acols.resize(0); + for (int i = 0; i <= mult; ++i) { + cols.push_back(0); + acols.push_back(0); + } + if (hasPartons && keepPartons && !setColours(event)) continue; + + // Check that enough phase space for decay. + if (mult > 1) { + double mDiff = mProd[0]; + for (int i = 1; i <= mult; ++i) mDiff -= mProd[i]; + if (mDiff < mSafety) continue; + } + + // End of inner trial loops. Check if succeeded or not. + foundMode = true; + break; + } + if (!foundMode) continue; + + // Store decay products in the event record. + int status = (hasOscillated) ? 92 : 91; + for (int i = 1; i <= mult; ++i) { + int iPos = event.append( idProd[i], status, iDec, 0, 0, 0, + cols[i], acols[i], Vec4(0., 0., 0., 0.), mProd[i], scale); + iProd.push_back( iPos); + } + hasStored = true; + + // Pick mass of Dalitz decay. Temporarily change multiplicity. + if ( (meMode == 11 || meMode == 12 || meMode == 13) + && !dalitzMass() ) continue; + + // Do a decay, split by multiplicity. + bool decayed = false; + if (mult == 1) decayed = oneBody(event); + else if (mult == 2) decayed = twoBody(event); + else if (mult == 3) decayed = threeBody(event); + else decayed = mGenerator(event); + if (!decayed) continue; + + // Kinematics of gamma* -> l- l+ in Dalitz decay. Restore multiplicity. + if (meMode == 11 || meMode == 12 || meMode == 13) + dalitzKinematics(event); + + // End of outer trial loops. + foundChannel = true; + break; + } + + // If the decay worked, then mark mother decayed and store daughters. + if (foundChannel) { + event[iDec].statusNeg(); + event[iDec].daughters( iProd[1], iProd[mult]); + + // Else remove unused daughters and return failure. + } else { + if (hasStored) event.popBack(mult); + infoPtr->errorMsg("Error in ParticleDecays::decay: " + "failed to find workable decay channel"); + return false; + } + + // Now finished normal internal decay treatment. + } + + // Set decay vertex when this is displaced. + if (event[iDec].hasVertex() || event[iDec].tau() > 0.) { + Vec4 vDec = event[iDec].vDec(); + for (int i = 1; i <= mult; ++i) event[iProd[i]].vProd( vDec ); + } + + // Set lifetime of daughters. + for (int i = 1; i <= mult; ++i) + event[iProd[i]].tau( event[iProd[i]].tau0() * rndmPtr->exp() ); + + // In a decay explicitly to partons then optionally do a shower, + // and always flag that partonic system should be fragmented. + if (hasPartons && keepPartons && doFSRinDecays) + timesDecPtr->shower( iProd[1], iProd.back(), event, mProd[0]); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Check whether a decay is allowed, given the upcoming decay vertex. + +bool ParticleDecays::checkVertex(Particle& decayer) { + + // Check whether any of the conditions are not fulfilled. + if (limitTau0 && decayer.tau0() > tau0Max) return false; + if (limitTau && decayer.tau() > tauMax) return false; + if (limitRadius && pow2(decayer.xDec()) + pow2(decayer.yDec()) + + pow2(decayer.zDec()) > pow2(rMax)) return false; + if (limitCylinder && (pow2(decayer.xDec()) + pow2(decayer.yDec()) + > pow2(xyMax) || abs(decayer.zDec()) > zMax) ) return false; + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Check for oscillations B0 <-> B0bar or B_s0 <-> B_s0bar. + +bool ParticleDecays::oscillateB(Particle& decayer) { + + // Extract relevant information and decide. + double xBmix = (abs(decayer.id()) == 511) ? xBdMix : xBsMix; + double tau = decayer.tau(); + double tau0 = decayer.tau0(); + double probosc = pow2(sin(0.5 * xBmix * tau / tau0)); + return (probosc > rndmPtr->flat()); + +} + +//-------------------------------------------------------------------------- + +// Do a one-body decay. (Rare; e.g. for K0 -> K0_short.) + +bool ParticleDecays::oneBody(Event& event) { + + // References to the particles involved. + Particle& decayer = event[iProd[0]]; + Particle& prod = event[iProd[1]]; + + // Set momentum and expand mother information. + prod.p( decayer.p() ); + prod.m( decayer.m() ); + prod.mother2( iProd[0] ); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Do a two-body decay. + +bool ParticleDecays::twoBody(Event& event) { + + // References to the particles involved. + Particle& decayer = event[iProd[0]]; + Particle& prod1 = event[iProd[1]]; + Particle& prod2 = event[iProd[2]]; + + // Masses. + double m0 = mProd[0]; + double m1 = mProd[1]; + double m2 = mProd[2]; + + // Energies and absolute momentum in the rest frame. + if (m1 + m2 + mSafety > m0) return false; + double e1 = 0.5 * (m0*m0 + m1*m1 - m2*m2) / m0; + double e2 = 0.5 * (m0*m0 + m2*m2 - m1*m1) / m0; + double pAbs = 0.5 * sqrtpos( (m0 - m1 - m2) * (m0 + m1 + m2) + * (m0 + m1 - m2) * (m0 - m1 + m2) ) / m0; + + // When meMode = 2, for V -> PS2 + PS3 (V = vector, pseudoscalar), + // need to check if production is PS0 -> PS1/gamma + V. + int iMother = event[iProd[0]].mother1(); + int idSister = 0; + if (meMode == 2) { + if (iMother <= 0 || iMother >= iProd[0]) meMode = 0; + else { + int iDaughter1 = event[iMother].daughter1(); + int iDaughter2 = event[iMother].daughter2(); + if (iDaughter2 != iDaughter1 + 1) meMode = 0; + else { + int idMother = abs( event[iMother].id() ); + if (idMother <= 100 || idMother%10 !=1 + || (idMother/1000)%10 != 0) meMode = 0; + else { + int iSister = (iProd[0] == iDaughter1) ? iDaughter2 : iDaughter1; + idSister = abs( event[iSister].id() ); + if ( (idSister <= 100 || idSister%10 !=1 + || (idSister/1000)%10 != 0) && idSister != 22) meMode = 0; + } + } + } + } + + // Begin loop over matrix-element corrections. + double wtME, wtMEmax; + int loop = 0; + do { + wtME = 1.; + wtMEmax = 1.; + ++loop; + + // Isotropic angles give three-momentum. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi = 2. * M_PI * rndmPtr->flat(); + double pX = pAbs * sinTheta * cos(phi); + double pY = pAbs * sinTheta * sin(phi); + double pZ = pAbs * cosTheta; + + // Fill four-momenta and boost them away from mother rest frame. + prod1.p( pX, pY, pZ, e1); + prod2.p( -pX, -pY, -pZ, e2); + prod1.bst( decayer.p(), decayer.m() ); + prod2.bst( decayer.p(), decayer.m() ); + + // Matrix element for PS0 -> PS1 + V1 -> PS1 + PS2 + PS3 of form + // cos**2(theta02) in V1 rest frame, and for PS0 -> gamma + V1 + // -> gamma + PS2 + PS3 of form sin**2(theta02). + if (meMode == 2) { + double p10 = decayer.p() * event[iMother].p(); + double p12 = decayer.p() * prod1.p(); + double p02 = event[iMother].p() * prod1.p(); + double s0 = pow2(event[iMother].m()); + double s1 = pow2(decayer.m()); + double s2 = pow2(prod1.m()); + if (idSister != 22) wtME = pow2(p10 * p12 - s1 * p02); + else wtME = s1 * (2. * p10 * p12 * p02 - s1 * p02*p02 + - s0 * p12*p12 - s2 * p10*p10 + s1 * s0 * s2); + wtME = max( wtME, 1e-6 * s1*s1 * s0 * s2); + wtMEmax = (p10*p10 - s1 * s0) * (p12*p12 - s1 * s2); + } + + // Break out of loop if no sensible ME weight. + if(loop > NTRYMEWT) { + infoPtr->errorMsg("ParticleDecays::twoBody: " + "caught in infinite ME weight loop"); + wtME = abs(wtMEmax); + } + + // If rejected, try again with new invariant masses. + } while ( wtME < rndmPtr->flat() * wtMEmax ); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Do a three-body decay (except Dalitz decays). + +bool ParticleDecays::threeBody(Event& event) { + + // References to the particles involved. + Particle& decayer = event[iProd[0]]; + Particle& prod1 = event[iProd[1]]; + Particle& prod2 = event[iProd[2]]; + Particle& prod3 = event[iProd[3]]; + + // Mother and sum daughter masses. Fail if too close. + double m0 = mProd[0]; + double m1 = mProd[1]; + double m2 = mProd[2]; + double m3 = mProd[3]; + double mSum = m1 + m2 + m3; + double mDiff = m0 - mSum; + if (mDiff < mSafety) return false; + + // Kinematical limits for 2+3 mass. Maximum phase-space weight. + double m23Min = m2 + m3; + double m23Max = m0 - m1; + double p1Max = 0.5 * sqrtpos( (m0 - m1 - m23Min) * (m0 + m1 + m23Min) + * (m0 + m1 - m23Min) * (m0 - m1 + m23Min) ) / m0; + double p23Max = 0.5 * sqrtpos( (m23Max - m2 - m3) * (m23Max + m2 + m3) + * (m23Max + m2 - m3) * (m23Max - m2 + m3) ) / m23Max; + double wtPSmax = 0.5 * p1Max * p23Max; + + // Begin loop over matrix-element corrections. + double wtME, wtMEmax, wtPS, m23, p1Abs, p23Abs; + do { + wtME = 1.; + wtMEmax = 1.; + + // Pick an intermediate mass m23 flat in the allowed range. + do { + m23 = m23Min + rndmPtr->flat() * mDiff; + + // Translate into relative momenta and find phase-space weight. + p1Abs = 0.5 * sqrtpos( (m0 - m1 - m23) * (m0 + m1 + m23) + * (m0 + m1 - m23) * (m0 - m1 + m23) ) / m0; + p23Abs = 0.5 * sqrtpos( (m23 - m2 - m3) * (m23 + m2 + m3) + * (m23 + m2 - m3) * (m23 - m2 + m3) ) / m23; + wtPS = p1Abs * p23Abs; + + // If rejected, try again with new invariant masses. + } while ( wtPS < rndmPtr->flat() * wtPSmax ); + + // Set up m23 -> m2 + m3 isotropic in its rest frame. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi = 2. * M_PI * rndmPtr->flat(); + double pX = p23Abs * sinTheta * cos(phi); + double pY = p23Abs * sinTheta * sin(phi); + double pZ = p23Abs * cosTheta; + double e2 = sqrt( m2*m2 + p23Abs*p23Abs); + double e3 = sqrt( m3*m3 + p23Abs*p23Abs); + prod2.p( pX, pY, pZ, e2); + prod3.p( -pX, -pY, -pZ, e3); + + // Set up m0 -> m1 + m23 isotropic in its rest frame. + cosTheta = 2. * rndmPtr->flat() - 1.; + sinTheta = sqrt(1. - cosTheta*cosTheta); + phi = 2. * M_PI * rndmPtr->flat(); + pX = p1Abs * sinTheta * cos(phi); + pY = p1Abs * sinTheta * sin(phi); + pZ = p1Abs * cosTheta; + double e1 = sqrt( m1*m1 + p1Abs*p1Abs); + double e23 = sqrt( m23*m23 + p1Abs*p1Abs); + prod1.p( pX, pY, pZ, e1); + + // Boost 2 + 3 to the 0 rest frame. + Vec4 p23( -pX, -pY, -pZ, e23); + prod2.bst( p23, m23 ); + prod3.bst( p23, m23 ); + + // Matrix-element weight for omega/phi -> pi+ pi- pi0. + if (meMode == 1) { + double p1p2 = prod1.p() * prod2.p(); + double p1p3 = prod1.p() * prod3.p(); + double p2p3 = prod2.p() * prod3.p(); + wtME = pow2(m1 * m2 * m3) - pow2(m1 * p2p3) - pow2(m2 * p1p3) + - pow2(m3 * p1p2) + 2. * p1p2 * p1p3 * p2p3; + wtMEmax = pow3(m0 * m0) / 150.; + + // Effective matrix element for nu spectrum in tau -> nu + hadrons. + } else if (meMode == 21) { + double x1 = 2. * prod1.e() / m0; + wtME = x1 * (3. - 2. * x1); + double xMax = min( 0.75, 2. * (1. - mSum / m0) ); + wtMEmax = xMax * (3. - 2. * xMax); + + // Matrix element for weak decay (only semileptonic for c and b). + } else if ((meMode == 22 || meMode == 23) && prod1.isLepton()) { + wtME = m0 * prod1.e() * (prod2.p() * prod3.p()); + wtMEmax = min( pow4(m0) / 16., m0 * (m0 - m1 - m2) * (m0 - m1 - m3) + * (m0 - m2 - m3) ); + + // Effective matrix element for weak decay to hadrons (B -> D, D -> K). + } else if (meMode == 22 || meMode == 23) { + double x1 = 2. * prod1.pAbs() / m0; + wtME = x1 * (3. - 2. * x1); + double xMax = min( 0.75, 2. * (1. - mSum / m0) ); + wtMEmax = xMax * (3. - 2. * xMax); + + // Effective matrix element for gamma spectrum in B -> gamma + hadrons. + } else if (meMode == 31) { + double x1 = 2. * prod1.e() / m0; + wtME = pow3(x1); + double x1Max = 1. - pow2(mSum / m0); + wtMEmax = pow3(x1Max); + + // Matrix-element weight for "onium" -> g + g + g or gamma + g + g. + } else if (meMode == 92) { + double x1 = 2. * prod1.e() / m0; + double x2 = 2. * prod2.e() / m0; + double x3 = 2. * prod3.e() / m0; + wtME = pow2( (1. - x1) / (x2 * x3) ) + pow2( (1. - x2) / (x1 * x3) ) + + pow2( (1. - x3) / (x1 * x2) ); + wtMEmax = 2.; + // For gamma + g + g require minimum mass for g + g system. + if (prod1.id() == 22 && sqrt(1. - x1) * m0 < 2. * stopMass) wtME = 0.; + if (prod2.id() == 22 && sqrt(1. - x2) * m0 < 2. * stopMass) wtME = 0.; + if (prod3.id() == 22 && sqrt(1. - x3) * m0 < 2. * stopMass) wtME = 0.; + } + + // If rejected, try again with new invariant masses. + } while ( wtME < rndmPtr->flat() * wtMEmax ); + + // Boost 1 + 2 + 3 to the current frame. + prod1.bst( decayer.p(), decayer.m() ); + prod2.bst( decayer.p(), decayer.m() ); + prod3.bst( decayer.p(), decayer.m() ); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Do a multibody decay using the M-generator algorithm. + +bool ParticleDecays::mGenerator(Event& event) { + + // Mother and sum daughter masses. Fail if too close or inconsistent. + double m0 = mProd[0]; + double mSum = mProd[1]; + for (int i = 2; i <= mult; ++i) mSum += mProd[i]; + double mDiff = m0 - mSum; + if (mDiff < mSafety) return false; + + // Begin setup of intermediate invariant masses. + mInv.resize(0); + for (int i = 0; i <= mult; ++i) mInv.push_back( mProd[i]); + + // Calculate the maximum weight in the decay. + double wtPS, wtME, wtMEmax; + double wtPSmax = 1. / WTCORRECTION[mult]; + double mMax = mDiff + mProd[mult]; + double mMin = 0.; + for (int i = mult - 1; i > 0; --i) { + mMax += mProd[i]; + mMin += mProd[i+1]; + double mNow = mProd[i]; + wtPSmax *= 0.5 * sqrtpos( (mMax - mMin - mNow) * (mMax + mMin + mNow) + * (mMax + mMin - mNow) * (mMax - mMin + mNow) ) / mMax; + } + + // Begin loop over matrix-element corrections. + do { + wtME = 1.; + wtMEmax = 1.; + + // Begin loop to find the set of intermediate invariant masses. + do { + wtPS = 1.; + + // Find and order random numbers in descending order. + rndmOrd.resize(0); + rndmOrd.push_back(1.); + for (int i = 1; i < mult - 1; ++i) { + double rndm = rndmPtr->flat(); + rndmOrd.push_back(rndm); + for (int j = i - 1; j > 0; --j) { + if (rndm > rndmOrd[j]) swap( rndmOrd[j], rndmOrd[j+1] ); + else break; + } + } + rndmOrd.push_back(0.); + + // Translate into intermediate masses and find weight. + for (int i = mult - 1; i > 0; --i) { + mInv[i] = mInv[i+1] + mProd[i] + (rndmOrd[i-1] - rndmOrd[i]) * mDiff; + wtPS *= 0.5 * sqrtpos( (mInv[i] - mInv[i+1] - mProd[i]) + * (mInv[i] + mInv[i+1] + mProd[i]) * (mInv[i] + mInv[i+1] - mProd[i]) + * (mInv[i] - mInv[i+1] + mProd[i]) ) / mInv[i]; + } + + // If rejected, try again with new invariant masses. + } while ( wtPS < rndmPtr->flat() * wtPSmax ); + + // Perform two-particle decays in the respective rest frame. + pInv.resize(mult + 1); + for (int i = 1; i < mult; ++i) { + double pAbs = 0.5 * sqrtpos( (mInv[i] - mInv[i+1] - mProd[i]) + * (mInv[i] + mInv[i+1] + mProd[i]) * (mInv[i] + mInv[i+1] - mProd[i]) + * (mInv[i] - mInv[i+1] + mProd[i]) ) / mInv[i]; + + // Isotropic angles give three-momentum. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi = 2. * M_PI * rndmPtr->flat(); + double pX = pAbs * sinTheta * cos(phi); + double pY = pAbs * sinTheta * sin(phi); + double pZ = pAbs * cosTheta; + + // Calculate energies, fill four-momenta. + double eHad = sqrt( mProd[i]*mProd[i] + pAbs*pAbs); + double eInv = sqrt( mInv[i+1]*mInv[i+1] + pAbs*pAbs); + event[iProd[i]].p( pX, pY, pZ, eHad); + pInv[i+1].p( -pX, -pY, -pZ, eInv); + } + + // Boost decay products to the mother rest frame. + event[iProd[mult]].p( pInv[mult] ); + for (int iFrame = mult - 1; iFrame > 1; --iFrame) + for (int i = iFrame; i <= mult; ++i) + event[iProd[i]].bst( pInv[iFrame], mInv[iFrame]); + + // Effective matrix element for nu spectrum in tau -> nu + hadrons. + if (meMode == 21 && event[iProd[1]].isLepton()) { + double x1 = 2. * event[iProd[1]].e() / m0; + wtME = x1 * (3. - 2. * x1); + double xMax = min( 0.75, 2. * (1. - mSum / m0) ); + wtMEmax = xMax * (3. - 2. * xMax); + + // Effective matrix element for weak decay (only semileptonic for c and b). + // Particles 4 onwards should be made softer explicitly? + } else if ((meMode == 22 || meMode == 23) && event[iProd[1]].isLepton()) { + Vec4 pRest = event[iProd[3]].p(); + for (int i = 4; i <= mult; ++i) pRest += event[iProd[i]].p(); + wtME = m0 * event[iProd[1]].e() * (event[iProd[2]].p() * pRest); + for (int i = 4; i <= mult; ++i) wtME + *= exp(- event[iProd[i]].pAbs2() / pow2(sigmaSoft) ); + wtMEmax = pow4(m0) / 16.; + + // Effective matrix element for weak decay to hadrons (B -> D, D -> K). + } else if (meMode == 22 || meMode == 23) { + double x1 = 2. * event[iProd[1]].pAbs() / m0; + wtME = x1 * (3. - 2. * x1); + double xMax = min( 0.75, 2. * (1. - mSum / m0) ); + wtMEmax = xMax * (3. - 2. * xMax); + + // Effective matrix element for gamma spectrum in B -> gamma + hadrons. + } else if (meMode == 31) { + double x1 = 2. * event[iProd[1]].e() / m0; + wtME = pow3(x1); + double x1Max = 1. - pow2(mSum / m0); + wtMEmax = pow3(x1Max); + } + + // If rejected, try again with new invariant masses. + } while ( wtME < rndmPtr->flat() * wtMEmax ); + + // Boost decay products to the current frame. + pInv[1].p( event[iProd[0]].p() ); + for (int i = 1; i <= mult; ++i) event[iProd[i]].bst( pInv[1], mInv[1] ); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Select mass of lepton pair in a Dalitz decay. + +bool ParticleDecays::dalitzMass() { + + // Mother and sum daughter masses. + double mSum1 = 0; + for (int i = 1; i <= mult - 2; ++i) mSum1 += mProd[i]; + if (meMode == 13) mSum1 *= MSAFEDALITZ; + double mSum2 = MSAFEDALITZ * (mProd[mult -1] + mProd[mult]); + double mDiff = mProd[0] - mSum1 - mSum2; + + // Fail if too close or inconsistent. + if (mDiff < mSafety) return false; + if (idProd[mult - 1] + idProd[mult] != 0 + || mProd[mult - 1] != mProd[mult]) { + infoPtr->errorMsg("Error in ParticleDecays::dalitzMass:" + " inconsistent flavour/mass assignments"); + return false; + } + if ( meMode == 13 && (idProd[1] + idProd[2] != 0 + || mProd[1] != mProd[2]) ) { + infoPtr->errorMsg("Error in ParticleDecays::dalitzMass:" + " inconsistent flavour/mass assignments"); + return false; + } + + // Case 1: one Dalitz pair. + if (meMode == 11 || meMode == 12) { + + // Kinematical limits for gamma* squared mass. + double sGamMin = pow2(mSum2); + double sGamMax = pow2(mProd[0] - mSum1); + // Select virtual gamma squared mass. Guessed form for meMode == 12. + double sGam, wtGam; + int loop = 0; + do { + if (++loop > NTRYDALITZ) return false; + sGam = sGamMin * pow( sGamMax / sGamMin, rndmPtr->flat() ); + wtGam = (1. + 0.5 * sGamMin / sGam) * sqrt(1. - sGamMin / sGam) + * pow3(1. - sGam / sGamMax) * sRhoDal * (sRhoDal + wRhoDal) + / ( pow2(sGam - sRhoDal) + sRhoDal * wRhoDal ); + } while ( wtGam < rndmPtr->flat() ); + + // Store results in preparation for doing a one-less-body decay. + --mult; + mProd[mult] = sqrt(sGam); + + // Case 2: two Dalitz pairs. + } else { + + // Kinematical limits for 1 + 2 and 3 + 4 gamma* masses. + double s0 = pow2(mProd[0]); + double s12Min = pow2(mSum1); + double s12Max = pow2(mProd[0] - mSum2); + double s34Min = pow2(mSum2); + double s34Max = pow2(mProd[0] - mSum1); + + // Select virtual gamma squared masses. Guessed form for meMode == 13. + double s12, s34, wt12, wt34, wtPAbs, wtAll; + int loop = 0; + do { + if (++loop > NTRYDALITZ) return false; + s12 = s12Min * pow( s12Max / s12Min, rndmPtr->flat() ); + wt12 = (1. + 0.5 * s12Min / s12) * sqrt(1. - s12Min / s12) + * sRhoDal * (sRhoDal + wRhoDal) + / ( pow2(s12 - sRhoDal) + sRhoDal * wRhoDal ); + s34 = s34Min * pow( s34Max / s34Min, rndmPtr->flat() ); + wt34 = (1. + 0.5 * s34Min / s34) * sqrt(1. - s34Min / s34) + * sRhoDal * (sRhoDal + wRhoDal) + / ( pow2(s34 - sRhoDal) + sRhoDal * wRhoDal ); + wtPAbs = sqrtpos( pow2(1. - (s12 + s34)/ s0) + - 4. * s12 * s34 / (s0 * s0) ); + wtAll = wt12 * wt34 * pow3(wtPAbs); + if (wtAll > 1.) infoPtr->errorMsg( + "Error in ParticleDecays::dalitzMass: weight > 1"); + } while (wtAll < rndmPtr->flat()); + + // Store results in preparation for doing a two-body decay. + mult = 2; + mProd[1] = sqrt(s12); + mProd[2] = sqrt(s34); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Do kinematics of gamma* -> l- l+ in Dalitz decay. + +bool ParticleDecays::dalitzKinematics(Event& event) { + + // Restore multiplicity. + int nDal = (meMode < 13) ? 1 : 2; + mult += nDal; + + // Loop over one or two lepton pairs. + for (int iDal = 0; iDal < nDal; ++iDal) { + + // References to the particles involved. + Particle& decayer = event[iProd[0]]; + Particle& prodA = (iDal == 0) ? event[iProd[mult - 1]] + : event[iProd[1]]; + Particle& prodB = (iDal == 0) ? event[iProd[mult]] + : event[iProd[2]]; + + // Reconstruct required rotations and boosts backwards. + Vec4 pDec = decayer.p(); + int iGam = (meMode < 13) ? mult - 1 : 2 - iDal; + Vec4 pGam = event[iProd[iGam]].p(); + pGam.bstback( pDec, decayer.m() ); + double phiGam = pGam.phi(); + pGam.rot( 0., -phiGam); + double thetaGam = pGam.theta(); + pGam.rot( -thetaGam, 0.); + + // Masses and phase space in gamma* rest frame. + double mGam = (meMode < 13) ? mProd[mult - 1] : mProd[2 - iDal]; + double mA = prodA.m(); + double mB = prodB.m(); + double mGamMin = MSAFEDALITZ * (mA + mB); + double mGamRat = pow2(mGamMin / mGam); + double pGamAbs = 0.5 * sqrtpos( (mGam - mA - mB) * (mGam + mA + mB) ); + + // Set up decay in gamma* rest frame, reference along +z axis. + double cosTheta, cos2Theta; + do { + cosTheta = 2. * rndmPtr->flat() - 1.; + cos2Theta = cosTheta * cosTheta; + } while ( 1. + cos2Theta + mGamRat * (1. - cos2Theta) + < 2. * rndmPtr->flat() ); + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi = 2. * M_PI * rndmPtr->flat(); + double pX = pGamAbs * sinTheta * cos(phi); + double pY = pGamAbs * sinTheta * sin(phi); + double pZ = pGamAbs * cosTheta; + double eA = sqrt( mA*mA + pGamAbs*pGamAbs); + double eB = sqrt( mB*mB + pGamAbs*pGamAbs); + prodA.p( pX, pY, pZ, eA); + prodB.p( -pX, -pY, -pZ, eB); + + // Boost to lab frame. + prodA.bst( pGam, mGam); + prodB.bst( pGam, mGam); + prodA.rot( thetaGam, phiGam); + prodB.rot( thetaGam, phiGam); + prodA.bst( pDec, decayer.m() ); + prodB.bst( pDec, decayer.m() ); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Translate a partonic content into a set of actual hadrons. + +bool ParticleDecays::pickHadrons() { + + // Find partonic decay products. Rest are known id's, mainly hadrons, + // when necessary shuffled to beginning of idProd list. + idPartons.resize(0); + int nPartons = 0; + int nKnown = 0; + bool closedGLoop = false; + for (int i = 1; i <= mult; ++i) { + int idAbs = abs(idProd[i]); + if ( idAbs < 9 || (idAbs > 1000 && idAbs < 10000 && (idAbs/10)%10 == 0) + || idAbs == 81 || idAbs == 82 || idAbs == 83) { + ++nPartons; + idPartons.push_back(idProd[i]); + if (idAbs == 83) closedGLoop = true; + } else { + ++nKnown; + if (nPartons > 0) { + idProd[nKnown] = idProd[i]; + mProd[nKnown] = mProd[i]; + } + } + } + + // Replace generic spectator flavour code by the actual one. + for (int i = 0; i < nPartons; ++i) { + int idPart = idPartons[i]; + int idNew = idPart; + if (idPart == 81) { + int idAbs = abs(idDec); + if ( (idAbs/1000)%10 == 0 ) { + idNew = -(idAbs/10)%10; + if ((idAbs/100)%2 == 1) idNew = -idNew; + } else if ( (idAbs/100)%10 >= (idAbs/10)%10 ) + idNew = 100 * ((idAbs/10)%100) + 3; + else idNew = 1000 * ((idAbs/10)%10) + 100 * ((idAbs/100)%10) + 1; + if (idDec < 0) idNew = -idNew; + + // Replace generic random flavour by a randomly selected one. + } else if (idPart == 82 || idPart == 83) { + double mFlav; + do { + int idDummy = -flavSelPtr->pickLightQ(); + FlavContainer flavDummy(idDummy, idPart - 82); + do idNew = flavSelPtr->pick(flavDummy).id; + while (idNew == 0); + mFlav = particleDataPtr->constituentMass(idNew); + } while (2. * mFlav + stopMass > mProd[0]); + } else if (idPart == -82 || idPart == -83) { + idNew = -idPartons[i-1]; + } + idPartons[i] = idNew; + } + + // Determine whether fixed multiplicity or to be selected at random. + int nMin = max( 2, nKnown + nPartons / 2); + if (meMode == 23) nMin = 3; + if (meMode > 41 && meMode <= 50) nMin = meMode - 40; + if (meMode > 51 && meMode <= 60) nMin = meMode - 50; + int nFix = 0; + if (meMode == 0) nFix = nMin; + if (meMode == 11) nFix = 3; + if (meMode == 12) nFix = 4; + if (meMode > 61 && meMode <= 70) nFix = meMode - 60; + if (meMode > 71 && meMode <= 80) nFix = meMode - 70; + if (nFix > 0 && nKnown + nPartons/2 > nFix) return false; + + // Initial values for loop to set new hadronic content. + int nFilled = nKnown + 1; + int nTotal, nNew, nSpec, nLeft; + double mDiff; + int nTry = 0; + bool diquarkClash = false; + bool usedChannel = false; + + // Begin loop; interrupt if multiple tries fail. + do { + ++nTry; + if (nTry > NTRYPICK) return false; + + // Initialize variables inside new try. + nFilled = nKnown + 1; + idProd.resize(nFilled); + mProd.resize(nFilled); + nTotal = nKnown; + nNew = 0; + nSpec = 0; + nLeft = nPartons; + mDiff = mProd[0]; + for (int i = 1; i < nFilled; ++i) mDiff -= mProd[i]; + diquarkClash = false; + usedChannel = false; + + // For weak decays collapse spectators to one particle. + if ( (meMode == 22 || meMode == 23) && nLeft > 1) { + FlavContainer flav1( idPartons[nPartons - 2] ); + FlavContainer flav2( idPartons[nPartons - 1] ); + int idHad; + do idHad = flavSelPtr->combine( flav1, flav2); + while (idHad == 0); + double mHad = particleDataPtr->mass(idHad); + mDiff -= mHad; + idProd.push_back( idHad); + mProd.push_back( mHad); + ++nFilled; + nSpec = 1; + nLeft -= 2; + } + + // If there are partons left, then determine how many hadrons to pick. + if (nLeft > 0) { + + // For B -> gamma + X use geometrical distribution. + if (meMode == 31) { + double geom = rndmPtr->flat(); + nTotal = 1; + do { + ++nTotal; + geom *= 2.; + } while (geom < 1. && nTotal < 10); + + // Calculate mass excess and from there average multiplicity. + } else if (nFix == 0) { + double mDiffPS = mDiff; + for (int i = 0; i < nLeft; ++i) + mDiffPS -= particleDataPtr->constituentMass( idPartons[i] ); + double average = 0.5 * (nKnown + nSpec) + 0.25 * nPartons + + multIncrease * log( max( 1.1, mDiffPS / multRefMass ) ); + if (closedGLoop) average += multGoffset; + + // Pick multiplicity according to Poissonian. + double value = 1.; + double sum = 1.; + for (int nNow = nMin + 1; nNow <= 10; ++nNow) { + value *= average / nNow; + sum += value; + } + nTotal = nMin; + value = 1.; + sum *= rndmPtr->flat(); + sum -= value; + if (sum > 0.) do { + ++nTotal; + value *= average / nTotal; + sum -= value; + } while (sum > 0. && nTotal < 10); + + // Alternatively predetermined multiplicity. + } else { + nTotal = nFix; + } + nNew = nTotal - nKnown - nSpec; + + // Set up ends of fragmented system, as copy of idPartons. + flavEnds.resize(0); + for (int i = 0; i < nLeft; ++i) { + flavEnds.push_back( FlavContainer(idPartons[i]) ); + if (abs(idPartons[i]) > 100) flavSelPtr->assignPopQ( flavEnds[i] ); + } + + // Fragment off at random, but save nLeft/2 for final recombination. + if (nNew > nLeft/2) { + FlavContainer flavNew; + int idHad; + for (int i = 0; i < nNew - nLeft/2; ++i) { + // When four quarks consider last one to be spectator. + int iEnd = int( (nLeft - 1.) * rndmPtr->flat() ); + // Pick new flavour and form a new hadron. + do { + flavNew = flavSelPtr->pick( flavEnds[iEnd] ); + idHad = flavSelPtr->combine( flavEnds[iEnd], flavNew); + } while (idHad == 0); + // Store new hadron and endpoint flavour. + idProd.push_back( idHad); + flavEnds[iEnd].anti(flavNew); + } + } + + // When only two quarks left, combine to form final hadron. + if (nLeft == 2) { + int idHad; + if ( abs(flavEnds[0].id) > 8 && abs(flavEnds[1].id) > 8) + diquarkClash = true; + else { + do idHad = flavSelPtr->combine( flavEnds[0], flavEnds[1]); + while (idHad == 0); + idProd.push_back( idHad); + } + + // If four quarks, decide how to pair them up. + } else { + int iEnd1 = 0; + int iEnd2 = 1; + int iEnd3 = 2; + int iEnd4 = 3; + if ( rndmPtr->flat() < colRearrange) iEnd2 = 3; + int relColSign = + ( (flavEnds[iEnd1].id > 0 && flavEnds[iEnd1].id < 9) + || flavEnds[iEnd1].id < -10 ) ? 1 : -1; + if ( (flavEnds[iEnd2].id < 0 && flavEnds[iEnd2].id > -9) + || flavEnds[iEnd2].id > 10 ) relColSign *= -1; + if (relColSign == 1) iEnd2 = 2; + if (iEnd2 == 2) iEnd3 = 1; + if (iEnd2 == 3) iEnd4 = 1; + + // Then combine to get final two hadrons. + int idHad; + if ( abs(flavEnds[iEnd1].id) > 8 && abs(flavEnds[iEnd2].id) > 8) + diquarkClash = true; + else { + do idHad = flavSelPtr->combine( flavEnds[iEnd1], flavEnds[iEnd2]); + while (idHad == 0); + idProd.push_back( idHad); + } + if ( abs(flavEnds[iEnd3].id) > 8 && abs(flavEnds[iEnd4].id) > 8) + diquarkClash = true; + else { + do idHad = flavSelPtr->combine( flavEnds[iEnd3], flavEnds[iEnd4]); + while (idHad == 0); + idProd.push_back( idHad); + } + } + + // Find masses of the new hadrons. + for (int i = nFilled; i < int(idProd.size()) ; ++i) { + double mHad = particleDataPtr->mass(idProd[i]); + mProd.push_back( mHad); + mDiff -= mHad; + } + } + + // Optional: check that this decay mode is not explicitly defined. + if ( (meMode > 61 && meMode <= 80) && mDiff > mSafety && !diquarkClash ) { + int idMatch[10], idPNow; + usedChannel = false; + bool matched = false; + // Loop through all channels. Done if not same multiplicity. + for (int i = 0; i < decDataPtr->sizeChannels(); ++i) { + DecayChannel& channel = decDataPtr->channel(i); + if (channel.multiplicity() != nTotal) continue; + for (int k = 0; k < nTotal; ++k) idMatch[k] = channel.product(k); + // Match particles one by one until fail. + // Do not distinguish K0/K0bar/K0short/K0long at this stage. + for (int j = 0; j < nTotal; ++j) { + matched = false; + idPNow = idProd[j + 1]; + if (idPNow == -311 || idPNow == 130 || idPNow == 310) idPNow = 311; + for (int k = 0; k < nTotal - j; ++k) + if (idMatch[k] == idPNow || (idMatch[k] == -311 && idPNow == 311)) { + // Compress list of unmatched when matching worked. + idMatch[k] = idMatch[nTotal - 1 - j]; + matched = true; + break; + } + if (!matched) break; + } + // If matching worked, then chosen channel to be rejected. + if (matched) {usedChannel = true; break;} + } + } + + // Keep on trying until enough phase space and no clash. + } while (mDiff < mSafety || diquarkClash || usedChannel); + + // Update particle multiplicity. + mult = idProd.size() - 1; + + // For Dalitz decays shuffle Dalitz pair to the end of the list. + if (meMode == 11 || meMode == 12) { + int iL1 = 0; + int iL2 = 0; + for (int i = 1; i <= mult; ++i) { + if (idProd[i] == 11 || idProd[i] == 13 || idProd[i] == 15) iL1 = i; + if (idProd[i] == -11 || idProd[i] == -13 || idProd[i] == -15) iL2 = i; + } + if (iL1 > 0 && iL2 > 0) { + int idL1 = idProd[iL1]; + int idL2 = idProd[iL2]; + double mL1 = mProd[iL1]; + double mL2 = mProd[iL2]; + int iMove = 0; + for (int i = 1; i <= mult; ++i) if (i != iL1 && i != iL2) { + ++iMove; + idProd[iMove] = idProd[i]; + mProd[iMove] = mProd[i]; + } + idProd[mult - 1] = idL1; + idProd[mult] = idL2; + mProd[mult - 1] = mL1; + mProd[mult] = mL2; + } + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Set colour flow and scale in a decay explicitly to partons. + +bool ParticleDecays::setColours(Event& event) { + + // Decay to q qbar (or qbar q). + if (meMode == 91 && idProd[1] > 0 && idProd[1] < 9) { + int newCol = event.nextColTag(); + cols[1] = newCol; + acols[2] = newCol; + } else if (meMode == 91 && idProd[1] < 0 && idProd[1] > -9) { + int newCol = event.nextColTag(); + cols[2] = newCol; + acols[1] = newCol; + + // Decay to g g. + } else if (meMode == 91 && idProd[1] == 21) { + int newCol1 = event.nextColTag(); + int newCol2 = event.nextColTag(); + cols[1] = newCol1; + acols[1] = newCol2; + cols[2] = newCol2; + acols[2] = newCol1; + + // Decay to g g g. + } else if (meMode == 92 && idProd[1] == 21 && idProd[2] == 21 + && idProd[3] == 21) { + int newCol1 = event.nextColTag(); + int newCol2 = event.nextColTag(); + int newCol3 = event.nextColTag(); + cols[1] = newCol1; + acols[1] = newCol2; + cols[2] = newCol2; + acols[2] = newCol3; + cols[3] = newCol3; + acols[3] = newCol1; + + // Decay to g g gamma: locate which is gamma. + } else if (meMode == 92) { + int iGlu1 = (idProd[1] == 21) ? 1 : 3; + int iGlu2 = (idProd[2] == 21) ? 2 : 3; + int newCol1 = event.nextColTag(); + int newCol2 = event.nextColTag(); + cols[iGlu1] = newCol1; + acols[iGlu1] = newCol2; + cols[iGlu2] = newCol2; + acols[iGlu2] = newCol1; + + // Unknown decay mode means failure. + } else return false; + + // Set maximum scale to be mass of decaying particle. + scale = mProd[0]; + + // Done. + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/PartonDistributions.cxx b/PYTHIA8/pythia8140/src/PartonDistributions.cxx new file mode 100644 index 00000000000..ae2a51275c0 --- /dev/null +++ b/PYTHIA8/pythia8140/src/PartonDistributions.cxx @@ -0,0 +1,2153 @@ +// PartonDistributions.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the PDF, LHAPDF, +// GRV94L, CTEQ5L, MSTWpdf, CTEQ6pdf, GRVpiL, PomFix, PomH1FitAB, +// PomH1Jets and Lepton classes. + +#include "PartonDistributions.h" +#include "LHAPDFInterface.h" + +namespace Pythia8 { + +//========================================================================== + +// Base class for parton distribution functions. + +//-------------------------------------------------------------------------- + +// Resolve valence content for assumed meson. Possibly modified later. + +void PDF::setValenceContent() { + + // Subdivide meson by flavour content. + if (idBeamAbs < 100 || idBeamAbs > 1000) return; + int idTmp1 = idBeamAbs/100; + int idTmp2 = (idBeamAbs/10)%10; + + // Find which is quark and which antiquark. + if (idTmp1%2 == 0) { + idVal1 = idTmp1; + idVal2 = -idTmp2; + } else { + idVal1 = idTmp2; + idVal2 = -idTmp1; + } + if (idBeam < 0) { + idVal1 = -idVal1; + idVal2 = -idVal2; + } + + // Special case for Pomeron, to start off. + if (idBeamAbs == 990) { + idVal1 = 1; + idVal2 = -1; + } +} + +//-------------------------------------------------------------------------- + +// Standard parton densities. + +double PDF::xf(int id, double x, double Q2) { + + // Need to update if flavour, x or Q2 changed. + // Use idSav = 9 to indicate that ALL flavours are up-to-date. + // Assume that flavour and antiflavour always updated simultaneously. + if ( (abs(idSav) != abs(id) && idSav != 9) || x != xSav || Q2 != Q2Sav) + {idSav = id; xfUpdate(id, x, Q2); xSav = x; Q2Sav = Q2;} + + // Baryon and nondiagonal meson beams: only p, pbar, pi+, pi- for now. + if (idBeamAbs == 2212 || idBeamAbs == 211) { + int idNow = (idBeam > 0) ? id : -id; + int idAbs = abs(id); + if (idNow == 0 || idAbs == 21) return max(0., xg); + if (idNow == 1) return max(0., xd); + if (idNow == -1) return max(0., xdbar); + if (idNow == 2) return max(0., xu); + if (idNow == -2) return max(0., xubar); + if (idNow == 3) return max(0., xs); + if (idNow == -3) return max(0., xsbar); + if (idAbs == 4) return max(0., xc); + if (idAbs == 5) return max(0., xb); + if (idAbs == 22) return max(0., xgamma); + return 0.; + + // Diagonal meson beams: only pi0, Pomeron for now. + } else if (idBeam == 111 || idBeam == 990) { + int idAbs = abs(id); + if (id == 0 || idAbs == 21) return max(0., xg); + if (id == idVal1 || id == idVal2) return max(0., xu); + if (idAbs <= 2) return max(0., xubar); + if (idAbs == 3) return max(0., xs); + if (idAbs == 4) return max(0., xc); + if (idAbs == 5) return max(0., xb); + if (idAbs == 22) return max(0., xgamma); + return 0.; + + + // Lepton beam. + } else { + if (id == idBeam ) return max(0., xlepton); + if (abs(id) == 22) return max(0., xgamma); + return 0.; + } + +} + +//-------------------------------------------------------------------------- + +// Only valence part of parton densities. + +double PDF::xfVal(int id, double x, double Q2) { + + // Need to update if flavour, x or Q2 changed. + // Use idSav = 9 to indicate that ALL flavours are up-to-date. + // Assume that flavour and antiflavour always updated simultaneously. + if ( (abs(idSav) != abs(id) && idSav != 9) || x != xSav || Q2 != Q2Sav) + {idSav = id; xfUpdate(id, x, Q2); xSav = x; Q2Sav = Q2;} + + // Baryon and nondiagonal meson beams: only p, pbar, pi+, pi- for now. + if (idBeamAbs == 2212) { + int idNow = (idBeam > 0) ? id : -id; + if (idNow == 1) return max(0., xdVal); + if (idNow == 2) return max(0., xuVal); + return 0.; + } else if (idBeamAbs == 211) { + int idNow = (idBeam > 0) ? id : -id; + if (idNow == 2 || idNow == -1) return max(0., xuVal); + return 0.; + + // Diagonal meson beams: only pi0, Pomeron for now. + } else if (idBeam == 111 || idBeam == 990) { + if (id == idVal1 || id == idVal2) return max(0., xuVal); + return 0.; + + // Lepton beam. + } else { + if (id == idBeam) return max(0., xlepton); + return 0.; + } + +} + +//-------------------------------------------------------------------------- + +// Only sea part of parton densities. + +double PDF::xfSea(int id, double x, double Q2) { + + // Need to update if flavour, x or Q2 changed. + // Use idSav = 9 to indicate that ALL flavours are up-to-date. + // Assume that flavour and antiflavour always updated simultaneously. + if ( (abs(idSav) != abs(id) && idSav != 9) || x != xSav || Q2 != Q2Sav) + {idSav = id; xfUpdate(id, x, Q2); xSav = x; Q2Sav = Q2;} + + // Hadron beams. + if (idBeamAbs > 100) { + int idNow = (idBeam > 0) ? id : -id; + int idAbs = abs(id); + if (idNow == 0 || idAbs == 21) return max(0., xg); + if (idBeamAbs == 2212) { + if (idNow == 1) return max(0., xdSea); + if (idNow == -1) return max(0., xdbar); + if (idNow == 2) return max(0., xuSea); + if (idNow == -2) return max(0., xubar); + } else { + if (idAbs <= 2) return max(0., xuSea); + } + if (idNow == 3) return max(0., xs); + if (idNow == -3) return max(0., xsbar); + if (idAbs == 4) return max(0., xc); + if (idAbs == 5) return max(0., xb); + if (idAbs == 22) return max(0., xgamma); + return 0.; + + // Lepton beam. + } else { + if (abs(id) == 22) return max(0., xgamma); + return 0.; + } + +} + +//========================================================================== + +// Interface to the LHAPDF library. + +//-------------------------------------------------------------------------- + +// Definitions of static variables. + +string LHAPDF::latestSetName = " "; +int LHAPDF::latestMember = -1; +int LHAPDF::latestNSet = 0; + +//-------------------------------------------------------------------------- + +// Initialize a parton density function from LHAPDF. + +void LHAPDF::init(string setName, int member, Info* infoPtr) { + + // If already initialized then need not do anything. + if (setName == latestSetName && member == latestMember + && nSet == latestNSet) return; + + // Initialize set. If first character is '/' then assume that name + // is given with path, else not. + if (setName[0] == '/') LHAPDFInterface::initPDFsetM( nSet, setName); + else LHAPDFInterface::initPDFsetByNameM( nSet, setName); + + // Check that not dummy library was linked and put nSet negative. + isSet = (nSet >= 0); + if (!isSet) { + if (infoPtr > 0) infoPtr->errorMsg("Error from LHAPDF::init: " + "you try to use LHAPDF but did not link it"); + else cout << " Error from LHAPDF::init: you try to use LHAPDF " + << "but did not link it" << endl; + } + + // Initialize member. + LHAPDFInterface::initPDFM(nSet, member); + + // Do not collect statistics on under/overflow to save time and space. + LHAPDFInterface::setPDFparm( "NOSTAT" ); + LHAPDFInterface::setPDFparm( "LOWKEY" ); + + // Save values to avoid unnecessary reinitializations. + latestSetName = setName; + latestMember = member; + latestNSet = nSet; + +} + +//-------------------------------------------------------------------------- + +// Allow optional extrapolation beyond boundaries. + +void LHAPDF::setExtrapolate(bool extrapol) { + + LHAPDFInterface::setPDFparm( (extrapol) ? "EXTRAPOLATE" : "18" ); + +} + +//-------------------------------------------------------------------------- + +// Give the parton distribution function set from LHAPDF. + +void LHAPDF::xfUpdate(int , double x, double Q2) { + + // Let LHAPDF do the evaluation of parton densities. + double Q = sqrt( max( 0., Q2)); + + // Use special call if photon included in proton (so far only MRST2004qed) + if (latestSetName == "MRST2004qed.LHgrid" ) { + LHAPDFInterface::evolvePDFPHOTONM( nSet, x, Q, xfArray, xPhoton); + } + // Else use default LHAPDF call + else { + LHAPDFInterface::evolvePDFM( nSet, x, Q, xfArray); + xPhoton=0.0; + } + + // Update values. + xg = xfArray[6]; + xu = xfArray[8]; + xd = xfArray[7]; + xs = xfArray[9]; + xubar = xfArray[4]; + xdbar = xfArray[5]; + xsbar = xfArray[3]; + xc = xfArray[10]; + xb = xfArray[11]; + xgamma = xPhoton; + + // Subdivision of valence and sea. + xuVal = xu - xubar; + xuSea = xubar; + xdVal = xd - xdbar; + xdSea = xdbar; + + // idSav = 9 to indicate that all flavours reset. + idSav = 9; + +} + +//========================================================================== + +// Gives the GRV 94 L (leading order) parton distribution function set +// in parametrized form. Authors: M. Glueck, E. Reya and A. Vogt. +// Ref: M. Glueck, E. Reya and A. Vogt, Z.Phys. C67 (1995) 433. + +void GRV94L::xfUpdate(int id, double x, double Q2) { + + // Common expressions. Constrain Q2 for which parametrization is valid. + double mu2 = 0.23; + double lam2 = 0.2322 * 0.2322; + double s = (Q2 > mu2) ? log( log(Q2/lam2) / log(mu2/lam2) ) : 0.; + double ds = sqrt(s); + double s2 = s * s; + double s3 = s2 * s; + + // uv : + double nu = 2.284 + 0.802 * s + 0.055 * s2; + double aku = 0.590 - 0.024 * s; + double bku = 0.131 + 0.063 * s; + double au = -0.449 - 0.138 * s - 0.076 * s2; + double bu = 0.213 + 2.669 * s - 0.728 * s2; + double cu = 8.854 - 9.135 * s + 1.979 * s2; + double du = 2.997 + 0.753 * s - 0.076 * s2; + double uv = grvv (x, nu, aku, bku, au, bu, cu, du); + + // dv : + double nd = 0.371 + 0.083 * s + 0.039 * s2; + double akd = 0.376; + double bkd = 0.486 + 0.062 * s; + double ad = -0.509 + 3.310 * s - 1.248 * s2; + double bd = 12.41 - 10.52 * s + 2.267 * s2; + double cd = 6.373 - 6.208 * s + 1.418 * s2; + double dd = 3.691 + 0.799 * s - 0.071 * s2; + double dv = grvv (x, nd, akd, bkd, ad, bd, cd, dd); + + // udb : + double alx = 1.451; + double bex = 0.271; + double akx = 0.410 - 0.232 * s; + double bkx = 0.534 - 0.457 * s; + double agx = 0.890 - 0.140 * s; + double bgx = -0.981; + double cx = 0.320 + 0.683 * s; + double dx = 4.752 + 1.164 * s + 0.286 * s2; + double ex = 4.119 + 1.713 * s; + double esx = 0.682 + 2.978 * s; + double udb = grvw (x, s, alx, bex, akx, bkx, agx, bgx, cx, + dx, ex, esx); + + // del : + double ne = 0.082 + 0.014 * s + 0.008 * s2; + double ake = 0.409 - 0.005 * s; + double bke = 0.799 + 0.071 * s; + double ae = -38.07 + 36.13 * s - 0.656 * s2; + double be = 90.31 - 74.15 * s + 7.645 * s2; + double ce = 0.; + double de = 7.486 + 1.217 * s - 0.159 * s2; + double del = grvv (x, ne, ake, bke, ae, be, ce, de); + + // sb : + double sts = 0.; + double als = 0.914; + double bes = 0.577; + double aks = 1.798 - 0.596 * s; + double as = -5.548 + 3.669 * ds - 0.616 * s; + double bs = 18.92 - 16.73 * ds + 5.168 * s; + double dst = 6.379 - 0.350 * s + 0.142 * s2; + double est = 3.981 + 1.638 * s; + double ess = 6.402; + double sb = grvs (x, s, sts, als, bes, aks, as, bs, dst, est, ess); + + // cb : + double stc = 0.888; + double alc = 1.01; + double bec = 0.37; + double akc = 0.; + double ac = 0.; + double bc = 4.24 - 0.804 * s; + double dct = 3.46 - 1.076 * s; + double ect = 4.61 + 1.49 * s; + double esc = 2.555 + 1.961 * s; + double chm = grvs (x, s, stc, alc, bec, akc, ac, bc, dct, ect, esc); + + // bb : + double stb = 1.351; + double alb = 1.00; + double beb = 0.51; + double akb = 0.; + double ab = 0.; + double bb = 1.848; + double dbt = 2.929 + 1.396 * s; + double ebt = 4.71 + 1.514 * s; + double esb = 4.02 + 1.239 * s; + double bot = grvs (x, s, stb, alb, beb, akb, ab, bb, dbt, ebt, esb); + + // gl : + double alg = 0.524; + double beg = 1.088; + double akg = 1.742 - 0.930 * s; + double bkg = - 0.399 * s2; + double ag = 7.486 - 2.185 * s; + double bg = 16.69 - 22.74 * s + 5.779 * s2; + double cg = -25.59 + 29.71 * s - 7.296 * s2; + double dg = 2.792 + 2.215 * s + 0.422 * s2 - 0.104 * s3; + double eg = 0.807 + 2.005 * s; + double esg = 3.841 + 0.316 * s; + double gl = grvw (x, s, alg, beg, akg, bkg, ag, bg, cg, + dg, eg, esg); + + // Update values + xg = gl; + xu = uv + 0.5*(udb - del); + xd = dv + 0.5*(udb + del); + xubar = 0.5*(udb - del); + xdbar = 0.5*(udb + del); + xs = sb; + xsbar = sb; + xc = chm; + xb = bot; + + // Subdivision of valence and sea. + xuVal = uv; + xuSea = xubar; + xdVal = dv; + xdSea = xdbar; + + // idSav = 9 to indicate that all flavours reset. id change dummy. + idSav = 9; + id = 0; + +} + +//-------------------------------------------------------------------------- + +double GRV94L::grvv (double x, double n, double ak, double bk, double a, + double b, double c, double d) { + + double dx = sqrt(x); + return n * pow(x, ak) * (1. + a * pow(x, bk) + x * (b + c * dx)) * + pow(1. - x, d); + +} + +//-------------------------------------------------------------------------- + +double GRV94L::grvw (double x, double s, double al, double be, double ak, + double bk, double a, double b, double c, double d, double e, double es) { + + double lx = log(1./x); + return (pow(x, ak) * (a + x * (b + x * c)) * pow(lx, bk) + pow(s, al) + * exp(-e + sqrt(es * pow(s, be) * lx))) * pow(1. - x, d); + +} + +//-------------------------------------------------------------------------- + +double GRV94L::grvs (double x, double s, double sth, double al, double be, + double ak, double ag, double b, double d, double e, double es) { + + if(s <= sth) { + return 0.; + } else { + double dx = sqrt(x); + double lx = log(1./x); + return pow(s - sth, al) / pow(lx, ak) * (1. + ag * dx + b * x) * + pow(1. - x, d) * exp(-e + sqrt(es * pow(s, be) * lx)); + } + +} + +//========================================================================== + +// Gives the CTEQ 5 L (leading order) parton distribution function set +// in parametrized form. Parametrization by J. Pumplin. +// Ref: CTEQ Collaboration, H.L. Lai et al., Eur.Phys.J. C12 (2000) 375. + +// The range of (x, Q) covered by this parametrization of the QCD +// evolved parton distributions is 1E-6 < x < 1, 1.1 GeV < Q < 10 TeV. +// In the current implementation, densities are frozen at borders. + +void CTEQ5L::xfUpdate(int id, double x, double Q2) { + + // Constrain x and Q2 to range for which parametrization is valid. + double Q = sqrt( max( 1., min( 1e8, Q2) ) ); + x = max( 1e-6, min( 1.-1e-10, x) ); + + // Derived kinematical quantities. + double y = - log(x); + double u = log( x / 0.00001); + double x1 = 1. - x; + double x1L = log(1. - x); + double sumUbarDbar = 0.; + + // Parameters of parametrizations. + const double Qmin[8] = { 0., 0., 0., 0., 0., 0., 1.3, 4.5}; + const double alpha[8] = { 0.2987216, 0.3407552, 0.4491863, 0.2457668, + 0.5293999, 0.3713141, 0.03712017, 0.004952010 }; + const double ut1[8] = { 4.971265, 2.612618, -0.4656819, 3.862583, + 0.1895615, 3.753257, 4.400772, 5.562568 }; + const double ut2[8] = { -1.105128, -1.258304e5, -274.2390, -1.265969, + -3.069097, -1.113085, -1.356116, -1.801317 }; + const double am[8][9][3] = { + // d. + { { 0.5292616E+01, -0.2751910E+01, -0.2488990E+01 }, + { 0.9714424E+00, 0.1011827E-01, -0.1023660E-01 }, + { -0.1651006E+02, 0.7959721E+01, 0.8810563E+01 }, + { -0.1643394E+02, 0.5892854E+01, 0.9348874E+01 }, + { 0.3067422E+02, 0.4235796E+01, -0.5112136E+00 }, + { 0.2352526E+02, -0.5305168E+01, -0.1169174E+02 }, + { -0.1095451E+02, 0.3006577E+01, 0.5638136E+01 }, + { -0.1172251E+02, -0.2183624E+01, 0.4955794E+01 }, + { 0.1662533E-01, 0.7622870E-02, -0.4895887E-03 } }, + // u. + { { 0.9905300E+00, -0.4502235E+00, 0.1624441E+00 }, + { 0.8867534E+00, 0.1630829E-01, -0.4049085E-01 }, + { 0.8547974E+00, 0.3336301E+00, 0.1371388E+00 }, + { 0.2941113E+00, -0.1527905E+01, 0.2331879E+00 }, + { 0.3384235E+02, 0.3715315E+01, 0.8276930E+00 }, + { 0.6230115E+01, 0.3134639E+01, -0.1729099E+01 }, + { -0.1186928E+01, -0.3282460E+00, 0.1052020E+00 }, + { -0.8545702E+01, -0.6247947E+01, 0.3692561E+01 }, + { 0.1724598E-01, 0.7120465E-02, 0.4003646E-04 } }, + // g. + { { 0.1193572E+03, -0.3886845E+01, -0.1133965E+01 }, + { -0.9421449E+02, 0.3995885E+01, 0.1607363E+01 }, + { 0.4206383E+01, 0.2485954E+00, 0.2497468E+00 }, + { 0.1210557E+03, -0.3015765E+01, -0.1423651E+01 }, + { -0.1013897E+03, -0.7113478E+00, 0.2621865E+00 }, + { -0.1312404E+01, -0.9297691E+00, -0.1562531E+00 }, + { 0.1627137E+01, 0.4954111E+00, -0.6387009E+00 }, + { 0.1537698E+00, -0.2487878E+00, 0.8305947E+00 }, + { 0.2496448E-01, 0.2457823E-02, 0.8234276E-03 } }, + // ubar + dbar. + { { 0.2647441E+02, 0.1059277E+02, -0.9176654E+00 }, + { 0.1990636E+01, 0.8558918E-01, 0.4248667E-01 }, + { -0.1476095E+02, -0.3276255E+02, 0.1558110E+01 }, + { -0.2966889E+01, -0.3649037E+02, 0.1195914E+01 }, + { -0.1000519E+03, -0.2464635E+01, 0.1964849E+00 }, + { 0.3718331E+02, 0.4700389E+02, -0.2772142E+01 }, + { -0.1872722E+02, -0.2291189E+02, 0.1089052E+01 }, + { -0.1628146E+02, -0.1823993E+02, 0.2537369E+01 }, + { -0.1156300E+01, -0.1280495E+00, 0.5153245E-01 } }, + // dbar/ubar. + { { -0.6556775E+00, 0.2490190E+00, 0.3966485E-01 }, + { 0.1305102E+01, -0.1188925E+00, -0.4600870E-02 }, + { -0.2371436E+01, 0.3566814E+00, -0.2834683E+00 }, + { -0.6152826E+01, 0.8339877E+00, -0.7233230E+00 }, + { -0.8346558E+01, 0.2892168E+01, 0.2137099E+00 }, + { 0.1279530E+02, 0.1021114E+00, 0.5787439E+00 }, + { 0.5858816E+00, -0.1940375E+01, -0.4029269E+00 }, + { -0.2795725E+02, -0.5263392E+00, 0.1290229E+01 }, + { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } }, + // sbar. + { { 0.1580931E+01, -0.2273826E+01, -0.1822245E+01 }, + { 0.2702644E+01, 0.6763243E+00, 0.7231586E-02 }, + { -0.1857924E+02, 0.3907500E+01, 0.5850109E+01 }, + { -0.3044793E+02, 0.2639332E+01, 0.5566644E+01 }, + { -0.4258011E+01, -0.5429244E+01, 0.4418946E+00 }, + { 0.3465259E+02, -0.5532604E+01, -0.4904153E+01 }, + { -0.1658858E+02, 0.2923275E+01, 0.2266286E+01 }, + { -0.1149263E+02, 0.2877475E+01, -0.7999105E+00 }, + { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } }, + // cbar. + { { -0.8293661E+00, -0.3982375E+01, -0.6494283E-01 }, + { 0.2754618E+01, 0.8338636E+00, -0.6885160E-01 }, + { -0.1657987E+02, 0.1439143E+02, -0.6887240E+00 }, + { -0.2800703E+02, 0.1535966E+02, -0.7377693E+00 }, + { -0.6460216E+01, -0.4783019E+01, 0.4913297E+00 }, + { 0.3141830E+02, -0.3178031E+02, 0.7136013E+01 }, + { -0.1802509E+02, 0.1862163E+02, -0.4632843E+01 }, + { -0.1240412E+02, 0.2565386E+02, -0.1066570E+02 }, + { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } }, + // bbar. + { { -0.6031237E+01, 0.1992727E+01, -0.1076331E+01 }, + { 0.2933912E+01, 0.5839674E+00, 0.7509435E-01 }, + { -0.8284919E+01, 0.1488593E+01, -0.8251678E+00 }, + { -0.1925986E+02, 0.2805753E+01, -0.3015446E+01 }, + { -0.9480483E+01, -0.9767837E+00, -0.1165544E+01 }, + { 0.2193195E+02, -0.1788518E+02, 0.9460908E+01 }, + { -0.1327377E+02, 0.1201754E+02, -0.6277844E+01 }, + { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 }, + { 0.0000000E+00, 0.0000000E+00, 0.0000000E+00 } } }; + + // Loop over 8 different parametrizations. Check if inside allowed region. + for (int i = 0; i < 8; ++i) { + double answer = 0.; + if (Q > max(Qmin[i], alpha[i])) { + + // Evaluate answer. + double tmp = log(Q / alpha[i]); + double sb = log(tmp); + double sb1 = sb - 1.2; + double sb2 = sb1*sb1; + double af[9]; + for (int j = 0; j < 9; ++j) + af[j] = am[i][j][0] + sb1 * am[i][j][1] + sb2 * am[i][j][2]; + double part1 = af[1] * pow( y, 1. + 0.01 * af[4]) * (1. + af[8] * u); + double part2 = af[0] * x1 + af[3] * x; + double part3 = x * x1 * (af[5] + af[6] * x1 + af[7] * x * x1); + double part4 = (ut2[i] < -100.) ? ut1[i] * x1L + af[2] * x1L + : ut1[i] * x1L + af[2] * log(x1 + exp(ut2[i])); + answer = x * exp( part1 + part2 + part3 + part4); + answer *= 1. - Qmin[i] / Q; + } + + // Store results. + if (i == 0) xd = x * answer; + else if (i == 1) xu = x * answer; + else if (i == 2) xg = x * answer; + else if (i == 3) sumUbarDbar = x * answer; + else if (i == 4) { xubar = sumUbarDbar / (1. + answer); + xdbar = sumUbarDbar * answer / (1. + answer); } + else if (i == 5) {xs = x * answer; xsbar = xs;} + else if (i == 6) xc = x * answer; + else if (i == 7) xb = x * answer; + } + + // Subdivision of valence and sea. + xuVal = xu - xubar; + xuSea = xubar; + xdVal = xd - xdbar; + xdSea = xdbar; + + // idSav = 9 to indicate that all flavours reset. id change is dummy here. + idSav = 9; + id = 0; + +} + +//========================================================================== + +// The MSTWpdf class. +// MSTW 2008 PDF's, specifically the LO one. +// Original C++ version by Jeppe Andersen. +// Modified by Graeme Watt . + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of parton flavours, x and Q2 grid points, +// bins below c and b thresholds. +const int MSTWpdf::np = 12; +const int MSTWpdf::nx = 64; +const int MSTWpdf::nq = 48; +const int MSTWpdf::nqc0 = 4; +const int MSTWpdf::nqb0 = 14; + +// Range of (x, Q2) grid. +const double MSTWpdf::xmin = 1e-6; +const double MSTWpdf::xmax = 1.0; +const double MSTWpdf::qsqmin = 1.0; +const double MSTWpdf::qsqmax = 1e9; + +// Array of x values. +const double MSTWpdf::xxInit[65] = {0., 1e-6, 2e-6, 4e-6, 6e-6, 8e-6, + 1e-5, 2e-5, 4e-5, 6e-5, 8e-5, 1e-4, 2e-4, 4e-4, 6e-4, 8e-4, + 1e-3, 2e-3, 4e-3, 6e-3, 8e-3, 1e-2, 1.4e-2, 2e-2, 3e-2, 4e-2, 6e-2, + 8e-2, 0.10, 0.125, 0.15, 0.175, 0.20, 0.225, 0.25, 0.275, 0.30, + 0.325, 0.35, 0.375, 0.40, 0.425, 0.45, 0.475, 0.50, 0.525, 0.55, + 0.575, 0.60, 0.625, 0.65, 0.675, 0.70, 0.725, 0.75, 0.775, 0.80, + 0.825, 0.85, 0.875, 0.90, 0.925, 0.95, 0.975, 1.0 }; + +// Array of Q values. +const double MSTWpdf::qqInit[49] = {0., 1.0, 1.25, 1.5, 0., 0., 2.5, 3.2, + 4.0, 5.0, 6.4, 8.0, 10., 12., 0., 0., 26.0, 40.0, 64.0, 1e2, 1.6e2, + 2.4e2, 4e2, 6.4e2, 1e3, 1.8e3, 3.2e3, 5.6e3, 1e4, 1.8e4, 3.2e4, 5.6e4, + 1e5, 1.8e5, 3.2e5, 5.6e5, 1e6, 1.8e6, 3.2e6, 5.6e6, 1e7, 1.8e7, 3.2e7, + 5.6e7, 1e8, 1.8e8, 3.2e8, 5.6e8, 1e9 }; + +//-------------------------------------------------------------------------- + +// Initialize PDF: read in data grid from file and set up interpolation. + +void MSTWpdf::init(int iFitIn, string xmlPath, Info* infoPtr) { + + // Choice of fit among possibilities. Counters and temporary variables. + iFit = iFitIn; + int i,n,m,k,l,j; + double dtemp; + + // Variables used for initialising c_ij array: + double f[np+1][nx+1][nq+1]; + double f1[np+1][nx+1][nq+1]; // derivative w.r.t. x + double f2[np+1][nx+1][nq+1]; // derivative w.r.t. q + double f12[np+1][nx+1][nq+1];// cross derivative + double f21[np+1][nx+1][nq+1];// cross derivative + int wt[16][16]={{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0}, + {-3,0,0,3,0,0,0,0,-2,0,0,-1,0,0,0,0}, + {2,0,0,-2,0,0,0,0,1,0,0,1,0,0,0,0}, + {0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0}, + {0,0,0,0,-3,0,0,3,0,0,0,0,-2,0,0,-1}, + {0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1}, + {-3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0}, + {9,-9,9,-9,6,3,-3,-6,6,-6,-3,3,4,2,1,2}, + {-6,6,-6,6,-4,-2,2,4,-3,3,3,-3,-2,-1,-1,-2}, + {2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0}, + {-6,6,-6,6,-3,-3,3,3,-4,4,2,-2,-2,-2,-1,-1}, + {4,-4,4,-4,2,2,-2,-2,2,-2,-2,2,1,1,1,1}}; + double xxd,d1d2,cl[16],x[16],d1,d2,y[5],y1[5],y2[5],y12[5]; + double mc2,mb2,eps=1e-6; // q^2 grid points at mc2+eps, mb2+eps + + // Select which data file to read for current fit. + if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; + string fileName = " "; + if (iFit == 1) fileName = "mrstlostar.00.dat"; + if (iFit == 2) fileName = "mrstlostarstar.00.dat"; + if (iFit == 3) fileName = "mstw2008lo.00.dat"; + if (iFit == 4) fileName = "mstw2008nlo.00.dat"; + + // Open data file. + ifstream data_file( (xmlPath + fileName).c_str() ); + if (!data_file.good()) { + if (infoPtr > 0) infoPtr->errorMsg("Error from MSTWpdf::init: " + "did not find parametrization file ", fileName); + else cout << " Error from MSTWpdf::init: " + << "did not find parametrization file " << fileName << endl; + isSet = false; + return; + } + + // Read distance, tolerance, heavy quark masses + // and alphaS values from file. + char comma; + int nExtraFlavours; + data_file.ignore(256,'\n'); + data_file.ignore(256,'\n'); + data_file.ignore(256,'='); data_file >> distance >> tolerance; + data_file.ignore(256,'='); data_file >> mCharm; + data_file.ignore(256,'='); data_file >> mBottom; + data_file.ignore(256,'='); data_file >> alphaSQ0; + data_file.ignore(256,'='); data_file >> alphaSMZ; + data_file.ignore(256,'='); data_file >> alphaSorder >> comma >> alphaSnfmax; + data_file.ignore(256,'='); data_file >> nExtraFlavours; + data_file.ignore(256,'\n'); + data_file.ignore(256,'\n'); + data_file.ignore(256,'\n'); + + // Use c and b quark masses for outlay of qq array. + for (int iqq = 0; iqq < 49; ++iqq) qq[iqq] = qqInit[iqq]; + mc2=mCharm*mCharm; + mb2=mBottom*mBottom; + qq[4]=mc2; + qq[5]=mc2+eps; + qq[14]=mb2; + qq[15]=mb2+eps; + + // Check that the heavy quark masses are sensible. + if (mc2 < qq[3] || mc2 > qq[6]) { + if (infoPtr > 0) infoPtr->errorMsg("Error from MSTWpdf::init: " + "invalid mCharm"); + else cout << " Error from MSTWpdf::init: invalid mCharm" << endl; + isSet = false; + return; + } + if (mb2 < qq[13] || mb2 > qq[16]) { + if (infoPtr > 0) infoPtr->errorMsg("Error from MSTWpdf::init: " + "invalid mBottom"); + else cout << " Error from MSTWpdf::init: invalid mBottom" << endl; + isSet = false; + return; + } + + // The nExtraFlavours variable is provided to aid compatibility + // with future grids where, for example, a photon distribution + // might be provided (cf. the MRST2004QED PDFs). + if (nExtraFlavours < 0 || nExtraFlavours > 1) { + if (infoPtr > 0) infoPtr->errorMsg("Error from MSTWpdf::init: " + "invalid nExtraFlavours"); + else cout << " Error from MSTWpdf::init: invalid nExtraFlavours" << endl; + isSet = false; + return; + } + + // Now read in the grids from the grid file. + for (n=1;n<=nx-1;n++) + for (m=1;m<=nq;m++) { + for (i=1;i<=9;i++) + data_file >> f[i][n][m]; + if (alphaSorder==2) { // only at NNLO + data_file >> f[10][n][m]; // = chm-cbar + data_file >> f[11][n][m]; // = bot-bbar + } + else { + f[10][n][m] = 0.; // = chm-cbar + f[11][n][m] = 0.; // = bot-bbar + } + if (nExtraFlavours>0) + data_file >> f[12][n][m]; // = photon + else + f[12][n][m] = 0.; // photon + if (data_file.eof()) { + if (infoPtr > 0) infoPtr->errorMsg("Error from MSTWpdf::init: " + "failed to read in data file"); + else cout << " Error from MSTWpdf::init: failed to read in data file" + << endl; + isSet = false; + return; + } + } + + // Check that ALL the file contents have been read in. + data_file >> dtemp; + if (!data_file.eof()) { + if (infoPtr > 0) infoPtr->errorMsg("Error from MSTWpdf::init: " + "failed to read in data file"); + else cout << " Error from MSTWpdf::init: failed to read in data file" + << endl; + isSet = false; + return; + } + + // Close the datafile. + data_file.close(); + + // PDFs are identically zero at x = 1. + for (i=1;i<=np;i++) + for (m=1;m<=nq;m++) + f[i][nx][m]=0.0; + + // Set up the new array in log10(x) and log10(qsq). + for (i=1;i<=nx;i++) + xx[i]=log10(xxInit[i]); + for (m=1;m<=nq;m++) + qq[m]=log10(qq[m]); + + // Now calculate the derivatives used for bicubic interpolation. + for (i=1;i<=np;i++) { + + // Start by calculating the first x derivatives + // along the first x value: + for (m=1;m<=nq;m++) { + f1[i][1][m]=polderivative1(xx[1],xx[2],xx[3],f[i][1][m],f[i][2][m], + f[i][3][m]); + // Then along the rest (up to the last): + for (k=2;kpow(10.,qq[nqc0]) && qsqpow(10.,qq[nqb0]) && qsqxmax) return 0.; + + if (qsqqsqmax) { + interpolate=0; + } + + if (f==0) ip=1; + else if (f>=1 && f<=5) ip=f+1; + else if (f<=-1 && f>=-5) ip=-f+1; + else if (f>=7 && f<=11) ip=f; + else if (f==13) ip=12; + else if (abs(f)==6 || f==12) return 0.; + else return 0.; + + // Interpolation in log10(x), log10(qsq): + xxx=log10(x); + qqq=log10(qsq); + + if (interpolate==1) { // do usual interpolation + parton_pdf=parton_interpolate(ip,xxx,qqq); + if (f<=-1 && f>=-5) // antiquark = quark - valence + parton_pdf -= parton_interpolate(ip+5,xxx,qqq); + } + else if (interpolate==-1) { // extrapolate to low Q^2 + + if (x=-5) { // antiquark = quark - valence + parton_pdf -= parton_extrapolate(ip+5,xxx,log10(qsqmin)); + parton_pdf1 -= parton_extrapolate(ip+5,xxx,log10(1.01*qsqmin)); + } + } + else { // do usual interpolation + parton_pdf = parton_interpolate(ip,xxx,log10(qsqmin)); + parton_pdf1 = parton_interpolate(ip,xxx,log10(1.01*qsqmin)); + if (f<=-1 && f>=-5) { // antiquark = quark - valence + parton_pdf -= parton_interpolate(ip+5,xxx,log10(qsqmin)); + parton_pdf1 -= parton_interpolate(ip+5,xxx,log10(1.01*qsqmin)); + } + } + // Calculate the anomalous dimension, dlog(xf)/dlog(qsq), + // evaluated at qsqmin. Then extrapolate the PDFs to low + // qsq < qsqmin by interpolating the anomalous dimenion between + // the value at qsqmin and a value of 1 for qsq << qsqmin. + // If value of PDF at qsqmin is very small, just set + // anomalous dimension to 1 to prevent rounding errors. + if (fabs(parton_pdf) >= 1.e-5) + anom = max(-2.5, (parton_pdf1-parton_pdf)/parton_pdf/0.01); + else anom = 1.; + parton_pdf = parton_pdf*pow(qsq/qsqmin,anom*qsq/qsqmin+1.-qsq/qsqmin); + + } + else { // extrapolate outside PDF grid to low x or high Q^2 + parton_pdf = parton_extrapolate(ip,xxx,qqq); + if (f<=-1 && f>=-5) // antiquark = quark - valence + parton_pdf -= parton_extrapolate(ip+5,xxx,qqq); + } + + return parton_pdf; +} + +//-------------------------------------------------------------------------- + +// Interpolate PDF value inside data grid. + +double MSTWpdf::parton_interpolate(int ip, double xxx, double qqq) { + + double g, t, u; + int n, m, l; + + n=locate(xx,nx,xxx); // 0: below xmin, nx: above xmax + m=locate(qq,nq,qqq); // 0: below qsqmin, nq: above qsqmax + + t=(xxx-xx[n])/(xx[n+1]-xx[n]); + u=(qqq-qq[m])/(qq[m+1]-qq[m]); + + // Assume PDF proportional to (1-x)^p as x -> 1. + if (n==nx-1) { + double g0=((c[ip][n][m][1][4]*u+c[ip][n][m][1][3])*u + +c[ip][n][m][1][2])*u+c[ip][n][m][1][1]; // value at xx[n] + double g1=((c[ip][n-1][m][1][4]*u+c[ip][n-1][m][1][3])*u + +c[ip][n-1][m][1][2])*u+c[ip][n-1][m][1][1]; // value at xx[n-1] + double p = 1.0; + if (g0>0.0&&g1>0.0) p = log(g1/g0)/log((xx[n+1]-xx[n-1])/(xx[n+1]-xx[n])); + if (p<=1.0) p=1.0; + g=g0*pow((xx[n+1]-xxx)/(xx[n+1]-xx[n]),p); + } + + // Usual interpolation. + else { + g=0.0; + for (l=4;l>=1;l--) { + g=t*g+((c[ip][n][m][l][4]*u+c[ip][n][m][l][3])*u + +c[ip][n][m][l][2])*u+c[ip][n][m][l][1]; + } + } + + return g; +} + +//-------------------------------------------------------------------------- + +// Extrapolate PDF value outside data grid. + + +double MSTWpdf::parton_extrapolate(int ip, double xxx, double qqq) { + + double parton_pdf=0.; + int n,m; + + n=locate(xx,nx,xxx); // 0: below xmin, nx: above xmax + m=locate(qq,nq,qqq); // 0: below qsqmin, nq: above qsqmax + + if (n==0&&(m>0&&m1e-3 && f1>1e-3 ) { // if values are positive, keep them so + f0=log(f0); + f1=log(f1); + parton_pdf=exp(f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1])); + } else // otherwise just extrapolate in the value + parton_pdf=f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1]); + + } if (n>0&&m==nq) { // if extrapolation into large q only + + double f0,f1; + f0=parton_interpolate(ip,xxx,qq[nq]); + f1=parton_interpolate(ip,xxx,qq[nq-1]); + if ( f0>1e-3 && f1>1e-3 ) { // if values are positive, keep them so + f0=log(f0); + f1=log(f1); + parton_pdf=exp(f0+(f0-f1)/(qq[nq]-qq[nq-1])*(qqq-qq[nq])); + } else // otherwise just extrapolate in the value + parton_pdf=f0+(f0-f1)/(qq[nq]-qq[nq-1])*(qqq-qq[nq]); + + } if (n==0&&m==nq) { // if extrapolation into large q AND small x + + double f0,f1; + f0=parton_extrapolate(ip,xx[1],qqq); + f1=parton_extrapolate(ip,xx[2],qqq); + if ( f0>1e-3 && f1>1e-3 ) { // if values are positive, keep them so + f0=log(f0); + f1=log(f1); + parton_pdf=exp(f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1])); + } else // otherwise just extrapolate in the value + parton_pdf=f0+(f1-f0)/(xx[2]-xx[1])*(xxx-xx[1]); + + } + + return parton_pdf; +} + +//-------------------------------------------------------------------------- + +// Returns an integer j such that x lies inbetween xloc[j] and xloc[j+1]. +// unit offset of increasing ordered array xloc assumed. +// n is the length of the array (xloc[n] highest element). + +int MSTWpdf::locate(double xloc[],int n,double x) { + int ju,jm,jl(0),j; + ju=n+1; + + while (ju-jl>1) { + jm=(ju+jl)/2; // compute a mid point. + if ( x>= xloc[jm]) + jl=jm; + else ju=jm; + } + if (x==xloc[1]) j=1; + else if (x==xloc[n]) j=n-1; + else j=jl; + + return j; +} + +//-------------------------------------------------------------------------- + +// Returns the estimate of the derivative at x1 obtained by a polynomial +// interpolation using the three points (x_i,y_i). + +double MSTWpdf::polderivative1(double x1, double x2, double x3, double y1, + double y2, double y3) { + + return (x3*x3*(y1-y2)+2.0*x1*(x3*(-y1+y2)+x2*(y1-y3))+x2*x2*(-y1+y3) + +x1*x1*(-y2+y3))/((x1-x2)*(x1-x3)*(x2-x3)); + +} + +//-------------------------------------------------------------------------- + +// Returns the estimate of the derivative at x2 obtained by a polynomial +// interpolation using the three points (x_i,y_i). + +double MSTWpdf::polderivative2(double x1, double x2, double x3, double y1, + double y2, double y3) { + + return (x3*x3*(y1-y2)-2.0*x2*(x3*(y1-y2)+x1*(y2-y3))+x2*x2*(y1-y3) + +x1*x1*(y2-y3))/((x1-x2)*(x1-x3)*(x2-x3)); + +} + +//-------------------------------------------------------------------------- + +// Returns the estimate of the derivative at x3 obtained by a polynomial +// interpolation using the three points (x_i,y_i). + +double MSTWpdf::polderivative3(double x1, double x2, double x3, double y1, + double y2, double y3) { + + return (x3*x3*(-y1+y2)+2.0*x2*x3*(y1-y3)+x1*x1*(y2-y3)+x2*x2*(-y1+y3) + +2.0*x1*x3*(-y2+y3))/((x1-x2)*(x1-x3)*(x2-x3)); + +} + +//========================================================================== + +// The CTEQ6pdf class. +// Code for handling CTEQ6L, CTEQ6L1, CTEQ66.00, CT09MC1, CT09MC2, (CT09MCS?). + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Stay away from xMin, xMax, Qmin, Qmax limits. +const double CTEQ6pdf::EPSILON = 1e-6; + +// Assumed approximate power of small-x behaviour for interpolation. +const double CTEQ6pdf::XPOWER = 0.3; + +//-------------------------------------------------------------------------- + +// Initialize PDF: read in data grid from file. + +void CTEQ6pdf::init(int iFitIn, string xmlPath, Info* infoPtr) { + + // Choice of fit among possibilities. + iFit = iFitIn; + + // Select which data file to read for current fit. + if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; + string fileName = " "; + if (iFit == 1) fileName = "cteq6l.tbl"; + if (iFit == 2) fileName = "cteq6l1.tbl"; + if (iFit == 3) fileName = "ctq66.00.pds"; + if (iFit == 4) fileName = "ct09mc1.pds"; + if (iFit == 5) fileName = "ct09mc2.pds"; + if (iFit == 6) fileName = "ct09mcs.pds"; + bool isPdsGrid = (iFit > 2); + + // Open data file. + ifstream pdfgrid( (xmlPath + fileName).c_str() ); + if (!pdfgrid.good()) { + if (infoPtr > 0) infoPtr->errorMsg("Error from CTEQ6pdf::init: " + "did not find parametrization file ", fileName); + else cout << " Error from CTEQ6pdf::init: " + << "did not find parametrization file " << fileName << endl; + isSet = false; + return; + } + + // Read in common information. + int iDum; + double orderTmp, nQTmp, qTmp, rDum; + string line; + getline( pdfgrid, line); + getline( pdfgrid, line); + getline( pdfgrid, line); + istringstream is1(line); + is1 >> orderTmp >> nQTmp >> lambda >> mQ[1] >> mQ[2] >> mQ[3] + >> mQ[4] >> mQ[5] >> mQ[6]; + order = int(orderTmp + 0.5); + nQuark = int(nQTmp + 0.5); + getline( pdfgrid, line); + + // Read in information for the .pds grid format. + if (isPdsGrid) { + getline( pdfgrid, line); + istringstream is2(line); + is2 >> iDum >> iDum >> iDum >> nfMx >> mxVal >> iDum; + if (mxVal > 4) mxVal = 3; + getline( pdfgrid, line); + getline( pdfgrid, line); + istringstream is3(line); + is3 >> nX >> nT >> iDum >> nG >> iDum; + for (int i = 0; i < nG + 2; ++i) getline( pdfgrid, line); + getline( pdfgrid, line); + istringstream is4(line); + is4 >> qIni >> qMax; + for (int iT = 0; iT <= nT; ++iT) { + getline( pdfgrid, line); + istringstream is5(line); + is5 >> qTmp; + tv[iT] = log( log( qTmp/lambda)); + } + getline( pdfgrid, line); + getline( pdfgrid, line); + istringstream is6(line); + is6 >> xMin >> rDum; + int nPackX = 6; + xv[0] = 0.; + for (int iXrng = 0; iXrng < int( (nX + nPackX - 1) / nPackX); ++iXrng) { + getline( pdfgrid, line); + istringstream is7(line); + for (int iX = nPackX * iXrng + 1; iX <= nPackX * (iXrng + 1); ++iX) + if (iX <= nX) is7 >> xv[iX]; + } + } + + // Read in information for the .tbl grid format. + else { + mxVal = 2; + getline( pdfgrid, line); + istringstream is2(line); + is2 >> nX >> nT >> nfMx; + getline( pdfgrid, line); + getline( pdfgrid, line); + istringstream is3(line); + is3 >> qIni >> qMax; + int nPackT = 6; + for (int iTrng = 0; iTrng < int( (nT + nPackT) / nPackT); ++iTrng) { + getline( pdfgrid, line); + istringstream is4(line); + for (int iT = nPackT * iTrng; iT < nPackT * (iTrng + 1); ++iT) + if (iT <= nT) { + is4 >> qTmp; + tv[iT] = log( log( qTmp / lambda) ); + } + } + getline( pdfgrid, line); + getline( pdfgrid, line); + istringstream is5(line); + is5 >> xMin; + int nPackX = 6; + for (int iXrng = 0; iXrng < int( (nX + nPackX) / nPackX); ++iXrng) { + getline( pdfgrid, line); + istringstream is6(line); + for (int iX = nPackX * iXrng; iX < nPackX * (iXrng + 1); ++iX) + if (iX <= nX) is6 >> xv[iX]; + } + } + + // Read in the grid proper. + getline( pdfgrid, line); + int nBlk = (nX + 1) * (nT + 1); + int nPts = nBlk * (nfMx + 1 + mxVal); + int nPack = (isPdsGrid) ? 6 : 5; + for (int iRng = 0; iRng < int( (nPts + nPack - 1) / nPack); ++iRng) { + getline( pdfgrid, line); + istringstream is8(line); + for (int i = nPack * iRng + 1; i <= nPack * (iRng + 1); ++i) + if (i <= nPts) is8 >> upd[i]; + } + + // Initialize x grid mapped to x^0.3. + xvpow[0] = 0.; + for (int iX = 1; iX <= nX; ++iX) xvpow[iX] = pow(xv[iX], XPOWER); + + // Set x and Q borders with some margin. + xMinEps = xMin * (1. + EPSILON); + xMaxEps = 1. - EPSILON; + qMinEps = qIni * (1. + EPSILON); + qMaxEps = qMax * (1. - EPSILON); + +} + +//-------------------------------------------------------------------------- + +// Update PDF values. + +void CTEQ6pdf::xfUpdate(int id, double x, double Q2) { + + // Update using CTEQ6 routine, within allowed (x, q) range. + double xEps = max( xMinEps, x); + double qEps = max( qMinEps, min( qMaxEps, sqrtpos(Q2) ) ); + + // Gluon: + double glu = xEps * parton6( 0, xEps, qEps); + // Sea quarks (note wrong order u, d): + double bot = xEps * parton6( 5, xEps, qEps); + double chm = xEps * parton6( 4, xEps, qEps); + double str = xEps * parton6( 3, xEps, qEps); + double usea = xEps * parton6(-1, xEps, qEps); + double dsea = xEps * parton6(-2, xEps, qEps); + // Valence quarks: + double upv = xEps * parton6( 1, xEps, qEps) - usea; + double dnv = xEps * parton6( 2, xEps, qEps) - dsea; + + // Transfer to Pythia notation. + xg = glu; + xu = upv + usea; + xd = dnv + dsea; + xubar = usea; + xdbar = dsea; + xs = str; + xsbar = str; + xc = chm; + xb = bot; + xgamma = 0.; + + // Subdivision of valence and sea. + xuVal = upv; + xuSea = usea; + xdVal = dnv; + xdSea = dsea; + + // idSav = 9 to indicate that all flavours reset. id change dummy. + idSav = 9; + id = 0; + +} + +//-------------------------------------------------------------------------- + +// Returns the PDF value for parton of flavour iParton at x, q. + +double CTEQ6pdf::parton6(int iParton, double x, double q) { + + // Put zero for large x. Parton table and interpolation variables. + if (x > xMaxEps) return 0.; + int iP = (iParton > mxVal) ? -iParton : iParton; + double ss = pow( x, XPOWER); + double tt = log( log(q / lambda) ); + + // Find location in grid.Skip if same as in latest call. + if (x != xLast || q != qLast) { + + // Binary search in x grid. + iGridX = 0; + iGridLX = -1; + int ju = nX + 1; + int jm = 0; + while (ju - iGridLX > 1 && jm >= 0) { + jm = (ju + iGridLX) / 2; + if (x >= xv[jm]) iGridLX = jm; + else ju = jm; + } + + // Separate acceptable from unacceptable grid points. + if (iGridLX <= -1) return 0.; + else if (iGridLX == 0) iGridX = 0; + else if (iGridLX <= nX - 2) iGridX = iGridLX - 1; + else if (iGridLX == nX - 1) iGridX = iGridLX - 2; + else return 0.; + + // Expressions for interpolation in x Grid. + if (iGridLX > 1 && iGridLX < nX - 1) { + double svec1 = xvpow[iGridX]; + double svec2 = xvpow[iGridX+1]; + double svec3 = xvpow[iGridX+2]; + double svec4 = xvpow[iGridX+3]; + double s12 = svec1 - svec2; + double s13 = svec1 - svec3; + xConst[8] = svec2 - svec3; + double s24 = svec2 - svec4; + double s34 = svec3 - svec4; + xConst[6] = ss - svec2; + xConst[7] = ss - svec3; + xConst[0] = s13 / xConst[8]; + xConst[1] = s12 / xConst[8]; + xConst[2] = s34 / xConst[8]; + xConst[3] = s24 / xConst[8]; + double s1213 = s12 + s13; + double s2434 = s24 + s34; + double sdet = s12 * s34 - s1213 * s2434; + double tmp = xConst[6] * xConst[7] / sdet; + xConst[4] = (s34 * xConst[6] - s2434 * xConst[7]) * tmp / s12; + xConst[5] = (s1213 * xConst[6] - s12 * xConst[7]) * tmp / s34; + } + + // Binary search in Q grid. + iGridQ = 0; + iGridLQ = -1; + ju = nT + 1; + jm = 0; + while (ju - iGridLQ > 1 && jm >= 0) { + jm = (ju + iGridLQ) / 2; + if (tt >= tv[jm]) iGridLQ = jm; + else ju = jm; + } + if (iGridLQ == 0) iGridQ = 0; + else if (iGridLQ <= nT - 2) iGridQ = iGridLQ - 1; + else iGridQ = nT - 3; + + // Expressions for interpolation in Q Grid. + if (iGridLQ > 0 && iGridLQ < nT - 1) { + double tvec1 = tv[iGridQ]; + double tvec2 = tv[iGridQ+1]; + double tvec3 = tv[iGridQ+2]; + double tvec4 = tv[iGridQ+3]; + double t12 = tvec1 - tvec2; + double t13 = tvec1 - tvec3; + tConst[8] = tvec2 - tvec3; + double t24 = tvec2 - tvec4; + double t34 = tvec3 - tvec4; + tConst[6] = tt - tvec2; + tConst[7] = tt - tvec3; + double tmp1 = t12 + t13; + double tmp2 = t24 + t34; + double tdet = t12 * t34 - tmp1 * tmp2; + tConst[0] = t13 / tConst[8]; + tConst[1] = t12 / tConst[8]; + tConst[2] = t34 / tConst[8]; + tConst[3] = t24 / tConst[8]; + tConst[4] = (t34 * tConst[6] - tmp2 * tConst[7]) / t12 + * tConst[6] * tConst[7] / tdet; + tConst[5] = (tmp1 * tConst[6] - t12 * tConst[7]) / t34 + * tConst[6] * tConst[7] / tdet; + } + + // Save x and q values so do not have to redo same again. + xLast = x; + qLast = q; + } + + // Jump to here if x and q are the same as for the last call. + int jtmp = ( (iP + nfMx) * (nT + 1) + (iGridQ - 1) ) * (nX + 1) + iGridX + 1; + + // Interpolate in x space for four different q values. + for(int it = 1; it <= 4; ++it) { + int j1 = jtmp + it * (nX + 1); + if (iGridX == 0) { + double fij[5]; + fij[1] = 0.; + fij[2] = upd[j1+1] * pow2(xv[1]); + fij[3] = upd[j1+2] * pow2(xv[2]); + fij[4] = upd[j1+3] * pow2(xv[3]); + double fX = polint4F( &xvpow[0], &fij[1], ss); + fVec[it] = (x > 0.) ? fX / pow2(x) : 0.; + } else if (iGridLX==nX-1) { + fVec[it] = polint4F( &xvpow[nX-3], &upd[j1], ss); + } else { + double sf2 = upd[j1+1]; + double sf3 = upd[j1+2]; + double g1 = sf2 * xConst[0] - sf3 * xConst[1]; + double g4 = -sf2 * xConst[2] + sf3 * xConst[3]; + fVec[it] = (xConst[4] * (upd[j1] - g1) + xConst[5] * (upd[j1+3] - g4) + + sf2 * xConst[7] - sf3 * xConst[6]) / xConst[8]; + } + } + + // Interpolate in q space for x-interpolated values found above. + double ff; + if( iGridLQ <= 0 ) { + ff = polint4F( &tv[0], &fVec[1], tt); + } else if (iGridLQ >= nT - 1) { + ff=polint4F( &tv[nT-3], &fVec[1], tt); + } else { + double tf2 = fVec[2]; + double tf3 = fVec[3]; + double g1 = tf2 * tConst[0] - tf3 * tConst[1]; + double g4 = -tf2 * tConst[2] + tf3 * tConst[3]; + ff = (tConst[4] * (fVec[1] - g1) + tConst[5] * (fVec[4] - g4) + + tf2 * tConst[7] - tf3 * tConst[6]) / tConst[8]; + } + + // Done. + return ff; +} + +//-------------------------------------------------------------------------- + +// The POLINT4 routine is based on the POLINT routine from "Numerical Recipes", +// but assuming N=4, and ignoring the error estimation. +// Suggested by Z. Sullivan. + +double CTEQ6pdf::polint4F(double xa[],double ya[],double x) { + + double y, h1, h2, h3, h4, w, den, d1, c1, d2, c2, d3, c3, cd1, cc1, + cd2, cc2, dd1, dc1; + + h1 = xa[0] - x; + h2 = xa[1] - x; + h3 = xa[2] - x; + h4 = xa[3] - x; + + w = ya[1] - ya[0]; + den = w / (h1 - h2); + d1 = h2 * den; + c1 = h1 * den; + + w = ya[2] - ya[1]; + den = w / (h2 - h3); + d2 = h3 * den; + c2 = h2 * den; + + w = ya[3] - ya[2]; + den = w / (h3 - h4); + d3 = h4 * den; + c3 = h3 * den; + + w = c2 - d1; + den = w / (h1 - h3); + cd1 = h3 * den; + cc1 = h1 * den; + + w = c3 - d2; + den = w / (h2 - h4); + cd2 = h4 * den; + cc2 = h2 * den; + + w = cc2 - cd1; + den = w / (h1 - h4); + dd1 = h4 * den; + dc1 = h1 * den; + + if (h3 + h4 < 0.) y = ya[3] + d3 + cd2 + dd1; + else if (h2 + h3 < 0.) y = ya[2] + d2 + cd1 + dc1; + else if (h1 + h2 < 0.) y = ya[1] + c2 + cd1 + dc1; + else y = ya[0] + c1 + cc1 + dc1; + + return y; + +} + +//========================================================================== + +// SA Unresolved proton: equivalent photon spectrum from +// V.M. Budnev, I.F. Ginzburg, G.V. Meledin and V.G. Serbo, +// Phys. Rept. 15 (1974/1975) 181. + +// Constants: +const double ProtonPoint::ALPHAEM = 0.00729735; +const double ProtonPoint::Q2MAX = 2.0; +const double ProtonPoint::Q20 = 0.71; +const double ProtonPoint::A = 7.16; +const double ProtonPoint::B = -3.96; +const double ProtonPoint::C = 0.028; + +//-------------------------------------------------------------------------- + +// Gives a generic Q2-independent equivalent photon spectrum. + +void ProtonPoint::xfUpdate(int id, double x, double /*Q2*/ ) { + + // Photon spectrum + double tmpQ2Min = 0.88 * pow2(x); + double phiMax = phiFunc(x, Q2MAX / Q20); + double phiMin = phiFunc(x, tmpQ2Min / Q20); + + double fgm = 0; + if (phiMax < phiMin && m_infoPtr != 0) { + m_infoPtr->errorMsg("Error from ProtonPoint::xfUpdate: phiMax - phiMin < 0!"); + } else { + // Corresponds to: x*f(x) + fgm = (ALPHAEM / M_PI) * (1 - x) * (phiMax - phiMin); + } + + // Update values + xg = 0.; + xu = 0.; + xd = 0.; + xubar = 0.; + xdbar = 0.; + xs = 0.; + xsbar = 0.; + xc = 0.; + xb = 0.; + xgamma = fgm; + + // Subdivision of valence and sea. + xuVal = 0.; + xuSea = 0; + xdVal = 0.; + xdSea = 0; + + // idSav = 9 to indicate that all flavours reset. id change dummy. + idSav = 9; + id = 0; + +} + +//-------------------------------------------------------------------------- + +// Function related to Q2 integration. + +double ProtonPoint::phiFunc(double x, double Q) { + + double tmpV = 1. + Q; + double tmpSum1 = 0; + double tmpSum2 = 0; + for (int k=1; k<4; ++k) { + tmpSum1 += 1. / (k * pow(tmpV, k)); + tmpSum2 += pow(B, k) / (k * pow(tmpV, k)); + } + + double tmpY = pow2(x) / (1 - x); + double funVal = (1 + A * tmpY) * (-1.*log(tmpV / Q) + tmpSum1) + + (1 - B) * tmpY / (4 * Q * pow(tmpV, 3)) + + C * (1 + tmpY/4.)* (log((tmpV - B)/tmpV) + tmpSum2); + + return funVal; + +} + +//========================================================================== + +// Gives the GRV 1992 pi+ (leading order) parton distribution function set +// in parametrized form. Authors: Glueck, Reya and Vogt. +// Ref: M. Glueck, E. Reya and A. Vogt, Z. Phys. C53 (1992) 651. +// Allowed variable range: 0.25 GeV^2 < Q^2 < 10^8 GeV^2 and 10^-5 < x < 1. + +void GRVpiL::xfUpdate(int id, double x, double Q2) { + + // Common expressions. Constrain Q2 for which parametrization is valid. + double mu2 = 0.25; + double lam2 = 0.232 * 0.232; + double s = (Q2 > mu2) ? log( log(Q2/lam2) / log(mu2/lam2) ) : 0.; + double s2 = s * s; + double x1 = 1. - x; + double xL = -log(x); + double xS = sqrt(x); + + // uv, dbarv. + double uv = (0.519 + 0.180 * s - 0.011 * s2) * pow(x, 0.499 - 0.027 * s) + * (1. + (0.381 - 0.419 * s) * xS) * pow(x1, 0.367 + 0.563 * s); + + // g. + double gl = ( pow(x, 0.482 + 0.341 * sqrt(s)) + * ( (0.678 + 0.877 * s - 0.175 * s2) + (0.338 - 1.597 * s) * xS + + (-0.233 * s + 0.406 * s2) * x) + pow(s, 0.599) + * exp(-(0.618 + 2.070 * s) + sqrt(3.676 * pow(s, 1.263) * xL) ) ) + * pow(x1, 0.390 + 1.053 * s); + + // sea: u, d, s. + double ub = pow(s, 0.55) * (1. - 0.748 * xS + (0.313 + 0.935 * s) * x) + * pow(x1, 3.359) * exp(-(4.433 + 1.301 * s) + sqrt((9.30 - 0.887 * s) + * pow(s, 0.56) * xL) ) / pow(xL, 2.538 - 0.763 * s); + + // c. + double chm = (s < 0.888) ? 0. : pow(s - 0.888, 1.02) * (1. + 1.008 * x) + * pow(x1, 1.208 + 0.771 * s) * exp(-(4.40 + 1.493 * s) + + sqrt( (2.032 + 1.901 * s) * pow(s, 0.39) * xL) ); + + // b. + double bot = (s < 1.351) ? 0. : pow(s - 1.351, 1.03) + * pow(x1, 0.697 + 0.855 * s) * exp(-(4.51 + 1.490 * s) + + sqrt( (3.056 + 1.694 * s) * pow(s, 0.39) * xL) ); + + // Update values. + xg = gl; + xu = uv + ub; + xd = ub; + xubar = ub; + xdbar = uv + ub; + xs = ub; + xsbar = ub; + xc = chm; + xb = bot; + + // Subdivision of valence and sea. + xuVal = uv; + xuSea = ub; + xdVal = uv; + xdSea = ub; + + // idSav = 9 to indicate that all flavours reset. id change dummy. + idSav = 9; + id = 0; + +} + +//========================================================================== + +// Pomeron PDF: simple Q2-independent parametrizations N x^a (1 - x)^b. + +//-------------------------------------------------------------------------- + +// Calculate normalization factors once and for all. + +void PomFix::init() { + + normGluon = GammaReal(PomGluonA + PomGluonB + 2.) + / (GammaReal(PomGluonA + 1.) * GammaReal(PomGluonB + 1.)); + normQuark = GammaReal(PomQuarkA + PomQuarkB + 2.) + / (GammaReal(PomQuarkA + 1.) * GammaReal(PomQuarkB + 1.)); + +} + +//-------------------------------------------------------------------------- + +// Gives a generic Q2-independent Pomeron PDF. + +void PomFix::xfUpdate(int id, double x, double) { + + // Gluon and quark distributions. + double gl = normGluon * pow(x, PomGluonA) * pow( (1. - x), PomGluonB); + double qu = normQuark * pow(x, PomQuarkA) * pow( (1. - x), PomQuarkB); + + // Update values + xg = (1. - PomQuarkFrac) * gl; + xu = (PomQuarkFrac / (4. + 2. * PomStrangeSupp) ) * qu; + xd = xu; + xubar = xu; + xdbar = xu; + xs = PomStrangeSupp * xu; + xsbar = xs; + xc = 0.; + xb = 0.; + + // Subdivision of valence and sea. + xuVal = 0.; + xuSea = xu; + xdVal = 0.; + xdSea = xd; + + // idSav = 9 to indicate that all flavours reset. id change dummy. + idSav = 9; + id = 0; + +} + +//========================================================================== + +// Pomeron PDF: the H1 2006 Fit A and Fit B Q2-dependent parametrizations. + +//-------------------------------------------------------------------------- + +void PomH1FitAB::init( int iFit, string xmlPath, Info* infoPtr) { + + // Open files from which grids should be read in. + if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; + string dataFile = "pomH1FitBlo.data"; + if (iFit == 1) dataFile = "pomH1FitA.data"; + if (iFit == 2) dataFile = "pomH1FitB.data"; + ifstream is( (xmlPath + dataFile).c_str() ); + if (!is.good()) { + if (infoPtr > 0) infoPtr->errorMsg("Error from PomH1FitAB::init: " + "the H1 Pomeron parametrization file was not found"); + else cout << " Error from PomH1FitAB::init: " + << "the H1 Pomeron parametrization file was not found" << endl; + isSet = false; + return; + } + + // Lower and upper bounds. Bin widths for logarithmic spacing. + nx = 100; + xlow = 0.001; + xupp = 0.99; + dx = log(xupp / xlow) / (nx - 1.); + nQ2 = 30; + Q2low = 1.0; + Q2upp = 30000.; + dQ2 = log(Q2upp / Q2low) / (nQ2 - 1.); + + // Read in quark data grid. + for (int i = 0; i < nx; ++i) + for (int j = 0; j < nQ2; ++j) + is >> quarkGrid[i][j]; + + // Read in gluon data grid. + for (int i = 0; i < nx; ++i) + for (int j = 0; j < nQ2; ++j) + is >> gluonGrid[i][j]; + + // Check for errors during read-in of file. + if (!is) { + if (infoPtr > 0) infoPtr->errorMsg("Error from PomH1FitAB::init: " + "the H1 Pomeron parametrization files could not be read"); + else cout << " Error from PomH1FitAB::init: " + << "the H1 Pomeron parametrization files could not be read" << endl; + isSet = false; + return; + } + + // Done. + isSet = true; + return; +} + +//-------------------------------------------------------------------------- + +void PomH1FitAB::xfUpdate(int id, double x, double Q2) { + + // Retrict input to validity range. + double xt = min( xupp, max( xlow, x) ); + double Q2t = min( Q2upp, max( Q2low, Q2) ); + + // Lower grid point and distance above it. + double dlx = log( xt / xlow) / dx; + int i = min( nx - 2, int(dlx) ); + dlx -= i; + double dlQ2 = log( Q2t / Q2low) / dQ2; + int j = min( nQ2 - 2, int(dlQ2) ); + dlQ2 -= j; + + // Interpolate to derive quark PDF. + double qu = (1. - dlx) * (1. - dlQ2) * quarkGrid[i][j] + + dlx * (1. - dlQ2) * quarkGrid[i + 1][j] + + (1. - dlx) * dlQ2 * quarkGrid[i][j + 1] + + dlx * dlQ2 * quarkGrid[i + 1][j + 1]; + + // Interpolate to derive gluon PDF. + double gl = (1. - dlx) * (1. - dlQ2) * gluonGrid[i][j] + + dlx * (1. - dlQ2) * gluonGrid[i + 1][j] + + (1. - dlx) * dlQ2 * gluonGrid[i][j + 1] + + dlx * dlQ2 * gluonGrid[i + 1][j + 1]; + + // Update values. + xg = rescale * gl; + xu = rescale * qu; + xd = xu; + xubar = xu; + xdbar = xu; + xs = xu; + xsbar = xu; + xc = 0.; + xb = 0.; + + // Subdivision of valence and sea. + xuVal = 0.; + xuSea = xu; + xdVal = 0.; + xdSea = xu; + + // idSav = 9 to indicate that all flavours reset. id change dummy. + idSav = 9; + id = 0; + +} + +//========================================================================== + +// Pomeron PDF: the H1 2007 Jets Q2-dependent parametrization. + +//-------------------------------------------------------------------------- + +void PomH1Jets::init( string xmlPath, Info* infoPtr) { + + // Open files from which grids should be read in. + if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; + ifstream isg( (xmlPath + "pomH1JetsGluon.data").c_str() ); + ifstream isq( (xmlPath + "pomH1JetsSinglet.data").c_str() ); + ifstream isc( (xmlPath + "pomH1JetsCharm.data").c_str() ); + if (!isg.good() || !isq.good() || !isc.good()) { + if (infoPtr > 0) infoPtr->errorMsg("Error from PomH1Jets::init: " + "the H1 Pomeron parametrization files were not found"); + else cout << " Error from PomH1Jets::init: " + << "the H1 Pomeron parametrization files were not found" << endl; + isSet = false; + return; + } + + // Read in x and Q grids. Do interpolation logarithmically in Q2. + for (int i = 0; i < 100; ++i) { + isg >> setw(13) >> xGrid[i]; + } + for (int j = 0; j < 88; ++j) { + isg >> setw(13) >> Q2Grid[j]; + Q2Grid[j] = log( Q2Grid[j] ); + } + + // Read in gluon data grid. + for (int j = 0; j < 88; ++j) { + for (int i = 0; i < 100; ++i) { + isg >> setw(13) >> gluonGrid[i][j]; + } + } + + // Identical x and Q2 grid for singlet, so skip ahead. + double dummy; + for (int i = 0; i < 188; ++i) isq >> setw(13) >> dummy; + + // Read in singlet data grid. + for (int j = 0; j < 88; ++j) { + for (int i = 0; i < 100; ++i) { + isq >> setw(13) >> singletGrid[i][j]; + } + } + + // Identical x and Q2 grid for charm, so skip ahead. + for (int i = 0; i < 188; ++i) isc >> setw(13) >> dummy; + + // Read in charm data grid. + for (int j = 0; j < 88; ++j) { + for (int i = 0; i < 100; ++i) { + isc >> setw(13) >> charmGrid[i][j]; + } + } + + // Check for errors during read-in of files. + if (!isg || !isq || !isc) { + if (infoPtr > 0) infoPtr->errorMsg("Error from PomH1Jets::init: " + "the H1 Pomeron parametrization files could not be read"); + else cout << " Error from PomH1Jets::init: " + << "the H1 Pomeron parametrization files could not be read" << endl; + isSet = false; + return; + } + + // Done. + isSet = true; + return; +} + +//-------------------------------------------------------------------------- + +void PomH1Jets::xfUpdate(int id, double x, double Q2) { + + // Find position in x array. + double xLog = log(x); + int i = 0; + double dx = 0.; + if (xLog <= xGrid[0]); + else if (xLog >= xGrid[99]) { + i = 98; + dx = 1.; + } else { + while (xLog > xGrid[i]) ++i; + --i; + dx = (xLog - xGrid[i]) / (xGrid[i + 1] - xGrid[i]); + } + + // Find position in y array. + double Q2Log = log(Q2); + int j = 0; + double dQ2 = 0.; + if (Q2Log <= Q2Grid[0]); + else if (Q2Log >= Q2Grid[87]) { + j = 86; + dQ2 = 1.; + } else { + while (Q2Log > Q2Grid[j]) ++j; + --j; + dQ2 = (Q2Log - Q2Grid[j]) / (Q2Grid[j + 1] - Q2Grid[j]); + } + + // Interpolate to derive gluon PDF. + double gl = (1. - dx) * (1. - dQ2) * gluonGrid[i][j] + + dx * (1. - dQ2) * gluonGrid[i + 1][j] + + (1. - dx) * dQ2 * gluonGrid[i][j + 1] + + dx * dQ2 * gluonGrid[i + 1][j + 1]; + + // Interpolate to derive singlet PDF. (Sum of u, d, s, ubar, dbar, sbar.) + double sn = (1. - dx) * (1. - dQ2) * singletGrid[i][j] + + dx * (1. - dQ2) * singletGrid[i + 1][j] + + (1. - dx) * dQ2 * singletGrid[i][j + 1] + + dx * dQ2 * singletGrid[i + 1][j + 1]; + + // Interpolate to derive charm PDF. (Charge-square times c and cbar.) + double ch = (1. - dx) * (1. - dQ2) * charmGrid[i][j] + + dx * (1. - dQ2) * charmGrid[i + 1][j] + + (1. - dx) * dQ2 * charmGrid[i][j + 1] + + dx * dQ2 * charmGrid[i + 1][j + 1]; + + // Update values. + xg = rescale * gl; + xu = rescale * sn / 6.; + xd = xu; + xubar = xu; + xdbar = xu; + xs = xu; + xsbar = xu; + xc = rescale * ch * 9./8.; + xb = 0.; + + // Subdivision of valence and sea. + xuVal = 0.; + xuSea = xu; + xdVal = 0.; + xdSea = xd; + + // idSav = 9 to indicate that all flavours reset. id change dummy. + idSav = 9; + id = 0; + +} + +//========================================================================== + +// Gives electron (or muon, or tau) parton distribution. + +// Constants: alphaEM(0), m_e, m_mu, m_tau. +const double Lepton::ALPHAEM = 0.00729735; +const double Lepton::ME = 0.0005109989; +const double Lepton::MMU = 0.10566; +const double Lepton::MTAU = 1.77699; + + +void Lepton::xfUpdate(int id, double x, double Q2) { + + // Squared mass of lepton species: electron, muon, tau. + if (!isInit) { + double mLep = ME; + if (abs(id) == 13) mLep = MMU; + if (abs(id) == 15) mLep = MTAU; + m2Lep = pow2( mLep ); + isInit = true; + } + + // Electron inside electron, see R. Kleiss et al., in Z physics at + // LEP 1, CERN 89-08, p. 34 + double xLog = log(max(1e-10,x)); + double xMinusLog = log( max(1e-10, 1. - x) ); + double Q2Log = log( max(3., Q2/m2Lep) ); + double beta = (ALPHAEM / M_PI) * (Q2Log - 1.); + double delta = 1. + (ALPHAEM / M_PI) * (1.5 * Q2Log + 1.289868) + + pow2(ALPHAEM / M_PI) * (-2.164868 * Q2Log*Q2Log + + 9.840808 * Q2Log - 10.130464); + double fPrel = beta * pow(1. - x, beta - 1.) * sqrtpos( delta ) + - 0.5 * beta * (1. + x) + 0.125 * beta*beta * ( (1. + x) + * (-4. * xMinusLog + 3. * xLog) - 4. * xLog / (1. - x) - 5. - x); + + // Zero distribution for very large x and rescale it for intermediate. + if (x > 1. - 1e-10) fPrel = 0.; + else if (x > 1. - 1e-7) fPrel *= pow(1000.,beta) / (pow(1000.,beta) - 1.); + xlepton = x * fPrel; + + // Photon inside electron (one possible scheme - primitive). + xgamma = (0.5 * ALPHAEM / M_PI) * Q2Log * (1. + pow2(1. - x)); + + // idSav = 9 to indicate that all flavours reset. id change is dummy here. + idSav = 9; + id = 0; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/PartonLevel.cxx b/PYTHIA8/pythia8140/src/PartonLevel.cxx new file mode 100644 index 00000000000..5dffdfc75db --- /dev/null +++ b/PYTHIA8/pythia8140/src/PartonLevel.cxx @@ -0,0 +1,1055 @@ +// PartonLevel.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the PartonLevel class. + +#include "PartonLevel.h" + +namespace Pythia8 { + +//========================================================================== + +// The PartonLevel class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Maximum number of tries to produce parton level from given input. +const int PartonLevel::NTRY = 10; + +//-------------------------------------------------------------------------- + +// Main routine to initialize the parton-level generation process. + +bool PartonLevel::init( Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + BeamParticle* beamPomAPtrIn, BeamParticle* beamPomBPtrIn, + CoupSM* coupSMPtrIn, PartonSystems* partonSystemsPtrIn, + SigmaTotal* sigmaTotPtr, TimeShower* timesDecPtrIn, TimeShower* timesPtrIn, + SpaceShower* spacePtrIn, UserHooks* userHooksPtrIn) { + + // Store input pointers and modes for future use. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + beamHadAPtr = beamAPtr; + beamHadBPtr = beamBPtr; + beamPomAPtr = beamPomAPtrIn; + beamPomBPtr = beamPomBPtrIn; + coupSMPtr = coupSMPtrIn; + partonSystemsPtr = partonSystemsPtrIn; + timesDecPtr = timesDecPtrIn; + timesPtr = timesPtrIn; + spacePtr = spacePtrIn; + userHooksPtr = userHooksPtrIn; + + // Min bias and single diffraction processes need special treatment. + doMinBias = settings.flag("SoftQCD:all") + || settings.flag("SoftQCD:minBias"); + doDiffraction = settings.flag("SoftQCD:all") + || settings.flag("SoftQCD:singleDiffractive") + || settings.flag("SoftQCD:doubleDiffractive"); + + // Separate low-mass (unresolved) and high-mass (perturbative) diffraction. + mMinDiff = settings.parm("Diffraction:mMinPert"); + mWidthDiff = settings.parm("Diffraction:mWidthPert"); + if (mMinDiff + mWidthDiff > infoPtr->eCM()) doDiffraction = false; + + // Need MI initialization for soft QCD processes, even if only first MI. + // But no need to initialize MI if never going to use it. + doMI = settings.flag("PartonLevel:MI"); + doMIMB = doMI; + doMISDA = doMI; + doMISDB = doMI; + doMIinit = doMI; + if (doMinBias || doDiffraction) doMIinit = true; + if (!settings.flag("PartonLevel:all")) doMIinit = false; + + // Flags for showers: ISR and FSR. + doISR = settings.flag("PartonLevel:ISR"); + bool FSR = settings.flag("PartonLevel:FSR"); + bool FSRinProcess = settings.flag("PartonLevel:FSRinProcess"); + bool interleaveFSR = settings.flag("TimeShower:interleave"); + doFSRduringProcess = FSR && FSRinProcess && interleaveFSR; + doFSRafterProcess = FSR && FSRinProcess && !interleaveFSR; + doFSRinResonances = FSR && settings.flag("PartonLevel:FSRinResonances"); + + // Some other flags. + doRemnants = settings.flag("PartonLevel:Remnants"); + doSecondHard = settings.flag("SecondHard:generate"); + + // Flag if lepton beams, and if non-resolved ones. May change main flags. + hasLeptonBeams = ( beamAPtr->isLepton() || beamBPtr->isLepton() ); + hasPointLeptons = ( hasLeptonBeams + && (beamAPtr->isUnresolved() || beamBPtr->isUnresolved() ) ); + if (hasLeptonBeams) { + doMIMB = false; + doMISDA = false; + doMISDB = false; + doMIinit = false; + } + if (hasPointLeptons) { + doISR = false; + doRemnants = false; + } + + // Possibility to allow user veto during evolution. + canVetoPT = (userHooksPtr > 0) ? userHooksPtr->canVetoPT() : false; + pTvetoPT = (canVetoPT) ? userHooksPtr->scaleVetoPT() : -1.; + canVetoStep = (userHooksPtr > 0) ? userHooksPtr->canVetoStep() : false; + nVetoStep = (canVetoStep) ? userHooksPtr->numberVetoStep() : -1; + canVetoMIStep = (userHooksPtr > 0) ? userHooksPtr->canVetoMIStep() : false; + nVetoMIStep = (canVetoStep) ? userHooksPtr->numberVetoMIStep() : -1; + + // Possibility to set maximal shower scale in resonance decays. + canSetScale = (userHooksPtr > 0) ? userHooksPtr->canSetResonanceScale() + : false; + + // Set info and initialize the respective program elements. + timesPtr->init( beamAPtr, beamBPtr); + if (doISR) spacePtr->init( beamAPtr, beamBPtr); + doMIMB = multiMB.init( doMIinit, 0, infoPtr, settings, particleDataPtr, + rndmPtr, beamAPtr, beamBPtr, coupSMPtr, partonSystemsPtr, sigmaTotPtr); + if (doDiffraction) doMISDA = multiSDA.init( doMIinit, 1, infoPtr, + settings, particleDataPtr, rndmPtr, beamPomBPtr, beamAPtr, coupSMPtr, + partonSystemsPtr, sigmaTotPtr); + if (doDiffraction) doMISDB = multiSDB.init( doMIinit, 2, infoPtr, + settings, particleDataPtr, rndmPtr, beamPomAPtr, beamBPtr, coupSMPtr, + partonSystemsPtr, sigmaTotPtr); + remnants.init( infoPtr, settings, rndmPtr, beamAPtr, beamBPtr, + partonSystemsPtr); + + // Succeeded, or not. + multiPtr = &multiMB; + if (doMIinit && !doMIMB) return false; + if (doMIinit && doDiffraction && (!doMISDA || !doMISDB)) return false; + if (!doMIMB || !doMISDA || !doMISDB) doMI = false; + return true; +} + +//-------------------------------------------------------------------------- + +// Main routine to do the parton-level evolution. + +bool PartonLevel::next( Event& process, Event& event) { + + // Current event classification. + isResolved = infoPtr->isResolved(); + isResolvedA = isResolved; + isResolvedB = isResolved; + isDiffA = infoPtr->isDiffractiveA(); + isDiffB = infoPtr->isDiffractiveB(); + isDiff = isDiffA || isDiffB; + isDoubleDiff = isDiffA && isDiffB; + isSingleDiff = isDiff && !isDoubleDiff; + isMinBias = infoPtr->isMinBias(); + + // nHardLoop counts how many hard-scattering subsystems are to be processed. + // Almost always 1, but elastic and low-mass diffraction gives 0, while + // double diffraction can give up to 2. Not to be confused with SecondHard. + int nHardLoop = 1; + if (!isResolved) nHardLoop = (isDiff) ? decideResolvedDiff( process) : 0; + + // Handle unresolved subsystems. Done if no resolved ones. + sizeProcess = 0; + sizeEvent = 0; + if (!isResolvedA || !isResolvedB) { + bool physical = setupUnresolvedSys( process, event); + if (!physical || nHardLoop == 0) return physical; + sizeProcess = process.size(); + sizeEvent = event.size(); + } + + // Big outer loop to handle up to two systems (in double diffraction), + // but normally one. (Not indented in following, but end clearly marked.) + for (int iHardLoop = 1; iHardLoop <= nHardLoop; ++iHardLoop) { + infoPtr->setCounter(20, iHardLoop); + infoPtr->setCounter(21); + + // Process and event records can be out of step for diffraction. + if (iHardLoop == 2) { + sizeProcess = process.size(); + sizeEvent = event.size(); + partonSystemsPtr->clear(); + } + + // If you need to restore then do not throw existing diffractive system. + if (isDiff) { + event.saveSize(); + event.saveJunctionSize(); + } + + // Allow special treatment of diffractive systems. + if (isDiff) setupResolvedDiff(iHardLoop, process); + + // Prepare to do multiple interactions; at new mass for diffraction. + if (doMIinit) multiPtr->reset(); + + // Special case if minimum bias: do hardest interaction. + if (isMinBias || isDiff) { + multiPtr->pTfirst(); + multiPtr->setupFirstSys( process); + } + + // Allow up to ten tries; failure possible for beam remnants. + // Main cause: inconsistent colour flow at the end of the day. + bool physical = true; + int nRad = 0; + for (int iTry = 0; iTry < NTRY; ++ iTry) { + infoPtr->addCounter(21); + for (int i = 22; i < 32; ++i) infoPtr->setCounter(i); + + // Reset flag, counters and max scales. + physical = true; + nMI = (doSecondHard) ? 2 : 1; + nISR = 0; + nFSRinProc = 0; + nFSRinRes = 0; + nISRhard = 0; + nFSRhard = 0; + pTsaveMI = 0.; + pTsaveISR = 0.; + pTsaveFSR = 0.; + + // Identify hard interaction system for showers. + setupHardSys( iHardLoop, process, event); + + // Optionally check for a veto after the hardest interaction. + if (canVetoMIStep) { + doVeto = userHooksPtr->doVetoMIStep( 1, event); + // Abort event if vetoed. + if (doVeto) { + if (isDiff) leaveResolvedDiff( iHardLoop, event); + return false; + } + } + + // Check matching of process scale to maximum ISR/FSR/MI scales. + double Q2Fac = infoPtr->Q2Fac(); + double Q2Ren = infoPtr->Q2Ren(); + bool limitPTmaxISR = (doISR) + ? spacePtr->limitPTmax( event, Q2Fac, Q2Ren) : false; + bool limitPTmaxFSR = (doFSRduringProcess) + ? timesPtr->limitPTmax( event, Q2Fac, Q2Ren) : false; + bool limitPTmaxMI = (doMI) ? multiPtr->limitPTmax( event) : false; + + // Set hard scale, maximum for showers and multiple interactions, + double pTscale = process.scale(); + if (doSecondHard) pTscale = max( pTscale, process.scaleSecond() ); + double pTmaxMI = (limitPTmaxMI) ? pTscale : infoPtr->eCM(); + double pTmaxISR = (limitPTmaxISR) ? spacePtr->enhancePTmax() * pTscale + : infoPtr->eCM(); + double pTmaxFSR = (limitPTmaxFSR) ? timesPtr->enhancePTmax() * pTscale + : infoPtr->eCM(); + double pTmax = max( pTmaxMI, max( pTmaxISR, pTmaxFSR) ); + pTsaveMI = pTmaxMI; + pTsaveISR = pTmaxISR; + pTsaveFSR = pTmaxFSR; + + // Prepare the classes to begin the generation. + if (doMI) multiPtr->prepare( pTmaxMI); + if (doISR) spacePtr->prepare( 0, event, limitPTmaxISR); + if (doFSRduringProcess) timesPtr->prepare( 0, event, limitPTmaxFSR); + if (doSecondHard && doISR) spacePtr->prepare( 1, event, limitPTmaxISR); + if (doSecondHard && doFSRduringProcess) + timesPtr->prepare( 1, event, limitPTmaxFSR); + + // Set up initial veto scale. + doVeto = false; + double pTveto = pTvetoPT; + typeLatest = 0; + + // Begin evolution down in pT from hard pT scale. + do { + infoPtr->addCounter(22); + typeVetoStep = 0; + nRad = nISR + nFSRinProc; + + // Find next pT value for FSR, MI and ISR. + // Order calls to minimize time expenditure. + double pTgen = 0.; + double pTtimes = (doFSRduringProcess) + ? timesPtr->pTnext( event, pTmaxFSR, pTgen) : -1.; + pTgen = max( pTgen, pTtimes); + double pTmulti = (doMI) + ? multiPtr->pTnext( pTmaxMI, pTgen, event) : -1.; + pTgen = max( pTgen, pTmulti); + double pTspace = (doISR) + ? spacePtr->pTnext( event, pTmaxISR, pTgen, nRad) : -1.; + double pTnow = max( pTtimes, max( pTmulti, pTspace)); + infoPtr->setPTnow( pTnow); + + // Allow a user veto. Only do it once, so remember to change pTveto. + if (pTveto > 0. && pTveto > pTnow) { + pTveto = -1.; + doVeto = userHooksPtr->doVetoPT( typeLatest, event); + // Abort event if vetoed. + if (doVeto) { + if (isDiff) leaveResolvedDiff( iHardLoop, event); + return false; + } + } + + // Do a multiple interaction (if allowed). + if (pTmulti > 0. && pTmulti > pTspace && pTmulti > pTtimes) { + infoPtr->addCounter(23); + multiPtr->scatter( event); + typeLatest = 1; + ++nMI; + if (canVetoMIStep && nMI <= nVetoMIStep) typeVetoStep = 1; + + // Update ISR and FSR dipoles. + if (doISR) spacePtr->prepare( nMI - 1, event); + if (doFSRduringProcess) timesPtr->prepare( nMI - 1, event); + + // Set maximal scales for next pT to pick. + pTmaxMI = pTmulti; + pTmaxISR = min( pTmulti, pTmaxISR); + pTmaxFSR = min( pTmulti, pTmaxFSR); + pTmax = pTmulti; + } + + // Do an initial-state emission (if allowed). + else if (pTspace > 0. && pTspace > pTtimes) { + infoPtr->addCounter(24); + if (spacePtr->branch( event)) { + typeLatest = 2; + iSysNow = spacePtr->system(); + ++nISR; + if (iSysNow == 0) ++nISRhard; + if (canVetoStep && iSysNow == 0 && nISRhard <= nVetoStep) + typeVetoStep = 2; + + // Update FSR dipoles. + if (doFSRduringProcess) timesPtr->update( iSysNow, event); + + // Rescatter: it is possible for kinematics to fail, in which + // case we need to restart the parton level processing. + } else if (spacePtr->doRestart()) { + physical = false; + break; + } + + // Set maximal scales for next pT to pick. + pTmaxMI = min( pTspace, pTmaxMI); + pTmaxISR = pTspace; + pTmaxFSR = min( pTspace, pTmaxFSR); + pTmax = pTspace; + } + + // Do a final-state emission (if allowed). + else if (pTtimes > 0.) { + infoPtr->addCounter(25); + if (timesPtr->branch( event, true)) { + typeLatest = 3; + iSysNow = timesPtr->system(); + ++nFSRinProc; + if (iSysNow == 0) ++nFSRhard; + if (canVetoStep && iSysNow == 0 && nFSRhard <= nVetoStep) + typeVetoStep = 3; + + // Update ISR dipoles. + if (doISR) spacePtr->update( iSysNow, event); + } + + // Set maximal scales for next pT to pick. + pTmaxMI = min( pTtimes, pTmaxMI); + pTmaxISR = min( pTtimes, pTmaxISR); + pTmaxFSR = pTtimes; + pTmax = pTtimes; + } + + // If no pT scales above zero then nothing to be done. + else pTmax = 0.; + + // Optionally check for a veto after the first few interactions, + // or after the first few emissions, ISR or FSR, in the hardest system. + if (typeVetoStep == 1) { + doVeto = userHooksPtr->doVetoMIStep( nMI, event); + } else if (typeVetoStep > 1) { + doVeto = userHooksPtr->doVetoStep( typeVetoStep, nISRhard, + nFSRhard, event); + } + + // Abort event if vetoed. + if (doVeto) { + if (isDiff) leaveResolvedDiff( iHardLoop, event); + return false; + } + + // Keep on evolving until nothing is left to be done. + if (typeLatest > 0 && typeLatest < 4) + infoPtr->addCounter(25 + typeLatest); + infoPtr->setPartEvolved( nMI, nISR); + } while (pTmax > 0.); + + // Do all final-state emissions if not already considered above. + if (doFSRafterProcess) { + + // Find largest scale for final partons. + pTmax = 0.; + for (int i = 0; i < event.size(); ++i) + if (event[i].isFinal() && event[i].scale() > pTmax) + pTmax = event[i].scale(); + pTsaveFSR = pTmax; + + // Prepare all subsystems for evolution. + for (int iSys = 0; iSys < partonSystemsPtr->sizeSys(); ++iSys) + timesPtr->prepare( iSys, event); + + // Set up initial veto scale. + doVeto = false; + pTveto = pTvetoPT; + + // Begin evolution down in pT from hard pT scale. + do { + infoPtr->addCounter(29); + typeVetoStep = 0; + double pTtimes = timesPtr->pTnext( event, pTmax, 0.); + infoPtr->setPTnow( pTtimes); + + // Allow a user veto. Only do it once, so remember to change pTveto. + if (pTveto > 0. && pTveto > pTtimes) { + pTveto = -1.; + doVeto = userHooksPtr->doVetoPT( 4, event); + // Abort event if vetoed. + if (doVeto) { + if (isDiff) leaveResolvedDiff( iHardLoop, event); + return false; + } + } + + // Do a final-state emission (if allowed). + if (pTtimes > 0.) { + infoPtr->addCounter(30); + if (timesPtr->branch( event, true)) { + iSysNow = timesPtr->system(); + ++nFSRinProc; + if (iSysNow == 0) ++nFSRhard; + if (canVetoStep && iSysNow == 0 && nFSRhard <= nVetoStep) + typeVetoStep = 4; + } + pTmax = pTtimes; + } + + // If no pT scales above zero then nothing to be done. + else pTmax = 0.; + + // Optionally check for a veto after the first few emissions. + if (typeVetoStep > 0) { + doVeto = userHooksPtr->doVetoStep( typeVetoStep, nISRhard, + nFSRhard, event); + // Abort event if vetoed. + if (doVeto) { + if (isDiff) leaveResolvedDiff( iHardLoop, event); + return false; + } + } + + // Keep on evolving until nothing is left to be done. + infoPtr->addCounter(31); + } while (pTmax > 0.); + } + + // Add beam remnants, including primordial kT kick and colour tracing. + if (physical && doRemnants && !remnants.add( event)) physical = false; + + // If no problems then done. + if (physical) break; + + // Else restore and loop, but do not throw existing diffractive system. + if (!isDiff) event.clear(); + else { + event.restoreSize(); + event.restoreJunctionSize(); + } + beamAPtr->clear(); + beamBPtr->clear(); + partonSystemsPtr->clear(); + + // End loop over ten tries. Restore from diffraction. Hopefully it worked. + } + if (isDiff) leaveResolvedDiff( iHardLoop, event); + if (!physical) return false; + + // End big outer loop to handle two systems in double diffraction. + } + + // Perform showers in resonance decay chains. + doVeto = !resonanceShowers( process, event); + // Abort event if vetoed. + if (doVeto) return false; + + // Store event properties. + infoPtr->setImpact( multiPtr->bMI(), multiPtr->enhanceMI()); + infoPtr->setEvolution( pTsaveMI, pTsaveISR, pTsaveFSR, + nMI, nISR, nFSRinProc, nFSRinRes); + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Decide which diffractive subsystems are resolved (= perturbative). + +int PartonLevel::decideResolvedDiff( Event& process) { + + // Loop over two systems. + int nHighMass = 0; + for (int iDiffSys = 1; iDiffSys <= 2; ++iDiffSys) { + int iDiffMot = iDiffSys + 2; + + // Only high-mass diffractive systems should be resolved. + double mDiff = process[iDiffMot].m(); + bool isHighMass = ( mDiff > mMinDiff + && rndmPtr->flat() < 1. - exp( -(mDiff - mMinDiff) / mWidthDiff ) ); + + // Set outcome and done. + if (isHighMass) ++nHighMass; + if (iDiffSys == 1) isResolvedA = isHighMass; + if (iDiffSys == 2) isResolvedB = isHighMass; + } + return nHighMass; + +} + +//-------------------------------------------------------------------------- + +// Set up an unresolved process, i.e. elastic or diffractive. + +bool PartonLevel::setupUnresolvedSys( Event& process, Event& event) { + + // No hard scale in event. + process.scale( 0.); + + // Copy particles from process to event. + for (int i = 0; i < process.size(); ++ i) event.append( process[i]); + + // Loop to find diffractively excited beams. + for (int i = 0; i < 2; ++i) + if ( (i == 0 && isDiffA && !isResolvedA) + || (i == 1 && isDiffB && !isResolvedB) ) { + int iBeam = i + 3; + BeamParticle* beamPtr = (i == 0) ? beamAPtr : beamBPtr; + + // Diffractive mass. Reconstruct boost and rotation to event cm frame. + double mDiff = process[iBeam].m(); + double m2Diff = mDiff*mDiff; + double beta = process[iBeam].pAbs() / process[iBeam].e(); + double theta = process[iBeam].theta(); + double phi = process[iBeam].phi(); + + // Pick quark or gluon kicked out and flavour subdivision. + bool gluonIsKicked = beamPtr->pickGluon(mDiff); + int id1 = beamPtr->pickValence(); + int id2 = beamPtr->pickRemnant(); + + // Find flavour masses. Scale them down if too big. + double m1 = particleDataPtr->constituentMass(id1); + double m2 = particleDataPtr->constituentMass(id2); + if (m1 + m2 > 0.5 * mDiff) { + double reduce = 0.5 * mDiff / (m1 + m2); + m1 *= reduce; + m2 *= reduce; + } + + // If quark is kicked out, then trivial kinematics in rest frame. + if (!gluonIsKicked) { + double pAbs = sqrt( pow2(m2Diff - m1*m1 - m2*m2) + - pow2(2. * m1 * m2) ) / (2. * mDiff); + double e1 = (m2Diff + m1*m1 - m2*m2) / (2. * mDiff); + double e2 = (m2Diff + m2*m2 - m1*m1) / (2. * mDiff); + Vec4 p1(0.,0., -pAbs, e1); + Vec4 p2(0.,0., pAbs, e2); + + // Boost and rotate to event cm frame. + p1.bst(0., 0., beta); p1.rot(theta, phi); + p2.bst(0., 0., beta); p2.rot(theta, phi); + + // Set colours. + int col1, acol1, col2, acol2; + if (particleDataPtr->colType(id1) == 1) { + col1 = event.nextColTag(); acol1 = 0; + col2 = 0; acol2 = col1; + } else { + col1 = 0; acol1 = event.nextColTag(); + col2 = acol1; acol2 = 0; + } + // Update process colours to stay in step. + process.nextColTag(); + + // Store partons of diffractive system and mark system decayed. + int iDauBeg = event.append( id1, 23, iBeam, 0, 0, 0, col1, acol1, + p1, m1); + int iDauEnd = event.append( id2, 63, iBeam, 0, 0, 0, col2, acol2, + p2, m2); + event[iBeam].statusNeg(); + event[iBeam].daughters(iDauBeg, iDauEnd); + + + // If gluon is kicked out: share momentum between two remnants. + } else { + double m2Sys, zSys, pxSys, pySys, mTS1, mTS2; + zSys = beamPtr->zShare(mDiff, m1, m2); + + // Provide relative pT kick in remnant. Construct (transverse) masses. + pxSys = beamPtr->pxShare(); + pySys = beamPtr->pyShare(); + mTS1 = m1*m1 + pxSys*pxSys + pySys*pySys; + mTS2 = m2*m2 + pxSys*pxSys + pySys*pySys; + m2Sys = mTS1 / zSys + mTS2 / (1. - zSys); + + // Momentum of kicked-out massless gluon in diffractive rest frame. + double pAbs = (m2Diff - m2Sys) / (2. * mDiff); + Vec4 pG(0., 0., -pAbs, pAbs); + Vec4 pRem(0., 0., pAbs, mDiff - pAbs); + + // Momenta of the two beam remnant flavours. (Lightcone p+ = m_diff!) + double e1 = 0.5 * (zSys * mDiff + mTS1 / (zSys * mDiff)); + double pL1 = 0.5 * (zSys * mDiff - mTS1 / (zSys * mDiff)); + Vec4 p1(pxSys, pySys, pL1, e1); + Vec4 p2 = pRem - p1; + + // Boost and rotate to event cm frame. + pG.bst(0., 0., beta); pG.rot(theta, phi); + p1.bst(0., 0., beta); p1.rot(theta, phi); + p2.bst(0., 0., beta); p2.rot(theta, phi); + + // Set colours. + int colG, acolG, col1, acol1, col2, acol2; + if (particleDataPtr->colType(id1) == 1) { + col1 = event.nextColTag(); acol1 = 0; + colG = event.nextColTag(); acolG = col1; + col2 = 0; acol2 = colG; + } else { + col1 = 0; acol1 = event.nextColTag(); + colG = acol1; acolG = event.nextColTag(); + col2 = acolG; acol2 = 0; + } + // Update process colours to stay in step. + process.nextColTag(); + process.nextColTag(); + + // Store partons of diffractive system and mark system decayed. + int iDauBeg = event.append( 21, 23, iBeam, 0, 0, 0, colG, acolG, + pG, m1); + event.append( id1, 63, iBeam, 0, 0, 0, col1, acol1, p1, m1); + int iDauEnd = event.append( id2, 63, iBeam, 0, 0, 0, col2, acol2, + p2, m2); + event[iBeam].statusNeg(); + event[iBeam].daughters(iDauBeg, iDauEnd); + } + + // End loop over beams. Done. + } + return true; + +} + +//-------------------------------------------------------------------------- + +// Set up the hard process(es), excluding subsequent resonance decays. + + void PartonLevel::setupHardSys( int iHardLoop, Event& process, + Event& event) { + + // Incoming partons to hard process are stored in slots 3 and 4. + int inS = 0; + int inP = 3; + int inM = 4; + + // Identify any diffractive system, mother, last entry. Offset. + int iDiffSys = (iHardLoop == 2 || !isResolvedA) ? 2 : 1; + int iDiffMot = iDiffSys + 2; + int iDiffDau = process.size() - 1; + int nOffset = sizeEvent - sizeProcess; + + // Resolved diffraction means more entries. + if (isDiff) { + inS = iDiffMot; + inP = iDiffDau - 3; + inM = iDiffDau - 2; + + // Diffractively excited particle described as Pomeron-hadron beams. + event[inS].statusNeg(); + event[inS].daughters( inP - 2 + nOffset, inM - 2 + nOffset); + } + + // If two hard interactions then find where second begins. + int iBeginSecond = process.size(); + if (doSecondHard) { + iBeginSecond = 5; + while (process[iBeginSecond].status() != -21) ++iBeginSecond; + } + + // If incoming partons are massive then recalculate to put them massless. + if (process[inP].m() != 0. || process[inM].m() != 0.) { + double pPos = process[inP].pPos() + process[inM].pPos(); + double pNeg = process[inP].pNeg() + process[inM].pNeg(); + process[inP].pz( 0.5 * pPos); + process[inP].e( 0.5 * pPos); + process[inP].m( 0.); + process[inM].pz(-0.5 * pNeg); + process[inM].e( 0.5 * pNeg); + process[inM].m( 0.); + } + + // Add incoming hard-scattering partons to list in beam remnants. + double x1 = process[inP].pPos() / process[inS].m(); + beamAPtr->append( inP + nOffset, process[inP].id(), x1); + double x2 = process[inM].pNeg() / process[inS].m(); + beamBPtr->append( inM + nOffset, process[inM].id(), x2); + + // Scale. Find whether incoming partons are valence or sea. Store. + double scale = process.scale(); + beamAPtr->xfISR( 0, process[inP].id(), x1, scale*scale); + int vsc1 = beamAPtr->pickValSeaComp(); + beamBPtr->xfISR( 0, process[inM].id(), x2, scale*scale); + int vsc2 = beamBPtr->pickValSeaComp(); + bool isVal1 = (vsc1 == -3); + bool isVal2 = (vsc2 == -3); + infoPtr->setValence( isVal1, isVal2); + + // Initialize info needed for subsequent sequential decays + showers. + nHardDone = sizeProcess; + iPosBefShow.resize( process.size() ); + + // Add the beam and hard subprocess partons to the event record. + for (int i = sizeProcess; i < iBeginSecond; ++ i) { + if (process[i].mother1() > inM) break; + int j = event.append(process[i]); + iPosBefShow[i] = i; + + // Offset history if process and event not in step. + if (nOffset != 0) { + int iOrd = i - iBeginSecond + 7; + if (iOrd == 1 || iOrd == 2) + event[j].offsetHistory( 0, 0, 0, nOffset); + else if (iOrd == 3 || iOrd == 4) + event[j].offsetHistory( 0, nOffset, 0, nOffset); + else if (iOrd == 5 || iOrd == 6) + event[j].offsetHistory( 0, nOffset, 0, 0); + } + + // Currently outgoing ones should not count as decayed. + if (event[j].status() == -22) { + event[j].statusPos(); + event[j].daughters(0, 0); + } + + // Complete task of copying hard subsystem into event record. + ++nHardDone; + } + + // Store participating partons as first set in list of all systems. + partonSystemsPtr->addSys(); + partonSystemsPtr->setInA(0, inP + nOffset); + partonSystemsPtr->setInB(0, inM + nOffset); + for (int i = inM + 1; i < nHardDone; ++i) + partonSystemsPtr->addOut(0, i + nOffset); + partonSystemsPtr->setSHat( 0, + (event[inP + nOffset].p() + event[inM + nOffset].p()).m2Calc() ); + + // Identify second hard process where applicable. + // Since internally generated incoming partons are guaranteed massless. + if (doSecondHard) { + int inP2 = iBeginSecond; + int inM2 = iBeginSecond + 1; + + // Add incoming hard-scattering partons to list in beam remnants. + // Not valid if not in rest frame?? + x1 = process[inP2].pPos() / process[0].e(); + beamAPtr->append( inP2, process[inP2].id(), x1); + x2 = process[inM2].pNeg() / process[0].e(); + beamBPtr->append( inM2, process[inM2].id(), x2); + + // Find whether incoming partons are valence or sea. + scale = process.scaleSecond(); + beamAPtr->xfISR( 1, process[inP2].id(), x1, scale*scale); + beamAPtr->pickValSeaComp(); + beamBPtr->xfISR( 1, process[inM2].id(), x2, scale*scale); + beamBPtr->pickValSeaComp(); + + // Add the beam and hard subprocess partons to the event record. + for (int i = inP2; i < process.size(); ++ i) { + int mother = process[i].mother1(); + if ( (mother > 2 && mother < inP2) || mother > inM2 ) break; + event.append(process[i]); + iPosBefShow[i] = i; + + // Currently outgoing ones should not count as decayed. + if (event[i].status() == -22) { + event[i].statusPos(); + event[i].daughters(0, 0); + } + + // Complete task of copying hard subsystem into event record. + ++nHardDone; + } + + // Store participating partons as second set in list of all systems. + partonSystemsPtr->addSys(); + partonSystemsPtr->setInA(1, inP2); + partonSystemsPtr->setInB(1, inM2); + for (int i = inM2 + 1; i < nHardDone; ++i) + partonSystemsPtr->addOut(1, i); + partonSystemsPtr->setSHat( 1, + (event[inP2].p() + event[inM2].p()).m2Calc() ); + + // End code for second hard process. + } + + // Update event colour tag to maximum in whole process. + int maxColTag = 0; + for (int i = 0; i < process.size(); ++ i) { + if (process[i].col() > maxColTag) maxColTag = process[i].col(); + if (process[i].acol() > maxColTag) maxColTag = process[i].acol(); + } + event.initColTag(maxColTag); + + // Copy junctions from process to event. + for (int i = 0; i < process.sizeJunction(); ++i) + event.appendJunction( process.getJunction(i)); + + // Done. +} + +//-------------------------------------------------------------------------- + +// Resolved diffraction: replace full event with diffractive subsystem. + +void PartonLevel::setupResolvedDiff(int iHardLoop, Event& process) { + + // Identify diffractive system, mother, last entry. + int iDiffSys = (iHardLoop == 2 || !isResolvedA) ? 2 : 1; + int iDiffMot = iDiffSys + 2; + int iDiffDau = process.size() - 1; + + // Diffractive system mass. + double mDiff = process[iDiffMot].m(); + double m2Diff = mDiff * mDiff; + + // Diffractively excited particle described as Pomeron-hadron beams. + process[iDiffMot].statusNeg(); + process[iDiffMot].daughters( iDiffDau + 1, iDiffDau + 2); + + // Set up Pomeron-proton system as if it were the complete collision. + int idHad = process[iDiffSys].id(); + double mHad = process[iDiffSys].m(); + double m2Had = mHad * mHad; + double m2Pom = (process[2].p() - process[4].p()).m2Calc(); + double mPom = (m2Pom >= 0.) ? sqrt(m2Pom) : -sqrt(-m2Pom); + double eHad = 0.5 * (m2Diff + m2Had - m2Pom) / mDiff; + double ePom = 0.5 * (m2Diff + m2Pom - m2Had) / mDiff; + double pzHP = 0.5 * sqrtpos( pow2(m2Diff - m2Had - m2Pom) + - 4. * m2Had * m2Pom ) / mDiff; + process.append( 990, 13, iDiffMot, 0, 0, 0, 0, 0, + 0., 0., pzHP, ePom, mPom); + process.append( idHad, 13, iDiffMot, 0, 0, 0, 0, 0, + 0., 0., -pzHP, eHad, mHad); + + // Reassign multiple interactions pointer to right object. + multiPtr = (iDiffSys == 1) ? &multiSDA : &multiSDB; + + // Reassign one beam pointer to refer to incoming Pomeron. + if (iDiffSys == 1) { + beamAPtr = beamPomBPtr; + beamBPtr = beamHadAPtr; + } else { + beamAPtr = beamPomAPtr; + beamBPtr = beamHadBPtr; + } + + // Beams not found in normal slots 1 and 2. + int beamOffset = (sizeEvent > 0) ? sizeEvent - 1 : 4; + + // Reassign beam pointers in other classes. + timesPtr->reassignBeamPtrs( beamAPtr, beamBPtr, beamOffset); + spacePtr->reassignBeamPtrs( beamAPtr, beamBPtr); + remnants.reassignBeamPtrs( beamAPtr, beamBPtr); + + // Pretend that the diffractive system is the whole collision. + eCMsave = infoPtr->eCM(); + infoPtr->setECM( mDiff); + beamAPtr->newPzE( pzHP, ePom); + beamBPtr->newPzE( -pzHP, eHad); + +} + +//-------------------------------------------------------------------------- + +// Resolved diffraction: restore to original behaviour. + +void PartonLevel::leaveResolvedDiff( int iHardLoop, Event& event) { + + // Identify diffractive system. + int iDiffSys = (iHardLoop == 2 || !isResolvedA) ? 2 : 1; + + // Reconstruct boost and rotation to event cm frame. + Vec4 pPom = event[3 - iDiffSys].p() - event[5 - iDiffSys].p(); + Vec4 pHad = event[iDiffSys].p(); + RotBstMatrix MtoCM; + MtoCM.fromCMframe( pPom, pHad); + + // Perform rotation and boost on diffractive system. + int iFirst = (iHardLoop == 1) ? 5 + sizeEvent - sizeProcess : sizeEvent; + for (int i = iFirst; i < event.size(); ++i) + event[i].rotbst( MtoCM); + + // Restore multiple interactions pointer to default object. + multiPtr = &multiMB; + + // Restore beam pointers to incoming hadrons. + beamAPtr = beamHadAPtr; + beamBPtr = beamHadBPtr; + + // Reassign beam pointers in other classes. + timesPtr->reassignBeamPtrs( beamAPtr, beamBPtr, 0); + spacePtr->reassignBeamPtrs( beamAPtr, beamBPtr); + remnants.reassignBeamPtrs( beamAPtr, beamBPtr); + + // Restore cm energy. + infoPtr->setECM( eCMsave); + beamAPtr->newPzE( event[1].pz(), event[1].e()); + beamBPtr->newPzE( event[2].pz(), event[2].e()); + +} + +//-------------------------------------------------------------------------- + +// Handle showers in successive resonance decays. + +bool PartonLevel::resonanceShowers( Event& process, Event& event) { + + // Isolate next system to be processed, if anything remains. + int nRes = 0; + int nFSRres = 0; + while (nHardDone < process.size()) { + ++nRes; + int iBegin = nHardDone; + + // Mother in hard process and in complete event (after shower). + int iHardMother = process[iBegin].mother1(); + Particle& hardMother = process[iHardMother]; + int iBefMother = iPosBefShow[iHardMother]; + int iAftMother = event.iBotCopyId(iBefMother); + Particle& aftMother = event[iAftMother]; + + // From now on mother counts as decayed. + aftMother.statusNeg(); + + // Mother can have been moved by showering (in any of previous steps), + // so prepare to update colour and momentum information for system. + int colBef = hardMother.col(); + int acolBef = hardMother.acol(); + int colAft = aftMother.col(); + int acolAft = aftMother.acol(); + RotBstMatrix M; + M.bst( hardMother.p(), aftMother.p()); + + // Extract next partons from hard event into normal event record. + for (int i = iBegin; i < process.size(); ++ i) { + if (process[i].mother1() != iHardMother) break; + int iNow = event.append( process[i] ); + iPosBefShow[i] = iNow; + Particle& now = event.back(); + + // Currently outgoing ones should not count as decayed. + if (now.status() == -22) { + now.statusPos(); + now.daughters(0, 0); + } + + // Update daughter and mother information. + if (i == iBegin) event[iAftMother].daughter1( iNow); + else event[iAftMother].daughter2( iNow); + now.mother1(iAftMother); + + // Update colour and momentum information. + if (now.col() == colBef) now.col( colAft); + if (now.acol() == acolBef) now.acol( acolAft); + now.rotbst( M); + + // Complete task of copying next subsystem into event record. + ++nHardDone; + } + int iEnd = nHardDone - 1; + + // Do parton showers inside subsystem: maximum scale by mother mass. + if (doFSRinResonances) { + double pTmax = 0.5 * hardMother.m(); + if (canSetScale) pTmax = userHooksPtr->scaleResonance( iAftMother, event); + nFSRhard = 0; + + // Add new system, automatically with two empty beam slots. + int iSys = partonSystemsPtr->addSys(); + partonSystemsPtr->setSHat(iSys, pow2(hardMother.m()) ); + + // Loop over allowed range to find all final-state particles. + for (int i = iPosBefShow[iBegin]; i <= iPosBefShow[iEnd]; ++i) + if (event[i].isFinal()) partonSystemsPtr->addOut( iSys, i); + + // Let prepare routine do the setup. + timesDecPtr->prepare( iSys, event); + + // Set up initial veto scale. + doVeto = false; + double pTveto = pTvetoPT; + + // Begin evolution down in pT from hard pT scale. + do { + typeVetoStep = 0; + double pTtimes = timesDecPtr->pTnext( event, pTmax, 0.); + + // Allow a user veto. Only do it once, so remember to change pTveto. + if (pTveto > 0. && pTveto > pTtimes) { + pTveto = -1.; + doVeto = userHooksPtr->doVetoPT( 5, event); + // Abort event if vetoed. + if (doVeto) return false; + } + + // Do a final-state emission (if allowed). + if (pTtimes > 0.) { + if (timesDecPtr->branch( event)) { + ++nFSRres; + ++nFSRhard; + if (canVetoStep && nFSRhard <= nVetoStep) typeVetoStep = 5; + } + pTmax = pTtimes; + } + + // If no pT scales above zero then nothing to be done. + else pTmax = 0.; + + // Optionally check for a veto after the first few emissions. + if (typeVetoStep > 0) { + doVeto = userHooksPtr->doVetoStep( typeVetoStep, 0, nFSRhard, + event); + // Abort event if vetoed. + if (doVeto) return false; + } + + // Keep on evolving until nothing is left to be done. + } while (pTmax > 0.); + + } + + // No more systems to be processed. Set total number of emissions. + } + nFSRinRes = nFSRres; + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/PartonSystems.cxx b/PYTHIA8/pythia8140/src/PartonSystems.cxx new file mode 100644 index 00000000000..a25fd9fe2ed --- /dev/null +++ b/PYTHIA8/pythia8140/src/PartonSystems.cxx @@ -0,0 +1,118 @@ +// PartonSystems.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// PartonSystem and PartonSystems classes. + +#include "PartonSystems.h" + +namespace Pythia8 { + +//========================================================================== + +// The PartonSystems class. + +//-------------------------------------------------------------------------- + +// Replace the index of an incoming or outgoing parton by a new index. + +void PartonSystems::replace(int iSys, int iPosOld, int iPosNew) { + + if (systems[iSys].iInA == iPosOld) { + systems[iSys].iInA = iPosNew; + return; + } + if (systems[iSys].iInB == iPosOld) { + systems[iSys].iInB = iPosNew; + return; + } + for (int i = 0; i < sizeOut(iSys); ++i) + if (systems[iSys].iOut[i] == iPosOld) { + systems[iSys].iOut[i] = iPosNew; + return; + } + +} + +//-------------------------------------------------------------------------- + +// Return index of any parton in system, list starting with beam remnants. + +int PartonSystems::getAll(int iSys, int iMem) const { + + if (hasInAB(iSys)) { + if (iMem == 0) return systems[iSys].iInA; + if (iMem == 1) return systems[iSys].iInB; + return systems[iSys].iOut[iMem - 2]; + } else return systems[iSys].iOut[iMem]; + +} + +//-------------------------------------------------------------------------- + +// Find system of given outgoing parton, optionally also incoming one. + +int PartonSystems::getSystemOf(int iPos, bool alsoIn) const { + + // Loop over systems and over final-state members in each system. + for (int iSys = 0; iSys < sizeSys(); ++iSys) { + if (alsoIn) { + if (systems[iSys].iInA == iPos) return iSys; + if (systems[iSys].iInB == iPos) return iSys; + } + for (int iMem = 0; iMem < sizeOut(iSys); ++iMem) + if (systems[iSys].iOut[iMem] == iPos) return iSys; + } + + // Failure signalled by return value -1. + return -1; + +} + +//-------------------------------------------------------------------------- + +// Get the iMem index of iOut for an index into the event record + +int PartonSystems::getIndexOfOut(int iSys, int iPos) const { + for (int iMem = 0; iMem < sizeOut(iSys); ++iMem) + if (systems[iSys].iOut[iMem] == iPos) return iMem; + + // Failure signalled by return value -1. + return -1; +} + + +//-------------------------------------------------------------------------- + +// Print members in systems; for debug mainly. + +void PartonSystems::list(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA Parton Systems Listing -------------------" + << "--------------------------------- " + << "\n \n no inA inB out members \n"; + + // Loop over system list and over members in each system. + for (int iSys = 0; iSys < sizeSys(); ++iSys) { + os << " " << setw(3) << iSys << " " << setw(4) << systems[iSys].iInA + << " " << setw(4) << systems[iSys].iInB; + for (int iMem = 0; iMem < sizeOut(iSys); ++iMem) { + if (iMem%16 == 0 && iMem > 0) os << "\n "; + os << " " << setw(4) << systems[iSys].iOut[iMem]; + } + os << "\n"; + } + + // Alternative if no systems. Done. + if (sizeSys() == 0) os << " no systems defined \n"; + os << "\n -------- End PYTHIA Parton Systems Listing ---------------" + << "---------------------------------" << endl; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/PhaseSpace.cxx b/PYTHIA8/pythia8140/src/PhaseSpace.cxx new file mode 100644 index 00000000000..7c20a47c8c7 --- /dev/null +++ b/PYTHIA8/pythia8140/src/PhaseSpace.cxx @@ -0,0 +1,3295 @@ +// PhaseSpace.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// PhaseSpace and PhaseSpace2to2tauyz classes. + +#include "PhaseSpace.h" + +namespace Pythia8 { + +//========================================================================== + +// The PhaseSpace class. +// Base class for phase space generators. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of trial maxima around which maximum search is performed. +const int PhaseSpace::NMAXTRY = 2; + +// Number of three-body trials in phase space optimization. +const int PhaseSpace::NTRY3BODY = 20; + +// Maximum cross section increase, just in case true maximum not found. +const double PhaseSpace::SAFETYMARGIN = 1.05; + +// Small number to avoid division by zero. +const double PhaseSpace::TINY = 1e-20; + +// Fraction of total weight that is shared evenly between all shapes. +const double PhaseSpace::EVENFRAC = 0.4; + +// Two cross sections with a small relative error are assumed same. +const double PhaseSpace::SAMESIGMA = 1e-6; + +// Do not include resonances peaked too far outside allowed mass region. +const double PhaseSpace::WIDTHMARGIN = 20.; + +// Special optimization treatment when two resonances at almost same mass. +const double PhaseSpace::SAMEMASS = 0.01; + +// Minimum phase space left when kinematics constraints are combined. +const double PhaseSpace::MASSMARGIN = 0.01; + +// When using Breit-Wigners in 2 -> 2 raise maximum weight estimate. +const double PhaseSpace::EXTRABWWTMAX = 1.25; + +// Size of Breit-Wigner threshold region, for mass selection biasing. +const double PhaseSpace::THRESHOLDSIZE = 3.; + +// Step size in optimal-mass search, for mass selection biasing. +const double PhaseSpace::THRESHOLDSTEP = 0.2; + +// Minimal rapidity range for allowed open range (in 2 -> 3). +const double PhaseSpace::YRANGEMARGIN = 1e-6; + +// Cutoff for f_e^e at x < 1 - 10^{-10} to be used in phase space selection. +// Note: the ...MIN quantities come from 1 - x_max or 1 - tau_max. +const double PhaseSpace::LEPTONXMIN = 1e-10; +const double PhaseSpace::LEPTONXMAX = 1. - 1e-10; +const double PhaseSpace::LEPTONXLOGMIN = log(1e-10); +const double PhaseSpace::LEPTONXLOGMAX = log(1. - 1e-10); +const double PhaseSpace::LEPTONTAUMIN = 2e-10; + +// Safety to avoid division with unreasonably small value for z selection. +const double PhaseSpace::SHATMINZ = 1.; + +// Regularization for small pT2min in z = cos(theta) selection. +const double PhaseSpace::PT2RATMINZ = 0.0001; + +// These numbers are hardwired empirical parameters, +// intended to speed up the M-generator. +const double PhaseSpace::WTCORRECTION[11] = { 1., 1., 1., + 2., 5., 15., 60., 250., 1250., 7000., 50000. }; + +//-------------------------------------------------------------------------- + +// Perform simple initialization and store pointers. + +void PhaseSpace::init(bool isFirst, SigmaProcess* sigmaProcessPtrIn, + Info* infoPtrIn, Settings* settingsPtrIn, ParticleData* particleDataPtrIn, + Rndm* rndmPtrIn, BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, + CoupSM* coupSMPtrIn, SigmaTotal* sigmaTotPtrIn, UserHooks* userHooksPtrIn) { + + // Store input pointers for future use. + sigmaProcessPtr = sigmaProcessPtrIn; + infoPtr = infoPtrIn; + settingsPtr = settingsPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + coupSMPtr = coupSMPtrIn; + sigmaTotPtr = sigmaTotPtrIn; + userHooksPtr = userHooksPtrIn; + + // Some commonly used beam information. + idA = beamAPtr->id(); + idB = beamBPtr->id(); + mA = beamAPtr->m(); + mB = beamBPtr->m(); + eCM = infoPtr->eCM(); + s = eCM * eCM; + + // Flag if lepton beams, and if non-resolved ones. + hasLeptonBeams = ( beamAPtr->isLepton() || beamBPtr->isLepton() ); + hasPointLeptons = ( hasLeptonBeams + && (beamAPtr->isUnresolved() || beamBPtr->isUnresolved() ) ); + + // Standard phase space cuts. + if (isFirst || settingsPtr->flag("PhaseSpace:sameForSecond")) { + mHatGlobalMin = settingsPtr->parm("PhaseSpace:mHatMin"); + mHatGlobalMax = settingsPtr->parm("PhaseSpace:mHatMax"); + pTHatGlobalMin = settingsPtr->parm("PhaseSpace:pTHatMin"); + pTHatGlobalMax = settingsPtr->parm("PhaseSpace:pTHatMax"); + + // Optionally separate phase space cuts for second hard process. + } else { + mHatGlobalMin = settingsPtr->parm("PhaseSpace:mHatMinSecond"); + mHatGlobalMax = settingsPtr->parm("PhaseSpace:mHatMaxSecond"); + pTHatGlobalMin = settingsPtr->parm("PhaseSpace:pTHatMinSecond"); + pTHatGlobalMax = settingsPtr->parm("PhaseSpace:pTHatMaxSecond"); + } + + // Cutoff against divergences at pT -> 0. + pTHatMinDiverge = settingsPtr->parm("PhaseSpace:pTHatMinDiverge"); + + // When to use Breit-Wigners. + useBreitWigners = settingsPtr->flag("PhaseSpace:useBreitWigners"); + minWidthBreitWigners = settingsPtr->parm("PhaseSpace:minWidthBreitWigners"); + + // Whether generation is with variable energy. + doEnergySpread = settingsPtr->flag("Beams:allowMomentumSpread"); + + // Flags for maximization information and violation handling. + showSearch = settingsPtr->flag("PhaseSpace:showSearch"); + showViolation = settingsPtr->flag("PhaseSpace:showViolation"); + increaseMaximum = settingsPtr->flag("PhaseSpace:increaseMaximum"); + + // Know whether a Z0 is pure Z0 or admixed with gamma*. + gmZmodeGlobal = settingsPtr->mode("WeakZ0:gmZmode"); + + // Default event-specific kinematics properties. + x1H = 1.; + x2H = 1.; + m3 = 0.; + m4 = 0.; + m5 = 0.; + s3 = m3 * m3; + s4 = m4 * m4; + s5 = m5 * m5; + mHat = eCM; + sH = s; + tH = 0.; + uH = 0.; + pTH = 0.; + theta = 0.; + phi = 0.; + runBW3H = 1.; + runBW4H = 1.; + runBW5H = 1.; + + // Default cross section information. + sigmaNw = 0.; + sigmaMx = 0.; + sigmaPos = 0.; + sigmaNeg = 0.; + newSigmaMx = false; + + // Flag if user should be allow to reweight cross section. + canModifySigma = (userHooksPtr > 0) + ? userHooksPtr->canModifySigma() : false; + +} + +//-------------------------------------------------------------------------- + +// Allow for nonisotropic decays when ME's available. + +void PhaseSpace::decayKinematics( Event& process) { + + // Identify sets of sister partons. + int iResEnd = 4; + for (int iResBeg = 5; iResBeg < process.size(); ++iResBeg) { + if (iResBeg <= iResEnd) continue; + iResEnd = iResBeg; + while ( iResEnd < process.size() - 1 + && process[iResEnd + 1].mother1() == process[iResBeg].mother1() + && process[iResEnd + 1].mother2() == process[iResBeg].mother2() ) + ++iResEnd; + + // Check that at least one of them is a resonance. + bool hasRes = false; + for (int iRes = iResBeg; iRes <= iResEnd; ++iRes) + if ( !process[iRes].isFinal() ) hasRes = true; + if ( !hasRes ) continue; + + // Evaluate matrix element and decide whether to keep kinematics. + double decWt = sigmaProcessPtr->weightDecay( process, iResBeg, iResEnd); + if (decWt < 0.) infoPtr->errorMsg("Warning in PhaseSpace::decay" + "Kinematics: negative angular weight"); + if (decWt > 1.) infoPtr->errorMsg("Warning in PhaseSpace::decay" + "Kinematics: angular weight above unity"); + while (decWt < rndmPtr->flat() ) { + + // Find resonances for which to redo decay angles. + for (int iRes = iResBeg; iRes < process.size(); ++iRes) { + if ( process[iRes].isFinal() ) continue; + int iResMother = iRes; + while (iResMother > iResEnd) + iResMother = process[iResMother].mother1(); + if (iResMother < iResBeg) continue; + + // Do decay of this mother isotropically in phase space. + decayKinematicsStep( process, iRes); + + // End loop over resonance decay chains. + } + + // Ready to allow new test of matrix element. + decWt = sigmaProcessPtr->weightDecay( process, iResBeg, iResEnd); + if (decWt < 0.) infoPtr->errorMsg("Warning in PhaseSpace::decay" + "Kinematics: negative angular weight"); + if (decWt > 1.) infoPtr->errorMsg("Warning in PhaseSpace::decay" + "Kinematics: angular weight above unity"); + } + + // End loop over sets of sister resonances/partons. + } + +} + +//-------------------------------------------------------------------------- + +// Reselect decay products momenta isotropically in phase space. +// Does not redo secondary vertex position! + +void PhaseSpace::decayKinematicsStep( Event& process, int iRes) { + + // Multiplicity and mother mass and four-momentum. + int i1 = process[iRes].daughter1(); + int mult = process[iRes].daughter2() + 1 - i1; + double m0 = process[iRes].m(); + Vec4 pRes = process[iRes].p(); + + // Description of two-body decays as simple special case. + if (mult == 2) { + + // Products and product masses. + int i2 = i1 + 1; + double m1t = process[i1].m(); + double m2t = process[i2].m(); + + // Energies and absolute momentum in the rest frame. + double e1 = 0.5 * (m0*m0 + m1t*m1t - m2t*m2t) / m0; + double e2 = 0.5 * (m0*m0 + m2t*m2t - m1t*m1t) / m0; + double p12 = 0.5 * sqrtpos( (m0 - m1t - m2t) * (m0 + m1t + m2t) + * (m0 + m1t - m2t) * (m0 - m1t + m2t) ) / m0; + + // Pick isotropic angles to give three-momentum. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi12 = 2. * M_PI * rndmPtr->flat(); + double pX = p12 * sinTheta * cos(phi12); + double pY = p12 * sinTheta * sin(phi12); + double pZ = p12 * cosTheta; + + // Fill four-momenta in mother rest frame and then boost to lab frame. + Vec4 p1( pX, pY, pZ, e1); + Vec4 p2( -pX, -pY, -pZ, e2); + p1.bst( pRes ); + p2.bst( pRes ); + + // Done for two-body decay. + process[i1].p( p1 ); + process[i2].p( p2 ); + return; + } + + // Description of three-body decays as semi-simple special case. + if (mult == 3) { + + // Products and product masses. + int i2 = i1 + 1; + int i3 = i2 + 1; + double m1t = process[i1].m(); + double m2t = process[i2].m(); + double m3t = process[i3].m(); + double mDiff = m0 - (m1t + m2t + m3t); + + // Kinematical limits for 2+3 mass. Maximum phase-space weight. + double m23Min = m2t + m3t; + double m23Max = m0 - m1t; + double p1Max = 0.5 * sqrtpos( (m0 - m1t - m23Min) + * (m0 + m1t + m23Min) * (m0 + m1t - m23Min) + * (m0 - m1t + m23Min) ) / m0; + double p23Max = 0.5 * sqrtpos( (m23Max - m2t - m3t) + * (m23Max + m2t + m3t) * (m23Max + m2t - m3t) + * (m23Max - m2t + m3t) ) / m23Max; + double wtPSmax = 0.5 * p1Max * p23Max; + + // Pick an intermediate mass m23 flat in the allowed range. + double wtPS, m23, p1Abs, p23Abs; + do { + m23 = m23Min + rndmPtr->flat() * mDiff; + + // Translate into relative momenta and find phase-space weight. + p1Abs = 0.5 * sqrtpos( (m0 - m1t - m23) * (m0 + m1t + m23) + * (m0 + m1t - m23) * (m0 - m1t + m23) ) / m0; + p23Abs = 0.5 * sqrtpos( (m23 - m2t - m3t) * (m23 + m2t + m3t) + * (m23 + m2t - m3t) * (m23 - m2t + m3t) ) / m23; + wtPS = p1Abs * p23Abs; + + // If rejected, try again with new invariant masses. + } while ( wtPS < rndmPtr->flat() * wtPSmax ); + + // Set up m23 -> m2 + m3 isotropic in its rest frame. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi23 = 2. * M_PI * rndmPtr->flat(); + double pX = p23Abs * sinTheta * cos(phi23); + double pY = p23Abs * sinTheta * sin(phi23); + double pZ = p23Abs * cosTheta; + double e2 = sqrt( m2t*m2t + p23Abs*p23Abs); + double e3 = sqrt( m3t*m3t + p23Abs*p23Abs); + Vec4 p2( pX, pY, pZ, e2); + Vec4 p3( -pX, -pY, -pZ, e3); + + // Set up 0 -> 1 + 23 isotropic in its rest frame. + cosTheta = 2. * rndmPtr->flat() - 1.; + sinTheta = sqrt(1. - cosTheta*cosTheta); + phi23 = 2. * M_PI * rndmPtr->flat(); + pX = p1Abs * sinTheta * cos(phi23); + pY = p1Abs * sinTheta * sin(phi23); + pZ = p1Abs * cosTheta; + double e1 = sqrt( m1t*m1t + p1Abs*p1Abs); + double e23 = sqrt( m23*m23 + p1Abs*p1Abs); + Vec4 p1( pX, pY, pZ, e1); + + // Boost 2 + 3 to the 0 rest frame and then boost to lab frame. + Vec4 p23( -pX, -pY, -pZ, e23); + p2.bst( p23 ); + p3.bst( p23 ); + p1.bst( pRes ); + p2.bst( pRes ); + p3.bst( pRes ); + + // Done for three-body decay. + process[i1].p( p1 ); + process[i2].p( p2 ); + process[i3].p( p3 ); + return; + } + + // Do a multibody decay using the M-generator algorithm. + + // Set up masses and four-momenta in a vector, with mother in slot 0. + vector mProd; + mProd.push_back( m0); + for (int i = i1; i <= process[iRes].daughter2(); ++i) + mProd.push_back( process[i].m() ); + vector pProd; + pProd.push_back( pRes); + + // Sum of daughter masses. + double mSum = mProd[1]; + for (int i = 2; i <= mult; ++i) mSum += mProd[i]; + double mDiff = m0 - mSum; + + // Begin setup of intermediate invariant masses. + vector mInv; + for (int i = 0; i <= mult; ++i) mInv.push_back( mProd[i]); + + // Calculate the maximum weight in the decay. + double wtPSmax = 1. / WTCORRECTION[mult]; + double mMaxWT = mDiff + mProd[mult]; + double mMinWT = 0.; + for (int i = mult - 1; i > 0; --i) { + mMaxWT += mProd[i]; + mMinWT += mProd[i+1]; + double mNow = mProd[i]; + wtPSmax *= 0.5 * sqrtpos( (mMaxWT - mMinWT - mNow) + * (mMaxWT + mMinWT + mNow) * (mMaxWT + mMinWT - mNow) + * (mMaxWT - mMinWT + mNow) ) / mMaxWT; + } + + // Begin loop to find the set of intermediate invariant masses. + vector rndmOrd; + double wtPS; + do { + wtPS = 1.; + + // Find and order random numbers in descending order. + rndmOrd.resize(0); + rndmOrd.push_back(1.); + for (int i = 1; i < mult - 1; ++i) { + double rndm = rndmPtr->flat(); + rndmOrd.push_back(rndm); + for (int j = i - 1; j > 0; --j) { + if (rndm > rndmOrd[j]) swap( rndmOrd[j], rndmOrd[j+1] ); + else break; + } + } + rndmOrd.push_back(0.); + + // Translate into intermediate masses and find weight. + for (int i = mult - 1; i > 0; --i) { + mInv[i] = mInv[i+1] + mProd[i] + (rndmOrd[i-1] - rndmOrd[i]) * mDiff; + wtPS *= 0.5 * sqrtpos( (mInv[i] - mInv[i+1] - mProd[i]) + * (mInv[i] + mInv[i+1] + mProd[i]) * (mInv[i] + mInv[i+1] - mProd[i]) + * (mInv[i] - mInv[i+1] + mProd[i]) ) / mInv[i]; + } + + // If rejected, try again with new invariant masses. + } while ( wtPS < rndmPtr->flat() * wtPSmax ); + + // Perform two-particle decays in the respective rest frame. + vector pInv; + pInv.resize(mult + 1); + for (int i = 1; i < mult; ++i) { + double p12 = 0.5 * sqrtpos( (mInv[i] - mInv[i+1] - mProd[i]) + * (mInv[i] + mInv[i+1] + mProd[i]) * (mInv[i] + mInv[i+1] - mProd[i]) + * (mInv[i] - mInv[i+1] + mProd[i]) ) / mInv[i]; + + // Isotropic angles give three-momentum. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phiLoc = 2. * M_PI * rndmPtr->flat(); + double pX = p12 * sinTheta * cos(phiLoc); + double pY = p12 * sinTheta * sin(phiLoc); + double pZ = p12 * cosTheta; + + // Calculate energies, fill four-momenta. + double eHad = sqrt( mProd[i]*mProd[i] + p12*p12); + double eInv = sqrt( mInv[i+1]*mInv[i+1] + p12*p12); + pProd.push_back( Vec4( pX, pY, pZ, eHad) ); + pInv[i+1].p( -pX, -pY, -pZ, eInv); + } + pProd.push_back( pInv[mult] ); + + // Boost decay products to the mother rest frame and on to lab frame. + pInv[1] = pProd[0]; + for (int iFrame = mult - 1; iFrame > 0; --iFrame) + for (int i = iFrame; i <= mult; ++i) pProd[i].bst(pInv[iFrame]); + + // Done for multibody decay. + for (int i = 1; i < mult; ++i) + process[i1 + i - 1].p( pProd[i] ); + return; + +} + +//-------------------------------------------------------------------------- + +// Determine how 3-body phase space should be sampled. + +void PhaseSpace::setup3Body() { + + // Check for massive t-channel propagator particles. + int idTchan1 = abs( sigmaProcessPtr->idTchan1() ); + int idTchan2 = abs( sigmaProcessPtr->idTchan2() ); + mTchan1 = (idTchan1 == 0) ? 0. : particleDataPtr->m0(idTchan1); + mTchan2 = (idTchan2 == 0) ? 0. : particleDataPtr->m0(idTchan2); + sTchan1 = mTchan1 * mTchan1; + sTchan2 = mTchan2 * mTchan2; + + // Find coefficients of different pT2 selection terms. Mirror choice. + frac3Pow1 = sigmaProcessPtr->tChanFracPow1(); + frac3Pow2 = sigmaProcessPtr->tChanFracPow2(); + frac3Flat = 1. - frac3Pow1 - frac3Pow2; + useMirrorWeight = sigmaProcessPtr->useMirrorWeight(); + +} + +//-------------------------------------------------------------------------- + +// Determine how phase space should be sampled. + +bool PhaseSpace::setupSampling123(bool is2, bool is3, ostream& os) { + + // Optional printout. + if (showSearch) os << "\n PYTHIA Optimization printout for " + << sigmaProcessPtr->name() << "\n \n" << scientific << setprecision(3); + + // Check that open range in tau (+ set tauMin, tauMax). + if (!limitTau(is2, is3)) return false; + + // Reset coefficients and matrices of equation system to solve. + int binTau[8], binY[8], binZ[8]; + double vecTau[8], matTau[8][8], vecY[8], matY[8][8], vecZ[8], matZ[8][8]; + for (int i = 0; i < 8; ++i) { + tauCoef[i] = 0.; + yCoef[i] = 0.; + zCoef[i] = 0.; + binTau[i] = 0; + binY[i] = 0; + binZ[i] = 0; + vecTau[i] = 0.; + vecY[i] = 0.; + vecZ[i] = 0.; + for (int j = 0; j < 8; ++j) { + matTau[i][j] = 0.; + matY[i][j] = 0.; + matZ[i][j] = 0.; + } + } + sigmaMx = 0.; + sigmaNeg = 0.; + + // Number of used coefficients/points for each dimension: tau, y, c. + nTau = (hasPointLeptons) ? 1 : 2; + nY = (hasPointLeptons) ? 1 : 5; + nZ = (is2) ? 5 : 1; + + // Identify if any resonances contribute in s-channel. + idResA = sigmaProcessPtr->resonanceA(); + if (idResA != 0) { + mResA = particleDataPtr->m0(idResA); + GammaResA = particleDataPtr->mWidth(idResA); + if (mHatMin > mResA + WIDTHMARGIN * GammaResA || (mHatMax > 0. + && mHatMax < mResA - WIDTHMARGIN * GammaResA) ) idResA = 0; + } + idResB = sigmaProcessPtr->resonanceB(); + if (idResB != 0) { + mResB = particleDataPtr->m0(idResB); + GammaResB = particleDataPtr->mWidth(idResB); + if (mHatMin > mResB + WIDTHMARGIN * GammaResB || (mHatMax > 0. + && mHatMax < mResB - WIDTHMARGIN * GammaResB) ) idResB = 0; + } + if (idResA == 0 && idResB != 0) { + idResA = idResB; + mResA = mResB; + GammaResA = GammaResB; + idResB = 0; + } + + // More sampling in tau if resonances in s-channel. + if (idResA !=0 && !hasPointLeptons) { + nTau += 2; + tauResA = mResA * mResA / s; + widResA = mResA * GammaResA / s; + } + if (idResB != 0 && !hasPointLeptons) { + nTau += 2; + tauResB = mResB * mResB / s; + widResB = mResB * GammaResB / s; + } + + // More sampling in tau (and different in y) if incoming lepton beams. + if (hasLeptonBeams && !hasPointLeptons) ++nTau; + + // Special case when both resonances have same mass. + sameResMass = false; + if (idResB != 0 && abs(mResA - mResB) < SAMEMASS * (GammaResA + GammaResB)) + sameResMass = true; + + // Default z value and weight required for 2 -> 1. Number of dimensions. + z = 0.; + wtZ = 1.; + int nVar = (is2) ? 3 : 2; + + // Initial values, to be modified later. + tauCoef[0] = 1.; + yCoef[1] = 0.5; + yCoef[2] = 0.5; + zCoef[0] = 1.; + + // Step through grid in tau. Set limits on y and z generation. + for (int iTau = 0; iTau < nTau; ++iTau) { + double posTau = 0.5; + if (sameResMass && iTau > 1 && iTau < 6) posTau = (iTau < 4) ? 0.4 : 0.6; + selectTau( iTau, posTau, is2); + if (!limitY()) continue; + if (is2 && !limitZ()) continue; + + // Step through grids in y and z. + for (int iY = 0; iY < nY; ++iY) { + selectY( iY, 0.5); + for (int iZ = 0; iZ < nZ; ++iZ) { + if (is2) selectZ( iZ, 0.5); + double sigmaTmp = 0.; + + // 2 -> 1: calculate cross section, weighted by phase-space volume. + if (!is2 && !is3) { + sigmaProcessPtr->set1Kin( x1H, x2H, sH); + sigmaTmp = sigmaProcessPtr->sigmaPDF(); + sigmaTmp *= wtTau * wtY; + + // 2 -> 2: calculate cross section, weighted by phase-space volume + // and Breit-Wigners for masses + } else if (is2) { + sigmaProcessPtr->set2Kin( x1H, x2H, sH, tH, m3, m4, + runBW3H, runBW4H); + sigmaTmp = sigmaProcessPtr->sigmaPDF(); + sigmaTmp *= wtTau * wtY * wtZ * wtBW; + + // 2 -> 3: repeat internal 3-body phase space several times and + // keep maximal cross section, weighted by phase-space volume + // and Breit-Wigners for masses + } else if (is3) { + for (int iTry3 = 0; iTry3 < NTRY3BODY; ++iTry3) { + if (!select3Body()) continue; + sigmaProcessPtr->set3Kin( x1H, x2H, sH, p3cm, p4cm, p5cm, + m3, m4, m5, runBW3H, runBW4H, runBW5H); + double sigmaTry = sigmaProcessPtr->sigmaPDF(); + sigmaTry *= wtTau * wtY * wt3Body * wtBW; + if (sigmaTry > sigmaTmp) sigmaTmp = sigmaTry; + } + } + + // Allow possibility for user to modify cross section. (3body??) + if (canModifySigma) sigmaTmp + *= userHooksPtr->multiplySigmaBy( sigmaProcessPtr, this, false); + + // Check if current maximum exceeded. + if (sigmaTmp > sigmaMx) sigmaMx = sigmaTmp; + + // Optional printout. Protect against negative cross sections. + if (showSearch) os << " tau =" << setw(11) << tau << " y =" + << setw(11) << y << " z =" << setw(11) << z + << " sigma =" << setw(11) << sigmaTmp << "\n"; + if (sigmaTmp < 0.) sigmaTmp = 0.; + + // Sum up tau cross-section pieces in points used. + if (!hasPointLeptons) { + binTau[iTau] += 1; + vecTau[iTau] += sigmaTmp; + matTau[iTau][0] += 1. / intTau0; + matTau[iTau][1] += (1. / intTau1) / tau; + if (idResA != 0) { + matTau[iTau][2] += (1. / intTau2) / (tau + tauResA); + matTau[iTau][3] += (1. / intTau3) + * tau / ( pow2(tau - tauResA) + pow2(widResA) ); + } + if (idResB != 0) { + matTau[iTau][4] += (1. / intTau4) / (tau + tauResB); + matTau[iTau][5] += (1. / intTau5) + * tau / ( pow2(tau - tauResB) + pow2(widResB) ); + } + if (hasLeptonBeams) matTau[iTau][nTau - 1] += (1. / intTau6) + * tau / max( LEPTONTAUMIN, 1. - tau); + } + + // Sum up y cross-section pieces in points used. + if (!hasPointLeptons) { + binY[iY] += 1; + vecY[iY] += sigmaTmp; + matY[iY][0] += (yMax / intY0) / cosh(y); + matY[iY][1] += (yMax / intY12) * (y + yMax); + matY[iY][2] += (yMax / intY12) * (yMax - y); + if (!hasLeptonBeams) { + matY[iY][3] += (yMax / intY34) * exp(y); + matY[iY][4] += (yMax / intY34) * exp(-y); + } else { + matY[iY][3] += (yMax / intY56) + / max( LEPTONXMIN, 1. - exp( y - yMax) ); + matY[iY][4] += (yMax / intY56) + / max( LEPTONXMIN, 1. - exp(-y - yMax) ); + } + } + + // Integrals over z expressions at tauMax, to be used below. + if (is2) { + double p2AbsMax = 0.25 * (pow2(tauMax * s - s3 - s4) + - 4. * s3 * s4) / (tauMax * s); + double zMaxMax = sqrtpos( 1. - pT2HatMin / p2AbsMax ); + double zPosMaxMax = max(ratio34, unity34 + zMaxMax); + double zNegMaxMax = max(ratio34, unity34 - zMaxMax); + double intZ0Max = 2. * zMaxMax; + double intZ12Max = log( zPosMaxMax / zNegMaxMax); + double intZ34Max = 1. / zNegMaxMax - 1. / zPosMaxMax; + + // Sum up z cross-section pieces in points used. + binZ[iZ] += 1; + vecZ[iZ] += sigmaTmp; + matZ[iZ][0] += 1.; + matZ[iZ][1] += (intZ0Max / intZ12Max) / zNeg; + matZ[iZ][2] += (intZ0Max / intZ12Max) / zPos; + matZ[iZ][3] += (intZ0Max / intZ34Max) / pow2(zNeg); + matZ[iZ][4] += (intZ0Max / intZ34Max) / pow2(zPos); + } + + // End of loops over phase space points. + } + } + } + + // Fail if no non-vanishing cross sections. + if (sigmaMx <= 0.) { + sigmaMx = 0.; + return false; + } + + // Solve respective equation system for better phase space coefficients. + if (!hasPointLeptons) solveSys( nTau, binTau, vecTau, matTau, tauCoef); + if (!hasPointLeptons) solveSys( nY, binY, vecY, matY, yCoef); + if (is2) solveSys( nZ, binZ, vecZ, matZ, zCoef); + if (showSearch) os << "\n"; + + // Provide cumulative sum of coefficients. + tauCoefSum[0] = tauCoef[0]; + yCoefSum[0] = yCoef[0]; + zCoefSum[0] = zCoef[0]; + for (int i = 1; i < 8; ++ i) { + tauCoefSum[i] = tauCoefSum[i - 1] + tauCoef[i]; + yCoefSum[i] = yCoefSum[i - 1] + yCoef[i]; + zCoefSum[i] = zCoefSum[i - 1] + zCoef[i]; + } + // The last element should be > 1 to be on safe side in selection below. + tauCoefSum[nTau - 1] = 2.; + yCoefSum[nY - 1] = 2.; + zCoefSum[nZ - 1] = 2.; + + + // Begin find two most promising maxima among same points as before. + int iMaxTau[NMAXTRY + 2], iMaxY[NMAXTRY + 2], iMaxZ[NMAXTRY + 2]; + double sigMax[NMAXTRY + 2]; + int nMax = 0; + + // Scan same grid as before in tau, y, z. + for (int iTau = 0; iTau < nTau; ++iTau) { + double posTau = 0.5; + if (sameResMass && iTau > 1 && iTau < 6) posTau = (iTau < 4) ? 0.4 : 0.6; + selectTau( iTau, posTau, is2); + if (!limitY()) continue; + if (is2 && !limitZ()) continue; + for (int iY = 0; iY < nY; ++iY) { + selectY( iY, 0.5); + for (int iZ = 0; iZ < nZ; ++iZ) { + if (is2) selectZ( iZ, 0.5); + double sigmaTmp = 0.; + + // 2 -> 1: calculate cross section, weighted by phase-space volume. + if (!is2 && !is3) { + sigmaProcessPtr->set1Kin( x1H, x2H, sH); + sigmaTmp = sigmaProcessPtr->sigmaPDF(); + sigmaTmp *= wtTau * wtY; + + // 2 -> 2: calculate cross section, weighted by phase-space volume + // and Breit-Wigners for masses + } else if (is2) { + sigmaProcessPtr->set2Kin( x1H, x2H, sH, tH, m3, m4, + runBW3H, runBW4H); + sigmaTmp = sigmaProcessPtr->sigmaPDF(); + sigmaTmp *= wtTau * wtY * wtZ * wtBW; + + // 2 -> 3: repeat internal 3-body phase space several times and + // keep maximal cross section, weighted by phase-space volume + // and Breit-Wigners for masses + } else if (is3) { + for (int iTry3 = 0; iTry3 < NTRY3BODY; ++iTry3) { + if (!select3Body()) continue; + sigmaProcessPtr->set3Kin( x1H, x2H, sH, p3cm, p4cm, p5cm, + m3, m4, m5, runBW3H, runBW4H, runBW5H); + double sigmaTry = sigmaProcessPtr->sigmaPDF(); + sigmaTry *= wtTau * wtY * wt3Body * wtBW; + if (sigmaTry > sigmaTmp) sigmaTmp = sigmaTry; + } + } + + // Allow possibility for user to modify cross section. (3body??) + if (canModifySigma) sigmaTmp + *= userHooksPtr->multiplySigmaBy( sigmaProcessPtr, this, false); + + // Optional printout. Protect against negative cross section. + if (showSearch) os << " tau =" << setw(11) << tau << " y =" + << setw(11) << y << " z =" << setw(11) << z + << " sigma =" << setw(11) << sigmaTmp << "\n"; + if (sigmaTmp < 0.) sigmaTmp = 0.; + + // Check that point is not simply mirror of already found one. + bool mirrorPoint = false; + for (int iMove = 0; iMove < nMax; ++iMove) + if (abs(sigmaTmp - sigMax[iMove]) < SAMESIGMA + * (sigmaTmp + sigMax[iMove])) mirrorPoint = true; + + // Add to or insert in maximum list. Only first two count. + if (!mirrorPoint) { + int iInsert = 0; + for (int iMove = nMax - 1; iMove >= -1; --iMove) { + iInsert = iMove + 1; + if (iInsert == 0 || sigmaTmp < sigMax[iMove]) break; + iMaxTau[iMove + 1] = iMaxTau[iMove]; + iMaxY[iMove + 1] = iMaxY[iMove]; + iMaxZ[iMove + 1] = iMaxZ[iMove]; + sigMax[iMove + 1] = sigMax[iMove]; + } + iMaxTau[iInsert] = iTau; + iMaxY[iInsert] = iY; + iMaxZ[iInsert] = iZ; + sigMax[iInsert] = sigmaTmp; + if (nMax < NMAXTRY) ++nMax; + } + + // Found two most promising maxima. + } + } + } + if (showSearch) os << "\n"; + + // Read out starting position for search. + sigmaMx = sigMax[0]; + int beginVar = (hasPointLeptons) ? 2 : 0; + for (int iMax = 0; iMax < nMax; ++iMax) { + int iTau = iMaxTau[iMax]; + int iY = iMaxY[iMax]; + int iZ = iMaxZ[iMax]; + double tauVal = 0.5; + double yVal = 0.5; + double zVal = 0.5; + int iGrid; + double varVal, varNew, deltaVar, marginVar, sigGrid[3]; + + // Starting point and step size in parameter space. + for (int iRepeat = 0; iRepeat < 2; ++iRepeat) { + // Run through (possibly a subset of) tau, y and z. + for (int iVar = beginVar; iVar < nVar; ++iVar) { + if (iVar == 0) varVal = tauVal; + else if (iVar == 1) varVal = yVal; + else varVal = zVal; + deltaVar = (iRepeat == 0) ? 0.1 + : max( 0.01, min( 0.05, min( varVal - 0.02, 0.98 - varVal) ) ); + marginVar = (iRepeat == 0) ? 0.02 : 0.002; + int moveStart = (iRepeat == 0 && iVar == 0) ? 0 : 1; + for (int move = moveStart; move < 9; ++move) { + + // Define new parameter-space point by step in one dimension. + if (move == 0) { + iGrid = 1; + varNew = varVal; + } else if (move == 1) { + iGrid = 2; + varNew = varVal + deltaVar; + } else if (move == 2) { + iGrid = 0; + varNew = varVal - deltaVar; + } else if (sigGrid[2] >= max( sigGrid[0], sigGrid[1]) + && varVal + 2. * deltaVar < 1. - marginVar) { + varVal += deltaVar; + sigGrid[0] = sigGrid[1]; + sigGrid[1] = sigGrid[2]; + iGrid = 2; + varNew = varVal + deltaVar; + } else if (sigGrid[0] >= max( sigGrid[1], sigGrid[2]) + && varVal - 2. * deltaVar > marginVar) { + varVal -= deltaVar; + sigGrid[2] = sigGrid[1]; + sigGrid[1] = sigGrid[0]; + iGrid = 0; + varNew = varVal - deltaVar; + } else if (sigGrid[2] >= sigGrid[0]) { + deltaVar *= 0.5; + varVal += deltaVar; + sigGrid[0] = sigGrid[1]; + iGrid = 1; + varNew = varVal; + } else { + deltaVar *= 0.5; + varVal -= deltaVar; + sigGrid[2] = sigGrid[1]; + iGrid = 1; + varNew = varVal; + } + + // Convert to relevant variables and find derived new limits. + bool insideLimits = true; + if (iVar == 0) { + tauVal = varNew; + selectTau( iTau, tauVal, is2); + if (!limitY()) insideLimits = false; + if (is2 && !limitZ()) insideLimits = false; + if (insideLimits) { + selectY( iY, yVal); + if (is2) selectZ( iZ, zVal); + } + } else if (iVar == 1) { + yVal = varNew; + selectY( iY, yVal); + } else if (iVar == 2) { + zVal = varNew; + selectZ( iZ, zVal); + } + + // Evaluate cross-section. + double sigmaTmp = 0.; + if (insideLimits) { + + // 2 -> 1: calculate cross section, weighted by phase-space volume. + if (!is2 && !is3) { + sigmaProcessPtr->set1Kin( x1H, x2H, sH); + sigmaTmp = sigmaProcessPtr->sigmaPDF(); + sigmaTmp *= wtTau * wtY; + + // 2 -> 2: calculate cross section, weighted by phase-space volume + // and Breit-Wigners for masses + } else if (is2) { + sigmaProcessPtr->set2Kin( x1H, x2H, sH, tH, m3, m4, + runBW3H, runBW4H); + sigmaTmp = sigmaProcessPtr->sigmaPDF(); + sigmaTmp *= wtTau * wtY * wtZ * wtBW; + + // 2 -> 3: repeat internal 3-body phase space several times and + // keep maximal cross section, weighted by phase-space volume + // and Breit-Wigners for masses + } else if (is3) { + for (int iTry3 = 0; iTry3 < NTRY3BODY; ++iTry3) { + if (!select3Body()) continue; + sigmaProcessPtr->set3Kin( x1H, x2H, sH, p3cm, p4cm, p5cm, + m3, m4, m5, runBW3H, runBW4H, runBW5H); + double sigmaTry = sigmaProcessPtr->sigmaPDF(); + sigmaTry *= wtTau * wtY * wt3Body * wtBW; + if (sigmaTry > sigmaTmp) sigmaTmp = sigmaTry; + } + } + + // Allow possibility for user to modify cross section. + if (canModifySigma) sigmaTmp + *= userHooksPtr->multiplySigmaBy( sigmaProcessPtr, this, false); + + // Optional printout. Protect against negative cross section. + if (showSearch) os << " tau =" << setw(11) << tau << " y =" + << setw(11) << y << " z =" << setw(11) << z + << " sigma =" << setw(11) << sigmaTmp << "\n"; + if (sigmaTmp < 0.) sigmaTmp = 0.; + } + + // Save new maximum. Final maximum. + sigGrid[iGrid] = sigmaTmp; + if (sigmaTmp > sigmaMx) sigmaMx = sigmaTmp; + } + } + } + } + sigmaMx *= SAFETYMARGIN; + sigmaPos = sigmaMx; + + // Optional printout. + if (showSearch) os << "\n Final maximum = " << setw(11) << sigmaMx << endl; + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Select a trial kinematics phase space point. +// Note: by In is meant the integral over the quantity multiplying +// coefficient cn. The sum of cn is normalized to unity. + +bool PhaseSpace::trialKin123(bool is2, bool is3, bool inEvent, ostream& os) { + + // Allow for possibility that energy varies from event to event. + if (doEnergySpread) { + eCM = infoPtr->eCM(); + s = eCM * eCM; + + // Find shifted tauRes values. + if (idResA !=0 && !hasPointLeptons) { + tauResA = mResA * mResA / s; + widResA = mResA * GammaResA / s; + } + if (idResB != 0 && !hasPointLeptons) { + tauResB = mResB * mResB / s; + widResB = mResB * GammaResB / s; + } + } + + // Choose tau according to h1(tau)/tau, where + // h1(tau) = c0/I0 + (c1/I1) * 1/tau + // + (c2/I2) / (tau + tauResA) + // + (c3/I3) * tau / ((tau - tauResA)^2 + widResA^2) + // + (c4/I4) / (tau + tauResB) + // + (c5/I5) * tau / ((tau - tauResB)^2 + widResB^2) + // + (c6/I6) * tau / (1 - tau). + if (!limitTau(is2, is3)) return false; + int iTau = 0; + if (!hasPointLeptons) { + double rTau = rndmPtr->flat(); + while (rTau > tauCoefSum[iTau]) ++iTau; + } + selectTau( iTau, rndmPtr->flat(), is2); + + // Choose y according to h2(y), where + // h2(y) = (c0/I0) * 1/cosh(y) + // + (c1/I1) * (y-ymin) + (c2/I2) * (ymax-y) + // + (c3/I3) * exp(y) + (c4/i4) * exp(-y) (for hadron; for lepton instead) + // + (c5/I5) * 1 / (1 - exp(y-ymax)) + (c6/I6) * 1 / (1 - exp(ymin-y)). + if (!limitY()) return false; + int iY = 0; + if (!hasPointLeptons) { + double rY = rndmPtr->flat(); + while (rY > yCoefSum[iY]) ++iY; + } + selectY( iY, rndmPtr->flat()); + + // Choose z = cos(thetaHat) according to h3(z), where + // h3(z) = c0/I0 + (c1/I1) * 1/(A - z) + (c2/I2) * 1/(A + z) + // + (c3/I3) * 1/(A - z)^2 + (c4/I4) * 1/(A + z)^2, + // where A = 1 + 2*(m3*m4/sH)^2 (= 1 for massless products). + if (is2) { + if (!limitZ()) return false; + int iZ = 0; + double rZ = rndmPtr->flat(); + while (rZ > zCoefSum[iZ]) ++iZ; + selectZ( iZ, rndmPtr->flat()); + } + + // 2 -> 1: calculate cross section, weighted by phase-space volume. + if (!is2 && !is3) { + sigmaProcessPtr->set1Kin( x1H, x2H, sH); + sigmaNw = sigmaProcessPtr->sigmaPDF(); + sigmaNw *= wtTau * wtY; + + // 2 -> 2: calculate cross section, weighted by phase-space volume + // and Breit-Wigners for masses + } else if (is2) { + sigmaProcessPtr->set2Kin( x1H, x2H, sH, tH, m3, m4, runBW3H, runBW4H); + sigmaNw = sigmaProcessPtr->sigmaPDF(); + sigmaNw *= wtTau * wtY * wtZ * wtBW; + + // 2 -> 3: also sample internal 3-body phase, weighted by + // 2 -> 1 phase-space volume and Breit-Wigners for masses + } else if (is3) { + if (!select3Body()) sigmaNw = 0.; + else { + sigmaProcessPtr->set3Kin( x1H, x2H, sH, p3cm, p4cm, p5cm, + m3, m4, m5, runBW3H, runBW4H, runBW5H); + sigmaNw = sigmaProcessPtr->sigmaPDF(); + sigmaNw *= wtTau * wtY * wt3Body * wtBW; + } + } + + // Allow possibility for user to modify cross section. + if (canModifySigma) sigmaNw + *= userHooksPtr->multiplySigmaBy( sigmaProcessPtr, this, inEvent); + + // Check if maximum violated. + newSigmaMx = false; + if (sigmaNw > sigmaMx) { + infoPtr->errorMsg("Warning in PhaseSpace2to2tauyz::trialKin: " + "maximum for cross section violated"); + + // Violation strategy 1: increase maximum (always during initialization). + if (increaseMaximum || !inEvent) { + double violFact = SAFETYMARGIN * sigmaNw / sigmaMx; + sigmaMx = SAFETYMARGIN * sigmaNw; + newSigmaMx = true; + if (showViolation) { + if (violFact < 9.99) os << fixed; + else os << scientific; + os << " PYTHIA Maximum for " << sigmaProcessPtr->name() + << " increased by factor " << setprecision(3) << violFact + << " to " << scientific << sigmaMx << endl; + } + + // Violation strategy 2: weight event (done in ProcessContainer). + } else if (showViolation && sigmaNw > sigmaPos) { + double violFact = sigmaNw / sigmaMx; + if (violFact < 9.99) os << fixed; + else os << scientific; + os << " PYTHIA Maximum for " << sigmaProcessPtr->name() + << " exceeded by factor " << setprecision(3) << violFact << endl; + sigmaPos = sigmaNw; + } + } + + // Check if negative cross section. + if (sigmaNw < sigmaNeg) { + infoPtr->errorMsg("Warning in PhaseSpace2to2tauyz::trialKin:" + " negative cross section set 0", "for " + sigmaProcessPtr->name() ); + sigmaNeg = sigmaNw; + + // Optional printout of (all) violations. + if (showViolation) os << " PYTHIA Negative minimum for " + << sigmaProcessPtr->name() << " changed to " << scientific + << setprecision(3) << sigmaNeg << endl; + } + if (sigmaNw < 0.) sigmaNw = 0.; + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Find range of allowed tau values. + +bool PhaseSpace::limitTau(bool is2, bool is3) { + + // Trivial reply for unresolved lepton beams. + if (hasPointLeptons) { + tauMin = 1.; + tauMax = 1.; + return true; + } + + // Requirements from allowed mHat range. + tauMin = sHatMin / s; + tauMax = (mHatMax < mHatMin) ? 1. : min( 1., sHatMax / s); + + // Requirements from allowed pT range and masses. + if (is2 || is3) { + double mT3Min = sqrt(s3 + pT2HatMin); + double mT4Min = sqrt(s4 + pT2HatMin); + double mT5Min = (is3) ? sqrt(s5 + pT2HatMin) : 0.; + tauMin = max( tauMin, pow2(mT3Min + mT4Min + mT5Min) / s); + } + + // Check that there is an open range. + return (tauMax > tauMin); +} + +//-------------------------------------------------------------------------- + +// Find range of allowed y values. + +bool PhaseSpace::limitY() { + + // Trivial reply for unresolved lepton beams. + if (hasPointLeptons) { + yMax = 1.; + return true; + } + + // Requirements from selected tau value. + yMax = -0.5 * log(tau); + + // For lepton beams requirements from cutoff for f_e^e. + double yMaxMargin = (hasLeptonBeams) ? yMax + LEPTONXLOGMAX : yMax; + + // Check that there is an open range. + return (yMaxMargin > 0.); +} + +//-------------------------------------------------------------------------- + +// Find range of allowed z = cos(theta) values. + +bool PhaseSpace::limitZ() { + + // Default limits. + zMin = 0.; + zMax = 1.; + + // Requirements from pTHat limits. + zMax = sqrtpos( 1. - pT2HatMin / p2Abs ); + if (pTHatMax > pTHatMin) zMin = sqrtpos( 1. - pT2HatMax / p2Abs ); + + // Check that there is an open range. + return (zMax > zMin); +} + +//-------------------------------------------------------------------------- + +// Select tau according to a choice of shapes. + +void PhaseSpace::selectTau(int iTau, double tauVal, bool is2) { + + // Trivial reply for unresolved lepton beams. + if (hasPointLeptons) { + tau = 1.; + wtTau = 1.; + sH = s; + mHat = sqrt(sH); + if (is2) { + p2Abs = 0.25 * (pow2(sH - s3 - s4) - 4. * s3 * s4) / sH; + pAbs = sqrtpos( p2Abs ); + } + return; + } + + // Contributions from s-channel resonances. + double tRatA = 0.; + double aLowA = 0.; + double aUppA = 0.; + if (idResA !=0) { + tRatA = ((tauResA + tauMax) / (tauResA + tauMin)) * (tauMin / tauMax); + aLowA = atan( (tauMin - tauResA) / widResA); + aUppA = atan( (tauMax - tauResA) / widResA); + } + double tRatB = 0.; + double aLowB = 0.; + double aUppB = 0.; + if (idResB != 0) { + tRatB = ((tauResB + tauMax) / (tauResB + tauMin)) * (tauMin / tauMax); + aLowB = atan( (tauMin - tauResB) / widResB); + aUppB = atan( (tauMax - tauResB) / widResB); + } + + // Contributions from 1 / (1 - tau) for lepton beams. + double aLowT = 0.; + double aUppT = 0.; + if (hasLeptonBeams) { + aLowT = log( max( LEPTONTAUMIN, 1. - tauMin) ); + aUppT = log( max( LEPTONTAUMIN, 1. - tauMax) ); + intTau6 = aLowT - aUppT; + } + + // Select according to 1/tau or 1/tau^2. + if (iTau == 0) tau = tauMin * pow( tauMax / tauMin, tauVal); + else if (iTau == 1) tau = tauMax * tauMin + / (tauMin + (tauMax - tauMin) * tauVal); + + // Select according to 1 / (1 - tau) for lepton beams. + else if (hasLeptonBeams && iTau == nTau - 1) + tau = 1. - exp( aUppT + intTau6 * tauVal ); + + // Select according to 1 / (tau * (tau + tauRes)) or + // 1 / ((tau - tauRes)^2 + widRes^2) for resonances A and B. + else if (iTau == 2) tau = tauResA * tauMin + / ((tauResA + tauMin) * pow( tRatA, tauVal) - tauMin); + else if (iTau == 3) tau = tauResA + widResA + * tan( aLowA + (aUppA - aLowA) * tauVal); + else if (iTau == 4) tau = tauResB * tauMin + / ((tauResB + tauMin) * pow( tRatB, tauVal) - tauMin); + else if (iTau == 5) tau = tauResB + widResB + * tan( aLowB + (aUppB - aLowB) * tauVal); + + // Phase space weight in tau. + intTau0 = log( tauMax / tauMin); + intTau1 = (tauMax - tauMin) / (tauMax * tauMin); + double invWtTau = (tauCoef[0] / intTau0) + (tauCoef[1] / intTau1) / tau; + if (idResA != 0) { + intTau2 = -log(tRatA) / tauResA; + intTau3 = (aUppA - aLowA) / widResA; + invWtTau += (tauCoef[2] / intTau2) / (tau + tauResA) + + (tauCoef[3] / intTau3) * tau / ( pow2(tau - tauResA) + pow2(widResA) ); + } + if (idResB != 0) { + intTau4 = -log(tRatB) / tauResB; + intTau5 = (aUppB - aLowB) / widResB; + invWtTau += (tauCoef[4] / intTau4) / (tau + tauResB) + + (tauCoef[5] / intTau5) * tau / ( pow2(tau - tauResB) + pow2(widResB) ); + } + if (hasLeptonBeams) + invWtTau += (tauCoef[nTau - 1] / intTau6) + * tau / max( LEPTONTAUMIN, 1. - tau); + wtTau = 1. / invWtTau; + + // Calculate sHat and absolute momentum of outgoing partons. + sH = tau * s; + mHat = sqrt(sH); + if (is2) { + p2Abs = 0.25 * (pow2(sH - s3 - s4) - 4. * s3 * s4) / sH; + pAbs = sqrtpos( p2Abs ); + } + +} + +//-------------------------------------------------------------------------- + +// Select y according to a choice of shapes. + +void PhaseSpace::selectY(int iY, double yVal) { + + // Trivial reply for unresolved lepton beams. + if (hasPointLeptons) { + y = 0.; + wtY = 1.; + x1H = 1.; + x2H = 1.; + return; + } + + // For lepton beams skip options 3&4 and go straight to 5&6. + if (hasLeptonBeams && iY > 2) iY += 2; + + // Standard expressions used below. + double expYMax = exp( yMax ); + double expYMin = exp(-yMax ); + double atanMax = atan( expYMax ); + double atanMin = atan( expYMin ); + double aUppY = (hasLeptonBeams) + ? log( max( LEPTONXMIN, LEPTONXMAX / tau - 1. ) ) : 0.; + double aLowY = LEPTONXLOGMIN; + + // 1 / cosh(y). + if (iY == 0) y = log( tan( atanMin + (atanMax - atanMin) * yVal ) ); + + // y - y_min or mirrored y_max - y. + else if (iY <= 2) y = yMax * (2. * sqrt(yVal) - 1.); + + // exp(y) or mirrored exp(-y). + else if (iY <= 4) y = log( expYMin + (expYMax - expYMin) * yVal ); + + // 1 / (1 - exp(y - y_max)) or mirrored 1 / (1 - exp(y_min - y)). + else y = yMax - log( 1. + exp(aLowY + (aUppY - aLowY) * yVal) ); + + // Mirror two cases. + if (iY == 2 || iY == 4 || iY == 6) y = -y; + + // Phase space integral in y. + intY0 = 2. * (atanMax - atanMin); + intY12 = 0.5 * pow2(2. * yMax); + intY34 = expYMax - expYMin; + intY56 = aUppY - aLowY; + double invWtY = (yCoef[0] / intY0) / cosh(y) + + (yCoef[1] / intY12) * (y + yMax) + (yCoef[2] / intY12) * (yMax - y); + if (!hasLeptonBeams) invWtY + += (yCoef[3] / intY34) * exp(y) + (yCoef[4] / intY34) * exp(-y); + else invWtY + += (yCoef[3] / intY56) / max( LEPTONXMIN, 1. - exp( y - yMax) ) + + (yCoef[4] / intY56) / max( LEPTONXMIN, 1. - exp(-y - yMax) ); + wtY = 1. / invWtY; + + // Calculate x1 and x2. + x1H = sqrt(tau) * exp(y); + x2H = sqrt(tau) * exp(-y); +} + +//-------------------------------------------------------------------------- + +// Select z = cos(theta) according to a choice of shapes. +// The selection is split in the positive- and negative-z regions, +// since a pTmax cut can remove the region around z = 0. + +void PhaseSpace::selectZ(int iZ, double zVal) { + + // Mass-dependent dampening of pT -> 0 limit. + ratio34 = max(TINY, 2. * s3 * s4 / pow2(sH)); + unity34 = 1. + ratio34; + double ratiopT2 = 2. * pT2HatMin / max( SHATMINZ, sH); + if (ratiopT2 < PT2RATMINZ) ratio34 = max( ratio34, ratiopT2); + + // Common expressions in z limits. + double zPosMax = max(ratio34, unity34 + zMax); + double zNegMax = max(ratio34, unity34 - zMax); + double zPosMin = max(ratio34, unity34 + zMin); + double zNegMin = max(ratio34, unity34 - zMin); + + // Flat in z. + if (iZ == 0) { + if (zVal < 0.5) z = -(zMax + (zMin - zMax) * 2. * zVal); + else z = zMin + (zMax - zMin) * (2. * zVal - 1.); + + // 1 / (unity34 - z). + } else if (iZ == 1) { + double areaNeg = log(zPosMax / zPosMin); + double areaPos = log(zNegMin / zNegMax); + double area = areaNeg + areaPos; + if (zVal * area < areaNeg) { + double zValMod = zVal * area / areaNeg; + z = unity34 - zPosMax * pow(zPosMin / zPosMax, zValMod); + } else { + double zValMod = (zVal * area - areaNeg)/ areaPos; + z = unity34 - zNegMin * pow(zNegMax / zNegMin, zValMod); + } + + // 1 / (unity34 + z). + } else if (iZ == 2) { + double areaNeg = log(zNegMin / zNegMax); + double areaPos = log(zPosMax / zPosMin); + double area = areaNeg + areaPos; + if (zVal * area < areaNeg) { + double zValMod = zVal * area / areaNeg; + z = zNegMax * pow(zNegMin / zNegMax, zValMod) - unity34; + } else { + double zValMod = (zVal * area - areaNeg)/ areaPos; + z = zPosMin * pow(zPosMax / zPosMin, zValMod) - unity34; + } + + // 1 / (unity34 - z)^2. + } else if (iZ == 3) { + double areaNeg = 1. / zPosMin - 1. / zPosMax; + double areaPos = 1. / zNegMax - 1. / zNegMin; + double area = areaNeg + areaPos; + if (zVal * area < areaNeg) { + double zValMod = zVal * area / areaNeg; + z = unity34 - 1. / (1./zPosMax + areaNeg * zValMod); + } else { + double zValMod = (zVal * area - areaNeg)/ areaPos; + z = unity34 - 1. / (1./zNegMin + areaPos * zValMod); + } + + // 1 / (unity34 + z)^2. + } else if (iZ == 4) { + double areaNeg = 1. / zNegMax - 1. / zNegMin; + double areaPos = 1. / zPosMin - 1. / zPosMax; + double area = areaNeg + areaPos; + if (zVal * area < areaNeg) { + double zValMod = zVal * area / areaNeg; + z = 1. / (1./zNegMax - areaNeg * zValMod) - unity34; + } else { + double zValMod = (zVal * area - areaNeg)/ areaPos; + z = 1. / (1./zPosMin - areaPos * zValMod) - unity34; + } + } + + // Safety check for roundoff errors. Combinations with z. + if (z < 0.) z = min(-zMin, max(-zMax, z)); + else z = min(zMax, max(zMin, z)); + zNeg = max(ratio34, unity34 - z); + zPos = max(ratio34, unity34 + z); + + // Phase space integral in z. + double intZ0 = 2. * (zMax - zMin); + double intZ12 = log( (zPosMax * zNegMin) / (zPosMin * zNegMax) ); + double intZ34 = 1. / zPosMin - 1. / zPosMax + 1. / zNegMax + - 1. / zNegMin; + wtZ = mHat * pAbs / ( (zCoef[0] / intZ0) + (zCoef[1] / intZ12) / zNeg + + (zCoef[2] / intZ12) / zPos + (zCoef[3] / intZ34) / pow2(zNeg) + + (zCoef[4] / intZ34) / pow2(zPos) ); + + // Calculate tHat and uHat. Also gives pTHat. + double sH34 = -0.5 * (sH - s3 - s4); + tH = sH34 + mHat * pAbs * z; + uH = sH34 - mHat * pAbs * z; + pTH = sqrtpos( (tH * uH - s3 * s4) / sH); + +} + +//-------------------------------------------------------------------------- + +// Select three-body phase space according to a cylindrically based form +// that can be chosen to favour low pT based on the form of propagators. + +bool PhaseSpace::select3Body() { + + // Upper and lower limits of pT choice for 4 and 5. + double m35S = pow2(m3 + m5); + double pT4Smax = 0.25 * ( pow2(sH - s4 - m35S) - 4. * s4 * m35S ) / sH; + if (pTHatMax > pTHatMin) pT4Smax = min( pT2HatMax, pT4Smax); + double pT4Smin = pT2HatMin; + double m34S = pow2(m3 + m4); + double pT5Smax = 0.25 * ( pow2(sH - s5 - m34S) - 4. * s5 * m34S ) / sH; + if (pTHatMax > pTHatMin) pT5Smax = min( pT2HatMax, pT5Smax); + double pT5Smin = pT2HatMin; + + // Check that pT ranges not closed. + if ( pT4Smax < pow2(pTHatMin + MASSMARGIN) ) return false; + if ( pT5Smax < pow2(pTHatMin + MASSMARGIN) ) return false; + + // Select pT4S according to c0 + c1/(M^2 + pT^2) + c2/(M^2 + pT^2)^2. + double pTSmaxProp = pT4Smax + sTchan1; + double pTSminProp = pT4Smin + sTchan1; + double pTSratProp = pTSmaxProp / pTSminProp; + double pTSdiff = pT4Smax - pT4Smin; + double rShape = rndmPtr->flat(); + double pT4S = 0.; + if (rShape < frac3Flat) pT4S = pT4Smin + rndmPtr->flat() * pTSdiff; + else if (rShape < frac3Flat + frac3Pow1) pT4S = max( pT2HatMin, + pTSminProp * pow( pTSratProp, rndmPtr->flat() ) - sTchan1 ); + else pT4S = max( pT2HatMin, pTSminProp * pTSmaxProp + / (pTSminProp + rndmPtr->flat()* pTSdiff) - sTchan1 ); + double wt4 = pTSdiff / ( frac3Flat + + frac3Pow1 * pTSdiff / (log(pTSratProp) * (pT4S + sTchan1)) + + frac3Pow2 * pTSminProp * pTSmaxProp / pow2(pT4S + sTchan1) ); + + // Select pT5S according to c0 + c1/(M^2 + pT^2) + c2/(M^2 + pT^2)^2. + pTSmaxProp = pT5Smax + sTchan2; + pTSminProp = pT5Smin + sTchan2; + pTSratProp = pTSmaxProp / pTSminProp; + pTSdiff = pT5Smax - pT5Smin; + rShape = rndmPtr->flat(); + double pT5S = 0.; + if (rShape < frac3Flat) pT5S = pT5Smin + rndmPtr->flat() * pTSdiff; + else if (rShape < frac3Flat + frac3Pow1) pT5S = max( pT2HatMin, + pTSminProp * pow( pTSratProp, rndmPtr->flat() ) - sTchan2 ); + else pT5S = max( pT2HatMin, pTSminProp * pTSmaxProp + / (pTSminProp + rndmPtr->flat()* pTSdiff) - sTchan2 ); + double wt5 = pTSdiff / ( frac3Flat + + frac3Pow1 * pTSdiff / (log(pTSratProp) * (pT5S + sTchan2)) + + frac3Pow2 * pTSminProp * pTSmaxProp / pow2(pT5S + sTchan2) ); + + // Select azimuthal angles and check that third pT in range. + double phi4 = 2. * M_PI * rndmPtr->flat(); + double phi5 = 2. * M_PI * rndmPtr->flat(); + double pT3S = max( 0., pT4S + pT5S + 2. * sqrt(pT4S * pT5S) + * cos(phi4 - phi5) ); + if ( pT3S < pT2HatMin || (pTHatMax > pTHatMin && pT3S > pT2HatMax) ) + return false; + + // Calculate transverse masses and check that phase space not closed. + double sT3 = s3 + pT3S; + double sT4 = s4 + pT4S; + double sT5 = s5 + pT5S; + double mT3 = sqrt(sT3); + double mT4 = sqrt(sT4); + double mT5 = sqrt(sT5); + if ( mT3 + mT4 + mT5 + MASSMARGIN > mHat ) return false; + + // Select rapidity for particle 3 and check that phase space not closed. + double m45S = pow2(mT4 + mT5); + double y3max = log( ( sH + sT3 - m45S + sqrtpos( pow2(sH - sT3 - m45S) + - 4 * sT3 * m45S ) ) / (2. * mHat * mT3) ); + if (y3max < YRANGEMARGIN) return false; + double y3 = (2. * rndmPtr->flat() - 1.) * (1. - YRANGEMARGIN) * y3max; + double pz3 = mT3 * sinh(y3); + double e3 = mT3 * cosh(y3); + + // Find momentum transfers in the two mirror solutions (in 4-5 frame). + double pz45 = -pz3; + double e45 = mHat - e3; + double sT45 = e45 * e45 - pz45 * pz45; + double lam45 = sqrtpos( pow2(sT45 - sT4 - sT5) - 4. * sT4 * sT5 ); + if (lam45 < YRANGEMARGIN * sH) return false; + double lam4e = sT45 + sT4 - sT5; + double lam5e = sT45 + sT5 - sT4; + double tFac = -0.5 * mHat / sT45; + double t1Pos = tFac * (e45 - pz45) * (lam4e - lam45); + double t1Neg = tFac * (e45 - pz45) * (lam4e + lam45); + double t2Pos = tFac * (e45 + pz45) * (lam5e - lam45); + double t2Neg = tFac * (e45 + pz45) * (lam5e + lam45); + + // Construct relative mirror weights and make choice. + double wtPosUnnorm = 1.; + double wtNegUnnorm = 1.; + if (useMirrorWeight) { + wtPosUnnorm = 1./ pow2( (t1Pos - sTchan1) * (t2Pos - sTchan2) ); + wtNegUnnorm = 1./ pow2( (t1Neg - sTchan1) * (t2Neg - sTchan2) ); + } + double wtPos = wtPosUnnorm / (wtPosUnnorm + wtNegUnnorm); + double wtNeg = wtNegUnnorm / (wtPosUnnorm + wtNegUnnorm); + double epsilon = (rndmPtr->flat() < wtPos) ? 1. : -1.; + + // Construct four-vectors in rest frame of subprocess. + double px4 = sqrt(pT4S) * cos(phi4); + double py4 = sqrt(pT4S) * sin(phi4); + double px5 = sqrt(pT5S) * cos(phi5); + double py5 = sqrt(pT5S) * sin(phi5); + double pz4 = 0.5 * (pz45 * lam4e + epsilon * e45 * lam45) / sT45; + double pz5 = pz45 - pz4; + double e4 = sqrt(sT4 + pz4 * pz4); + double e5 = sqrt(sT5 + pz5 * pz5); + p3cm = Vec4( -(px4 + px5), -(py4 + py5), pz3, e3); + p4cm = Vec4( px4, py4, pz4, e4); + p5cm = Vec4( px5, py5, pz5, e5); + + // Total weight to associate with kinematics choice. + wt3Body = wt4 * wt5 * (2. * y3max) / (128. * pow3(M_PI) * lam45); + wt3Body *= (epsilon > 0.) ? 1. / wtPos : 1. / wtNeg; + + // Cross section of form |M|^2/(2 sHat) dPS_3 so need 1/(2 sHat). + wt3Body /= (2. * sH); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Solve linear equation system for better phase space coefficients. + +void PhaseSpace::solveSys( int n, int bin[8], double vec[8], + double mat[8][8], double coef[8], ostream& os) { + + // Optional printout. + if (showSearch) { + os << "\n Equation system: " << setw(5) << bin[0]; + for (int j = 0; j < n; ++j) os << setw(12) << mat[0][j]; + os << setw(12) << vec[0] << "\n"; + for (int i = 1; i < n; ++i) { + os << " " << setw(5) << bin[i]; + for (int j = 0; j < n; ++j) os << setw(12) << mat[i][j]; + os << setw(12) << vec[i] << "\n"; + } + } + + // Local variables. + double vecNor[8], coefTmp[8]; + for (int i = 0; i < n; ++i) coefTmp[i] = 0.; + + // Check if equation system solvable. + bool canSolve = true; + for (int i = 0; i < n; ++i) if (bin[i] == 0) canSolve = false; + double vecSum = 0.; + for (int i = 0; i < n; ++i) vecSum += vec[i]; + if (abs(vecSum) < TINY) canSolve = false; + + // Solve to find relative importance of cross-section pieces. + if (canSolve) { + for (int i = 0; i < n; ++i) vecNor[i] = max( 0.1, vec[i] / vecSum); + for (int k = 0; k < n - 1; ++k) { + for (int i = k + 1; i < n; ++i) { + if (abs(mat[k][k]) < TINY) {canSolve = false; break;} + double ratio = mat[i][k] / mat[k][k]; + vec[i] -= ratio * vec[k]; + for (int j = k; j < n; ++j) mat[i][j] -= ratio * mat[k][j]; + } + if (!canSolve) break; + } + if (canSolve) { + for (int k = n - 1; k >= 0; --k) { + for (int j = k + 1; j < n; ++j) vec[k] -= mat[k][j] * coefTmp[j]; + coefTmp[k] = vec[k] / mat[k][k]; + } + } + } + + // Share evenly if failure. + if (!canSolve) for (int i = 0; i < n; ++i) { + coefTmp[i] = 1.; + vecNor[i] = 0.1; + if (vecSum > TINY) vecNor[i] = max(0.1, vec[i] / vecSum); + } + + // Normalize coefficients, with piece shared democratically. + double coefSum = 0.; + vecSum = 0.; + for (int i = 0; i < n; ++i) { + coefTmp[i] = max( 0., coefTmp[i]); + coefSum += coefTmp[i]; + vecSum += vecNor[i]; + } + if (coefSum > 0.) for (int i = 0; i < n; ++i) coef[i] = EVENFRAC / n + + (1. - EVENFRAC) * 0.5 * (coefTmp[i] / coefSum + vecNor[i] / vecSum); + else for (int i = 0; i < n; ++i) coef[i] = 1. / n; + + // Optional printout. + if (showSearch) { + os << " Solution: "; + for (int i = 0; i < n; ++i) os << setw(12) << coef[i]; + os << "\n"; + } +} + +//-------------------------------------------------------------------------- + +// Setup mass selection for one resonance at a time - part 1. + +void PhaseSpace::setupMass1(int iM) { + + // Identity for mass seletion; is 0 also for light quarks (not yet selected). + if (iM == 3) idMass[iM] = abs(sigmaProcessPtr->id3Mass()); + if (iM == 4) idMass[iM] = abs(sigmaProcessPtr->id4Mass()); + if (iM == 5) idMass[iM] = abs(sigmaProcessPtr->id5Mass()); + + // Masses and widths of resonances. + if (idMass[iM] == 0) { + mPeak[iM] = 0.; + mWidth[iM] = 0.; + mMin[iM] = 0.; + mMax[iM] = 0.; + } else { + mPeak[iM] = particleDataPtr->m0(idMass[iM]); + mWidth[iM] = particleDataPtr->mWidth(idMass[iM]); + mMin[iM] = particleDataPtr->mMin(idMass[iM]); + mMax[iM] = particleDataPtr->mMax(idMass[iM]); + // gmZmode == 1 means pure photon propagator; set at lower mass limit. + if (idMass[iM] == 23 && gmZmode == 1) mPeak[iM] = mMin[iM]; + } + + // Mass and width combinations for Breit-Wigners. + sPeak[iM] = mPeak[iM] * mPeak[iM]; + useBW[iM] = useBreitWigners && (mWidth[iM] > minWidthBreitWigners); + if (!useBW[iM]) mWidth[iM] = 0.; + mw[iM] = mPeak[iM] * mWidth[iM]; + wmRat[iM] = (idMass[iM] == 0 || mPeak[iM] == 0.) + ? 0. : mWidth[iM] / mPeak[iM]; + + // Simple Breit-Wigner range, upper edge to be corrected subsequently. + if (useBW[iM]) { + mLower[iM] = mMin[iM]; + mUpper[iM] = mHatMax; + } + +} + +//-------------------------------------------------------------------------- + +// Setup mass selection for one resonance at a time - part 2. + +void PhaseSpace::setupMass2(int iM, double distToThresh) { + + // Store reduced Breit-Wigner range. + if (mMax[iM] > mMin[iM]) mUpper[iM] = min( mUpper[iM], mMax[iM]); + sLower[iM] = mLower[iM] * mLower[iM]; + sUpper[iM] = mUpper[iM] * mUpper[iM]; + + // Prepare to select m3 by BW + flat + 1/s_3. + // Determine relative coefficients by allowed mass range. + if (distToThresh > THRESHOLDSIZE) { + fracFlat[iM] = 0.1; + fracInv[iM] = 0.1; + } else if (distToThresh > - THRESHOLDSIZE) { + fracFlat[iM] = 0.25 - 0.15 * distToThresh / THRESHOLDSIZE; + fracInv [iM] = 0.15 - 0.05 * distToThresh / THRESHOLDSIZE; + } else { + fracFlat[iM] = 0.4; + fracInv[iM] = 0.2; + } + + // For gamma*/Z0: increase 1/s_i part and introduce 1/s_i^2 part. + fracInv2[iM] = 0.; + if (idMass[iM] == 23 && gmZmode == 0) { + fracFlat[iM] *= 0.5; + fracInv[iM] = 0.5 * fracInv[iM] + 0.25; + fracInv2[iM] = 0.25; + } else if (idMass[iM] == 23 && gmZmode == 1) { + fracFlat[iM] = 0.1; + fracInv[iM] = 0.4; + fracInv2[iM] = 0.4; + } + + // Normalization integrals for the respective contribution. + atanLower[iM] = atan( (sLower[iM] - sPeak[iM])/ mw[iM] ); + atanUpper[iM] = atan( (sUpper[iM] - sPeak[iM])/ mw[iM] ); + intBW[iM] = atanUpper[iM] - atanLower[iM]; + intFlat[iM] = sUpper[iM] - sLower[iM]; + intInv[iM] = log( sUpper[iM] / sLower[iM] ); + intInv2[iM] = 1./sLower[iM] - 1./sUpper[iM]; + +} + +//-------------------------------------------------------------------------- + +// Select Breit-Wigner-distributed or fixed masses. + +void PhaseSpace::trialMass(int iM) { + + // References to masses to be set. + double& mSet = (iM == 3) ? m3 : ( (iM == 4) ? m4 : m5 ); + double& sSet = (iM == 3) ? s3 : ( (iM == 4) ? s4 : s5 ); + + // Distribution for m_i is BW + flat + 1/s_i + 1/s_i^2. + if (useBW[iM]) { + double pickForm = rndmPtr->flat(); + if (pickForm > fracFlat[iM] + fracInv[iM] + fracInv2[iM]) + sSet = sPeak[iM] + mw[iM] * tan( atanLower[iM] + + rndmPtr->flat() * intBW[iM] ); + else if (pickForm > fracInv[iM] + fracInv2[iM]) + sSet = sLower[iM] + rndmPtr->flat() * (sUpper[iM] - sLower[iM]); + else if (pickForm > fracInv2[iM]) + sSet = sLower[iM] * pow( sUpper[iM] / sLower[iM], rndmPtr->flat() ); + else sSet = sLower[iM] * sUpper[iM] + / (sLower[iM] + rndmPtr->flat() * (sUpper[iM] - sLower[iM])); + mSet = sqrt(sSet); + + // Else m_i is fixed at peak value. + } else { + mSet = mPeak[iM]; + sSet = sPeak[iM]; + } + +} + +//-------------------------------------------------------------------------- + +// Naively a fixed-width Breit-Wigner is used to pick the mass. +// Here come the correction factors for +// (i) preselection according to BW + flat in s_i + 1/s_i + 1/s_i^2, +// (ii) reduced allowed mass range, +// (iii) running width, i.e. m0*Gamma0 -> s*Gamma0/m0. +// In the end, the weighted distribution is a running-width BW. + +double PhaseSpace::weightMass(int iM) { + + // Reference to mass and to Breit-Wigner weight to be set. + double& sSet = (iM == 3) ? s3 : ( (iM == 4) ? s4 : s5 ); + double& runBWH = (iM == 3) ? runBW3H : ( (iM == 4) ? runBW4H : runBW5H ); + + // Default weight if no Breit-Wigner. + runBWH = 1.; + if (!useBW[iM]) return 1.; + + // Weight of generated distribution. + double genBW = (1. - fracFlat[iM] - fracInv[iM] - fracInv2[iM]) + * mw[iM] / ( (pow2(sSet - sPeak[iM]) + pow2(mw[iM])) * intBW[iM]) + + fracFlat[iM] / intFlat[iM] + fracInv[iM] / (sSet * intInv[iM]) + + fracInv2[iM] / (sSet*sSet * intInv2[iM]); + + // Weight of distribution with running width in Breit-Wigner. + double mwRun = sSet * wmRat[iM]; + runBWH = mwRun / (pow2(sSet - sPeak[iM]) + pow2(mwRun)) / M_PI; + + // Done. + return (runBWH / genBW); + +} + +//========================================================================== + +// PhaseSpace2to1tauy class. +// 2 -> 1 kinematics for normal subprocesses. + +//-------------------------------------------------------------------------- + +// Set limits for resonance mass selection. + +bool PhaseSpace2to1tauy::setupMass() { + + // Treat Z0 as such or as gamma*/Z0 + gmZmode = gmZmodeGlobal; + int gmZmodeProc = sigmaProcessPtr->gmZmode(); + if (gmZmodeProc >= 0) gmZmode = gmZmodeProc; + + // Mass limits for current resonance. + int idRes = abs(sigmaProcessPtr->resonanceA()); + int idTmp = abs(sigmaProcessPtr->resonanceB()); + if (idTmp > 0) idRes = idTmp; + double mResMin = (idRes == 0) ? 0. : particleDataPtr->mMin(idRes); + double mResMax = (idRes == 0) ? 0. : particleDataPtr->mMax(idRes); + + // Compare with global mass limits and pick tighter of them. + mHatMin = max( mResMin, mHatGlobalMin); + sHatMin = mHatMin*mHatMin; + mHatMax = eCM; + if (mResMax > mResMin) mHatMax = min( mHatMax, mResMax); + if (mHatGlobalMax > mHatGlobalMin) mHatMax = min( mHatMax, mHatGlobalMax); + sHatMax = mHatMax*mHatMax; + + // Default Breit-Wigner weight. + wtBW = 1.; + + // Fail if mass window (almost) closed. + return (mHatMax > mHatMin + MASSMARGIN); + +} + +//-------------------------------------------------------------------------- + +// Construct the four-vector kinematics from the trial values. + +bool PhaseSpace2to1tauy::finalKin() { + + // Particle masses; incoming always on mass shell. + mH[1] = 0.; + mH[2] = 0.; + mH[3] = mHat; + + // Incoming partons along beam axes. Outgoing has sum of momenta. + pH[1] = Vec4( 0., 0., 0.5 * eCM * x1H, 0.5 * eCM * x1H); + pH[2] = Vec4( 0., 0., -0.5 * eCM * x2H, 0.5 * eCM * x2H); + pH[3] = pH[1] + pH[2]; + + // Done. + return true; +} + +//========================================================================== + +// PhaseSpace2to2tauyz class. +// 2 -> 2 kinematics for normal subprocesses. + +//-------------------------------------------------------------------------- + +// Set up for fixed or Breit-Wigner mass selection. + +bool PhaseSpace2to2tauyz::setupMasses() { + + // Treat Z0 as such or as gamma*/Z0 + gmZmode = gmZmodeGlobal; + int gmZmodeProc = sigmaProcessPtr->gmZmode(); + if (gmZmodeProc >= 0) gmZmode = gmZmodeProc; + + // Set sHat limits - based on global limits only. + mHatMin = mHatGlobalMin; + sHatMin = mHatMin*mHatMin; + mHatMax = eCM; + if (mHatGlobalMax > mHatGlobalMin) mHatMax = min( eCM, mHatGlobalMax); + sHatMax = mHatMax*mHatMax; + + // Masses and widths of resonances. + setupMass1(3); + setupMass1(4); + + // Reduced mass range when two massive particles. + if (useBW[3]) mUpper[3] -= (useBW[4]) ? mMin[4] : mPeak[4]; + if (useBW[4]) mUpper[4] -= (useBW[3]) ? mMin[3] : mPeak[3]; + + // If closed phase space then unallowed process. + bool physical = true; + if (useBW[3] && mUpper[3] < mLower[3] + MASSMARGIN) physical = false; + if (useBW[4] && mUpper[4] < mLower[4] + MASSMARGIN) physical = false; + if (!useBW[3] && !useBW[4] && mHatMax < mPeak[3] + mPeak[4] + MASSMARGIN) + physical = false; + if (!physical) return false; + + // If either particle is massless then need extra pTHat cut. + pTHatMin = pTHatGlobalMin; + if (mPeak[3] < pTHatMinDiverge || mPeak[4] < pTHatMinDiverge) + pTHatMin = max( pTHatMin, pTHatMinDiverge); + pT2HatMin = pTHatMin * pTHatMin; + pTHatMax = pTHatGlobalMax; + pT2HatMax = pTHatMax * pTHatMax; + + // Prepare to select m3 by BW + flat + 1/s_3. + if (useBW[3]) { + double distToThreshA = (mHatMax - mPeak[3] - mPeak[4]) * mWidth[3] + / (pow2(mWidth[3]) + pow2(mWidth[4])); + double distToThreshB = (mHatMax - mPeak[3] - mMin[4]) / mWidth[3]; + double distToThresh = min( distToThreshA, distToThreshB); + setupMass2(3, distToThresh); + } + + // Prepare to select m4 by BW + flat + 1/s_4. + if (useBW[4]) { + double distToThreshA = (mHatMax - mPeak[3] - mPeak[4]) * mWidth[4] + / (pow2(mWidth[3]) + pow2(mWidth[4])); + double distToThreshB = (mHatMax - mMin[3] - mPeak[4]) / mWidth[4]; + double distToThresh = min( distToThreshA, distToThreshB); + setupMass2(4, distToThresh); + } + + // Initialization masses. Special cases when constrained phase space. + m3 = (useBW[3]) ? min(mPeak[3], mUpper[3]) : mPeak[3]; + m4 = (useBW[4]) ? min(mPeak[4], mUpper[4]) : mPeak[4]; + if (m3 + m4 + THRESHOLDSIZE * (mWidth[3] + mWidth[4]) + MASSMARGIN + > mHatMax) { + if (useBW[3] && useBW[4]) physical = constrainedM3M4(); + else if (useBW[3]) physical = constrainedM3(); + else if (useBW[4]) physical = constrainedM4(); + } + s3 = m3*m3; + s4 = m4*m4; + + // Correct selected mass-spectrum to running-width Breit-Wigner. + // Extra safety margin for maximum search. + wtBW = 1.; + if (useBW[3]) wtBW *= weightMass(3) * EXTRABWWTMAX; + if (useBW[4]) wtBW *= weightMass(4) * EXTRABWWTMAX; + + // Done. + return physical; + +} + + +//-------------------------------------------------------------------------- + +// Select Breit-Wigner-distributed or fixed masses. + +bool PhaseSpace2to2tauyz::trialMasses() { + + // By default vanishing cross section. + sigmaNw = 0.; + wtBW = 1.; + + // Pick m3 and m4 independently. + trialMass(3); + trialMass(4); + + // If outside phase space then reject event. + if (m3 + m4 + MASSMARGIN > mHatMax) return false; + + // Correct selected mass-spectrum to running-width Breit-Wigner. + if (useBW[3]) wtBW *= weightMass(3); + if (useBW[4]) wtBW *= weightMass(4); + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Construct the four-vector kinematics from the trial values. + +bool PhaseSpace2to2tauyz::finalKin() { + + // Assign masses to particles assumed massless in matrix elements. + int id3 = sigmaProcessPtr->id(3); + int id4 = sigmaProcessPtr->id(4); + if (idMass[3] == 0) { m3 = particleDataPtr->m0(id3); s3 = m3*m3; } + if (idMass[4] == 0) { m4 = particleDataPtr->m0(id4); s4 = m4*m4; } + + // Sometimes swap tHat <-> uHat to reflect chosen final-state order. + if (sigmaProcessPtr->swappedTU()) { + swap(tH, uH); + z = -z; + } + + // Check that phase space still open after new mass assignment. + if (m3 + m4 + MASSMARGIN > mHat) { + infoPtr->errorMsg("Warning in PhaseSpace2to2tauyz::finalKin: " + "failed after mass assignment"); + return false; + } + p2Abs = 0.25 * (pow2(sH - s3 - s4) - 4. * s3 * s4) / sH; + pAbs = sqrtpos( p2Abs ); + + // Particle masses; incoming always on mass shell. + mH[1] = 0.; + mH[2] = 0.; + mH[3] = m3; + mH[4] = m4; + + // Incoming partons along beam axes. + pH[1] = Vec4( 0., 0., 0.5 * eCM * x1H, 0.5 * eCM * x1H); + pH[2] = Vec4( 0., 0., -0.5 * eCM * x2H, 0.5 * eCM * x2H); + + // Outgoing partons initially in collision CM frame along beam axes. + pH[3] = Vec4( 0., 0., pAbs, 0.5 * (sH + s3 - s4) / mHat); + pH[4] = Vec4( 0., 0., -pAbs, 0.5 * (sH + s4 - s3) / mHat); + + // Then rotate and boost them to overall CM frame + theta = acos(z); + phi = 2. * M_PI * rndmPtr->flat(); + betaZ = (x1H - x2H)/(x1H + x2H); + pH[3].rot( theta, phi); + pH[4].rot( theta, phi); + pH[3].bst( 0., 0., betaZ); + pH[4].bst( 0., 0., betaZ); + pTH = pAbs * sin(theta); + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Special choice of m3 and m4 when mHatMax push them off mass shell. +// Vary x in expression m3 + m4 = mHatMax - x * (Gamma3 + Gamma4). +// For each x try to put either 3 or 4 as close to mass shell as possible. +// Maximize BW_3 * BW_4 * beta_34, where latter approximate phase space. + +bool PhaseSpace2to2tauyz::constrainedM3M4() { + + // Initial values. + bool foundNonZero = false; + double wtMassMax = 0.; + double m3WtMax = 0.; + double m4WtMax = 0.; + double xMax = (mHatMax - mLower[3] - mLower[4]) / (mWidth[3] + mWidth[4]); + double xStep = THRESHOLDSTEP * min(1., xMax); + double xNow = 0.; + double wtMassXbin, wtMassMaxOld, m34, mT34Min, wtMassNow, + wtBW3Now, wtBW4Now, beta34Now; + + // Step through increasing x values. + do { + xNow += xStep; + wtMassXbin = 0.; + wtMassMaxOld = wtMassMax; + m34 = mHatMax - xNow * (mWidth[3] + mWidth[4]); + + // Study point where m3 as close as possible to on-shell. + m3 = min( mUpper[3], m34 - mLower[4]); + if (m3 > mPeak[3]) m3 = max( mLower[3], mPeak[3]); + m4 = m34 - m3; + if (m4 < mLower[4]) {m4 = mLower[4]; m3 = m34 - m4;} + + // Check that inside phase space limit set by pTmin. + mT34Min = sqrt(m3*m3 + pT2HatMin) + sqrt(m4*m4 + pT2HatMin); + if (mT34Min < mHatMax) { + + // Breit-Wigners and beta factor give total weight. + wtMassNow = 0.; + if (m3 > mLower[3] && m3 < mUpper[3] && m4 > mLower[4] + && m4 < mUpper[4]) { + wtBW3Now = mw[3] / ( pow2(m3*m3 - sPeak[3]) + pow2(mw[3]) ); + wtBW4Now = mw[4] / ( pow2(m4*m4 - sPeak[4]) + pow2(mw[4]) ); + beta34Now = sqrt( pow2(mHatMax*mHatMax - m3*m3 - m4*m4) + - pow2(2. * m3 * m4) ) / (mHatMax*mHatMax); + wtMassNow = wtBW3Now * wtBW4Now * beta34Now; + } + + // Store new maximum, if any. + if (wtMassNow > wtMassXbin) wtMassXbin = wtMassNow; + if (wtMassNow > wtMassMax) { + foundNonZero = true; + wtMassMax = wtMassNow; + m3WtMax = m3; + m4WtMax = m4; + } + } + + // Study point where m4 as close as possible to on-shell. + m4 = min( mUpper[4], m34 - mLower[3]); + if (m4 > mPeak[4]) m4 = max( mLower[4], mPeak[4]); + m3 = m34 - m4; + if (m3 < mLower[3]) {m3 = mLower[3]; m4 = m34 - m3;} + + // Check that inside phase space limit set by pTmin. + mT34Min = sqrt(m3*m3 + pT2HatMin) + sqrt(m4*m4 + pT2HatMin); + if (mT34Min < mHatMax) { + + // Breit-Wigners and beta factor give total weight. + wtMassNow = 0.; + if (m3 > mLower[3] && m3 < mUpper[3] && m4 > mLower[4] + && m4 < mUpper[4]) { + wtBW3Now = mw[3] / ( pow2(m3*m3 - sPeak[3]) + pow2(mw[3]) ); + wtBW4Now = mw[4] / ( pow2(m4*m4 - sPeak[4]) + pow2(mw[4]) ); + beta34Now = sqrt( pow2(mHatMax*mHatMax - m3*m3 - m4*m4) + - pow2(2. * m3 * m4) ) / (mHatMax*mHatMax); + wtMassNow = wtBW3Now * wtBW4Now * beta34Now; + } + + // Store new maximum, if any. + if (wtMassNow > wtMassXbin) wtMassXbin = wtMassNow; + if (wtMassNow > wtMassMax) { + foundNonZero = true; + wtMassMax = wtMassNow; + m3WtMax = m3; + m4WtMax = m4; + } + } + + // Continue stepping if increasing trend and more x range available. + } while ( (!foundNonZero || wtMassXbin > wtMassMaxOld) + && xNow < xMax - xStep); + + // Restore best values for subsequent maximization. Return. + m3 = m3WtMax; + m4 = m4WtMax; + return foundNonZero; + +} + +//-------------------------------------------------------------------------- + +// Special choice of m3 when mHatMax pushes it off mass shell. +// Vary x in expression m3 = mHatMax - m4 - x * Gamma3. +// Maximize BW_3 * beta_34, where latter approximate phase space. + +bool PhaseSpace2to2tauyz::constrainedM3() { + + // Initial values. + bool foundNonZero = false; + double wtMassMax = 0.; + double m3WtMax = 0.; + double mT4Min = sqrt(m4*m4 + pT2HatMin); + double xMax = (mHatMax - mLower[3] - m4) / mWidth[3]; + double xStep = THRESHOLDSTEP * min(1., xMax); + double xNow = 0.; + double wtMassNow, mT34Min, wtBW3Now, beta34Now; + + // Step through increasing x values; gives m3 unambiguously. + do { + xNow += xStep; + wtMassNow = 0.; + m3 = mHatMax - m4 - xNow * mWidth[3]; + + // Check that inside phase space limit set by pTmin. + mT34Min = sqrt(m3*m3 + pT2HatMin) + mT4Min; + if (mT34Min < mHatMax) { + + // Breit-Wigner and beta factor give total weight. + wtBW3Now = mw[3] / ( pow2(m3*m3 - sPeak[3]) + pow2(mw[3]) ); + beta34Now = sqrt( pow2(mHatMax*mHatMax - m3*m3 - m4*m4) + - pow2(2. * m3 * m4) ) / (mHatMax*mHatMax); + wtMassNow = wtBW3Now * beta34Now; + + // Store new maximum, if any. + if (wtMassNow > wtMassMax) { + foundNonZero = true; + wtMassMax = wtMassNow; + m3WtMax = m3; + } + } + + // Continue stepping if increasing trend and more x range available. + } while ( (!foundNonZero || wtMassNow > wtMassMax) + && xNow < xMax - xStep); + + // Restore best value for subsequent maximization. Return. + m3 = m3WtMax; + return foundNonZero; + +} + +//-------------------------------------------------------------------------- + +// Special choice of m4 when mHatMax pushes it off mass shell. +// Vary x in expression m4 = mHatMax - m3 - x * Gamma4. +// Maximize BW_4 * beta_34, where latter approximate phase space. + +bool PhaseSpace2to2tauyz::constrainedM4() { + + // Initial values. + bool foundNonZero = false; + double wtMassMax = 0.; + double m4WtMax = 0.; + double mT3Min = sqrt(m3*m3 + pT2HatMin); + double xMax = (mHatMax - mLower[4] - m3) / mWidth[4]; + double xStep = THRESHOLDSTEP * min(1., xMax); + double xNow = 0.; + double wtMassNow, mT34Min, wtBW4Now, beta34Now; + + // Step through increasing x values; gives m4 unambiguously. + do { + xNow += xStep; + wtMassNow = 0.; + m4 = mHatMax - m3 - xNow * mWidth[4]; + + // Check that inside phase space limit set by pTmin. + mT34Min = mT3Min + sqrt(m4*m4 + pT2HatMin); + if (mT34Min < mHatMax) { + + // Breit-Wigner and beta factor give total weight. + wtBW4Now = mw[4] / ( pow2(m4*m4 - sPeak[4]) + pow2(mw[4]) ); + beta34Now = sqrt( pow2(mHatMax*mHatMax - m3*m3 - m4*m4) + - pow2(2. * m3 * m4) ) / (mHatMax*mHatMax); + wtMassNow = wtBW4Now * beta34Now; + + // Store new maximum, if any. + if (wtMassNow > wtMassMax) { + foundNonZero = true; + wtMassMax = wtMassNow; + m4WtMax = m4; + } + } + + // Continue stepping if increasing trend and more x range available. + } while ( (!foundNonZero || wtMassNow > wtMassMax) + && xNow < xMax - xStep); + + // Restore best value for subsequent maximization. + m4 = m4WtMax; + return foundNonZero; + +} + +//========================================================================== + +// PhaseSpace2to2elastic class. +// 2 -> 2 kinematics set up for elastic scattering. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Maximum positive/negative argument for exponentiation. +const double PhaseSpace2to2elastic::EXPMAX = 50.; + +// Conversion coefficients = 1/(16pi) * (mb <-> GeV^2). +const double PhaseSpace2to2elastic::CONVERTEL = 0.0510925; + +//-------------------------------------------------------------------------- + +// Form of phase space sampling already fixed, so no optimization. +// However, need to read out relevant parameters from SigmaTotal. + +bool PhaseSpace2to2elastic::setupSampling() { + + // Find maximum = value of cross section. + sigmaNw = sigmaProcessPtr->sigmaHatWrap(); + sigmaMx = sigmaNw; + + // Squared masses of particles. + s1 = mA * mA; + s2 = mB * mB; + + // Elastic slope. + bSlope = sigmaTotPtr->bSlopeEl(); + + // Determine maximum possible t range. + lambda12S = pow2(s - s1 - s2) - 4. * s1 * s2 ; + tLow = - lambda12S / s; + tUpp = 0; + + // Production model with Coulomb corrections need more parameters. + useCoulomb = settingsPtr->flag("SigmaTotal:setOwn") + && settingsPtr->flag("SigmaElastic:setOwn"); + if (useCoulomb) { + sigmaTot = sigmaTotPtr->sigmaTot(); + rho = settingsPtr->parm("SigmaElastic:rho"); + lambda = settingsPtr->parm("SigmaElastic:lambda"); + tAbsMin = settingsPtr->parm("SigmaElastic:tAbsMin"); + phaseCst = settingsPtr->parm("SigmaElastic:phaseConst"); + alphaEM0 = settingsPtr->parm("StandardModel:alphaEM0"); + + // Relative rate of nuclear and Coulombic parts in trials. + tUpp = -tAbsMin; + sigmaNuc = CONVERTEL * pow2(sigmaTot) * (1. + rho*rho) / bSlope + * exp(-bSlope * tAbsMin); + sigmaCou = (useCoulomb) ? + pow2(alphaEM0) / (4. * CONVERTEL * tAbsMin) : 0.; + signCou = (idA == idB) ? 1. : -1.; + + // Dummy values. + } else { + sigmaNuc = sigmaNw; + sigmaCou = 0.; + } + + // Calculate coefficient of generation. + tAux = exp( max(-EXPMAX, bSlope * (tLow - tUpp)) ) - 1.; + + return true; + +} + +//-------------------------------------------------------------------------- + +// Select a trial kinematics phase space point. Perform full +// Monte Carlo acceptance/rejection at this stage. + +bool PhaseSpace2to2elastic::trialKin( bool, bool ) { + + // Select t according to exp(bSlope*t). + if (!useCoulomb || sigmaNuc > rndmPtr->flat() * (sigmaNuc + sigmaCou)) + tH = tUpp + log(1. + tAux * rndmPtr->flat()) / bSlope; + + // Select t according to 1/t^2. + else tH = tLow * tUpp / (tUpp + rndmPtr->flat() * (tLow - tUpp)); + + // Correction factor for ratio full/simulated. + if (useCoulomb) { + double sigmaN = CONVERTEL * pow2(sigmaTot) * (1. + rho*rho) + * exp(bSlope * tH); + double alpEM = coupSMPtr->alphaEM(-tH); + double sigmaC = pow2(alpEM) / (4. * CONVERTEL * tH*tH); + double sigmaGen = 2. * (sigmaN + sigmaC); + double form2 = pow4(lambda/(lambda - tH)); + double phase = signCou * alpEM + * (-phaseCst - log(-0.5 * bSlope * tH)); + double sigmaCor = sigmaN + pow2(form2) * sigmaC + - signCou * alpEM * sigmaTot * (form2 / (-tH)) + * exp(0.5 * bSlope * tH) * (rho * cos(phase) + sin(phase)); + sigmaNw = sigmaMx * sigmaCor / sigmaGen; + } + + // Careful reconstruction of scattering angle. + double tRat = s * tH / lambda12S; + double cosTheta = min(1., max(-1., 1. + 2. * tRat ) ); + double sinTheta = 2. * sqrtpos( -tRat * (1. + tRat) ); + theta = asin( min(1., sinTheta)); + if (cosTheta < 0.) theta = M_PI - theta; + + return true; + +} + +//-------------------------------------------------------------------------- + +// Construct the four-vector kinematics from the trial values. + +bool PhaseSpace2to2elastic::finalKin() { + + // Particle masses. + mH[1] = mA; + mH[2] = mB; + mH[3] = m3; + mH[4] = m4; + + // Incoming particles along beam axes. + pAbs = 0.5 * sqrtpos(lambda12S) / eCM; + pH[1] = Vec4( 0., 0., pAbs, 0.5 * (s + s1 - s2) / eCM); + pH[2] = Vec4( 0., 0., -pAbs, 0.5 * (s + s2 - s1) / eCM); + + // Outgoing particles initially along beam axes. + pH[3] = Vec4( 0., 0., pAbs, 0.5 * (s + s1 - s2) / eCM); + pH[4] = Vec4( 0., 0., -pAbs, 0.5 * (s + s2 - s1) / eCM); + + // Then rotate them + phi = 2. * M_PI * rndmPtr->flat(); + pH[3].rot( theta, phi); + pH[4].rot( theta, phi); + + // Set some further info for completeness. + x1H = 1.; + x2H = 1.; + sH = s; + uH = 2. * (s1 + s2) - sH - tH; + mHat = eCM; + p2Abs = pAbs * pAbs; + betaZ = 0.; + pTH = pAbs * sin(theta); + + // Done. + return true; + +} + +//========================================================================== + +// PhaseSpace2to2diffractive class. +// 2 -> 2 kinematics set up for diffractive scattering. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of tries to find acceptable (m^2, t) set. +const int PhaseSpace2to2diffractive::NTRY = 500; + +// Maximum positive/negative argument for exponentiation. +const double PhaseSpace2to2diffractive::EXPMAX = 50.; + +// Safety margin so sum of diffractive masses not too close to eCM. +const double PhaseSpace2to2diffractive::DIFFMASSMAX = 1e-8; + +//-------------------------------------------------------------------------- + +// Form of phase space sampling already fixed, so no optimization. +// However, need to read out relevant parameters from SigmaTotal. + +bool PhaseSpace2to2diffractive::setupSampling() { + + // Pomeron flux parametrization, and parameters of some options. + PomFlux = settingsPtr->mode("Diffraction:PomFlux"); + epsilonPF = settingsPtr->parm("Diffraction:PomFluxEpsilon"); + alphaPrimePF = settingsPtr->parm("Diffraction:PomFluxAlphaPrime"); + + // Find maximum = value of cross section. + sigmaNw = sigmaProcessPtr->sigmaHatWrap(); + sigmaMx = sigmaNw; + + // Masses of particles and minimal masses of diffractive states. + m3ElDiff = (isDiffA) ? sigmaTotPtr->mMinXB() : mA; + m4ElDiff = (isDiffB) ? sigmaTotPtr->mMinAX() : mB; + s1 = mA * mA; + s2 = mB * mB; + s3 = pow2( m3ElDiff); + s4 = pow2( m4ElDiff); + + // Determine maximum possible t range and coefficient of generation. + lambda12 = sqrtpos( pow2( s - s1 - s2) - 4. * s1 * s2 ); + lambda34 = sqrtpos( pow2( s - s3 - s4) - 4. * s3 * s4 ); + double tempA = s - (s1 + s2 + s3 + s4) + (s1 - s2) * (s3 - s4) / s; + double tempB = lambda12 * lambda34 / s; + double tempC = (s3 - s1) * (s4 - s2) + (s1 + s4 - s2 - s3) + * (s1 * s4 - s2 * s3) / s; + tLow = -0.5 * (tempA + tempB); + tUpp = tempC / tLow; + + // Default for all parametrization-specific parameters. + cRes = sResXB = sResAX = sProton = bMin = bSlope = bSlope1 = bSlope2 + = probSlope1 = xIntPF = xtCorPF = mp24DL = coefDL = tAux + = tAux1 = tAux2 = 0.; + + // Schuler&Sjostrand: parameters of low-mass-resonance enhancement. + if (PomFlux == 1) { + cRes = sigmaTotPtr->cRes(); + sResXB = pow2( sigmaTotPtr->mResXB()); + sResAX = pow2( sigmaTotPtr->mResAX()); + sProton = sigmaTotPtr->sProton(); + + // Schuler&Sjostrand: lower limit diffractive slope. + if (!isDiffB) bMin = sigmaTotPtr->bMinSlopeXB(); + else if (!isDiffA) bMin = sigmaTotPtr->bMinSlopeAX(); + else bMin = sigmaTotPtr->bMinSlopeXX(); + tAux = exp( max(-EXPMAX, bMin * (tLow - tUpp)) ) - 1.; + + // Bruni&Ingelman: relative weight of two diffractive slopes. + } else if (PomFlux == 2) { + bSlope1 = 8.0; + probSlope1 = 6.38 * ( exp(max(-EXPMAX, bSlope1 * tUpp)) + - exp(max(-EXPMAX, bSlope1 * tLow)) ) / bSlope1; + bSlope2 = 3.0; + double pS2 = 0.424 * ( exp(max(-EXPMAX, bSlope2 * tUpp)) + - exp(max(-EXPMAX, bSlope2 * tLow)) ) / bSlope2; + probSlope1 /= probSlope1 + pS2; + tAux1 = exp( max(-EXPMAX, bSlope1 * (tLow - tUpp)) ) - 1.; + tAux2 = exp( max(-EXPMAX, bSlope2 * (tLow - tUpp)) ) - 1.; + + // Streng&Berger (RapGap): diffractive slope, power of mass spectrum. + } else if (PomFlux == 3) { + bSlope = 4.7; + double xPowPF = 1. - 2. * (1. + epsilonPF); + xIntPF = 2. * (1. + xPowPF); + xtCorPF = 2. * alphaPrimePF; + tAux = exp( max(-EXPMAX, bSlope * (tLow - tUpp)) ) - 1.; + + // Donnachie&Landshoff (RapGap): power of mass spectrum. + } else if (PomFlux == 4) { + mp24DL = 4. * pow2(particleDataPtr->m0(2212)); + double xPowPF = 1. - 2. * (1. + epsilonPF); + xIntPF = 2. * (1. + xPowPF); + xtCorPF = 2. * alphaPrimePF; + // Upper estimate of t dependence, for preliminary choice. + coefDL = 0.85; + tAux1 = 1. / pow3(1. - coefDL * tLow); + tAux2 = 1. / pow3(1. - coefDL * tUpp); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Select a trial kinematics phase space point. Perform full +// Monte Carlo acceptance/rejection at this stage. + +bool PhaseSpace2to2diffractive::trialKin( bool, bool ) { + + // Loop over attempts to set up masses and t consistently. + for (int loop = 0; ; ++loop) { + if (loop == NTRY) { + infoPtr->errorMsg("Error in PhaseSpace2to2diffractive::trialKin: " + " quit after repeated tries"); + return false; + } + + // Schuler and Sjostrand: + if (PomFlux == 1) { + + // Select diffractive mass(es) according to dm^2/m^2. + m3 = (isDiffA) ? m3ElDiff * pow( max(mA, eCM - m4ElDiff) / m3ElDiff, + rndmPtr->flat()) : m3ElDiff; + m4 = (isDiffB) ? m4ElDiff * pow( max(mB, eCM - m3ElDiff) / m4ElDiff, + rndmPtr->flat()) : m4ElDiff; + s3 = m3 * m3; + s4 = m4 * m4; + + // Additional mass factors, including resonance enhancement. + if (m3 + m4 >= eCM) continue; + if (isDiffA && !isDiffB) { + double facXB = (1. - s3 / s) + * (1. + cRes * sResXB / (sResXB + s3)); + if (facXB < rndmPtr->flat() * (1. + cRes)) continue; + } else if (isDiffB && !isDiffA) { + double facAX = (1. - s4 / s) + * (1. + cRes * sResAX / (sResAX + s4)); + if (facAX < rndmPtr->flat() * (1. + cRes)) continue; + } else { + double facXX = (1. - pow2(m3 + m4) / s) + * (s * sProton / (s * sProton + s3 * s4)) + * (1. + cRes * sResXB / (sResXB + s3)) + * (1. + cRes * sResAX / (sResAX + s4)); + if (facXX < rndmPtr->flat() * pow2(1. + cRes)) continue; + } + + // Select t according to exp(bMin*t) and correct to right slope. + tH = tUpp + log(1. + tAux * rndmPtr->flat()) / bMin; + double bDiff = 0.; + if (isDiffA && !isDiffB) bDiff = sigmaTotPtr->bSlopeXB(s3) - bMin; + else if (!isDiffA) bDiff = sigmaTotPtr->bSlopeAX(s4) - bMin; + else bDiff = sigmaTotPtr->bSlopeXX(s3, s4) - bMin; + bDiff = max(0., bDiff); + if (exp( max(-EXPMAX, bDiff * (tH - tUpp)) ) < rndmPtr->flat()) continue; + + // Bruni and Ingelman: + } else if (PomFlux == 2) { + + // Select diffractive mass(es) according to dm^2/m^2. + m3 = (isDiffA) ? m3ElDiff * pow( max(mA, eCM - m4ElDiff) / m3ElDiff, + rndmPtr->flat()) : m3ElDiff; + m4 = (isDiffB) ? m4ElDiff * pow( max(mB, eCM - m3ElDiff) / m4ElDiff, + rndmPtr->flat()) : m4ElDiff; + s3 = m3 * m3; + s4 = m4 * m4; + + // Select t according to exp(bSlope*t) with two possible slopes. + tH = (rndmPtr->flat() < probSlope1) + ? tUpp + log(1. + tAux1 * rndmPtr->flat()) / bSlope1 + : tUpp + log(1. + tAux2 * rndmPtr->flat()) / bSlope2; + + // Streng and Berger et al. (RapGap): + } else if (PomFlux == 3) { + + // Select diffractive mass(es) according to dm^2/(m^2)^(1 + 2 epsilon). + m3 = m3ElDiff; + m4 = m4ElDiff; + if (isDiffA) { + double s3MinPow = pow( m3ElDiff, xIntPF ); + double s3MaxPow = pow( max(mA, eCM - m4ElDiff), xIntPF ); + m3 = pow( s3MinPow + rndmPtr->flat() * (s3MaxPow - s3MinPow), + 1. / xIntPF ); + } + if (isDiffB) { + double s4MinPow = pow( m4ElDiff, xIntPF ); + double s4MaxPow = pow( max(mB, eCM - m3ElDiff), xIntPF ); + m4 = pow( s4MinPow + rndmPtr->flat() * (s4MaxPow - s4MinPow), + 1. / xIntPF ); + } + s3 = m3 * m3; + s4 = m4 * m4; + + // Select t according to exponential and weigh by x_P^(2 alpha' |t|). + tH = tUpp + log(1. + tAux * rndmPtr->flat()) / bSlope; + if ( isDiffA && pow( s3 / s, xtCorPF * abs(tH) ) < rndmPtr->flat() ) + continue; + if ( isDiffB && pow( s4 / s, xtCorPF * abs(tH) ) < rndmPtr->flat() ) + continue; + + // Donnachie and Landshoff (RapGap): + } else if (PomFlux == 4) { + + // Select diffractive mass(es) according to dm^2/(m^2)^(1 + 2 epsilon). + m3 = m3ElDiff; + m4 = m4ElDiff; + if (isDiffA) { + double s3MinPow = pow( m3ElDiff, xIntPF ); + double s3MaxPow = pow( max(mA, eCM - m4ElDiff), xIntPF ); + m3 = pow( s3MinPow + rndmPtr->flat() * (s3MaxPow - s3MinPow), + 1. / xIntPF ); + } + if (isDiffB) { + double s4MinPow = pow( m4ElDiff, xIntPF ); + double s4MaxPow = pow( max(mB, eCM - m3ElDiff), xIntPF ); + m4 = pow( s4MinPow + rndmPtr->flat() * (s4MaxPow - s4MinPow), + 1. / xIntPF ); + } + s3 = m3 * m3; + s4 = m4 * m4; + + // Select t according to power and weigh by x_P^(2 alpha' |t|). + tH = - (1. / pow( tAux1 + rndmPtr->flat() * (tAux2 - tAux1), 1./3.) + - 1.) / coefDL; + double wDL = pow2( (mp24DL - 2.8 * tH) / (mp24DL - tH) ) + / pow4( 1. - tH / 0.7); + double wMX = 1. / pow4( 1. - coefDL * tH); + if (wDL < rndmPtr->flat() * wMX) continue; + if ( isDiffA && pow( s3 / s, xtCorPF * abs(tH) ) < rndmPtr->flat() ) + continue; + if ( isDiffB && pow( s4 / s, xtCorPF * abs(tH) ) < rndmPtr->flat() ) + continue; + } + + // Check whether m^2 and t choices are consistent. + lambda34 = sqrtpos( pow2( s - s3 - s4) - 4. * s3 * s4 ); + double tempA = s - (s1 + s2 + s3 + s4) + (s1 - s2) * (s3 - s4) / s; + double tempB = lambda12 * lambda34 / s; + if (tempB < DIFFMASSMAX) continue; + double tempC = (s3 - s1) * (s4 - s2) + (s1 + s4 - s2 - s3) + * (s1 * s4 - s2 * s3) / s; + double tLowNow = -0.5 * (tempA + tempB); + double tUppNow = tempC / tLowNow; + if (tH < tLowNow || tH > tUppNow) continue; + + // Careful reconstruction of scattering angle. + double cosTheta = min(1., max(-1., (tempA + 2. * tH) / tempB)); + double sinTheta = 2. * sqrtpos( -(tempC + tempA * tH + tH * tH) ) + / tempB; + theta = asin( min(1., sinTheta)); + if (cosTheta < 0.) theta = M_PI - theta; + + // Found acceptable kinematics, so no more looping. Done + break; + } + return true; + +} + +//-------------------------------------------------------------------------- + +// Construct the four-vector kinematics from the trial values. + +bool PhaseSpace2to2diffractive::finalKin() { + + // Particle masses; incoming always on mass shell. + mH[1] = mA; + mH[2] = mB; + mH[3] = m3; + mH[4] = m4; + + // Incoming particles along beam axes. + pAbs = 0.5 * lambda12 / eCM; + pH[1] = Vec4( 0., 0., pAbs, 0.5 * (s + s1 - s2) / eCM); + pH[2] = Vec4( 0., 0., -pAbs, 0.5 * (s + s2 - s1) / eCM); + + // Outgoing particles initially along beam axes. + pAbs = 0.5 * lambda34 / eCM; + pH[3] = Vec4( 0., 0., pAbs, 0.5 * (s + s3 - s4) / eCM); + pH[4] = Vec4( 0., 0., -pAbs, 0.5 * (s + s4 - s3) / eCM); + + // Then rotate them + phi = 2. * M_PI * rndmPtr->flat(); + pH[3].rot( theta, phi); + pH[4].rot( theta, phi); + + // Set some further info for completeness. + x1H = 1.; + x2H = 1.; + sH = s; + uH = s1 + s2 + s3 + s4 - sH - tH; + mHat = eCM; + p2Abs = pAbs * pAbs; + betaZ = 0.; + pTH = pAbs * sin(theta); + + // Done. + return true; + +} + +//========================================================================== + +// PhaseSpace2to3tauycyl class. +// 2 -> 3 kinematics for normal subprocesses. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of Newton-Raphson iterations of kinematics when masses introduced. +const int PhaseSpace2to3tauycyl::NITERNR = 5; + +//-------------------------------------------------------------------------- + +// Set up for fixed or Breit-Wigner mass selection. + +bool PhaseSpace2to3tauycyl::setupMasses() { + + // Treat Z0 as such or as gamma*/Z0 + gmZmode = gmZmodeGlobal; + int gmZmodeProc = sigmaProcessPtr->gmZmode(); + if (gmZmodeProc >= 0) gmZmode = gmZmodeProc; + + // Set sHat limits - based on global limits only. + mHatMin = mHatGlobalMin; + sHatMin = mHatMin*mHatMin; + mHatMax = eCM; + if (mHatGlobalMax > mHatGlobalMin) mHatMax = min( eCM, mHatGlobalMax); + sHatMax = mHatMax*mHatMax; + + // Masses and widths of resonances. + setupMass1(3); + setupMass1(4); + setupMass1(5); + + // Reduced mass range - do not make it as fancy as in two-body case. + if (useBW[3]) mUpper[3] -= (mPeak[4] + mPeak[5]); + if (useBW[4]) mUpper[4] -= (mPeak[3] + mPeak[5]); + if (useBW[5]) mUpper[5] -= (mPeak[3] + mPeak[4]); + + // If closed phase space then unallowed process. + bool physical = true; + if (useBW[3] && mUpper[3] < mLower[3] + MASSMARGIN) physical = false; + if (useBW[4] && mUpper[4] < mLower[4] + MASSMARGIN) physical = false; + if (useBW[5] && mUpper[5] < mLower[5] + MASSMARGIN) physical = false; + if (!useBW[3] && !useBW[4] && !useBW[5] && mHatMax < mPeak[3] + + mPeak[4] + mPeak[5] + MASSMARGIN) physical = false; + if (!physical) return false; + + // No extra pT precautions in massless limit - assumed fixed by ME's. + pTHatMin = pTHatGlobalMin; + pT2HatMin = pTHatMin * pTHatMin; + pTHatMax = pTHatGlobalMax; + pT2HatMax = pTHatMax * pTHatMax; + + // Prepare to select m3 by BW + flat + 1/s_3. + if (useBW[3]) { + double distToThreshA = (mHatMax - mPeak[3] - mPeak[4] - mPeak[5]) + * mWidth[3] / (pow2(mWidth[3]) + pow2(mWidth[4]) + pow2(mWidth[5])); + double distToThreshB = (mHatMax - mPeak[3] - mMin[4] - mMin[5]) + / mWidth[3]; + double distToThresh = min( distToThreshA, distToThreshB); + setupMass2(3, distToThresh); + } + + // Prepare to select m4 by BW + flat + 1/s_3. + if (useBW[4]) { + double distToThreshA = (mHatMax - mPeak[3] - mPeak[4] - mPeak[5]) + * mWidth[4] / (pow2(mWidth[3]) + pow2(mWidth[4]) + pow2(mWidth[5])); + double distToThreshB = (mHatMax - mPeak[4] - mMin[3] - mMin[5]) + / mWidth[4]; + double distToThresh = min( distToThreshA, distToThreshB); + setupMass2(4, distToThresh); + } + + // Prepare to select m5 by BW + flat + 1/s_3. + if (useBW[5]) { + double distToThreshA = (mHatMax - mPeak[3] - mPeak[4] - mPeak[5]) + * mWidth[5] / (pow2(mWidth[3]) + pow2(mWidth[4]) + pow2(mWidth[5])); + double distToThreshB = (mHatMax - mPeak[5] - mMin[3] - mMin[4]) + / mWidth[5]; + double distToThresh = min( distToThreshA, distToThreshB); + setupMass2(5, distToThresh); + } + + // Initialization masses. For now give up when constrained phase space. + m3 = (useBW[3]) ? min(mPeak[3], mUpper[3]) : mPeak[3]; + m4 = (useBW[4]) ? min(mPeak[4], mUpper[4]) : mPeak[4]; + m5 = (useBW[5]) ? min(mPeak[5], mUpper[5]) : mPeak[5]; + if (m3 + m4 + m5 + MASSMARGIN > mHatMax) physical = false; + s3 = m3*m3; + s4 = m4*m4; + s5 = m5*m5; + + // Correct selected mass-spectrum to running-width Breit-Wigner. + // Extra safety margin for maximum search. + wtBW = 1.; + if (useBW[3]) wtBW *= weightMass(3) * EXTRABWWTMAX; + if (useBW[4]) wtBW *= weightMass(4) * EXTRABWWTMAX; + if (useBW[5]) wtBW *= weightMass(5) * EXTRABWWTMAX; + + // Done. + return physical; + +} + +//-------------------------------------------------------------------------- + +// Select Breit-Wigner-distributed or fixed masses. + +bool PhaseSpace2to3tauycyl::trialMasses() { + + // By default vanishing cross section. + sigmaNw = 0.; + wtBW = 1.; + + // Pick m3, m4 and m5 independently. + trialMass(3); + trialMass(4); + trialMass(5); + + // If outside phase space then reject event. + if (m3 + m4 + m5 + MASSMARGIN > mHatMax) return false; + + // Correct selected mass-spectrum to running-width Breit-Wigner. + if (useBW[3]) wtBW *= weightMass(3); + if (useBW[4]) wtBW *= weightMass(4); + if (useBW[5]) wtBW *= weightMass(5); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Construct the four-vector kinematics from the trial values. + +bool PhaseSpace2to3tauycyl::finalKin() { + + // Assign masses to particles assumed massless in matrix elements. + int id3 = sigmaProcessPtr->id(3); + int id4 = sigmaProcessPtr->id(4); + int id5 = sigmaProcessPtr->id(5); + if (idMass[3] == 0) { m3 = particleDataPtr->m0(id3); s3 = m3*m3; } + if (idMass[4] == 0) { m4 = particleDataPtr->m0(id4); s4 = m4*m4; } + if (idMass[5] == 0) { m5 = particleDataPtr->m0(id5); s5 = m5*m5; } + + // Check that phase space still open after new mass assignment. + if (m3 + m4 + m5 + MASSMARGIN > mHat) { + infoPtr->errorMsg("Warning in PhaseSpace2to3tauycyl::finalKin: " + "failed after mass assignment"); + return false; + } + + // Particle masses; incoming always on mass shell. + mH[1] = 0.; + mH[2] = 0.; + mH[3] = m3; + mH[4] = m4; + mH[5] = m5; + + // Incoming partons along beam axes. + pH[1] = Vec4( 0., 0., 0.5 * eCM * x1H, 0.5 * eCM * x1H); + pH[2] = Vec4( 0., 0., -0.5 * eCM * x2H, 0.5 * eCM * x2H); + + // Begin three-momentum rescaling to compensate for masses. + if (idMass[3] == 0 || idMass[4] == 0 || idMass[5] == 0) { + double p3S = p3cm.pAbs2(); + double p4S = p4cm.pAbs2(); + double p5S = p5cm.pAbs2(); + double fac = 1.; + double e3, e4, e5, value, deriv; + + // Iterate rescaling solution five times, using Newton-Raphson. + for (int i = 0; i < NITERNR; ++i) { + e3 = sqrt(s3 + fac * p3S); + e4 = sqrt(s4 + fac * p4S); + e5 = sqrt(s5 + fac * p5S); + value = e3 + e4 + e5 - mHat; + deriv = 0.5 * (p3S / e3 + p4S / e4 + p5S / e5); + fac -= value / deriv; + } + + // Rescale momenta appropriately. + double facRoot = sqrt(fac); + p3cm.rescale3( facRoot ); + p4cm.rescale3( facRoot ); + p5cm.rescale3( facRoot ); + p3cm.e( sqrt(s3 + fac * p3S) ); + p4cm.e( sqrt(s4 + fac * p4S) ); + p5cm.e( sqrt(s5 + fac * p5S) ); + } + + // Outgoing partons initially in collision CM frame along beam axes. + pH[3] = p3cm; + pH[4] = p4cm; + pH[5] = p5cm; + + // Then boost them to overall CM frame + betaZ = (x1H - x2H)/(x1H + x2H); + pH[3].rot( theta, phi); + pH[4].rot( theta, phi); + pH[3].bst( 0., 0., betaZ); + pH[4].bst( 0., 0., betaZ); + pH[5].bst( 0., 0., betaZ); + + // Store average pT of three final particles for documentation. + pTH = (p3cm.pT() + p4cm.pT() + p5cm.pT()) / 3.; + + // Done. + return true; +} + +//========================================================================== + +// The PhaseSpace2to3yyycyl class. +// Phase space for 2 -> 3 QCD processes, 1 + 2 -> 3 + 4 + 5 set up in +// y3, y4, y5, pT2_3, pT2_5, phi_3 and phi_5, and with R separation cut. +// Note: here cout is used for output, not os. Change?? + +//-------------------------------------------------------------------------- + +// Sample the phase space of the process. + +bool PhaseSpace2to3yyycyl::setupSampling() { + + // Phase space cuts specifically for 2 -> 3 QCD processes. + pTHat3Min = settingsPtr->parm("PhaseSpace:pTHat3Min"); + pTHat3Max = settingsPtr->parm("PhaseSpace:pTHat3Max"); + pTHat5Min = settingsPtr->parm("PhaseSpace:pTHat5Min"); + pTHat5Max = settingsPtr->parm("PhaseSpace:pTHat5Max"); + RsepMin = settingsPtr->parm("PhaseSpace:RsepMin"); + R2sepMin = pow2(RsepMin); + + // If both beams are baryons then softer PDF's than for mesons/Pomerons. + hasBaryonBeams = ( beamAPtr->isBaryon() && beamBPtr->isBaryon() ); + + // Work with massless partons. + for (int i = 0; i < 6; ++i) mH[i] = 0.; + + // Constrain to possible cuts at current CM energy and check consistency. + pT3Min = pTHat3Min; + pT3Max = pTHat3Max; + if (pT3Max < pT3Min) pT3Max = 0.5 * eCM; + pT5Min = pTHat5Min; + pT5Max = pTHat5Max; + if (pT5Max < pT5Min) pT5Max = 0.5 * eCM; + if (pT5Max > pT3Max || pT5Min > pT3Min || pT3Min + 2. * pT5Min > eCM) { + infoPtr->errorMsg("Error in PhaseSpace2to3yyycyl::setupSampling: " + "inconsistent pT limits in 3-body phase space"); + return false; + } + + // Loop over some configurations where cross section could be maximal. + // In all cases all sum p_z = 0, for maximal PDF weights. + // Also pT3 and R45 are minimal, while pT5 may vary. + sigmaMx = 0.; + double pT5EffMax = min( pT5Max, 0.5 * pT3Min / cos(0.5 * RsepMin) ); + double pT3EffMin = max( pT3Min, 2.0 * pT5Min * cos(0.5 * RsepMin) ) ; + double sinhR = sinh(0.5 * RsepMin); + double coshR = cosh(0.5 * RsepMin); + for (int iStep = 0; iStep < 120; ++iStep) { + + // First kind: |phi4 - phi5| = R, all p_z = 0, i.e. separation in phi. + if (iStep < 10) { + pT3 = pT3EffMin; + pT5 = pT5Min * pow( pT5EffMax / pT5Min, iStep / 9.); + double pTRat = pT5 / pT3; + double sin2Rsep = pow2( sin(RsepMin) ); + double cosPhi35 = - cos(RsepMin) * sqrtpos(1. - sin2Rsep + * pow2(pTRat)) - sin2Rsep * pTRat; + cosPhi35 = max( cosPhi35, cos(M_PI - 0.5 * RsepMin) ); + double sinPhi35 = sqrt(1. - pow2(cosPhi35)); + pT4 = sqrt( pow2(pT3) + pow2(pT5) + 2. * pT3 * pT5 * cosPhi35); + p3cm = pT3 * Vec4( 1., 0., 0., 1.); + p4cm = Vec4(-pT3 - pT5 * cosPhi35, -pT5 * sinPhi35, 0., pT4); + p5cm = pT5 * Vec4( cosPhi35, sinPhi35, 0., 1.); + + // Second kind: |y4 - y5| = R, phi4 = phi5, i.e. separation in y. + } else { + pT5 = pT5Min * pow( pT5Max / pT5Min, iStep%10 / 9. ); + pT3 = max( pT3Min, 2. * pT5); + pT4 = pT3 - pT5; + p4cm = pT4 * Vec4( -1., 0., sinhR, coshR ); + p5cm = pT5 * Vec4( -1., 0., -sinhR, coshR ); + y3 = -1.2 + 0.2 * (iStep/10); + p3cm = pT3 * Vec4( 1., 0., sinh(y3), cosh(y3)); + betaZ = (p3cm.pz() + p4cm.pz() + p5cm.pz()) + / (p3cm.e() + p4cm.e() + p5cm.e()); + p3cm.bst( 0., 0., -betaZ); + p4cm.bst( 0., 0., -betaZ); + p5cm.bst( 0., 0., -betaZ); + } + + // Find cross section in chosen phase space point. + pInSum = p3cm + p4cm + p5cm; + x1H = pInSum.e() / eCM; + x2H = x1H; + sH = pInSum.m2Calc(); + sigmaProcessPtr->set3Kin( x1H, x2H, sH, p3cm, p4cm, p5cm, + 0., 0., 0., 1., 1., 1.); + sigmaNw = sigmaProcessPtr->sigmaPDF(); + + // Multiply by Jacobian. + double flux = 1. /(8. * pow2(sH) * pow5(2. * M_PI)); + double pTRng = pow2(M_PI) + * pow4(pT3) * (1./pow2(pT3Min) - 1./pow2(pT3Max)) + * pow2(pT5) * 2.* log(pT5Max/pT5Min); + double yRng = 8. * log(eCM / pT3) * log(eCM / pT4) * log(eCM / pT5); + sigmaNw *= SAFETYMARGIN * flux * pTRng * yRng; + + // Update to largest maximum. + if (showSearch && sigmaNw > sigmaMx) cout << "\n New sigmamax is " + << scientific << setprecision(3) << sigmaNw << " for x1 = " << x1H + << " x2 = " << x2H << " sH = " << sH << endl << " p3 = " << p3cm + << " p4 = " << p4cm << " p5 = " << p5cm; + if (sigmaNw > sigmaMx) sigmaMx = sigmaNw; + } + sigmaPos = sigmaMx; + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Sample the phase space of the process. + +bool PhaseSpace2to3yyycyl::trialKin(bool inEvent, bool) { + + // Allow for possibility that energy varies from event to event. + if (doEnergySpread) { + eCM = infoPtr->eCM(); + s = eCM * eCM; + } + sigmaNw = 0.; + + // Constrain to possible cuts at current CM energy and check consistency. + pT3Min = pTHat3Min; + pT3Max = pTHat3Max; + if (pT3Max < pT3Min) pT3Max = 0.5 * eCM; + pT5Min = pTHat5Min; + pT5Max = pTHat5Max; + if (pT5Max < pT5Min) pT5Max = 0.5 * eCM; + if (pT5Max > pT3Max || pT5Min > pT3Min || pT3Min + 2. * pT5Min > eCM) { + infoPtr->errorMsg("Error in PhaseSpace2to3yyycyl::trialKin: " + "inconsistent pT limits in 3-body phase space"); + return false; + } + + // Pick pT3 according to d^2(pT3)/pT3^4 and pT5 to d^2(pT5)/pT5^2. + pT3 = pT3Min * pT3Max / sqrt( pow2(pT3Min) + + rndmPtr->flat() * (pow2(pT3Max) - pow2(pT3Min)) ); + pT5Max = min(pT5Max, pT3); + if (pT5Max < pT5Min) return false; + pT5 = pT5Min * pow( pT5Max / pT5Min, rndmPtr->flat() ); + + // Pick azimuthal angles flat and reconstruct pT4, between pT3 and pT5. + phi3 = 2. * M_PI * rndmPtr->flat(); + phi5 = 2. * M_PI * rndmPtr->flat(); + pT4 = sqrt( pow2(pT3) + pow2(pT5) + 2. * pT3 * pT5 * cos(phi3 - phi5) ); + if (pT4 > pT3 || pT4 < pT5) return false; + phi4 = atan2( -(pT3 * sin(phi3) + pT5 * sin(phi5)), + -(pT3 * cos(phi3) + pT5 * cos(phi5)) ); + + // Pick rapidities flat in allowed ranges. + y3Max = log(eCM / pT3); + y4Max = log(eCM / pT4); + y5Max = log(eCM / pT5); + y3 = y3Max * (2. * rndmPtr->flat() - 1.); + y4 = y4Max * (2. * rndmPtr->flat() - 1.); + y5 = y5Max * (2. * rndmPtr->flat() - 1.); + + // Reject some events at large rapidities to improve efficiency. + // (Works for baryons, not pions or Pomerons if they have hard PDF's.) + double WTy = (hasBaryonBeams) ? (1. - pow2(y3/y3Max)) + * (1. - pow2(y4/y4Max)) * (1. - pow2(y5/y5Max)) : 1.; + if (WTy < rndmPtr->flat()) return false; + + // Check that any pair separated more then RsepMin in (y, phi) space. + dphi = abs(phi3 - phi4); + if (dphi > M_PI) dphi = 2. * M_PI - dphi; + if (pow2(y3 - y4) + pow2(dphi) < R2sepMin) return false; + dphi = abs(phi3 - phi5); + if (dphi > M_PI) dphi = 2. * M_PI - dphi; + if (pow2(y3 - y5) + pow2(dphi) < R2sepMin) return false; + dphi = abs(phi4 - phi5); + if (dphi > M_PI) dphi = 2. * M_PI - dphi; + if (pow2(y4 - y5) + pow2(dphi) < R2sepMin) return false; + + // Reconstruct all four-vectors. + pH[3] = pT3 * Vec4( cos(phi3), sin(phi3), sinh(y3), cosh(y3) ); + pH[4] = pT4 * Vec4( cos(phi4), sin(phi4), sinh(y4), cosh(y4) ); + pH[5] = pT5 * Vec4( cos(phi5), sin(phi5), sinh(y5), cosh(y5) ); + pInSum = pH[3] + pH[4] + pH[5]; + + // Check that x values physical and sHat in allowed range. + x1H = (pInSum.e() + pInSum.pz()) / eCM; + x2H = (pInSum.e() - pInSum.pz()) / eCM; + if (x1H >= 1. || x2H >= 1.) return false; + sH = pInSum.m2Calc(); + if ( sH < pow2(mHatGlobalMin) || + (mHatGlobalMax > mHatGlobalMin && sH > pow2(mHatGlobalMax)) ) + return false; + + // Boost four-vectors to rest frame of collision. + betaZ = (x1H - x2H)/(x1H + x2H); + p3cm = pH[3]; p3cm.bst( 0., 0., -betaZ); + p4cm = pH[4]; p4cm.bst( 0., 0., -betaZ); + p5cm = pH[5]; p5cm.bst( 0., 0., -betaZ); + + // Find cross section in chosen phase space point. + sigmaProcessPtr->set3Kin( x1H, x2H, sH, p3cm, p4cm, p5cm, + 0., 0., 0., 1., 1., 1.); + sigmaNw = sigmaProcessPtr->sigmaPDF(); + + // Multiply by Jacobian. Correct for rejection of large rapidities. + double flux = 1. /(8. * pow2(sH) * pow5(2. * M_PI)); + double yRng = 8. * y3Max * y4Max * y5Max; + double pTRng = pow2(M_PI) + * pow4(pT3) * (1./pow2(pT3Min) - 1./pow2(pT3Max)) + * pow2(pT5) * 2.* log(pT5Max/pT5Min); + sigmaNw *= flux * yRng * pTRng / WTy; + + // Allow possibility for user to modify cross section. + if (canModifySigma) sigmaNw + *= userHooksPtr->multiplySigmaBy( sigmaProcessPtr, this, inEvent); + + // Check if maximum violated. + newSigmaMx = false; + if (sigmaNw > sigmaMx) { + infoPtr->errorMsg("Warning in PhaseSpace2to3yyycyl::trialKin: " + "maximum for cross section violated"); + + // Violation strategy 1: increase maximum (always during initialization). + if (increaseMaximum || !inEvent) { + double violFact = SAFETYMARGIN * sigmaNw / sigmaMx; + sigmaMx = SAFETYMARGIN * sigmaNw; + newSigmaMx = true; + if (showViolation) { + if (violFact < 9.99) cout << fixed; + else cout << scientific; + cout << " PYTHIA Maximum for " << sigmaProcessPtr->name() + << " increased by factor " << setprecision(3) << violFact + << " to " << scientific << sigmaMx << endl; + } + + // Violation strategy 2: weight event (done in ProcessContainer). + } else if (showViolation && sigmaNw > sigmaPos) { + double violFact = sigmaNw / sigmaMx; + if (violFact < 9.99) cout << fixed; + else cout << scientific; + cout << " PYTHIA Maximum for " << sigmaProcessPtr->name() + << " exceeded by factor " << setprecision(3) << violFact << endl; + sigmaPos = sigmaNw; + } + } + + // Check if negative cross section. + if (sigmaNw < sigmaNeg) { + infoPtr->errorMsg("Warning in PhaseSpace2to3yyycyl::trialKin:" + " negative cross section set 0", "for " + sigmaProcessPtr->name() ); + sigmaNeg = sigmaNw; + + // Optional printout of (all) violations. + if (showViolation) cout << " PYTHIA Negative minimum for " + << sigmaProcessPtr->name() << " changed to " << scientific + << setprecision(3) << sigmaNeg << endl; + } + if (sigmaNw < 0.) sigmaNw = 0.; + + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Construct the final kinematics of the process: not much left + +bool PhaseSpace2to3yyycyl::finalKin() { + + // Work with massless partons. + for (int i = 0; i < 6; ++i) mH[i] = 0.; + + // Ibncoming partons to collision. + pH[1] = 0.5 * (pInSum.e() + pInSum.pz()) * Vec4( 0., 0., 1., 1.); + pH[2] = 0.5 * (pInSum.e() - pInSum.pz()) * Vec4( 0., 0., -1., 1.); + + // Some quantities meaningless for 2 -> 3. pT devined as average value. + tH = 0.; + uH = 0.; + pTH = (pH[3].pT() + pH[4].pT() + pH[5].pT()) / 3.; + theta = 0.; + phi = 0.; + + return true; +} + + +//========================================================================== + +// The PhaseSpaceLHA class. +// A derived class for Les Houches events. +// Note: arbitrary subdivision into PhaseSpaceLHA and SigmaLHAProcess tasks. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// LHA convention with cross section in pb forces conversion to mb. +const double PhaseSpaceLHA::CONVERTPB2MB = 1e-9; + +//-------------------------------------------------------------------------- + +// Find maximal cross section for comparison with internal processes. + +bool PhaseSpaceLHA::setupSampling() { + + // Find which strategy Les Houches events are produced with. + strategy = lhaUpPtr->strategy(); + stratAbs = abs(strategy); + if (strategy == 0 || stratAbs > 4) { + ostringstream stratCode; + stratCode << strategy; + infoPtr->errorMsg("Error in PhaseSpaceLHA::setupSampling: unknown " + "Les Houches Accord weighting stategy", stratCode.str()); + return false; + } + + // Number of contributing processes. + nProc = lhaUpPtr->sizeProc(); + + // Loop over all processes. Read out maximum and cross section. + xMaxAbsSum = 0.; + xSecSgnSum = 0.; + int idPr; + double xMax, xSec, xMaxAbs; + for (int iProc = 0 ; iProc < nProc; ++iProc) { + idPr = lhaUpPtr->idProcess(iProc); + xMax = lhaUpPtr->xMax(iProc); + xSec = lhaUpPtr->xSec(iProc); + + // Check for inconsistencies between strategy and stored values. + if ( (strategy == 1 || strategy == 2) && xMax < 0.) { + infoPtr->errorMsg("Error in PhaseSpaceLHA::setupSampling: " + "negative maximum not allowed"); + return false; + } + if ( ( strategy == 2 || strategy == 3) && xSec < 0.) { + infoPtr->errorMsg("Error in PhaseSpaceLHA::setupSampling: " + "negative cross section not allowed"); + return false; + } + + // Store maximal cross sections for later choice. + if (stratAbs == 1) xMaxAbs = abs(xMax); + else if (stratAbs < 4) xMaxAbs = abs(xSec); + else xMaxAbs = 1.; + idProc.push_back( idPr ); + xMaxAbsProc.push_back( xMaxAbs ); + + // Find sum and convert to mb. + xMaxAbsSum += xMaxAbs; + xSecSgnSum += xSec; + } + sigmaMx = xMaxAbsSum * CONVERTPB2MB; + sigmaSgn = xSecSgnSum * CONVERTPB2MB; + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Construct the next process, by interface to Les Houches class. + +bool PhaseSpaceLHA::trialKin( bool, bool repeatSame ) { + + // Must select process type in some cases. + int idProcNow = 0; + if (repeatSame) idProcNow = idProcSave; + else if (stratAbs <= 2) { + double xMaxAbsRndm = xMaxAbsSum * rndmPtr->flat(); + int iProc = -1; + do xMaxAbsRndm -= xMaxAbsProc[++iProc]; + while (xMaxAbsRndm > 0. && iProc < nProc - 1); + idProcNow = idProc[iProc]; + } + + // Generate Les Houches event. Return if fail (= end of file). + bool physical = lhaUpPtr->setEvent(idProcNow); + if (!physical) return false; + + // Find which process was generated. + int idPr = lhaUpPtr->idProcess(); + int iProc = 0; + for (int iP = 0; iP < int(idProc.size()); ++iP) + if (idProc[iP] == idPr) iProc = iP; + idProcSave = idPr; + + // Extract cross section and rescale according to strategy. + double wtPr = lhaUpPtr->weight(); + if (stratAbs == 1) sigmaNw = wtPr * CONVERTPB2MB + * xMaxAbsSum / xMaxAbsProc[iProc]; + else if (stratAbs == 2) sigmaNw = (wtPr / abs(lhaUpPtr->xMax(iProc))) + * sigmaMx; + else if (strategy == 3) sigmaNw = sigmaMx; + else if (strategy == -3 && wtPr > 0.) sigmaNw = sigmaMx; + else if (strategy == -3) sigmaNw = -sigmaMx; + else if (stratAbs == 4) sigmaNw = wtPr * CONVERTPB2MB; + + // Set x scales. + x1H = lhaUpPtr->x1(); + x2H = lhaUpPtr->x2(); + + // Done. + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/ProcessContainer.cxx b/PYTHIA8/pythia8140/src/ProcessContainer.cxx new file mode 100644 index 00000000000..1974ab536da --- /dev/null +++ b/PYTHIA8/pythia8140/src/ProcessContainer.cxx @@ -0,0 +1,2298 @@ +// ProcessContainer.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// ProcessContainer and SetupContainers classes. + +#include "ProcessContainer.h" + +// Internal headers for special processes. +#include "SigmaCompositeness.h" +#include "SigmaEW.h" +#include "SigmaExtraDim.h" +#include "SigmaGeneric.h" +#include "SigmaHiggs.h" +#include "SigmaLeftRightSym.h" +#include "SigmaLeptoquark.h" +#include "SigmaNewGaugeBosons.h" +#include "SigmaOnia.h" +#include "SigmaQCD.h" +#include "SigmaSUSY.h" + +namespace Pythia8 { + +//========================================================================== + +// ProcessContainer class. +// Information allowing the generation of a specific process. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of event tries to check maximization finding reliability. +const int ProcessContainer::N12SAMPLE = 100; + +// Ditto, but increased for 2 -> 3 processes. +const int ProcessContainer::N3SAMPLE = 1000; + +//-------------------------------------------------------------------------- + +// Initialize phase space and counters. +// Argument isFirst distinguishes two hard processes in same event. + +bool ProcessContainer::init(bool isFirst, Info* infoPtrIn, + Settings& settings, ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + BeamParticle* beamAPtr, BeamParticle* beamBPtr, CoupSM* coupSMPtr, + SigmaTotal* sigmaTotPtr, CoupSUSY* coupSUSYPtr, + ResonanceDecays* resDecaysPtrIn, SusyLesHouches* slhaPtr, + UserHooks* userHooksPtr) { + + // Extract info about current process from SigmaProcess object. + isLHA = sigmaProcessPtr->isLHA(); + isMinBias = sigmaProcessPtr->isMinBias(); + isResolved = sigmaProcessPtr->isResolved(); + isDiffA = sigmaProcessPtr->isDiffA(); + isDiffB = sigmaProcessPtr->isDiffB(); + isQCD3body = sigmaProcessPtr->isQCD3body(); + int nFin = sigmaProcessPtr->nFinal(); + lhaStrat = (isLHA) ? lhaUpPtr->strategy() : 0; + lhaStratAbs = abs(lhaStrat); + allowNegSig = sigmaProcessPtr->allowNegativeSigma(); + + // Flag for maximum violation handling. + increaseMaximum = settings.flag("PhaseSpace:increaseMaximum"); + + // Pick and create phase space generator. Send pointers where required. + if (isLHA) phaseSpacePtr = new PhaseSpaceLHA(); + else if (isMinBias) phaseSpacePtr = new PhaseSpace2to2minbias(); + else if (!isResolved && !isDiffA && !isDiffB ) + phaseSpacePtr = new PhaseSpace2to2elastic(); + else if (!isResolved) phaseSpacePtr = new PhaseSpace2to2diffractive( + isDiffA, isDiffB); + else if (nFin == 1) phaseSpacePtr = new PhaseSpace2to1tauy(); + else if (nFin == 2) phaseSpacePtr = new PhaseSpace2to2tauyz(); + else if (isQCD3body) phaseSpacePtr = new PhaseSpace2to3yyycyl(); + else phaseSpacePtr = new PhaseSpace2to3tauycyl(); + + // Store pointers and perform simple initialization. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + resDecaysPtr = resDecaysPtrIn; + if (isLHA) { + sigmaProcessPtr->setLHAPtr(lhaUpPtr); + phaseSpacePtr->setLHAPtr(lhaUpPtr); + } + sigmaProcessPtr->init(infoPtr, &settings, particleDataPtr, rndmPtr, + beamAPtr, beamBPtr, coupSMPtr, sigmaTotPtr, coupSUSYPtr, slhaPtr); + phaseSpacePtr->init( isFirst, sigmaProcessPtr, infoPtr, &settings, + particleDataPtr, rndmPtr, beamAPtr, beamBPtr, coupSMPtr, sigmaTotPtr, + userHooksPtr); + + // Reset cross section statistics. + nTry = 0; + nSel = 0; + nAcc = 0; + nTryStat = 0; + sigmaMx = 0.; + sigmaSum = 0.; + sigma2Sum = 0.; + sigmaNeg = 0.; + sigmaAvg = 0.; + sigmaFin = 0.; + deltaFin = 0.; + + // Initialize process and allowed incoming partons. + sigmaProcessPtr->initProc(); + if (!sigmaProcessPtr->initFlux()) return false; + + // Find maximum of differential cross section * phasespace. + bool physical = phaseSpacePtr->setupSampling(); + sigmaMx = phaseSpacePtr->sigmaMax(); + double sigmaHalfWay = sigmaMx; + + // Separate signed maximum needed for LHA with negative weight. + sigmaSgn = phaseSpacePtr->sigmaSumSigned(); + + // Check maximum by a few events, and extrapolate a further increase. + if (physical & !isLHA) { + int nSample = (nFin < 3) ? N12SAMPLE : N3SAMPLE; + for (int iSample = 0; iSample < nSample; ++iSample) + while (!phaseSpacePtr->trialKin(false)) { + if (iSample == nSample/2) sigmaHalfWay = phaseSpacePtr->sigmaMax(); + } + sigmaMx = pow2(phaseSpacePtr->sigmaMax()) / sigmaHalfWay; + phaseSpacePtr->setSigmaMax(sigmaMx); + } + + // Done. + return physical; +} + +//-------------------------------------------------------------------------- + +// Generate a trial event; selected or not. + +bool ProcessContainer::trialProcess() { + + // Loop over tries only occurs for Les Houches strategy = +-2. + for (int iTry = 0; ; ++iTry) { + + // Generate a trial phase space point, if meaningful. + if (sigmaMx == 0.) return false; + infoPtr->setEndOfFile(false); + bool repeatSame = (iTry > 0); + bool physical = phaseSpacePtr->trialKin(true, repeatSame); + + // Possibly fail, e.g. if at end of Les Houches file, else cross section. + if (isLHA && !physical) infoPtr->setEndOfFile(true); + else ++nTry; + if (!physical) return false; + double sigmaNow = phaseSpacePtr->sigmaNow(); + + // Tell if this event comes with negative weight, or weight at all. + double weight = 1.; + if (!isLHA && !increaseMaximum && sigmaNow > sigmaMx) + weight = sigmaNow / sigmaMx; + if ( lhaStrat < 0 && sigmaNow < 0.) weight = -1.; + if ( lhaStratAbs == 4) weight = sigmaNow; + infoPtr->setWeight( weight); + + // Check that not negative cross section when not allowed. + if (!allowNegSig) { + if (sigmaNow < sigmaNeg) { + infoPtr->errorMsg("Warning in ProcessContainer::trialProcess: neg" + "ative cross section set 0", "for " + sigmaProcessPtr->name() ); + sigmaNeg = sigmaNow; + } + if (sigmaNow < 0.) sigmaNow = 0.; + } + + // Update statistics. Check if maximum violated. + double sigmaAdd = sigmaNow; + if (lhaStratAbs == 2 || lhaStratAbs == 3) sigmaAdd = sigmaSgn; + sigmaSum += sigmaAdd; + sigma2Sum += pow2(sigmaAdd); + newSigmaMx = phaseSpacePtr->newSigmaMax(); + if (newSigmaMx) sigmaMx = phaseSpacePtr->sigmaMax(); + + // Select or reject trial point. + bool select = true; + if (lhaStratAbs < 3) select + = (newSigmaMx || rndmPtr->flat() * abs(sigmaMx) < abs(sigmaNow)); + if (select) ++nSel; + if (select || lhaStratAbs != 2) return select; + } + +} + + +//-------------------------------------------------------------------------- + +// Give the hard subprocess. + +bool ProcessContainer::constructProcess( Event& process, bool isHardest) { + + // Construct flavour and colours for selected event. + if (isResolved && !isMinBias) sigmaProcessPtr->pickInState(); + sigmaProcessPtr->setIdColAcol(); + + // Construct kinematics from selected phase space point. + if (!phaseSpacePtr->finalKin()) return false; + int nFin = sigmaProcessPtr->nFinal(); + + // Basic info on process. + if (isHardest) infoPtr->setType( name(), code(), nFin, isMinBias, + isResolved, isDiffA, isDiffB, isLHA); + + // Let hard process record begin with the event as a whole and + // the two incoming beam particles. + process.append( 90, -11, 0, 0, 0, 0, 0, 0, + Vec4(0., 0., 0., infoPtr->eCM()), infoPtr->eCM(), 0. ); + process.append( infoPtr->idA(), -12, 0, 0, 0, 0, 0, 0, + Vec4(0., 0., infoPtr->pzA(), infoPtr->eA()), infoPtr->mA(), 0. ); + process.append( infoPtr->idB(), -12, 0, 0, 0, 0, 0, 0, + Vec4(0., 0., infoPtr->pzB(), infoPtr->eB()), infoPtr->mB(), 0. ); + + // For minbias process no interaction selected so far, so done. + if (isMinBias) return true; + + // Entries 3 and 4, now to be added, come from 1 and 2. + process[1].daughter1(3); + process[2].daughter1(4); + double scale = 0.; + + // Insert the subprocess partons - resolved processes. + int idRes = sigmaProcessPtr->idSChannel(); + if (isResolved && !isLHA) { + + // NOAM: Mothers and daughters without/with intermediate state. + int m_M1 = 3; + int m_M2 = 4; + int m_D1 = 5; + int m_D2 = 4 + nFin; + if (idRes != 0) { + m_M1 = 5; + m_M2 = 0; + m_D1 = 5; + m_D2 = 0; + } + + // Find scale from which to begin MI/ISR/FSR evolution. + scale = sqrt(Q2Fac()); + process.scale( scale ); + + // Loop over incoming and outgoing partons. + int colOffset = process.lastColTag(); + for (int i = 1; i <= 2 + nFin; ++i) { + + // Read out particle info from SigmaProcess object. + int id = sigmaProcessPtr->id(i); + int status = (i <= 2) ? -21 : 23; + int mother1 = (i <= 2) ? i : m_M1 ; + int mother2 = (i <= 2) ? 0 : m_M2 ; + int daughter1 = (i <= 2) ? m_D1 : 0; + int daughter2 = (i <= 2) ? m_D2 : 0; + int col = sigmaProcessPtr->col(i); + if (col > 0) col += colOffset; + int acol = sigmaProcessPtr->acol(i); + if (acol > 0) acol += colOffset; + + // Append to process record. + int iNow = process.append( id, status, mother1, mother2, + daughter1, daughter2, col, acol, phaseSpacePtr->p(i), + phaseSpacePtr->m(i), scale); + + // NOAM: If there is an intermediate state, insert the it in + // the process record after the two incoming particles. + if (i == 2 && idRes != 0) { + + // Sign of intermediate state: go by charge. + if (particleDataPtr->hasAnti(idRes) + && process[3].chargeType() + process[4].chargeType() < 0) + idRes *= -1; + + // The colour configuration of the intermediate state has to be + // resolved separately. + col = 0; + acol = 0; + int m_col1 = sigmaProcessPtr->col(1); + int m_acol1 = sigmaProcessPtr->acol(1); + int m_col2 = sigmaProcessPtr->col(2); + int m_acol2 = sigmaProcessPtr->acol(2); + if (m_col1 == m_acol2 && m_col2 != m_acol1) { + col = m_col2; + acol = m_acol1; + } else if (m_col2 == m_acol1 && m_col1 != m_acol2) { + col = m_col1; + acol = m_acol2; + } + if (col > 0) col += colOffset; + if (acol > 0) acol += colOffset; + + // Insert the intermediate state into the event record. + Vec4 pIntMed = phaseSpacePtr->p(1) + phaseSpacePtr->p(2); + process.append( idRes, -22, 3, 4, 6, 5 + nFin, col, acol, + pIntMed, pIntMed.mCalc(), scale); + } + + // Pick lifetime where relevant, else not. + if (process[iNow].tau0() > 0.) process[iNow].tau( + process[iNow].tau0() * rndmPtr->exp() ); + } + } + + // Insert the outgoing particles - unresolved processes. + else if (!isLHA) { + int id3 = sigmaProcessPtr->id(3); + int status3 = (id3 == process[1].id()) ? 14 : 15; + process.append( id3, status3, 1, 0, 0, 0, 0, 0, + phaseSpacePtr->p(3), phaseSpacePtr->m(3)); + int id4 = sigmaProcessPtr->id(4); + int status4 = (id4 == process[2].id()) ? 14 : 15; + process.append( id4, status4, 2, 0, 0, 0, 0, 0, + phaseSpacePtr->p(4), phaseSpacePtr->m(4)); + } + + // Insert the outgoing particles - Les Houches Accord processes. + else { + + // Since LHA partons may be out of order, determine correct one. + // (Recall that zeroth particle is empty.) + vector newPos; + newPos.reserve(lhaUpPtr->sizePart()); + newPos.push_back(0); + for (int iNew = 0; iNew < lhaUpPtr->sizePart(); ++iNew) { + // For iNew == 0 look for the two incoming partons, then for + // partons having them as mothers, and so on layer by layer. + for (int i = 1; i < lhaUpPtr->sizePart(); ++i) + if (lhaUpPtr->mother1(i) == newPos[iNew]) newPos.push_back(i); + if (int(newPos.size()) <= iNew) break; + } + + // Find scale from which to begin MI/ISR/FSR evolution. + scale = lhaUpPtr->scale(); + double scalePr = (scale < 0.) ? sqrt(Q2Fac()) : scale; + process.scale( scalePr); + + // Copy over info from LHA event to process, in proper order. + for (int i = 1; i < lhaUpPtr->sizePart(); ++i) { + int iOld = newPos[i]; + int id = lhaUpPtr->id(iOld); + + // Translate from LHA status codes. + int lhaStatus = lhaUpPtr->status(iOld); + int status = -21; + if (lhaStatus == 2 || lhaStatus == 3) status = -22; + if (lhaStatus == 1) status = 23; + + // Find where mothers have been moved by reordering. + int mother1Old = lhaUpPtr->mother1(iOld); + int mother2Old = lhaUpPtr->mother2(iOld); + int mother1 = 0; + int mother2 = 0; + for (int im = 1; im < i; ++im) { + if (mother1Old == newPos[im]) mother1 = im + 2; + if (mother2Old == newPos[im]) mother2 = im + 2; + } + if (i <= 2) mother1 = i; + + // Ensure that second mother = 0 except for bona fide carbon copies. + if (mother1 > 0 && mother2 == mother1) { + int sister1 = process[mother1].daughter1(); + int sister2 = process[mother1].daughter2(); + if (sister2 != sister1 && sister2 != 0) mother2 = 0; + } + + // Find daughters and where they have been moved by reordering. + // (Values shifted two steps to account for inserted beams.) + int daughter1 = 0; + int daughter2 = 0; + for (int im = i + 1; im < lhaUpPtr->sizePart(); ++im) { + if (lhaUpPtr->mother1(newPos[im]) == iOld + || lhaUpPtr->mother2(newPos[im]) == iOld) { + if (daughter1 == 0 || im + 2 < daughter1) daughter1 = im + 2; + if (daughter2 == 0 || im + 2 > daughter2) daughter2 = im + 2; + } + } + // For 2 -> 1 hard scatterings reset second daughter to 0. + if (daughter2 == daughter1) daughter2 = 0; + + // Colour trivial, except reset irrelevant colour indices. + int colType = particleDataPtr->colType(id); + int col1 = (colType == 1 || colType == 2) + ? lhaUpPtr->col1(iOld) : 0; + int col2 = (colType == -1 || colType == 2) + ? lhaUpPtr->col2(iOld) : 0; + + // Momentum trivial. + double px = lhaUpPtr->px(iOld); + double py = lhaUpPtr->py(iOld); + double pz = lhaUpPtr->pz(iOld); + double e = lhaUpPtr->e(iOld); + double m = lhaUpPtr->m(iOld); + + // For resonance decay products use resonance mass as scale. + double scaleNow = scalePr; + if (mother1 > 4) scaleNow = process[mother1].m(); + + // Store Les Houches Accord partons. + int iNow = process.append( id, status, mother1, mother2, daughter1, + daughter2, col1, col2, Vec4(px, py, pz, e), m, scaleNow); + + // Check if need to store lifetime. + double tau = lhaUpPtr->tau(iOld); + if (tau > 0.) process[iNow].tau(tau); + } + } + + // Loop through decay chains and set secondary vertices when needed. + for (int i = 3; i < process.size(); ++i) { + int iMother = process[i].mother1(); + + // If sister to already assigned vertex then assign same. + if ( process[i - 1].mother1() == iMother && process[i - 1].hasVertex() ) + process[i].vProd( process[i - 1].vProd() ); + + // Else if mother already has vertex and/or lifetime then assign. + else if ( process[iMother].hasVertex() || process[iMother].tau() > 0.) + process[i].vProd( process[iMother].vDec() ); + } + + // Further info on process. Reset quantities that may or may not be known. + int id1Now = process[3].id(); + int id2Now = process[4].id(); + double pdf1 = 0.; + double pdf2 = 0.; + double tHat = 0.; + double uHat = 0.; + double pTHatL = 0.; + double m3 = 0.; + double m4 = 0.; + double theta = 0.; + double phi = 0.; + double Q2FacNow, alphaEM, alphaS, Q2Ren, x1Now, x2Now, sHat; + + // Internally generated and stored information. + if (!isLHA) { + pdf1 = sigmaProcessPtr->pdf1(); + pdf2 = sigmaProcessPtr->pdf2(); + Q2FacNow = sigmaProcessPtr->Q2Fac(); + alphaEM = sigmaProcessPtr->alphaEMRen(); + alphaS = sigmaProcessPtr->alphaSRen(); + Q2Ren = sigmaProcessPtr->Q2Ren(); + x1Now = phaseSpacePtr->x1(); + x2Now = phaseSpacePtr->x2(); + sHat = phaseSpacePtr->sHat(); + tHat = phaseSpacePtr->tHat(); + uHat = phaseSpacePtr->uHat(); + pTHatL = phaseSpacePtr->pTHat(); + m3 = phaseSpacePtr->m(3); + m4 = phaseSpacePtr->m(4); + theta = phaseSpacePtr->thetaHat(); + phi = phaseSpacePtr->phiHat(); + } + + // Les Houches Accord process partly available, partly to be constructed. + else { + Q2FacNow = (scale < 0.) ? sigmaProcessPtr->Q2Fac() : pow2(scale); + alphaEM = lhaUpPtr->alphaQED(); + if (alphaEM < 0.001) alphaEM = sigmaProcessPtr->alphaEMRen(); + alphaS = lhaUpPtr->alphaQCD(); + if (alphaS < 0.001) alphaS = sigmaProcessPtr->alphaSRen(); + Q2Ren = (scale < 0.) ? sigmaProcessPtr->Q2Ren() : pow2(scale); + x1Now = 2. * process[3].e() / infoPtr->eCM(); + x2Now = 2. * process[4].e() / infoPtr->eCM(); + Vec4 pSum = process[3].p() + process[4].p(); + sHat = pSum * pSum; + + // Read info on parton densities if provided. + if (lhaUpPtr->pdfIsSet()) { + pdf1 = lhaUpPtr->xpdf1(); + pdf2 = lhaUpPtr->xpdf2(); + Q2FacNow = pow2(lhaUpPtr->scalePDF()); + x1Now = lhaUpPtr->x1(); + x2Now = lhaUpPtr->x2(); + } + + // Reconstruct kinematics of 2 -> 2 processes from momenta. + if (nFin == 2) { + Vec4 pDifT = process[3].p() - process[5].p(); + tHat = pDifT * pDifT; + Vec4 pDifU = process[3].p() - process[6].p(); + uHat = pDifU * pDifU; + pTHatL = process[5].pT(); + m3 = process[5].m(); + m4 = process[6].m(); + Vec4 p5 = process[5].p(); + p5.bstback(pSum); + theta = p5.theta(); + phi = process[5].phi(); + } + } + + // Store information. + if (isHardest) { + infoPtr->setPDFalpha( id1Now, id2Now, pdf1, pdf2, Q2FacNow, + alphaEM, alphaS, Q2Ren); + infoPtr->setKin( x1Now, x2Now, sHat, tHat, uHat, pTHatL, m3, m4, + theta, phi); + } + infoPtr->setTypeMI( code(), pTHatL); + + // For Les Houches event store subprocess classification. + if (isLHA) { + int codeSub = lhaUpPtr->idProcess(); + ostringstream nameSub; + nameSub << "user process " << codeSub; + infoPtr->setSubType( nameSub.str(), codeSub, nFin); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Handle resonance decays. + +bool ProcessContainer::decayResonances( Event& process) { + + // Save current event-record size. + process.saveSize(); + bool physical = true; + bool newFlavours = false; + + // Do sequential chain of uncorrelated isotropic decays. + do { + physical = resDecaysPtr->next( process); + if (!physical) return false; + + // Check whether flavours should be correlated. + // (Currently only relevant for f fbar -> gamma*/Z0 gamma*/Z0.) + newFlavours = ( sigmaProcessPtr->weightDecayFlav( process) + < rndmPtr->flat() ); + + // Reset the decay chains if have to redo. + if (newFlavours) { + process.restoreSize(); + for (int i = 5; i < process.size(); ++i) process[i].statusPos(); + } + + // Loop back where required to generate new decays with new flavours. + } while (newFlavours); + + // Correct to nonisotropic decays. + phaseSpacePtr->decayKinematics( process); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Reset event generation statistics; but NOT maximum of cross section. + +void ProcessContainer::reset() { + + nTry = 0; + nSel = 0; + nAcc = 0; + nTryStat = 0; + sigmaSum = 0.; + sigma2Sum = 0.; + sigmaNeg = 0.; + sigmaAvg = 0.; + sigmaFin = 0.; + deltaFin = 0.; + +} + +//-------------------------------------------------------------------------- + +// Estimate integrated cross section and its uncertainty. + +void ProcessContainer::sigmaDelta() { + + // Initial values. No analysis meaningful unless accepted events. + nTryStat = nTry; + sigmaAvg = 0.; + sigmaFin = 0.; + deltaFin = 0.; + if (nAcc == 0) return; + + // Average value. + double nTryInv = 1. / nTry; + double nSelInv = 1. / nSel; + double nAccInv = 1. / nAcc; + sigmaAvg = sigmaSum * nTryInv ; + double fracAcc = nAcc * nSelInv; + sigmaFin = sigmaAvg * fracAcc; + + // Estimated error. Quadratic sum of cross section term and + // binomial from accept/reject step. + deltaFin = sigmaFin; + if (nAcc == 1) return; + double delta2Sig = (sigma2Sum *nTryInv - pow2(sigmaAvg)) * nTryInv + / pow2(sigmaAvg); + double delta2Veto = (nSel - nAcc) * nAccInv * nSelInv; + double delta2Sum = delta2Sig + delta2Veto; + deltaFin = sqrtpos(delta2Sum) * sigmaFin; + +} + +//========================================================================== + +// SetupContainer class. +// Turns list of user-desired processes into a vector of containers. + +//-------------------------------------------------------------------------- + +// Main routine to initialize list of processes. + +bool SetupContainers::init(vector& containerPtrs, + Settings& settings, ParticleData* particleDataPtr, CoupSUSY& coupSUSY) { + + // Reset process list, if filled in previous subrun. + if (containerPtrs.size() > 0) { + for (int i = 0; i < int(containerPtrs.size()); ++i) + delete containerPtrs[i]; + containerPtrs.clear(); + } + SigmaProcess* sigmaPtr; + + // Set up requested objects for soft QCD processes. + bool softQCD = settings.flag("SoftQCD:all"); + if (softQCD || settings.flag("SoftQCD:minBias")) { + sigmaPtr = new Sigma0minBias; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (softQCD || settings.flag("SoftQCD:elastic")) { + sigmaPtr = new Sigma0AB2AB; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (softQCD || settings.flag("SoftQCD:singleDiffractive")) { + sigmaPtr = new Sigma0AB2XB; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma0AB2AX; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (softQCD || settings.flag("SoftQCD:doubleDiffractive")) { + sigmaPtr = new Sigma0AB2XX; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for hard QCD processes. + bool hardQCD = settings.flag("HardQCD:all"); + if (hardQCD || settings.flag("HardQCD:gg2gg")) { + sigmaPtr = new Sigma2gg2gg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:gg2qqbar")) { + sigmaPtr = new Sigma2gg2qqbar; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:qg2qg")) { + sigmaPtr = new Sigma2qg2qg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:qq2qq")) { + sigmaPtr = new Sigma2qq2qq; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:qqbar2gg")) { + sigmaPtr = new Sigma2qqbar2gg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:qqbar2qqbarNew")) { + sigmaPtr = new Sigma2qqbar2qqbarNew; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for c cbar and b bbar, also hard QCD. + if (hardQCD || settings.flag("HardQCD:gg2ccbar")) { + sigmaPtr = new Sigma2gg2QQbar(4, 121); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:qqbar2ccbar")) { + sigmaPtr = new Sigma2qqbar2QQbar(4, 122); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:gg2bbbar")) { + sigmaPtr = new Sigma2gg2QQbar(5, 123); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD || settings.flag("HardQCD:qqbar2bbbar")) { + sigmaPtr = new Sigma2qqbar2QQbar(5, 124); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for hard QCD 2 -> 3 processes. + bool hardQCD3parton = settings.flag("HardQCD:3parton"); + if (hardQCD3parton || settings.flag("HardQCD:gg2ggg")) { + sigmaPtr = new Sigma3gg2ggg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qqbar2ggg")) { + sigmaPtr = new Sigma3qqbar2ggg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qg2qgg")) { + sigmaPtr = new Sigma3qg2qgg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qq2qqgDiff")) { + sigmaPtr = new Sigma3qq2qqgDiff; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qq2qqgSame")) { + sigmaPtr = new Sigma3qq2qqgSame; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qqbar2qqbargDiff")) { + sigmaPtr = new Sigma3qqbar2qqbargDiff; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qqbar2qqbargSame")) { + sigmaPtr = new Sigma3qqbar2qqbargSame; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:gg2qqbarg")) { + sigmaPtr = new Sigma3gg2qqbarg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qg2qqqbarDiff")) { + sigmaPtr = new Sigma3qg2qqqbarDiff; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hardQCD3parton || settings.flag("HardQCD:qg2qqqbarSame")) { + sigmaPtr = new Sigma3qg2qqqbarSame; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for prompt photon processes. + bool promptPhotons = settings.flag("PromptPhoton:all"); + if (promptPhotons + || settings.flag("PromptPhoton:qg2qgamma")) { + sigmaPtr = new Sigma2qg2qgamma; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (promptPhotons + || settings.flag("PromptPhoton:qqbar2ggamma")) { + sigmaPtr = new Sigma2qqbar2ggamma; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (promptPhotons + || settings.flag("PromptPhoton:gg2ggamma")) { + sigmaPtr = new Sigma2gg2ggamma; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (promptPhotons + || settings.flag("PromptPhoton:ffbar2gammagamma")) { + sigmaPtr = new Sigma2ffbar2gammagamma; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (promptPhotons + || settings.flag("PromptPhoton:gg2gammagamma")) { + sigmaPtr = new Sigma2gg2gammagamma; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for weak gauge boson t-channel exchange. + bool weakBosonExchanges = settings.flag("WeakBosonExchange:all"); + if (weakBosonExchanges + || settings.flag("WeakBosonExchange:ff2ff(t:gmZ)")) { + sigmaPtr = new Sigma2ff2fftgmZ; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonExchanges + || settings.flag("WeakBosonExchange:ff2ff(t:W)")) { + sigmaPtr = new Sigma2ff2fftW; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for weak gauge boson processes. + bool weakSingleBosons = settings.flag("WeakSingleBoson:all"); + if (weakSingleBosons + || settings.flag("WeakSingleBoson:ffbar2gmZ")) { + sigmaPtr = new Sigma1ffbar2gmZ; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakSingleBosons + || settings.flag("WeakSingleBoson:ffbar2W")) { + sigmaPtr = new Sigma1ffbar2W; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested object for s-channel gamma exchange. + // Subset of gamma*/Z0 above, intended for Multiple interactions. + if (settings.flag("WeakSingleBoson:ffbar2ffbar(s:gm)")) { + sigmaPtr = new Sigma2ffbar2ffbarsgm; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for weak gauge boson pair processes. + bool weakDoubleBosons = settings.flag("WeakDoubleBoson:all"); + if (weakDoubleBosons + || settings.flag("WeakDoubleBoson:ffbar2gmZgmZ")) { + sigmaPtr = new Sigma2ffbar2gmZgmZ; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakDoubleBosons + || settings.flag("WeakDoubleBoson:ffbar2ZW")) { + sigmaPtr = new Sigma2ffbar2ZW; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakDoubleBosons + || settings.flag("WeakDoubleBoson:ffbar2WW")) { + sigmaPtr = new Sigma2ffbar2WW; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for weak gauge boson + parton processes. + bool weakBosonAndPartons = settings.flag("WeakBosonAndParton:all"); + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:qqbar2gmZg")) { + sigmaPtr = new Sigma2qqbar2gmZg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:qg2gmZq")) { + sigmaPtr = new Sigma2qg2gmZq; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:ffbar2gmZgm")) { + sigmaPtr = new Sigma2ffbar2gmZgm; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:fgm2gmZf")) { + sigmaPtr = new Sigma2fgm2gmZf; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:qqbar2Wg")) { + sigmaPtr = new Sigma2qqbar2Wg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:qg2Wq")) { + sigmaPtr = new Sigma2qg2Wq; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:ffbar2Wgm")) { + sigmaPtr = new Sigma2ffbar2Wgm; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (weakBosonAndPartons + || settings.flag("WeakBosonAndParton:fgm2Wf")) { + sigmaPtr = new Sigma2fgm2Wf; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for photon collision processes. + bool photonCollisions = settings.flag("PhotonCollision:all"); + if (photonCollisions || settings.flag("PhotonCollision:gmgm2qqbar")) { + sigmaPtr = new Sigma2gmgm2ffbar(1, 261); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (photonCollisions || settings.flag("PhotonCollision:gmgm2ccbar")) { + sigmaPtr = new Sigma2gmgm2ffbar(4, 262); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (photonCollisions || settings.flag("PhotonCollision:gmgm2bbbar")) { + sigmaPtr = new Sigma2gmgm2ffbar(5, 263); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (photonCollisions || settings.flag("PhotonCollision:gmgm2ee")) { + sigmaPtr = new Sigma2gmgm2ffbar(11, 264); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (photonCollisions || settings.flag("PhotonCollision:gmgm2mumu")) { + sigmaPtr = new Sigma2gmgm2ffbar(13, 265); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (photonCollisions || settings.flag("PhotonCollision:gmgm2tautau")) { + sigmaPtr = new Sigma2gmgm2ffbar(15, 266); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for charmonium production + bool charmoniums = settings.flag("Charmonium:all"); + if (charmoniums || settings.flag("Charmonium:gg2QQbar[3S1(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3S11g(4, 401); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:gg2QQbar[3P0(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3PJ1g(4, 0, 402); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:gg2QQbar[3P1(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3PJ1g(4, 1, 403); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:gg2QQbar[3P2(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3PJ1g(4, 2, 404); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qg2QQbar[3P0(1)]q")) { + sigmaPtr = new Sigma2qg2QQbar3PJ1q(4, 0, 405); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qg2QQbar[3P1(1)]q")) { + sigmaPtr = new Sigma2qg2QQbar3PJ1q(4, 1, 406); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qg2QQbar[3P2(1)]q")) { + sigmaPtr = new Sigma2qg2QQbar3PJ1q(4, 2, 407); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qqbar2QQbar[3P0(1)]g")) { + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(4, 0, 408); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qqbar2QQbar[3P1(1)]g")) { + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(4, 1, 409); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qqbar2QQbar[3P2(1)]g")) { + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(4, 2, 410); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:gg2QQbar[3S1(8)]g")) { + sigmaPtr = new Sigma2gg2QQbarX8g(4, 0, 411); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:gg2QQbar[1S0(8)]g")) { + sigmaPtr = new Sigma2gg2QQbarX8g(4, 1, 412); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:gg2QQbar[3PJ(8)]g")) { + sigmaPtr = new Sigma2gg2QQbarX8g(4, 2, 413); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qg2QQbar[3S1(8)]q")) { + sigmaPtr = new Sigma2qg2QQbarX8q(4, 0, 414); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qg2QQbar[1S0(8)]q")) { + sigmaPtr = new Sigma2qg2QQbarX8q(4, 1, 415); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qg2QQbar[3PJ(8)]q")) { + sigmaPtr = new Sigma2qg2QQbarX8q(4, 2, 416); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qqbar2QQbar[3S1(8)]g")) { + sigmaPtr = new Sigma2qqbar2QQbarX8g(4, 0, 417); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qqbar2QQbar[1S0(8)]g")) { + sigmaPtr = new Sigma2qqbar2QQbarX8g(4, 1, 418); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (charmoniums || settings.flag("Charmonium:qqbar2QQbar[3PJ(8)]g")) { + sigmaPtr = new Sigma2qqbar2QQbarX8g(4, 2, 419); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for bottomonium production + bool bottomoniums = settings.flag("Bottomonium:all"); + if (bottomoniums || settings.flag("Bottomonium:gg2QQbar[3S1(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3S11g(5, 501); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:gg2QQbar[3P0(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3PJ1g(5, 0, 502); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:gg2QQbar[3P1(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3PJ1g(5, 1, 503); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:gg2QQbar[3P2(1)]g")) { + sigmaPtr = new Sigma2gg2QQbar3PJ1g(5, 2, 504); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qg2QQbar[3P0(1)]q")) { + sigmaPtr = new Sigma2qg2QQbar3PJ1q(5, 0, 505); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qg2QQbar[3P1(1)]q")) { + sigmaPtr = new Sigma2qg2QQbar3PJ1q(5, 1, 506); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qg2QQbar[3P2(1)]q")) { + sigmaPtr = new Sigma2qg2QQbar3PJ1q(5, 2, 507); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qqbar2QQbar[3P0(1)]g")) { + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(5, 0, 508); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qqbar2QQbar[3P1(1)]g")) { + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(5, 1, 509); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qqbar2QQbar[3P2(1)]g")) { + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(5, 2, 510); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:gg2QQbar[3S1(8)]g")) { + sigmaPtr = new Sigma2gg2QQbarX8g(5, 0, 511); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:gg2QQbar[1S0(8)]g")) { + sigmaPtr = new Sigma2gg2QQbarX8g(5, 1, 512); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:gg2QQbar[3PJ(8)]g")) { + sigmaPtr = new Sigma2gg2QQbarX8g(5, 2, 513); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qg2QQbar[3S1(8)]q")) { + sigmaPtr = new Sigma2qg2QQbarX8q(5, 0, 514); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qg2QQbar[1S0(8)]q")) { + sigmaPtr = new Sigma2qg2QQbarX8q(5, 1, 515); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qg2QQbar[3PJ(8)]q")) { + sigmaPtr = new Sigma2qg2QQbarX8q(5, 2, 516); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qqbar2QQbar[3S1(8)]g")) { + sigmaPtr = new Sigma2qqbar2QQbarX8g(5, 0, 517); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qqbar2QQbar[1S0(8)]g")) { + sigmaPtr = new Sigma2qqbar2QQbarX8g(5, 1, 518); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bottomoniums || settings.flag("Bottomonium:qqbar2QQbar[3PJ(8)]g")) { + sigmaPtr = new Sigma2qqbar2QQbarX8g(5, 2, 519); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for top production + bool tops = settings.flag("Top:all"); + if (tops || settings.flag("Top:gg2ttbar")) { + sigmaPtr = new Sigma2gg2QQbar(6, 601); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tops || settings.flag("Top:qqbar2ttbar")) { + sigmaPtr = new Sigma2qqbar2QQbar(6, 602); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tops || settings.flag("Top:qq2tq(t:W)")) { + sigmaPtr = new Sigma2qq2QqtW(6, 603); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tops || settings.flag("Top:ffbar2ttbar(s:gmZ)")) { + sigmaPtr = new Sigma2ffbar2FFbarsgmZ(6, 604); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tops || settings.flag("Top:ffbar2tqbar(s:W)")) { + sigmaPtr = new Sigma2ffbar2FfbarsW(6, 0, 605); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tops || settings.flag("Top:gmgm2ttbar")) { + sigmaPtr = new Sigma2gmgm2ffbar(6, 606); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for fourth-generation b' production + bool bPrimes = settings.flag("FourthBottom:all"); + if (bPrimes || settings.flag("FourthBottom:gg2bPrimebPrimebar")) { + sigmaPtr = new Sigma2gg2QQbar(7, 801); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bPrimes || settings.flag("FourthBottom:qqbar2bPrimebPrimebar")) { + sigmaPtr = new Sigma2qqbar2QQbar(7, 802); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bPrimes || settings.flag("FourthBottom:qq2bPrimeq(t:W)")) { + sigmaPtr = new Sigma2qq2QqtW(7, 803); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bPrimes || settings.flag("FourthBottom:ffbar2bPrimebPrimebar(s:gmZ)")) { + sigmaPtr = new Sigma2ffbar2FFbarsgmZ(7, 804); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bPrimes || settings.flag("FourthBottom:ffbar2bPrimeqbar(s:W)")) { + sigmaPtr = new Sigma2ffbar2FfbarsW(7, 0, 805); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (bPrimes || settings.flag("FourthBottom:ffbar2bPrimetbar(s:W)")) { + sigmaPtr = new Sigma2ffbar2FfbarsW(7, 6, 806); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for fourth-generation t' production + bool tPrimes = settings.flag("FourthTop:all"); + if (tPrimes || settings.flag("FourthTop:gg2tPrimetPrimebar")) { + sigmaPtr = new Sigma2gg2QQbar(8, 821); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tPrimes || settings.flag("FourthTop:qqbar2tPrimetPrimebar")) { + sigmaPtr = new Sigma2qqbar2QQbar(8, 822); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tPrimes || settings.flag("FourthTop:qq2tPrimeq(t:W)")) { + sigmaPtr = new Sigma2qq2QqtW(8, 823); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tPrimes || settings.flag("FourthTop:ffbar2tPrimetPrimebar(s:gmZ)")) { + sigmaPtr = new Sigma2ffbar2FFbarsgmZ(8, 824); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (tPrimes || settings.flag("FourthTop:ffbar2tPrimeqbar(s:W)")) { + sigmaPtr = new Sigma2ffbar2FfbarsW(8, 0, 825); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for two different fourth-generation fermions. + if (bPrimes || tPrimes + || settings.flag("FourthPair:ffbar2tPrimebPrimebar(s:W)")) { + sigmaPtr = new Sigma2ffbar2FfbarsW(8, 7, 841); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("FourthPair:ffbar2tauPrimenuPrimebar(s:W)")) { + sigmaPtr = new Sigma2ffbar2FfbarsW(17, 18, 842); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Flag for global choice between SM and BSM Higgses. + bool useBSMHiggses = settings.flag("Higgs:useBSM"); + + // Set up requested objects for Standard-Model Higgs production. + if (!useBSMHiggses) { + bool HiggsesSM = settings.flag("HiggsSM:all"); + if (HiggsesSM || settings.flag("HiggsSM:ffbar2H")) { + sigmaPtr = new Sigma1ffbar2H(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:gg2H")) { + sigmaPtr = new Sigma1gg2H(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:gmgm2H")) { + sigmaPtr = new Sigma1gmgm2H(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:ffbar2HZ")) { + sigmaPtr = new Sigma2ffbar2HZ(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:ffbar2HW")) { + sigmaPtr = new Sigma2ffbar2HW(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:ff2Hff(t:ZZ)")) { + sigmaPtr = new Sigma3ff2HfftZZ(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:ff2Hff(t:WW)")) { + sigmaPtr = new Sigma3ff2HfftWW(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:gg2Httbar")) { + sigmaPtr = new Sigma3gg2HQQbar(6,0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesSM || settings.flag("HiggsSM:qqbar2Httbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(6,0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Further Standard-Model Higgs processes, not included in "all". + if (settings.flag("HiggsSM:qg2Hq")) { + sigmaPtr = new Sigma2qg2Hq(4,0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2Hq(5,0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsSM:gg2Hbbbar")) { + sigmaPtr = new Sigma3gg2HQQbar(5,0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsSM:qqbar2Hbbbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(5,0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsSM:gg2Hg(l:t)")) { + sigmaPtr = new Sigma2gg2Hglt(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsSM:qg2Hq(l:t)")) { + sigmaPtr = new Sigma2qg2Hqlt(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsSM:qqbar2Hg(l:t)")) { + sigmaPtr = new Sigma2qqbar2Hglt(0); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + + // Common switch for the group of Higgs production BSM. + if (useBSMHiggses) { + bool HiggsesBSM = settings.flag("HiggsBSM:all"); + + // Set up requested objects for BSM H1 production. + bool HiggsesH1 = settings.flag("HiggsBSM:allH1"); + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:ffbar2H1")) { + sigmaPtr = new Sigma1ffbar2H(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:gg2H1")) { + sigmaPtr = new Sigma1gg2H(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:gmgm2H1")) { + sigmaPtr = new Sigma1gmgm2H(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:ffbar2H1Z")) { + sigmaPtr = new Sigma2ffbar2HZ(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:ffbar2H1W")) { + sigmaPtr = new Sigma2ffbar2HW(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:ff2H1ff(t:ZZ)")) { + sigmaPtr = new Sigma3ff2HfftZZ(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:ff2H1ff(t:WW)")) { + sigmaPtr = new Sigma3ff2HfftWW(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:gg2H1ttbar")) { + sigmaPtr = new Sigma3gg2HQQbar(6,1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH1 || settings.flag("HiggsBSM:qqbar2H1ttbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(6,1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Further BSM H1 processes, not included in "all". + if (settings.flag("HiggsBSM:qg2H1q")) { + sigmaPtr = new Sigma2qg2Hq(4,1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2Hq(5,1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:gg2H1bbbar")) { + sigmaPtr = new Sigma3gg2HQQbar(5,1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qqbar2H1bbbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(5,1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:gg2H1g(l:t)")) { + sigmaPtr = new Sigma2gg2Hglt(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qg2H1q(l:t)")) { + sigmaPtr = new Sigma2qg2Hqlt(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qqbar2H1g(l:t)")) { + sigmaPtr = new Sigma2qqbar2Hglt(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for BSM H2 production. + bool HiggsesH2 = settings.flag("HiggsBSM:allH2"); + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:ffbar2H2")) { + sigmaPtr = new Sigma1ffbar2H(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:gg2H2")) { + sigmaPtr = new Sigma1gg2H(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:gmgm2H2")) { + sigmaPtr = new Sigma1gmgm2H(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:ffbar2H2Z")) { + sigmaPtr = new Sigma2ffbar2HZ(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:ffbar2H2W")) { + sigmaPtr = new Sigma2ffbar2HW(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:ff2H2ff(t:ZZ)")) { + sigmaPtr = new Sigma3ff2HfftZZ(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:ff2H2ff(t:WW)")) { + sigmaPtr = new Sigma3ff2HfftWW(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:gg2H2ttbar")) { + sigmaPtr = new Sigma3gg2HQQbar(6,2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesH2 || settings.flag("HiggsBSM:qqbar2H2ttbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(6,2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Further BSM H2 processes, not included in "all". + if (settings.flag("HiggsBSM:qg2H2q")) { + sigmaPtr = new Sigma2qg2Hq(4,2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2Hq(5,2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:gg2H2bbbar")) { + sigmaPtr = new Sigma3gg2HQQbar(5,2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qqbar2H2bbbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(5,2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:gg2H2g(l:t)")) { + sigmaPtr = new Sigma2gg2Hglt(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qg2H2q(l:t)")) { + sigmaPtr = new Sigma2qg2Hqlt(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qqbar2H2g(l:t)")) { + sigmaPtr = new Sigma2qqbar2Hglt(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for BSM A3 production. + bool HiggsesA3 = settings.flag("HiggsBSM:allA3"); + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:ffbar2A3")) { + sigmaPtr = new Sigma1ffbar2H(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:gg2A3")) { + sigmaPtr = new Sigma1gg2H(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:gmgm2A3")) { + sigmaPtr = new Sigma1gmgm2H(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:ffbar2A3Z")) { + sigmaPtr = new Sigma2ffbar2HZ(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:ffbar2A3W")) { + sigmaPtr = new Sigma2ffbar2HW(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:ff2A3ff(t:ZZ)")) { + sigmaPtr = new Sigma3ff2HfftZZ(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:ff2A3ff(t:WW)")) { + sigmaPtr = new Sigma3ff2HfftWW(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:gg2A3ttbar")) { + sigmaPtr = new Sigma3gg2HQQbar(6,3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesA3 || settings.flag("HiggsBSM:qqbar2A3ttbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(6,3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Further BSM A3 processes, not included in "all". + if (settings.flag("HiggsBSM:qg2A3q")) { + sigmaPtr = new Sigma2qg2Hq(4,3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2Hq(5,3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:gg2A3bbbar")) { + sigmaPtr = new Sigma3gg2HQQbar(5,3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qqbar2A3bbbar")) { + sigmaPtr = new Sigma3qqbar2HQQbar(5,3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:gg2A3g(l:t)")) { + sigmaPtr = new Sigma2gg2Hglt(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qg2A3q(l:t)")) { + sigmaPtr = new Sigma2qg2Hqlt(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("HiggsBSM:qqbar2A3g(l:t)")) { + sigmaPtr = new Sigma2qqbar2Hglt(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for Charged Higgs production + bool HiggsesChg = settings.flag("HiggsBSM:allH+-"); + if (HiggsesBSM || HiggsesChg || settings.flag("HiggsBSM:ffbar2H+-")) { + sigmaPtr = new Sigma1ffbar2Hchg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesChg || settings.flag("HiggsBSM:bg2H+-t")) { + sigmaPtr = new Sigma2qg2Hchgq(6, 1062, "b g -> H+- t"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for Higgs pair-production + bool HiggsesPairs = settings.flag("HiggsBSM:allHpair"); + if (HiggsesBSM || HiggsesPairs || settings.flag("HiggsBSM:ffbar2A3H1")) { + sigmaPtr = new Sigma2ffbar2A3H12(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesPairs || settings.flag("HiggsBSM:ffbar2A3H2")) { + sigmaPtr = new Sigma2ffbar2A3H12(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesPairs || settings.flag("HiggsBSM:ffbar2H+-H1")) { + sigmaPtr = new Sigma2ffbar2HchgH12(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesPairs || settings.flag("HiggsBSM:ffbar2H+-H2")) { + sigmaPtr = new Sigma2ffbar2HchgH12(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (HiggsesBSM || HiggsesPairs || settings.flag("HiggsBSM:ffbar2H+H-")) { + sigmaPtr = new Sigma2ffbar2HposHneg(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + + // Set up requested objects for SUSY pair processes. + bool SUSYs = settings.flag("SUSY:all"); + bool nmssm = settings.flag("SLHA:NMSSM"); + + // Preselected SUSY codes + int codeA = max( abs(settings.mode("SUSY:idA")), + abs(settings.mode("SUSY:idB"))); + int codeB = min( abs(settings.mode("SUSY:idA")), + abs(settings.mode("SUSY:idB"))); + + // MSSM: 4 neutralinos + int nNeut = 4; + if (nmssm) nNeut = 5; + + // Gluino-gluino + if (SUSYs || settings.flag("SUSY:gg2gluinogluino")) { + sigmaPtr = new Sigma2gg2gluinogluino(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (SUSYs || settings.flag("SUSY:qqbar2gluinogluino")) { + sigmaPtr = new Sigma2qqbar2gluinogluino(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Gluino-squark + if (SUSYs || settings.flag("SUSY:qg2squarkgluino")) { + int iproc = 1202; + for (int idx = 1; idx <= 6; ++idx) { + for (int iso = 1; iso <= 2; ++iso) { + iproc++; + int id3 = iso + ((idx <= 3) ? 1000000+2*(idx-1) : 2000000+2*(idx-4)); + int id4 = 1000021; + // Skip if specific codes not asked for + if (codeA != 0 && codeA != abs(id3) && codeA != abs(id4)) continue; + if (codeB != 0 && ( codeA != max(abs(id3),abs(id4)) + || codeB != min(abs(id3),abs(id4)) ) ) continue; + sigmaPtr = new Sigma2qg2squarkgluino(id3,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + + // Squark-antisquark (gg initiated) + if (SUSYs || settings.flag("SUSY:gg2squarkantisquark")) { + int iproc = 1214; + for (int idx = 1; idx <= 6; ++idx) { + for (int iso = 1; iso <= 2; ++iso) { + iproc++; + int id = iso + ((idx <= 3) ? 1000000+2*(idx-1) : 2000000+2*(idx-4)); + + // Skip if specific codes not asked for + if (codeA != 0 && codeA != abs(id)) continue; + if (codeA != 0 && codeB != 0 && codeB != abs(id)) continue; + sigmaPtr = new Sigma2gg2squarkantisquark(id,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + + // Squark-antisquark (qqbar initiated) + if (SUSYs || settings.flag("SUSY:qqbar2squarkantisquark")) { + int iproc = 1230; + for (int idx = 1; idx <= 6; ++idx) { + for (int iso = 1; iso <= 2; ++iso) { + for (int jso = iso; jso >= 1; --jso) { + for (int jdx = 1; jdx <= 6; ++jdx) { + if (iso == jso && jdx < idx) continue; + int id1 = iso + ((idx <= 3) ? 1000000+2*(idx-1) + : 2000000+2*(idx-4)); + int id2 = jso + ((jdx <= 3) ? 1000000+2*(jdx-1) + : 2000000+2*(jdx-4)); + // Update process number counter (for ~q~q, +2 if not self-conj) + //if (iproc == 1302) iproc=1310; + iproc++; + if (iso == jso && id1 != id2) iproc++; + // Skip if specific codes not asked for + if (codeA != 0 && codeA != abs(id1) && codeA != abs(id2)) continue; + if (codeB != 0 && ( codeA != max(abs(id1),abs(id2)) || + codeB != min(abs(id1),abs(id2)) ) ) continue; + if (iso == jso && id1 != id2) { + sigmaPtr = new Sigma2qqbar2squarkantisquark(id1,-id2,iproc-1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2squarkantisquark(id2,-id1,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } else { + sigmaPtr = new Sigma2qqbar2squarkantisquark(id1,-id2,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + } + } + } + + // Squark-squark + if (SUSYs || settings.flag("SUSY:qq2squarksquark")) { + int iproc = 1350; + for (int idx = 1; idx <= 6; ++idx) { + for (int iso = 1; iso <= 2; ++iso) { + for (int jso = iso; jso >= 1; jso--) { + for (int jdx = 1; jdx <= 6; ++jdx) { + if (iso == jso && jdx < idx) continue; + iproc++; + int id1 = iso + ((idx <= 3) ? 1000000+2*(idx-1) : 2000000+2*(idx-4)); + int id2 = jso + ((jdx <= 3) ? 1000000+2*(jdx-1) : 2000000+2*(jdx-4)); + // Skip if specific codes not asked for + if (codeA != 0 && codeA != abs(id1) && codeA != abs(id2)) continue; + if (codeB != 0 && ( codeA != max(abs(id1),abs(id2)) + || codeB != min(abs(id1),abs(id2)) ) ) continue; + sigmaPtr = new Sigma2qq2squarksquark(id1,id2,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + } + } + + // Neutralino + squark + if (SUSYs || settings.flag("SUSY:qg2chi0squark")) { + int iproc = 1430; + for (int iNeut= 1; iNeut <= nNeut; iNeut++) { + for (int idx = 1; idx <= 6; idx++) { + bool isUp = false; + for (int iso = 1; iso <= 2; iso++) { + if (iso == 2) isUp = true; + iproc++; + int id3 = coupSUSY.idNeut(iNeut); + int id4 = iso + ((idx <= 3) ? 1000000+2*(idx-1) : 2000000+2*(idx-4)); + if (codeA != 0 && codeA != abs(id3) && codeA != abs(id4)) continue; + if (codeB != 0 && codeB != min(abs(id3),abs(id4)) ) continue; + sigmaPtr = new Sigma2qg2chi0squark(iNeut,idx,isUp,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + } + + // Chargino + squark + if (SUSYs || settings.flag("SUSY:qg2chi+-squark")) { + int iproc = 1490; + for (int iChar = 1; iChar <= 2; iChar++) { + for (int idx = 1; idx <= 6; idx++) { + bool isUp = false; + for (int iso = 1; iso <= 2; iso++) { + if (iso == 2) isUp = true; + iproc++; + int id3 = coupSUSY.idChar(iChar); + int id4 = iso + ((idx <= 3) ? 1000000+2*(idx-1) : 2000000+2*(idx-4)); + if (codeA != 0 && codeA != abs(id3) && codeA != abs(id4)) continue; + if (codeB != 0 && codeB != min(abs(id3),abs(id4)) ) continue; + sigmaPtr = new Sigma2qg2charsquark(iChar,idx,isUp,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + } + + // Neutralino pairs + if (SUSYs || settings.flag("SUSY:qqbar2chi0chi0")) { + int iproc = 1550; + for (int iNeut2 = 1; iNeut2 <= nNeut; iNeut2++) { + for (int iNeut1 = 1; iNeut1 <= iNeut2; iNeut1++) { + iproc++; + if (codeA != 0 && codeA != abs(coupSUSY.idNeut(iNeut1)) + && codeA != abs(coupSUSY.idNeut(iNeut2))) continue; + if (codeB != 0 && codeB != min(abs(coupSUSY.idNeut(iNeut1)), + abs(coupSUSY.idNeut(iNeut2))) ) continue; + sigmaPtr = new Sigma2qqbar2chi0chi0(iNeut1, iNeut2,iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + + // Neutralino-Chargino + if (SUSYs || settings.flag("SUSY:qqbar2chi+-chi0")) { + int iproc = 1570; + for (int iNeut = 1; iNeut <= nNeut; iNeut++) { + for (int iChar = 1; iChar <= 2; ++iChar) { + iproc += 2; + if (codeA != 0 && codeA != coupSUSY.idNeut(iNeut) + && codeA != coupSUSY.idChar(iChar)) continue; + if (codeB != 0 + && ( codeA != max(coupSUSY.idNeut(iNeut),coupSUSY.idChar(iChar)) + || codeB != min(coupSUSY.idNeut(iNeut),coupSUSY.idChar(iChar))) + ) continue; + sigmaPtr = new Sigma2qqbar2charchi0( iChar, iNeut, iproc-1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2charchi0(-iChar, iNeut, iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + + // Chargino-Chargino + if (SUSYs || settings.flag("SUSY:qqbar2chi+chi-")) { + int iproc = 1590; + for (int i = 1; i <= 2; ++i) { + for (int j = 1; j <= 2; ++j) { + iproc++; + if (codeA != 0 && codeA != abs(coupSUSY.idChar(i)) + && codeA != abs(coupSUSY.idChar(j))) continue; + if (codeB != 0 + && ( codeA != max(coupSUSY.idChar(i),coupSUSY.idChar(j)) + || codeB != min(coupSUSY.idChar(i),coupSUSY.idChar(j)) ) ) + continue; + sigmaPtr = new Sigma2qqbar2charchar( i,-j, iproc); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + } + } + + // Set up requested objects for New-Gauge-Boson processes. + if (settings.flag("NewGaugeBoson:ffbar2gmZZprime")) { + sigmaPtr = new Sigma1ffbar2gmZZprime(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("NewGaugeBoson:ffbar2Wprime")) { + sigmaPtr = new Sigma1ffbar2Wprime(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("NewGaugeBoson:ffbar2R0")) { + sigmaPtr = new Sigma1ffbar2Rhorizontal(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for Left-Right-Symmetry processes. + bool leftrights = settings.flag("LeftRightSymmmetry:all"); + if (leftrights || settings.flag("LeftRightSymmmetry:ffbar2ZR")) { + sigmaPtr = new Sigma1ffbar2ZRight(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:ffbar2WR")) { + sigmaPtr = new Sigma1ffbar2WRight(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:ll2HL")) { + sigmaPtr = new Sigma1ll2Hchgchg(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:lgm2HLe")) { + sigmaPtr = new Sigma2lgm2Hchgchgl(1, 11); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:lgm2HLmu")) { + sigmaPtr = new Sigma2lgm2Hchgchgl(1, 13); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:lgm2HLtau")) { + sigmaPtr = new Sigma2lgm2Hchgchgl(1, 15); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:ff2HLff")) { + sigmaPtr = new Sigma3ff2HchgchgfftWW(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:ffbar2HLHL")) { + sigmaPtr = new Sigma2ffbar2HchgchgHchgchg(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:ll2HR")) { + sigmaPtr = new Sigma1ll2Hchgchg(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:lgm2HRe")) { + sigmaPtr = new Sigma2lgm2Hchgchgl(2, 11); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:lgm2HRmu")) { + sigmaPtr = new Sigma2lgm2Hchgchgl(2, 13); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:lgm2HRtau")) { + sigmaPtr = new Sigma2lgm2Hchgchgl(2, 15); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:ff2HRff")) { + sigmaPtr = new Sigma3ff2HchgchgfftWW(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leftrights || settings.flag("LeftRightSymmmetry:ffbar2HRHR")) { + sigmaPtr = new Sigma2ffbar2HchgchgHchgchg(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for leptoquark LQ processes. + bool leptoquarks = settings.flag("LeptoQuark:all"); + if (leptoquarks || settings.flag("LeptoQuark:ql2LQ")) { + sigmaPtr = new Sigma1ql2LeptoQuark; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leptoquarks || settings.flag("LeptoQuark:qg2LQl")) { + sigmaPtr = new Sigma2qg2LeptoQuarkl; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leptoquarks || settings.flag("LeptoQuark:gg2LQLQbar")) { + sigmaPtr = new Sigma2gg2LQLQbar; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (leptoquarks || settings.flag("LeptoQuark:qqbar2LQLQbar")) { + sigmaPtr = new Sigma2qqbar2LQLQbar; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for excited-fermion processes. + bool excitedfermions = settings.flag("ExcitedFermion:all"); + if (excitedfermions || settings.flag("ExcitedFermion:dg2dStar")) { + sigmaPtr = new Sigma1qg2qStar(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:ug2uStar")) { + sigmaPtr = new Sigma1qg2qStar(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:sg2sStar")) { + sigmaPtr = new Sigma1qg2qStar(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:cg2cStar")) { + sigmaPtr = new Sigma1qg2qStar(4); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:bg2bStar")) { + sigmaPtr = new Sigma1qg2qStar(5); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:egm2eStar")) { + sigmaPtr = new Sigma1lgm2lStar(11); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:mugm2muStar")) { + sigmaPtr = new Sigma1lgm2lStar(13); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:taugm2tauStar")) { + sigmaPtr = new Sigma1lgm2lStar(15); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qq2dStarq")) { + sigmaPtr = new Sigma2qq2qStarq(1); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qq2uStarq")) { + sigmaPtr = new Sigma2qq2qStarq(2); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qq2sStarq")) { + sigmaPtr = new Sigma2qq2qStarq(3); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qq2cStarq")) { + sigmaPtr = new Sigma2qq2qStarq(4); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qq2bStarq")) { + sigmaPtr = new Sigma2qq2qStarq(5); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qqbar2eStare")) { + sigmaPtr = new Sigma2qqbar2lStarlbar(11); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qqbar2nueStarnue")) { + sigmaPtr = new Sigma2qqbar2lStarlbar(12); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qqbar2muStarmu")) { + sigmaPtr = new Sigma2qqbar2lStarlbar(13); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qqbar2numuStarnumu")) { + sigmaPtr = new Sigma2qqbar2lStarlbar(14); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qqbar2tauStartau")) { + sigmaPtr = new Sigma2qqbar2lStarlbar(15); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (excitedfermions || settings.flag("ExcitedFermion:qqbar2nutauStarnutau")) { + sigmaPtr = new Sigma2qqbar2lStarlbar(16); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for contact interaction processes. + if (settings.flag("ContactInteractions:QCqq2qq")) { + sigmaPtr = new Sigma2QCqq2qq(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ContactInteractions:QCqqbar2qqbar")) { + sigmaPtr = new Sigma2QCqqbar2qqbar(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set spin of particles in the Hidden Valley scenario. + int spinFv = settings.mode("HiddenValley:spinFv"); + for (int i = 1; i < 7; ++i) { + if (particleDataPtr->spinType( 4900000 + i) != spinFv + 1) + particleDataPtr->spinType( 4900000 + i, spinFv + 1); + if (particleDataPtr->spinType( 4900010 + i) != spinFv + 1) + particleDataPtr->spinType( 4900010 + i, spinFv + 1); + } + if (spinFv != 1) { + if (particleDataPtr->spinType( 4900101) != 2) + particleDataPtr->spinType( 4900101, 2); + } else { + int spinqv = settings.mode("HiddenValley:spinqv"); + if (particleDataPtr->spinType( 4900101) != 2 * spinqv + 1) + particleDataPtr->spinType( 4900101, 2 * spinqv + 1); + } + + // Set up requested objects for HiddenValley processes. + bool hiddenvalleys = settings.flag("HiddenValley:all"); + if (hiddenvalleys || settings.flag("HiddenValley:gg2DvDvbar")) { + sigmaPtr = new Sigma2gg2qGqGbar( 4900001, 4901, spinFv, + "g g -> Dv Dvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:gg2UvUvbar")) { + sigmaPtr = new Sigma2gg2qGqGbar( 4900002, 4902, spinFv, + "g g -> Uv Uvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:gg2SvSvbar")) { + sigmaPtr = new Sigma2gg2qGqGbar( 4900003, 4903, spinFv, + "g g -> Sv Svbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:gg2CvCvbar")) { + sigmaPtr = new Sigma2gg2qGqGbar( 4900004, 4904, spinFv, + "g g -> Cv Cvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:gg2BvBvbar")) { + sigmaPtr = new Sigma2gg2qGqGbar( 4900005, 4905, spinFv, + "g g -> Bv Bvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:gg2TvTvbar")) { + sigmaPtr = new Sigma2gg2qGqGbar( 4900006, 4906, spinFv, + "g g -> Tv Tvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:qqbar2DvDvbar")) { + sigmaPtr = new Sigma2qqbar2qGqGbar( 4900001, 4911, spinFv, + "q qbar -> Dv Dvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:qqbar2UvUvbar")) { + sigmaPtr = new Sigma2qqbar2qGqGbar( 4900002, 4912, spinFv, + "q qbar -> Uv Uvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:qqbar2SvSvbar")) { + sigmaPtr = new Sigma2qqbar2qGqGbar( 4900003, 4913, spinFv, + "q qbar -> Sv Svbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:qqbar2CvCvbar")) { + sigmaPtr = new Sigma2qqbar2qGqGbar( 4900004, 4914, spinFv, + "q qbar -> Cv Cvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:qqbar2BvBvbar")) { + sigmaPtr = new Sigma2qqbar2qGqGbar( 4900005, 4915, spinFv, + "q qbar -> Bv Bvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:qqbar2TvTvbar")) { + sigmaPtr = new Sigma2qqbar2qGqGbar( 4900006, 4916, spinFv, + "q qbar -> Tv Tvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2DvDvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900001, 4921, spinFv, + "f fbar -> Dv Dvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2UvUvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900002, 4922, spinFv, + "f fbar -> Uv Uvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2SvSvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900003, 4923, spinFv, + "f fbar -> Sv Svbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2CvCvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900004, 4924, spinFv, + "f fbar -> Cv Cvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2BvBvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900005, 4925, spinFv, + "f fbar -> Bv Bvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2TvTvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900006, 4926, spinFv, + "f fbar -> Tv Tvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2EvEvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900011, 4931, spinFv, + "f fbar -> Ev Evbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2nuEvnuEvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900012, 4932, spinFv, + "f fbar -> nuEv nuEvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2MUvMUvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900013, 4933, spinFv, + "f fbar -> MUv MUvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2nuMUvnuMUvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900014, 4934, spinFv, + "f fbar -> nuMUv nuMUvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2TAUvTAUvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900015, 4935, spinFv, + "f fbar -> TAUv TAUvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (hiddenvalleys || settings.flag("HiddenValley:ffbar2nuTAUvnuTAUvbar")) { + sigmaPtr = new Sigma2ffbar2fGfGbar( 4900016, 4936, spinFv, + "f fbar -> nuTAUv nuTAUvbar"); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for RS extra-dimensional G* processes. + bool extraDimGstars = settings.flag("ExtraDimensionsG*:all"); + if (extraDimGstars || settings.flag("ExtraDimensionsG*:gg2G*")) { + sigmaPtr = new Sigma1gg2GravitonStar; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (extraDimGstars || settings.flag("ExtraDimensionsG*:ffbar2G*")) { + sigmaPtr = new Sigma1ffbar2GravitonStar; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsG*:gg2G*g")) { + sigmaPtr = new Sigma2gg2GravitonStarg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsG*:qg2G*q")) { + sigmaPtr = new Sigma2qg2GravitonStarq; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsG*:qqbar2G*g")) { + sigmaPtr = new Sigma2qqbar2GravitonStarg; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for RS extra-dimensional KKgluon processes. + if (settings.flag("ExtraDimensionsG*:qqbar2KKgluon*")) { + sigmaPtr = new Sigma1qqbar2KKgluonStar; + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // NOAM: Set up requested objects for TEV extra-dimensional processes. + if (settings.flag("ExtraDimensionsTEV:ffbar2ffbar")) { + sigmaPtr = new Sigma2ffbar2TEVffbar(13); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for large extra-dimensional G processes. + bool extraDimLEDmono = settings.flag("ExtraDimensionsLED:monojet"); + if (extraDimLEDmono || settings.flag("ExtraDimensionsLED:gg2Gg")) { + sigmaPtr = new Sigma2gg2LEDUnparticleg( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (extraDimLEDmono || settings.flag("ExtraDimensionsLED:qg2Gq")) { + sigmaPtr = new Sigma2qg2LEDUnparticleq( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (extraDimLEDmono || settings.flag("ExtraDimensionsLED:qqbar2Gg")) { + sigmaPtr = new Sigma2qqbar2LEDUnparticleg( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsLED:ffbar2GZ")) { + sigmaPtr = new Sigma2ffbar2LEDUnparticleZ( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsLED:ffbar2Ggamma")) { + sigmaPtr = new Sigma2ffbar2LEDUnparticlegamma( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsLED:ffbar2gammagamma")) { + sigmaPtr = new Sigma2ffbar2LEDgammagamma( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsLED:gg2gammagamma")) { + sigmaPtr = new Sigma2gg2LEDgammagamma( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsLED:ffbar2llbar")) { + sigmaPtr = new Sigma2ffbar2LEDllbar( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsLED:gg2llbar")) { + sigmaPtr = new Sigma2gg2LEDllbar( true ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Set up requested objects for unparticle processes. + bool extraDimUnpartmono = settings.flag("ExtraDimensionsUnpart:monojet"); + if (extraDimUnpartmono || settings.flag("ExtraDimensionsUnpart:gg2Ug")) { + sigmaPtr = new Sigma2gg2LEDUnparticleg( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (extraDimUnpartmono || settings.flag("ExtraDimensionsUnpart:qg2Uq")) { + sigmaPtr = new Sigma2qg2LEDUnparticleq( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (extraDimUnpartmono || settings.flag("ExtraDimensionsUnpart:qqbar2Ug")) { + sigmaPtr = new Sigma2qqbar2LEDUnparticleg( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsUnpart:ffbar2UZ")) { + sigmaPtr = new Sigma2ffbar2LEDUnparticleZ( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsUnpart:ffbar2Ugamma")) { + sigmaPtr = new Sigma2ffbar2LEDUnparticlegamma( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsUnpart:ffbar2gammagamma")) { + sigmaPtr = new Sigma2ffbar2LEDgammagamma( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsUnpart:gg2gammagamma")) { + sigmaPtr = new Sigma2gg2LEDgammagamma( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsUnpart:ffbar2llbar")) { + sigmaPtr = new Sigma2ffbar2LEDllbar( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + if (settings.flag("ExtraDimensionsUnpart:gg2llbar")) { + sigmaPtr = new Sigma2gg2LEDllbar( false ); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Routine to initialize list of second hard processes. + +bool SetupContainers::init2(vector& container2Ptrs, + Settings& settings) { + + // Reset process list, if filled in previous subrun. + if (container2Ptrs.size() > 0) { + for (int i = 0; i < int(container2Ptrs.size()); ++i) + delete container2Ptrs[i]; + container2Ptrs.clear(); + } + SigmaProcess* sigmaPtr; + + // Two hard QCD jets. + if (settings.flag("SecondHard:TwoJets")) { + sigmaPtr = new Sigma2gg2gg; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2qqbar; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2qg; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qq2qq; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2gg; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2qqbarNew; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar(4, 121); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar(4, 122); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar(5, 123); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar(5, 124); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // A prompt photon and a hard jet. + if (settings.flag("SecondHard:PhotonAndJet")) { + sigmaPtr = new Sigma2qg2qgamma; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2ggamma; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2ggamma; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Two prompt photons. + if (settings.flag("SecondHard:TwoPhotons")) { + sigmaPtr = new Sigma2ffbar2gammagamma; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2gammagamma; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Charmonium production. + if (settings.flag("SecondHard:Charmonium")) { + sigmaPtr = new Sigma2gg2QQbar3S11g(4, 401); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar3PJ1g(4, 0, 402); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar3PJ1g(4, 1, 403); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar3PJ1g(4, 2, 404); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbar3PJ1q(4, 0, 405); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbar3PJ1q(4, 1, 406); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbar3PJ1q(4, 2, 407); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(4, 0, 408); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(4, 1, 409); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(4, 2, 410); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbarX8g(4, 0, 411); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbarX8g(4, 1, 412); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbarX8g(4, 2, 413); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbarX8q(4, 0, 414); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbarX8q(4, 1, 415); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbarX8q(4, 2, 416); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbarX8g(4, 0, 417); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbarX8g(4, 1, 418); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbarX8g(4, 2, 419); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Bottomonium production. + if (settings.flag("SecondHard:Bottomonium")) { + sigmaPtr = new Sigma2gg2QQbar3S11g(5, 501); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar3PJ1g(5, 0, 502); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar3PJ1g(5, 1, 503); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbar3PJ1g(5, 2, 504); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbar3PJ1q(5, 0, 505); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbar3PJ1q(5, 1, 506); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbar3PJ1q(5, 2, 507); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(5, 0, 508); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(5, 1, 509); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar3PJ1g(5, 2, 510); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbarX8g(5, 0, 511); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbarX8g(5, 1, 512); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2gg2QQbarX8g(5, 2, 513); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbarX8q(5, 0, 514); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbarX8q(5, 1, 515); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2QQbarX8q(5, 2, 516); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbarX8g(5, 0, 517); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbarX8g(5, 1, 518); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbarX8g(5, 2, 519); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // A single gamma*/Z0. + if (settings.flag("SecondHard:SingleGmZ")) { + sigmaPtr = new Sigma1ffbar2gmZ; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // A single W+-. + if (settings.flag("SecondHard:SingleW")) { + sigmaPtr = new Sigma1ffbar2W; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // A gamma*/Z0 and a hard jet. + if (settings.flag("SecondHard:GmZAndJet")) { + sigmaPtr = new Sigma2qqbar2gmZg; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2gmZq; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // A W+- and a hard jet. + if (settings.flag("SecondHard:WAndJet")) { + sigmaPtr = new Sigma2qqbar2Wg; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qg2Wq; + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Top pair production. + if (settings.flag("SecondHard:TopPair")) { + sigmaPtr = new Sigma2gg2QQbar(6, 601); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar(6, 602); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2ffbar2FFbarsgmZ(6, 604); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Single top production. + if (settings.flag("SecondHard:SingleTop")) { + sigmaPtr = new Sigma2qq2QqtW(6, 603); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2ffbar2FfbarsW(6, 0, 605); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Two b jets - already part of TwoJets sample above. + if (settings.flag("SecondHard:TwoBJets")) { + sigmaPtr = new Sigma2gg2QQbar(5, 123); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + sigmaPtr = new Sigma2qqbar2QQbar(5, 124); + container2Ptrs.push_back( new ProcessContainer(sigmaPtr) ); + } + + // Done. + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/ProcessLevel.cxx b/PYTHIA8/pythia8140/src/ProcessLevel.cxx new file mode 100644 index 00000000000..0260c244e3d --- /dev/null +++ b/PYTHIA8/pythia8140/src/ProcessLevel.cxx @@ -0,0 +1,1373 @@ +// ProcessLevel.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the ProcessLevel class. + +#include "ProcessLevel.h" + +namespace Pythia8 { + +//========================================================================== + +// The ProcessLevel class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Allow a few failures in final construction of events. +const int ProcessLevel::MAXLOOP = 5; + +//-------------------------------------------------------------------------- + +// Destructor. + +ProcessLevel::~ProcessLevel() { + + // Run through list of first hard processes and delete them. + for (int i = 0; i < int(containerPtrs.size()); ++i) + delete containerPtrs[i]; + + // Run through list of second hard processes and delete them. + for (int i =0; i < int(container2Ptrs.size()); ++i) + delete container2Ptrs[i]; + +} + +//-------------------------------------------------------------------------- + +// Main routine to initialize generation process. + +bool ProcessLevel::init( Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, + BeamParticle* beamAPtrIn, BeamParticle* beamBPtrIn, CoupSM* coupSMPtrIn, + SigmaTotal* sigmaTotPtrIn, bool doLHA, SusyLesHouches* slhaPtrIn, + UserHooks* userHooksPtrIn, vector& sigmaPtrs, ostream& os) { + + // Store input pointers for future use. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + coupSMPtr = coupSMPtrIn; + sigmaTotPtr = sigmaTotPtrIn; + userHooksPtr = userHooksPtrIn; + slhaPtr = slhaPtrIn; + + // Send on some input pointers. + resonanceDecays.init( infoPtr, particleDataPtr, rndmPtr); + + // Set up SigmaTotal. Store sigma_nondiffractive for future use. + sigmaTotPtr->init( infoPtr, settings, particleDataPtr); + int idA = infoPtr->idA(); + int idB = infoPtr->idB(); + double eCM = infoPtr->eCM(); + sigmaTotPtr->calc( idA, idB, eCM); + sigmaND = sigmaTotPtr->sigmaND(); + + // Options to allow second hard interaction and resonance decays. + doSecondHard = settings.flag("SecondHard:generate"); + doSameCuts = settings.flag("PhaseSpace:sameForSecond"); + doResDecays = settings.flag("ProcessLevel:resonanceDecays"); + startColTag = settings.mode("Event:startColTag"); + + // Mass and pT cuts for two hard processes. + mHatMin1 = settings.parm("PhaseSpace:mHatMin"); + mHatMax1 = settings.parm("PhaseSpace:mHatMax"); + if (mHatMax1 < mHatMin1) mHatMax1 = eCM; + pTHatMin1 = settings.parm("PhaseSpace:pTHatMin"); + pTHatMax1 = settings.parm("PhaseSpace:pTHatMax"); + if (pTHatMax1 < pTHatMin1) pTHatMax1 = eCM; + mHatMin2 = settings.parm("PhaseSpace:mHatMinSecond"); + mHatMax2 = settings.parm("PhaseSpace:mHatMaxSecond"); + if (mHatMax2 < mHatMin2) mHatMax2 = eCM; + pTHatMin2 = settings.parm("PhaseSpace:pTHatMinSecond"); + pTHatMax2 = settings.parm("PhaseSpace:pTHatMaxSecond"); + if (pTHatMax2 < pTHatMin2) pTHatMax2 = eCM; + + // Check whether mass and pT ranges agree or overlap. + cutsAgree = doSameCuts; + if (mHatMin2 == mHatMin1 && mHatMax2 == mHatMax1 && pTHatMin2 == pTHatMin1 + && pTHatMax2 == pTHatMax1) cutsAgree = true; + cutsOverlap = cutsAgree; + if (!cutsAgree) { + bool mHatOverlap = (max( mHatMin1, mHatMin2) + < min( mHatMax1, mHatMax2)); + bool pTHatOverlap = (max( pTHatMin1, pTHatMin2) + < min( pTHatMax1, pTHatMax2)); + if (mHatOverlap && pTHatOverlap) cutsOverlap = true; + } + + // Initialize SUSY Les Houches Accord data + if (!initSLHA(settings)) return false; + + // Set up containers for all the internal hard processes. + SetupContainers setupContainers; + setupContainers.init(containerPtrs, settings, particleDataPtr, coupSUSY); + + // Append containers for external hard processes, if any. + if (sigmaPtrs.size() > 0) { + for (int iSig = 0; iSig < int(sigmaPtrs.size()); ++iSig) + containerPtrs.push_back( new ProcessContainer(sigmaPtrs[iSig], + true) ); + } + + // Append single container for Les Houches processes, if any. + if (doLHA) { + SigmaProcess* sigmaPtr = new SigmaLHAProcess(); + containerPtrs.push_back( new ProcessContainer(sigmaPtr) ); + + // Store location of this container, and send in LHA pointer. + iLHACont = containerPtrs.size() - 1; + containerPtrs[iLHACont]->setLHAPtr(lhaUpPtr); + } + + // If no processes found then refuse to do anything. + if ( int(containerPtrs.size()) == 0) { + infoPtr->errorMsg("Error in ProcessLevel::init: " + "no process switched on"); + return false; + } + + // Check that SUSY couplings were indeed initialized where necessary. + bool hasSUSY = false; + for (int i = 0; i < int(containerPtrs.size()); ++i) + if (containerPtrs[i]->isSUSY()) hasSUSY = true; + if (hasSUSY && !coupSUSY.isInit) coupSUSY.init(slhaPtr, &settings, + particleDataPtr, coupSMPtr); + + // Initialize each process. + int numberOn = 0; + for (int i = 0; i < int(containerPtrs.size()); ++i) + if (containerPtrs[i]->init(true, infoPtr, settings, particleDataPtr, + rndmPtr, beamAPtr, beamBPtr, coupSMPtr, sigmaTotPtr, &coupSUSY, + &resonanceDecays, slhaPtr, userHooksPtr)) ++numberOn; + + // Sum maxima for Monte Carlo choice. + sigmaMaxSum = 0.; + for (int i = 0; i < int(containerPtrs.size()); ++i) + sigmaMaxSum += containerPtrs[i]->sigmaMax(); + + // Option to pick a second hard interaction: repeat as above. + int number2On = 0; + if (doSecondHard) { + setupContainers.init2(container2Ptrs, settings); + if ( int(container2Ptrs.size()) == 0) { + infoPtr->errorMsg("Error in ProcessLevel::init: " + "no second hard process switched on"); + return false; + } + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + if (container2Ptrs[i2]->init(false, infoPtr, settings, particleDataPtr, + rndmPtr, beamAPtr, beamBPtr, coupSMPtr, sigmaTotPtr, &coupSUSY, + &resonanceDecays, slhaPtr, userHooksPtr)) ++number2On; + sigma2MaxSum = 0.; + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + sigma2MaxSum += container2Ptrs[i2]->sigmaMax(); + } + + // Construct string with incoming beams and for cm energy. + string collision = "We collide " + particleDataPtr->name(idA) + + " with " + particleDataPtr->name(idB) + " at a CM energy of "; + string pad( 51 - collision.length(), ' '); + + // Print initialization information: header. + os << "\n *------- PYTHIA Process Initialization ---------" + << "-----------------*\n" + << " | " + << " |\n" + << " | " << collision << scientific << setprecision(3)<< setw(9) << eCM + << " GeV" << pad << " |\n" + << " | " + << " |\n" + << " |---------------------------------------------------" + << "---------------|\n" + << " | " + << " | |\n" + << " | Subprocess Code" + << " | Estimated |\n" + << " | " + << " | max (mb) |\n" + << " | " + << " | |\n" + << " |---------------------------------------------------" + << "---------------|\n" + << " | " + << " | |\n"; + + + // Loop over existing processes: print individual process info. + for (int i = 0; i < int(containerPtrs.size()); ++i) + os << " | " << left << setw(45) << containerPtrs[i]->name() + << right << setw(5) << containerPtrs[i]->code() << " | " + << scientific << setprecision(3) << setw(11) + << containerPtrs[i]->sigmaMax() << " |\n"; + + // Loop over second hard processes, if any, and repeat as above. + if (doSecondHard) { + os << " | " + << " | |\n" + << " |---------------------------------------------------" + <<"---------------|\n" + << " | " + <<" | |\n"; + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + os << " | " << left << setw(45) << container2Ptrs[i2]->name() + << right << setw(5) << container2Ptrs[i2]->code() << " | " + << scientific << setprecision(3) << setw(11) + << container2Ptrs[i2]->sigmaMax() << " |\n"; + } + + // Listing finished. + os << " | " + << " |\n" + << " *------- End PYTHIA Process Initialization ----------" + <<"-------------*" << endl; + + // If sum of maxima vanishes then refuse to do anything. + if ( numberOn == 0 || sigmaMaxSum <= 0.) { + infoPtr->errorMsg("Error in ProcessLevel::init: " + "all processes have vanishing cross sections"); + return false; + } + if ( doSecondHard && (number2On == 0 || sigma2MaxSum <= 0.) ) { + infoPtr->errorMsg("Error in ProcessLevel::init: " + "all second hard processes have vanishing cross sections"); + return false; + } + + // If two hard processes then check whether some (but not all) agree. + allHardSame = true; + noneHardSame = true; + if (doSecondHard) { + bool foundMatch = false; + + // Check for each first process if matched in second. + for (int i = 0; i < int(containerPtrs.size()); ++i) { + foundMatch = false; + if (cutsOverlap) + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + if (container2Ptrs[i2]->code() == containerPtrs[i]->code()) + foundMatch = true; + containerPtrs[i]->isSame( foundMatch ); + if (!foundMatch) allHardSame = false; + if ( foundMatch) noneHardSame = false; + } + + // Check for each second process if matched in first. + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) { + foundMatch = false; + if (cutsOverlap) + for (int i = 0; i < int(containerPtrs.size()); ++i) + if (containerPtrs[i]->code() == container2Ptrs[i2]->code()) + foundMatch = true; + container2Ptrs[i2]->isSame( foundMatch ); + if (!foundMatch) allHardSame = false; + if ( foundMatch) noneHardSame = false; + } + } + + // Concluding classification, including cuts. + if (!cutsAgree) allHardSame = false; + someHardSame = !allHardSame && !noneHardSame; + + // Reset counters for average impact-parameter enhancement. + nImpact = 0; + sumImpactFac = 0.; + sum2ImpactFac = 0.; + + // Statistics for LHA events. + codeLHA.resize(0); + nEvtLHA.resize(0); + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Main routine to generate the hard process. + +bool ProcessLevel::next( Event& process) { + + // Generate the next event with two or one hard interactions. + bool physical = (doSecondHard) ? nextTwo( process) : nextOne( process); + + // Check that colour assignments make sense. + if (physical) physical = checkColours( process); + + // Done. + return physical; +} + +//-------------------------------------------------------------------------- + +// Accumulate and update statistics (after possible user veto). + +void ProcessLevel::accumulate() { + + // Increase number of accepted events. + containerPtrs[iContainer]->accumulate(); + + // Provide current generated cross section estimate. + long nTrySum = 0; + long nSelSum = 0; + long nAccSum = 0; + double sigmaSum = 0.; + double delta2Sum = 0.; + double sigSelSum = 0.; + for (int i = 0; i < int(containerPtrs.size()); ++i) + if (containerPtrs[i]->sigmaMax() != 0.) { + nTrySum += containerPtrs[i]->nTried(); + nSelSum += containerPtrs[i]->nSelected(); + nAccSum += containerPtrs[i]->nAccepted(); + sigmaSum += containerPtrs[i]->sigmaMC(); + delta2Sum += pow2(containerPtrs[i]->deltaMC()); + sigSelSum += containerPtrs[i]->sigmaSelMC(); + } + + // For Les Houches events find subprocess type and update counter. + if (infoPtr->isLHA()) { + int codeLHANow = infoPtr->codeSub(); + int iFill = -1; + for (int i = 0; i < int(codeLHA.size()); ++i) + if (codeLHANow == codeLHA[i]) iFill = i; + if (iFill >= 0) ++nEvtLHA[iFill]; + + // Add new process when new code and then arrange in order. + else { + codeLHA.push_back(codeLHANow); + nEvtLHA.push_back(1); + for (int i = int(codeLHA.size()) - 1; i > 0; --i) { + if (codeLHA[i] < codeLHA[i - 1]) { + swap(codeLHA[i], codeLHA[i - 1]); + swap(nEvtLHA[i], nEvtLHA[i - 1]); + } + else break; + } + } + } + + // Normally only one hard interaction. Then store info and done. + if (!doSecondHard) { + double deltaSum = sqrtpos(delta2Sum); + infoPtr->setSigma( nTrySum, nSelSum, nAccSum, sigmaSum, deltaSum); + return; + } + + // Increase counter for a second hard interaction. + container2Ptrs[i2Container]->accumulate(); + + // Update statistics on average impact factor. + ++nImpact; + sumImpactFac += infoPtr->enhanceMI(); + sum2ImpactFac += pow2(infoPtr->enhanceMI()); + + // Cross section estimate for second hard process. + double sigma2Sum = 0.; + double sig2SelSum = 0.; + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + if (container2Ptrs[i2]->sigmaMax() != 0.) { + nTrySum += container2Ptrs[i2]->nTried(); + sigma2Sum += container2Ptrs[i2]->sigmaMC(); + sig2SelSum += container2Ptrs[i2]->sigmaSelMC(); + } + + // Average impact-parameter factor and error. + double invN = 1. / max(1, nImpact); + double impactFac = max( 1., sumImpactFac * invN); + double impactErr2 = ( sum2ImpactFac * invN / pow2(impactFac) - 1.) * invN; + + // Cross section estimate for combination of first and second process. + // Combine two possible ways and take average. + double sigmaComb = 0.5 * (sigmaSum * sig2SelSum + sigSelSum * sigma2Sum); + sigmaComb *= impactFac / sigmaND; + if (allHardSame) sigmaComb *= 0.5; + double deltaComb = sqrtpos(2. / nAccSum + impactErr2) * sigmaComb; + + // Store info and done. + infoPtr->setSigma( nTrySum, nSelSum, nAccSum, sigmaComb, deltaComb); + +} + +//-------------------------------------------------------------------------- + +// Print statistics on cross sections and number of events. + +void ProcessLevel::statistics(bool reset, ostream& os) { + + // Special processing if two hard interactions selected. + if (doSecondHard) { + statistics2(reset, os); + return; + } + + // Header. + os << "\n *------- PYTHIA Event and Cross Section Statistics ------" + << "-------------------------------------------------------*\n" + << " | " + << " |\n" + << " | Subprocess Code | " + << " Number of events | sigma +- delta |\n" + << " | | " + << "Tried Selected Accepted | (estimated) (mb) |\n" + << " | | " + << " | |\n" + << " |------------------------------------------------------------" + << "-----------------------------------------------------|\n" + << " | | " + << " | |\n"; + + // Reset sum counters. + long nTrySum = 0; + long nSelSum = 0; + long nAccSum = 0; + double sigmaSum = 0.; + double delta2Sum = 0.; + + // Loop over existing processes. + for (int i = 0; i < int(containerPtrs.size()); ++i) + if (containerPtrs[i]->sigmaMax() != 0.) { + + // Read info for process. Sum counters. + long nTry = containerPtrs[i]->nTried(); + long nSel = containerPtrs[i]->nSelected(); + long nAcc = containerPtrs[i]->nAccepted(); + double sigma = containerPtrs[i]->sigmaMC(); + double delta = containerPtrs[i]->deltaMC(); + nTrySum += nTry; + nSelSum += nSel; + nAccSum += nAcc; + sigmaSum += sigma; + delta2Sum += pow2(delta); + + // Print individual process info. + os << " | " << left << setw(45) << containerPtrs[i]->name() + << right << setw(5) << containerPtrs[i]->code() << " | " + << setw(11) << nTry << " " << setw(10) << nSel << " " + << setw(10) << nAcc << " | " << scientific << setprecision(3) + << setw(11) << sigma << setw(11) << delta << " |\n"; + + // Print subdivision by user code for Les Houches process. + if (containerPtrs[i]->code() == 9999) + for (int j = 0; j < int(codeLHA.size()); ++j) + os << " | ... whereof user classification code " << setw(10) + << codeLHA[j] << " | " << setw(10) + << nEvtLHA[j] << " | | \n"; + } + + // Print summed process info. + os << " | | " + << " | |\n" + << " | " << left << setw(50) << "sum" << right << " | " << setw(11) + << nTrySum << " " << setw(10) << nSelSum << " " << setw(10) + << nAccSum << " | " << scientific << setprecision(3) << setw(11) + << sigmaSum << setw(11) << sqrtpos(delta2Sum) << " |\n"; + + // Listing finished. + os << " | " + << " |\n" + << " *------- End PYTHIA Event and Cross Section Statistics -----" + << "-----------------------------------------------------*" << endl; + + // Optionally reset statistics contants. + if (reset) for (int i = 0; i < int(containerPtrs.size()); ++i) + containerPtrs[i]->reset(); + +} + +//-------------------------------------------------------------------------- + +// Initialize SUSY Les Houches Accord data. + +bool ProcessLevel::initSLHA(Settings& settings) { + + // Initial and settings values. + int ifailLHE = 1; + int ifailSpc = 1; + int ifailDec = 1; + int readFrom = settings.mode("SLHA:readFrom"); + string lhefFile = settings.word("Beams:LHEF"); + string slhaFile = settings.word("SLHA:file"); + int verboseSLHA = settings.mode("SLHA:verbose"); + + // Option with no SLHA read-in at all. + if (readFrom == 0) return true; + + // First check LHEF header (if reading from LHEF) + if (readFrom == 1 && lhefFile != "void") { + ifailLHE = slhaPtr->readFile(lhefFile, verboseSLHA); + } + + // If LHEF read successful, everything needed should already be ready + if (ifailLHE == 0) { + ifailSpc = 0; + ifailDec = 0; + // If no LHEF file or no SLHA info in header, read from SLHA:file + } else { + lhefFile = "void"; + if ( settings.word("SLHA:file") == "none" + || settings.word("SLHA:file") == "void" + || settings.word("SLHA:file") == "" + || settings.word("SLHA:file") == " ") return true; + ifailSpc = slhaPtr->readFile(slhaFile,verboseSLHA); + } + + // In case of problems, print error and fail init. + if (ifailSpc != 0) { + infoPtr->errorMsg("Error in ProcessLevel::initSLHA: " + "problem reading SLHA file", slhaFile); + return false; + }; + + /* + // Check decays for consistency (replaced by internal Pythia check below) + ifailDec = slhaPtr->checkDecays(); + if (ifailDec != 0) { + infoPtr->errorMsg("Warning in ProcessLevel::initSLHA: " + "Problem with SLHA decay tables."); + } + */ + + // Check spectrum for consistency. Switch off SUSY if necessary. + ifailSpc = slhaPtr->checkSpectrum(); + // ifail > 1 : no MODSEL found -> don't switch on SUSY + if (ifailSpc == 1) { + // no SUSY, but MASS ok + } else if (ifailSpc >= 2) { + // no SUSY, but problems + infoPtr->errorMsg("Warning in ProcessLevel::initSLHA: " + "Problem with SLHA MASS or QNUMBERS."); + } + // ifail = 0 : MODSEL found, spectrum OK + else if (ifailSpc == 0) { + // Print spectrum. Done. + slhaPtr->printSpectrum(); + } + else if (ifailSpc < 0) { + infoPtr->errorMsg("Warning in ProcessLevel::initSLHA: " + "Problem with SLHA spectrum.", + "\n Only using masses and switching off SUSY."); + settings.flag("SUSY:all", false); + slhaPtr->printSpectrum(); + } + + // Import mass spectrum. + bool keepSM = settings.flag("SLHA:keepSM"); + double minMassSM = settings.parm("SLHA:minMassSM"); + if (ifailSpc == 1 || ifailSpc == 0) { + + // Loop through to update particle data. + int id = slhaPtr->mass.first(); + for (int i = 1; i <= slhaPtr->mass.size() ; i++) { + double mass = abs(slhaPtr->mass(id)); + + // Ignore masses for known SM particles or particles with + // default masses < minMassSM; overwrite masses for rest. + if (keepSM && (id < 25 || (id > 80 && id < 1000000))) ; + else if (id < 1000000 && particleDataPtr->m0(id) < minMassSM) { + ostringstream idCode; + idCode << id; + infoPtr->errorMsg("Warning in ProcessLevel::initSLHA: " + "ignoring MASS entry", "for id = "+idCode.str() + +" (m0 < SLHA:minMassSM)", true); + } + else particleDataPtr->m0(id,mass); + id = slhaPtr->mass.next(); + }; + + // Init SUSY couplings + if (ifailSpc == 0) coupSUSY.init(slhaPtr, &settings, particleDataPtr, + coupSMPtr); + + } + + // Update decay data. + for (int iTable=0; iTable < int(slhaPtr->decays.size()); iTable++) { + + // Pointer to this SLHA table + SusyLesHouches::decayTable* slhaTable=&slhaPtr->decays[iTable]; + + // Extract ID and create pointer to corresponding particle data object + int idRes = slhaTable->getId(); + ParticleDataEntry* particlePtr + = particleDataPtr->particleDataEntryPtr(idRes); + + // Ignore decay channels for known SM particles or particles with + // default masses < minMassSM; overwrite masses for rest. + if (keepSM && (idRes < 25 || (idRes > 80 && idRes < 1000000))) continue; + else if (idRes < 1000000 && particleDataPtr->m0(idRes) < minMassSM) { + ostringstream idCode; + idCode << idRes; + infoPtr->errorMsg("Warning in ProcessLevel::initSLHA: " + "ignoring DECAY table", "for id = " + idCode.str() + + " (m0 < SLHA:minMassSM)", true); + continue; + } + + // Extract and store total width (absolute value, neg -> switch off) + double widRes = abs(slhaTable->getWidth()); + particlePtr->setMWidth(widRes); + + // Reset decay table of the particle. Allow decays. + if (slhaTable->size() > 0) { + particlePtr->clearChannels(); + particleDataPtr->mayDecay(idRes,true); + } + + // Reset to stable if width <= 0.0 + if (slhaTable->getWidth() <= 0.0) particleDataPtr->mayDecay(idRes,false); + + // Mass margin between lowest mass allowed and "average" decay channel. + double massMargin = 1.; + + // Set initial minimum mass. + double brWTsum = 0.; + double massWTsum = 0.; + + // Loop over SLHA channels, import into Pythia, treating channels + // with negative branching fractions as having the equivalent positive + // branching fraction, but being switched off for this run + for (int iChannel=0 ; iChannelsize(); iChannel++) { + SusyLesHouches::decayChannel slhaChannel = slhaTable->getChannel(iChannel); + double brat = slhaChannel.getBrat(); + vector idDa = slhaChannel.getIdDa(); + if (idDa.size() >= 9) { + infoPtr->errorMsg("Error in ProcessLevel::initSLHA: " + "max number of decay products is 8."); + } else if (idDa.size() <= 1) { + infoPtr->errorMsg("Error in ProcessLevel::initSLHA: " + "min number of decay products is 2."); + } + else { + int onMode = 1; + if (brat < 0.0) onMode = 0; + + // Check phase space, including margin + double massSum = massMargin; + for (int jDa=0; jDam0( idDa[jDa] ); + if (onMode == 1 && brat > 0.0 && massSum > particleDataPtr->m0(idRes) ) { + // String containing decay name + ostringstream errCode; + errCode << idRes <<" ->"; + for (int jDa=0; jDaerrorMsg("Warning in ProcessLevel::initSLHA: " + "switching off decay", errCode.str() + " (mRes - mDa < massMargin)" + "\n (Note: cross sections will be scaled by remaining" + " open branching fractions!)" , true); + onMode=0; + } + + // Branching-ratio-weighted average mass in decay. + brWTsum += abs(brat); + massWTsum += abs(brat) * massSum; + + // Add channel + int id0 = idDa[0]; + int id1 = idDa[1]; + int id2 = (idDa.size() >= 3) ? idDa[2] : 0; + int id3 = (idDa.size() >= 4) ? idDa[3] : 0; + int id4 = (idDa.size() >= 5) ? idDa[4] : 0; + int id5 = (idDa.size() >= 6) ? idDa[5] : 0; + int id6 = (idDa.size() >= 7) ? idDa[6] : 0; + int id7 = (idDa.size() >= 8) ? idDa[7] : 0; + particlePtr->addChannel(onMode,abs(brat),101, + id0,id1,id2,id3,id4,id5,id6,id7); + + } + } + + // Set minimal mass, but always below nominal one. + if (slhaTable->size() > 0) { + double massAvg = massWTsum / brWTsum; + double massMin = min( massAvg, particlePtr->m0()) - massMargin; + particlePtr->setMMin(massMin); + } + } + + return true; + +} + +//-------------------------------------------------------------------------- + +// Generate the next event with one interaction. + +bool ProcessLevel::nextOne( Event& process) { + + // Update CM energy for phase space selection. + double eCM = infoPtr->eCM(); + for (int i = 0; i < int(containerPtrs.size()); ++i) + containerPtrs[i]->newECM(eCM); + + // Outer loop in case of rare failures. + bool physical = true; + for (int loop = 0; loop < MAXLOOP; ++loop) { + if (!physical) process.clear(); + physical = true; + + // Loop over tries until trial event succeeds. + for ( ; ; ) { + + // Pick one of the subprocesses. + double sigmaMaxNow = sigmaMaxSum * rndmPtr->flat(); + int iMax = containerPtrs.size() - 1; + iContainer = -1; + do sigmaMaxNow -= containerPtrs[++iContainer]->sigmaMax(); + while (sigmaMaxNow > 0. && iContainer < iMax); + + // Do a trial event of this subprocess; accept or not. + if (containerPtrs[iContainer]->trialProcess()) break; + + // Check for end-of-file condition for Les Houches events. + if (infoPtr->atEndOfFile()) return false; + } + + // Update sum of maxima if current maximum violated. + if (containerPtrs[iContainer]->newSigmaMax()) { + sigmaMaxSum = 0.; + for (int i = 0; i < int(containerPtrs.size()); ++i) + sigmaMaxSum += containerPtrs[i]->sigmaMax(); + } + + // Construct kinematics of acceptable process. + if ( !containerPtrs[iContainer]->constructProcess( process) ) + physical = false; + + // Do all resonance decays. + if ( physical && doResDecays + && !containerPtrs[iContainer]->decayResonances( process) ) + physical = false; + + // Add any junctions to the process event record list. + if (physical) findJunctions( process); + + // Outer loop should normally work first time around. + if (physical) break; + } + + // Done. + return physical; +} + +//-------------------------------------------------------------------------- + +// Generate the next event with two hard interactions. + +bool ProcessLevel::nextTwo( Event& process) { + + // Update CM energy for phase space selection. + double eCM = infoPtr->eCM(); + for (int i = 0; i < int(containerPtrs.size()); ++i) + containerPtrs[i]->newECM(eCM); + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + container2Ptrs[i2]->newECM(eCM); + + // Outer loop in case of rare failures. + bool physical = true; + for (int loop = 0; loop < MAXLOOP; ++loop) { + if (!physical) process.clear(); + physical = true; + + // Loop over both hard processes to find consistent common kinematics. + for ( ; ; ) { + + // Loop internally over tries for hardest process until succeeds. + for ( ; ; ) { + + // Pick one of the subprocesses. + double sigmaMaxNow = sigmaMaxSum * rndmPtr->flat(); + int iMax = containerPtrs.size() - 1; + iContainer = -1; + do sigmaMaxNow -= containerPtrs[++iContainer]->sigmaMax(); + while (sigmaMaxNow > 0. && iContainer < iMax); + + // Do a trial event of this subprocess; accept or not. + if (containerPtrs[iContainer]->trialProcess()) break; + + // Check for end-of-file condition for Les Houches events. + if (infoPtr->atEndOfFile()) return false; + } + + // Update sum of maxima if current maximum violated. + if (containerPtrs[iContainer]->newSigmaMax()) { + sigmaMaxSum = 0.; + for (int i = 0; i < int(containerPtrs.size()); ++i) + sigmaMaxSum += containerPtrs[i]->sigmaMax(); + } + + // Loop internally over tries for second hardest process until succeeds. + for ( ; ; ) { + + // Pick one of the subprocesses. + double sigma2MaxNow = sigma2MaxSum * rndmPtr->flat(); + int i2Max = container2Ptrs.size() - 1; + i2Container = -1; + do sigma2MaxNow -= container2Ptrs[++i2Container]->sigmaMax(); + while (sigma2MaxNow > 0. && i2Container < i2Max); + + // Do a trial event of this subprocess; accept or not. + if (container2Ptrs[i2Container]->trialProcess()) break; + } + + // Update sum of maxima if current maximum violated. + if (container2Ptrs[i2Container]->newSigmaMax()) { + sigma2MaxSum = 0.; + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + sigma2MaxSum += container2Ptrs[i2]->sigmaMax(); + } + + // Check whether common set of x values is kinematically possible. + double xA1 = containerPtrs[iContainer]->x1(); + double xB1 = containerPtrs[iContainer]->x2(); + double xA2 = container2Ptrs[i2Container]->x1(); + double xB2 = container2Ptrs[i2Container]->x2(); + if (xA1 + xA2 >= 1. || xB1 + xB2 >= 1.) continue; + + // Reset beam contents. Naive parton densities for second interaction. + // (Subsequent procedure could be symmetrized, but would be overkill.) + beamAPtr->clear(); + beamBPtr->clear(); + int idA1 = containerPtrs[iContainer]->id1(); + int idB1 = containerPtrs[iContainer]->id2(); + int idA2 = container2Ptrs[i2Container]->id1(); + int idB2 = container2Ptrs[i2Container]->id2(); + double Q2Fac1 = containerPtrs[iContainer]->Q2Fac(); + double Q2Fac2 = container2Ptrs[i2Container]->Q2Fac(); + double pdfA2Raw = beamAPtr->xf( idA2, xA2,Q2Fac2); + double pdfB2Raw = beamBPtr->xf( idB2, xB2,Q2Fac2); + + // Remove partons in first interaction from beams. + beamAPtr->append( 3, idA1, xA1); + beamAPtr->xfISR( 0, idA1, xA1, Q2Fac1); + beamAPtr->pickValSeaComp(); + beamBPtr->append( 4, idB1, xB1); + beamBPtr->xfISR( 0, idB1, xB1, Q2Fac1); + beamBPtr->pickValSeaComp(); + + // Reevaluate pdf's for second interaction and weight by reduction. + double pdfA2Mod = beamAPtr->xfMI( idA2, xA2,Q2Fac2); + double pdfB2Mod = beamBPtr->xfMI( idB2, xB2,Q2Fac2); + double wtPdfMod = (pdfA2Mod * pdfB2Mod) / (pdfA2Raw * pdfB2Raw); + if (wtPdfMod < rndmPtr->flat()) continue; + + // Reduce by a factor of 2 for identical processes when others not, + // and when in same phase space region. + bool toLoop = false; + if ( someHardSame && containerPtrs[iContainer]->isSame() + && container2Ptrs[i2Container]->isSame()) { + if (cutsAgree) { + if (rndmPtr->flat() > 0.5) toLoop = true; + } else { + double mHat1 = containerPtrs[iContainer]->mHat(); + double pTHat1 = containerPtrs[iContainer]->pTHat(); + double mHat2 = container2Ptrs[i2Container]->mHat(); + double pTHat2 = container2Ptrs[i2Container]->pTHat(); + if (mHat1 > mHatMin2 && mHat1 < mHatMax2 + && pTHat1 > pTHatMin2 && pTHat1 < pTHatMax2 + && mHat2 > mHatMin1 && mHat2 < mHatMax1 + && pTHat2 > pTHatMin1 && pTHat2 < pTHatMax1 + && rndmPtr->flat() > 0.5) toLoop = true; + } + } + if (toLoop) continue; + + // If come this far then acceptable event. + break; + } + + // Construct kinematics of acceptable processes. + Event process2; + process2.init( "(second hard)", particleDataPtr, startColTag); + process2.initColTag(); + if ( !containerPtrs[iContainer]->constructProcess( process) ) + physical = false; + if (physical && !container2Ptrs[i2Container]->constructProcess( process2, + false) ) physical = false; + + // Do all resonance decays. + if ( physical && doResDecays + && !containerPtrs[iContainer]->decayResonances( process) ) + physical = false; + if ( physical && doResDecays + && !container2Ptrs[i2Container]->decayResonances( process2) ) + physical = false; + + // Append second hard interaction to normal process object. + if (physical) combineProcessRecords( process, process2); + + // Add any junctions to the process event record list. + if (physical) findJunctions( process); + + // Outer loop should normally work first time around. + if (physical) break; + } + + // Done. + return physical; +} + +//-------------------------------------------------------------------------- + +// Append second hard interaction to normal process object. +// Complication: all resonance decay chains must be put at the end. + +void ProcessLevel::combineProcessRecords( Event& process, Event& process2) { + + // Find first event record size, excluding resonances. + int nSize = process.size(); + int nHard = 5; + while (nHard < nSize && process[nHard].mother1() == 3) ++nHard; + + // Save resonance products temporarily elsewhere. + vector resProd; + if (nSize > nHard) { + for (int i = nHard; i < nSize; ++i) resProd.push_back( process[i] ); + process.popBack(nSize - nHard); + } + + // Find second event record size, excluding resonances. + int nSize2 = process2.size(); + int nHard2 = 5; + while (nHard2 < nSize2 && process2[nHard2].mother1() == 3) ++nHard2; + + // Find amount of necessary position and colour offset for second process. + int addPos = nHard - 3; + int addCol = process.lastColTag() - startColTag; + + // Loop over all particles (except beams) from second process. + for (int i = 3; i < nSize2; ++i) { + + // Offset mother and daughter pointers and colour tags of particle. + process2[i].offsetHistory( 2, addPos, 2, addPos); + process2[i].offsetCol( addCol); + + // Append hard-process particles from process2 to process. + if (i < nHard2) process.append( process2[i] ); + } + + // Reinsert resonance decay chains of first hard process. + int addPos2 = nHard2 - 3; + if (nHard < nSize) { + + // Offset daughter pointers of unmoved mothers. + for (int i = 5; i < nHard; ++i) + process[i].offsetHistory( 0, 0, nHard - 1, addPos2); + + // Modify history of resonance products when restoring. + for (int i = 0; i < int(resProd.size()); ++i) { + resProd[i].offsetHistory( nHard - 1, addPos2, nHard - 1, addPos2); + process.append( resProd[i] ); + } + } + + // Insert resonance decay chains of second hard process. + if (nHard2 < nSize2) { + int nHard3 = nHard + nHard2 - 3; + int addPos3 = nSize - nHard; + + // Offset daughter pointers of second-process mothers. + for (int i = nHard + 2; i < nHard3; ++i) + process[i].offsetHistory( 0, 0, nHard3 - 1, addPos3); + + // Modify history of second-process resonance products and insert. + for (int i = nHard2; i < nSize2; ++i) { + process2[i].offsetHistory( nHard3 - 1, addPos3, nHard3 - 1, addPos3); + process.append( process2[i] ); + } + } + + // Store PDF scale for second interaction. + process.scaleSecond( process2.scale() ); + +} + +//-------------------------------------------------------------------------- + +// Add any junctions to the process event record list. +// First try, so still incomplete. ?? +// Also check that do not doublebook if called repeatedly. + +void ProcessLevel::findJunctions( Event& junEvent) { + + // Loop though event; isolate all uncoloured particles. + for (int i = 0; i < junEvent.size(); ++i) + if ( junEvent[i].col() == 0 && junEvent[i].acol() == 0) { + + // Find all daughters and store daughter colours and anticolours. + vector daughters = junEvent.daughterList(i); + // Debug?? + if (junEvent.size() == 3 && daughters.size() > 0) { + cout << " warning: daughtersize = " << daughters.size() << endl; + junEvent.list(); + } + // End debug??? + vector cols, acols; + for (int j = 0; j < int(daughters.size()); ++j) { + int colDau = junEvent[ daughters[j] ].col(); + int acolDau = junEvent[ daughters[j] ].acol(); + if (colDau > 0) cols.push_back( colDau); + if (acolDau > 0) acols.push_back( acolDau); + } + + // Remove all matching colour-anticolour pairs. + bool foundPair = true; + while (foundPair && cols.size() > 0 && acols.size() > 0) { + foundPair = false; + for (int j = 0; j < int(cols.size()); ++j) { + for (int k = 0; k < int(acols.size()); ++k) { + if (acols[k] == cols[j]) { + cols[j] = cols.back(); + cols.pop_back(); + acols[k] = acols.back(); + acols.pop_back(); + foundPair = true; + break; + } + } if (foundPair) break; + } + } + + // Store an (anti)junction when three (anti)coloured daughters. + // But first check that junction not already exists. + if (cols.size() == 3 && acols.size() == 0) { + bool foundMatch = false; + for (int iJun = 0; iJun < junEvent.sizeJunction(); ++iJun) + if (junEvent.kindJunction(iJun) == 1) { + int nMatch = 0; + for (int j = 0; j < 3; ++j) { + int colNow = junEvent.colJunction(iJun, j); + if (colNow == cols[0] || colNow == cols[1] + || colNow == cols[2]) ++nMatch; + } + if (nMatch == 3) foundMatch = true; + } + if (!foundMatch) + junEvent.appendJunction( 1, cols[0], cols[1], cols[2]); + } + if (acols.size() == 3 && cols.size() == 0) { + bool foundMatch = false; + for (int iJun = 0; iJun < junEvent.sizeJunction(); ++iJun) + if (junEvent.kindJunction(iJun) == 2) { + int nMatch = 0; + for (int j = 0; j < 3; ++j) { + int colNow = junEvent.colJunction(iJun, j); + if (colNow == acols[0] || colNow == acols[1] + || colNow == acols[2]) ++nMatch; + } + if (nMatch == 3) foundMatch = true; + } + if (!foundMatch) + junEvent.appendJunction( 2, acols[0], acols[1], acols[2]); + } + } + + // Done. +} + +//-------------------------------------------------------------------------- + +// Check that colours match up. + +bool ProcessLevel::checkColours( Event& process) { + + // Variables and arrays for common usage. + bool physical = true; + bool match; + int colType, col, acol, iPos, iNow, iNowA; + vector colTags, colPos, acolPos; + + // Check that each particle has the kind of colours expected of it. + for (int i = 0; i < process.size(); ++i) { + colType = process[i].colType(); + col = process[i].col(); + acol = process[i].acol(); + if (colType == 0 && (col != 0 || acol != 0)) physical = false; + else if (colType == 1 && (col <= 0 || acol != 0)) physical = false; + else if (colType == -1 && (col != 0 || acol <= 0)) physical = false; + else if (colType == 2 && (col <= 0 || acol <= 0)) physical = false; + else if (colType < -1 || colType > 2) physical = false; + + // Add to the list of colour tags. + if (col > 0) { + match = false; + for (int ic = 0; ic < int(colTags.size()) ; ++ic) + if (col == colTags[ic]) match = true; + if (!match) colTags.push_back(col); + } else if (acol > 0) { + match = false; + for (int ic = 0; ic < int(colTags.size()) ; ++ic) + if (acol == colTags[ic]) match = true; + if (!match) colTags.push_back(acol); + } + } + + // Warn and give up if particles did not have the expected colours. + if (!physical) { + infoPtr->errorMsg("Error in ProcessLevel::checkColours: " + "incorrect colour assignment"); + return false; + } + + // Remove (anti)colours coming from an (anti)junction. + // Temporary solution; only relevant for some cases?? + for (int iJun = 0; iJun < process.sizeJunction(); ++iJun) + if ( process.kindJunction(iJun) == 1 + || process.kindJunction(iJun) == 2) { + for (int j = 0; j < 3; ++j) { + int colJun = process.colJunction(iJun, j); + for (int ic = 0; ic < int(colTags.size()) ; ++ic) + if (colJun == colTags[ic]) { + colTags[ic] = colTags[colTags.size() - 1]; + colTags.pop_back(); + break; + } + } + } + + // Loop through all colour tags and find their positions (by sign). + for (int ic = 0; ic < int(colTags.size()); ++ic) { + col = colTags[ic]; + colPos.resize(0); + acolPos.resize(0); + for (int i = 0; i < process.size(); ++i) { + if (process[i].col() == col) colPos.push_back(i); + if (process[i].acol() == col) acolPos.push_back(i); + } + + // Trace colours back through decays; remove daughters. + while (colPos.size() > 1) { + iPos = colPos.size() - 1; + iNow = colPos[iPos]; + if ( process[iNow].mother1() == colPos[iPos - 1] + && process[iNow].mother2() == 0) colPos.pop_back(); + else break; + } + while (acolPos.size() > 1) { + iPos = acolPos.size() - 1; + iNow = acolPos[iPos]; + if ( process[iNow].mother1() == acolPos[iPos - 1] + && process[iNow].mother2() == 0) acolPos.pop_back(); + else break; + } + + // Now colour should exist in only 2 copies. + if (colPos.size() + acolPos.size() != 2) physical = false; + + // If both colours or both anticolours then one mother of the other. + else if (colPos.size() == 2) { + iNow = colPos[1]; + if ( process[iNow].mother1() != colPos[0] + && process[iNow].mother2() != colPos[0] ) physical = false; + } + else if (acolPos.size() == 2) { + iNowA = acolPos[1]; + if ( process[iNowA].mother1() != acolPos[0] + && process[iNowA].mother2() != acolPos[0] ) physical = false; + } + + // If one of each then should have same mother(s), or point to beams. + else { + iNow = colPos[0]; + iNowA = acolPos[0]; + if ( process[iNow].status() == -21 && process[iNowA].status() == -21 ); + else if ( (process[iNow].mother1() != process[iNowA].mother1()) + || (process[iNow].mother2() != process[iNowA].mother2()) ) + physical = false; + } + + } + + // Error message if problem found. Done. + if (!physical) infoPtr->errorMsg("Error in ProcessLevel::checkColours: " + "unphysical colour flow"); + return physical; + +} + +//-------------------------------------------------------------------------- + +// Print statistics when two hard processes allowed. + +void ProcessLevel::statistics2(bool reset, ostream& os) { + + // Average impact-parameter factor and error. + double invN = 1. / max(1, nImpact); + double impactFac = max( 1., sumImpactFac * invN); + double impactErr2 = ( sum2ImpactFac * invN / pow2(impactFac) - 1.) * invN; + + // Derive scaling factor to be applied to first set of processes. + double sigma2SelSum = 0.; + int n2SelSum = 0; + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) { + sigma2SelSum += container2Ptrs[i2]->sigmaSelMC(); + n2SelSum += container2Ptrs[i2]->nSelected(); + } + double factor1 = impactFac * sigma2SelSum / sigmaND; + double rel1Err = sqrt(1. / max(1, n2SelSum) + impactErr2); + if (allHardSame) factor1 *= 0.5; + + // Derive scaling factor to be applied to second set of processes. + double sigma1SelSum = 0.; + int n1SelSum = 0; + for (int i = 0; i < int(containerPtrs.size()); ++i) { + sigma1SelSum += containerPtrs[i]->sigmaSelMC(); + n1SelSum += containerPtrs[i]->nSelected(); + } + double factor2 = impactFac * sigma1SelSum / sigmaND; + if (allHardSame) factor2 *= 0.5; + double rel2Err = sqrt(1. / max(1, n1SelSum) + impactErr2); + + // Header. + os << "\n *------- PYTHIA Event and Cross Section Statistics ------" + << "--------------------------------------------------*\n" + << " | " + << " |\n" + << " | Subprocess Code | " + << "Number of events | sigma +- delta |\n" + << " | | Tried" + << " Selected Accepted | (estimated) (mb) |\n" + << " | | " + << " | |\n" + << " |------------------------------------------------------------" + << "------------------------------------------------|\n" + << " | | " + << " | |\n" + << " | First hard process: | " + << " | |\n" + << " | | " + << " | |\n"; + + // Reset sum counters. + long nTrySum = 0; + long nSelSum = 0; + long nAccSum = 0; + double sigmaSum = 0.; + double delta2Sum = 0.; + + // Loop over existing first processes. + for (int i = 0; i < int(containerPtrs.size()); ++i) + if (containerPtrs[i]->sigmaMax() != 0.) { + + // Read info for process. Sum counters. + long nTry = containerPtrs[i]->nTried(); + long nSel = containerPtrs[i]->nSelected(); + long nAcc = containerPtrs[i]->nAccepted(); + double sigma = containerPtrs[i]->sigmaMC() * factor1; + double delta2 = pow2( containerPtrs[i]->deltaMC() * factor1 ); + nTrySum += nTry; + nSelSum += nSel; + nAccSum += nAcc; + sigmaSum += sigma; + delta2Sum += delta2; + delta2 += pow2( sigma * rel1Err ); + + // Print individual process info. + os << " | " << left << setw(40) << containerPtrs[i]->name() + << right << setw(5) << containerPtrs[i]->code() << " | " + << setw(11) << nTry << " " << setw(10) << nSel << " " + << setw(10) << nAcc << " | " << scientific << setprecision(3) + << setw(11) << sigma << setw(11) << sqrtpos(delta2) << " |\n"; + } + + // Print summed info for first processes. + delta2Sum += pow2( sigmaSum * rel1Err ); + os << " | | " + << " | |\n" + << " | " << left << setw(45) << "sum" << right << " | " << setw(11) + << nTrySum << " " << setw(10) << nSelSum << " " << setw(10) + << nAccSum << " | " << scientific << setprecision(3) << setw(11) + << sigmaSum << setw(11) << sqrtpos(delta2Sum) << " |\n"; + + + // Separation lines to second hard processes. + os << " | | " + << " | |\n" + << " |------------------------------------------------------------" + << "------------------------------------------------|\n" + << " | | " + << " | |\n" + << " | Second hard process: | " + << " | |\n" + << " | | " + << " | |\n"; + + // Reset sum counters. + nTrySum = 0; + nSelSum = 0; + nAccSum = 0; + sigmaSum = 0.; + delta2Sum = 0.; + + // Loop over existing second processes. + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + if (container2Ptrs[i2]->sigmaMax() != 0.) { + + // Read info for process. Sum counters. + long nTry = container2Ptrs[i2]->nTried(); + long nSel = container2Ptrs[i2]->nSelected(); + long nAcc = container2Ptrs[i2]->nAccepted(); + double sigma = container2Ptrs[i2]->sigmaMC() * factor2; + double delta2 = pow2( container2Ptrs[i2]->deltaMC() * factor2 ); + nTrySum += nTry; + nSelSum += nSel; + nAccSum += nAcc; + sigmaSum += sigma; + delta2Sum += delta2; + delta2 += pow2( sigma * rel2Err ); + + // Print individual process info. + os << " | " << left << setw(40) << container2Ptrs[i2]->name() + << right << setw(5) << container2Ptrs[i2]->code() << " | " + << setw(11) << nTry << " " << setw(10) << nSel << " " + << setw(10) << nAcc << " | " << scientific << setprecision(3) + << setw(11) << sigma << setw(11) << sqrtpos(delta2) << " |\n"; + } + + // Print summed info for second processes. + delta2Sum += pow2( sigmaSum * rel2Err ); + os << " | | " + << " | |\n" + << " | " << left << setw(45) << "sum" << right << " | " << setw(11) + << nTrySum << " " << setw(10) << nSelSum << " " << setw(10) + << nAccSum << " | " << scientific << setprecision(3) << setw(11) + << sigmaSum << setw(11) << sqrtpos(delta2Sum) << " |\n"; + + // Print information on how the two processes were combined. + os << " | | " + << " | |\n" + << " |------------------------------------------------------------" + << "------------------------------------------------|\n" + << " | " + << " |\n" + << " | Uncombined cross sections for the two event sets were " + << setw(10) << sigma1SelSum << " and " << sigma2SelSum << " mb, " + << "respectively, combined |\n" + << " | using a sigma(nonDiffractive) of " << setw(10) << sigmaND + << " mb and an impact-parameter enhancement factor of " + << setw(10) << impactFac << ". |\n"; + + // Listing finished. + os << " | " + << " |\n" + << " *------- End PYTHIA Event and Cross Section Statistics -----" + << "------------------------------------------------*" << endl; + + // Optionally reset statistics contants. + if (reset) { + for (int i = 0; i < int(containerPtrs.size()); ++i) + containerPtrs[i]->reset(); + for (int i2 = 0; i2 < int(container2Ptrs.size()); ++i2) + container2Ptrs[i2]->reset(); + } + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/Pythia.cxx b/PYTHIA8/pythia8140/src/Pythia.cxx new file mode 100644 index 00000000000..8bc3c4a5090 --- /dev/null +++ b/PYTHIA8/pythia8140/src/Pythia.cxx @@ -0,0 +1,1912 @@ +// Pythia.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the Pythia class. + +#include "Pythia.h" + +// Access time information. +#include + +// Allow string and character manipulation. +#include + +namespace Pythia8 { + +//========================================================================== + +// The Pythia class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Maximum number of tries to produce parton level from given input. +const int Pythia::NTRY = 10; + +// Negative integer to denote that no subrun has been set. +const int Pythia::SUBRUNDEFAULT = -999; + +//-------------------------------------------------------------------------- + +// Constructor. + +Pythia::Pythia(string xmlDir) { + + // Initial values for pointers to PDF's. + useNewPdfA = false; + useNewPdfB = false; + useNewPdfHard = false; + useNewPdfPomA = false; + useNewPdfPomB = false; + pdfAPtr = 0; + pdfBPtr = 0; + pdfHardAPtr = 0; + pdfHardBPtr = 0; + pdfPomAPtr = 0; + pdfPomBPtr = 0; + + // Initial values for pointers to Les Houches Event objects. + doLHA = false; + useNewLHA = false; + lhaUpPtr = 0; + + // Initial value for pointer to external decay handler. + decayHandlePtr = 0; + + // Initial value for pointer to user hooks. + userHooksPtr = 0; + + // Initial value for pointer to beam shape. + useNewBeamShape = false; + beamShapePtr = 0; + + // Initial values for pointers to timelike and spacelike showers. + useNewTimes = false; + useNewSpace = false; + timesDecPtr = 0; + timesPtr = 0; + spacePtr = 0; + + // Find path to data files, i.e. xmldoc directory location. + // Environment variable takes precedence, else use constructor input. + xmlPath = ""; + const char* PYTHIA8DATA = "PYTHIA8DATA"; + char* envPath = getenv(PYTHIA8DATA); + if (envPath != 0 && *envPath != '\0') { + int i = 0; + while (*(envPath+i) != '\0') xmlPath += *(envPath+(i++)); + } + else xmlPath = xmlDir; + if (xmlPath[ xmlPath.length() - 1 ] != '/') xmlPath += "/"; + + // Read in files with all flags, modes, parms and words. + settings.initPtr( &info); + string initFile = xmlPath + "Index.xml"; + isConstructed = settings.init( initFile); + if (!isConstructed) { + info.errorMsg("Abort from Pythia::Pythia: settings unavailable"); + return; + } + + // Read in files with all particle data. + particleData.initPtr( &info, &settings, &rndm, &coupSM); + string dataFile = xmlPath + "ParticleData.xml"; + isConstructed = particleData.init( dataFile); + if (!isConstructed) { + info.errorMsg("Abort from Pythia::Pythia: particle data unavailable"); + return; + } + + // Write the Pythia banner to output. + banner(); + + // Set headers to distinguish the two event listing kinds. + int startColTag = settings.mode("Event:startColTag"); + process.init("(hard process)", &particleData, startColTag); + event.init("(complete event)", &particleData, startColTag); + + // Not initialized until at the end of initInternal. + isInit = false; + info.addCounter(0); + +} + +//-------------------------------------------------------------------------- + +// Destructor. + +Pythia::~Pythia() { + + // Delete the PDF's created with new. + if (useNewPdfHard && pdfHardAPtr != pdfAPtr) delete pdfHardAPtr; + if (useNewPdfHard && pdfHardBPtr != pdfBPtr) delete pdfHardBPtr; + if (useNewPdfA) delete pdfAPtr; + if (useNewPdfB) delete pdfBPtr; + if (useNewPdfPomA) delete pdfPomAPtr; + if (useNewPdfPomB) delete pdfPomBPtr; + + // Delete the Les Houches object created with new. + if (useNewLHA) delete lhaUpPtr; + + // Delete the BeamShape object created with new. + if (useNewBeamShape) delete beamShapePtr; + + // Delete the timelike and spacelike showers created with new. + if (useNewTimes) delete timesPtr; + if (useNewSpace) delete spacePtr; + +} + +//-------------------------------------------------------------------------- + +// Read in one update for a setting or particle data from a single line. + +bool Pythia::readString(string line, bool warn) { + + // Check that constructor worked. + if (!isConstructed) return false; + + // If empty line then done. + if (line.find_first_not_of(" \n\t\v\b\r\f\a") == string::npos) return true; + + // If first character is not a letter/digit, then taken to be a comment. + int firstChar = line.find_first_not_of(" \n\t\v\b\r\f\a"); + if (!isalnum(line[firstChar])) return true; + + // Send on particle data to the ParticleData database. + if (isdigit(line[firstChar])) + return particleData.readString(line, warn); + + // Everything else sent on to Settings. + return settings.readString(line, warn); + +} + +//-------------------------------------------------------------------------- + +// Read in updates for settings or particle data from user-defined file. + +bool Pythia::readFile(string fileName, bool warn, int subrun) { + + // Check that constructor worked. + if (!isConstructed) return false; + + // Open file for reading. + const char* cstring = fileName.c_str(); + ifstream is(cstring); + if (!is.good()) { + info.errorMsg("Error in Pythia::readFile: did not find file", fileName); + return false; + } + + // Hand over real work to next method. + return readFile( is, warn, subrun); + +} + +//-------------------------------------------------------------------------- + +// Read in updates for settings or particle data +// from user-defined stream (or file). + +bool Pythia::readFile(istream& is, bool warn, int subrun) { + + // Check that constructor worked. + if (!isConstructed) return false; + + // Read in one line at a time. + string line; + bool accepted = true; + int subrunNow = SUBRUNDEFAULT; + while ( getline(is, line) ) { + + // Check whether entered new subrun. + int subrunLine = readSubrun( line, warn); + if (subrunLine >= 0) subrunNow = subrunLine; + + // Process the line if in correct subrun. + if ( (subrunNow == subrun || subrunNow == SUBRUNDEFAULT) + && !readString( line, warn) ) accepted = false; + + // Reached end of input file. + }; + return accepted; + +} + +//-------------------------------------------------------------------------- + +// Routine to pass in pointers to PDF's. Usage optional. + +bool Pythia::setPDFPtr( PDF* pdfAPtrIn, PDF* pdfBPtrIn, PDF* pdfHardAPtrIn, + PDF* pdfHardBPtrIn, PDF* pdfPomAPtrIn, PDF* pdfPomBPtrIn) { + + // Delete any PDF's created in a previous initInternal call. + if (useNewPdfHard && pdfHardAPtr != pdfAPtr) delete pdfHardAPtr; + if (useNewPdfHard && pdfHardBPtr != pdfBPtr) delete pdfHardBPtr; + if (useNewPdfA) delete pdfAPtr; + if (useNewPdfB) delete pdfBPtr; + if (useNewPdfPomA) delete pdfPomAPtr; + if (useNewPdfPomB) delete pdfPomBPtr; + + // Reset pointers to be empty. + useNewPdfA = false; + useNewPdfB = false; + useNewPdfHard = false; + useNewPdfPomA = false; + useNewPdfPomB = false; + pdfAPtr = 0; + pdfBPtr = 0; + pdfHardAPtr = 0; + pdfHardBPtr = 0; + pdfPomAPtr = 0; + pdfPomBPtr = 0; + + // Switch off external PDF's by zero as input. + if (pdfAPtrIn == 0 && pdfBPtrIn == 0) return true; + + // The two PDF objects cannot be one and the same. + if (pdfAPtrIn == pdfBPtrIn) return false; + + // Save pointers. + pdfAPtr = pdfAPtrIn; + pdfBPtr = pdfBPtrIn; + + // By default same pointers for hard-process PDF's. + pdfHardAPtr = pdfAPtrIn; + pdfHardBPtr = pdfBPtrIn; + + // Optionally allow separate pointers for hard process. + if (pdfHardAPtrIn != 0 && pdfHardBPtrIn != 0) { + if (pdfHardAPtrIn == pdfHardBPtrIn) return false; + pdfHardAPtr = pdfHardAPtrIn; + pdfHardBPtr = pdfHardBPtrIn; + } + + // Optionally allow pointers for Pomerons in the proton. + if (pdfPomAPtrIn != 0 && pdfPomBPtrIn != 0) { + if (pdfPomAPtrIn == pdfPomBPtrIn) return false; + pdfPomAPtr = pdfPomAPtrIn; + pdfPomBPtr = pdfPomBPtrIn; + } + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Routine to initialize with CM energy. + +bool Pythia::init( int idAin, int idBin, double eCMin) { + + // Read in and set values. + info.addCounter(1); + idA = idAin; + idB = idBin; + frameType = 1; + eCM = eCMin; + doLHA = false; + + // Send on to common initialization. + bool status = initInternal(); + if (status) info.addCounter(2); + else info.errorMsg("Abort from Pythia::init: initialization failed"); + return status; + +} + +//-------------------------------------------------------------------------- + +// Routine to initialize with two collinear beams, energies specified. + +bool Pythia::init( int idAin, int idBin, double eAin, double eBin) { + + // Read in and set values. + info.addCounter(1); + idA = idAin; + idB = idBin; + frameType = 2; + eA = eAin; + eB = eBin; + doLHA = false; + + // Send on to common initialization. + bool status = initInternal(); + if (status) info.addCounter(2); + else info.errorMsg("Abort from Pythia::init: initialization failed"); + return status; + +} + +//-------------------------------------------------------------------------- + +// Routine to initialize with two beams specified by three-momenta. + +bool Pythia::init( int idAin, int idBin, double pxAin, double pyAin, + double pzAin, double pxBin, double pyBin, double pzBin) { + + // Read in and set values. + info.addCounter(1); + idA = idAin; + idB = idBin; + frameType = 3; + pxA = pxAin; + pyA = pyAin; + pzA = pzAin; + pxB = pxBin; + pyB = pyBin; + pzB = pzBin; + doLHA = false; + + // Send on to common initialization. + bool status = initInternal(); + if (status) info.addCounter(2); + else info.errorMsg("Abort from Pythia::init: initialization failed"); + return status; + +} + +//-------------------------------------------------------------------------- + +// Routine to initialize when all info is given in a Les Houches Event File. + +bool Pythia::init( string LesHouchesEventFile, bool skipInit) { + + // Destroy any previous LHAup object. + info.addCounter(1); + if (useNewLHA) delete lhaUpPtr; + + // Create LHAup object. Send in pointer to info. + const char* cstring = LesHouchesEventFile.c_str(); + lhaUpPtr = new LHAupLHEF(cstring); + lhaUpPtr->setPtr( &info); + doLHA = true; + useNewLHA = true; + + // Check that file was properly opened. + if (!lhaUpPtr->fileFound()) { + info.errorMsg("Abort from Pythia::init: Les Houches Event File not found"); + return false; + } + + // Store LHEF name in Beams if not already set (for SLHA reader) + // (also makes sure information is consistent, overwriting any other + // name given in Beams:LHEF by the name of the LHEF file actually used) + if (word("Beams:LHEF") != LesHouchesEventFile) { + settings.word("Beams:LHEF", LesHouchesEventFile); + } + + // Store or replace LHA pointer in other classes. + processLevel.setLHAPtr( lhaUpPtr); + + // If second time around, only with new file, then simplify. + if (skipInit) return true; + + // Set LHAinit information (in some external program). + if (!lhaUpPtr->setInit()) { + info.errorMsg("Abort from Pythia::init: " + "Les Houches initialization failed"); + return false; + } + + // Extract beams from values set in an LHAinit object. + idA = lhaUpPtr->idBeamA(); + idB = lhaUpPtr->idBeamB(); + eA = lhaUpPtr->eBeamA(); + eB = lhaUpPtr->eBeamB(); + frameType = 2; + + // Now do normal initialization. List info if there. + bool status = initInternal(); + lhaUpPtr->listInit(); + if (status) info.addCounter(2); + else info.errorMsg("Abort from Pythia::init: initialization failed"); + return status; + +} + +//-------------------------------------------------------------------------- + +// Routine to initialize with the variable values of the Beams kind. + +bool Pythia::init() { + + // Check if to read from Les Houches Event File set, and is so send on. + info.addCounter(1); + if (mode("Beams:frameType") == 4) { + string lhef = word("Beams:LHEF"); + bool skipInit = flag("Main:LHEFskipInit"); + return init( lhef, skipInit); + } + + // Read in and set values. + idA = mode("Beams:idA"); + idB = mode("Beams:idB"); + frameType = mode("Beams:frameType"); + eCM = parm("Beams:eCM"); + eA = parm("Beams:eA"); + eB = parm("Beams:eB"); + pxA = parm("Beams:pxA"); + pyA = parm("Beams:pyA"); + pzA = parm("Beams:pzA"); + pxB = parm("Beams:pxB"); + pyB = parm("Beams:pyB"); + pzB = parm("Beams:pzB"); + doLHA = false; + + // Send on to common initialization. + bool status = initInternal(); + if (status) info.addCounter(2); + else info.errorMsg("Abort from Pythia::init: initialization failed"); + return status; + +} + +//-------------------------------------------------------------------------- + +// Routine to initialize when beam info is given in an LHAup object. + +bool Pythia::init( LHAup* lhaUpPtrIn) { + + // Save and set flag for subsequent usage of LHAup object. + info.addCounter(1); + lhaUpPtr = lhaUpPtrIn; + doLHA = true; + + // Send in pointer to info. Store LHA pointer in other classes. + lhaUpPtr->setPtr( &info); + processLevel.setLHAPtr( lhaUpPtr); + + // Set LHAinit information (in some external program). + if (!lhaUpPtr->setInit()) { + info.errorMsg("Abort from Pythia::init: " + "Les Houches initialization failed"); + return false; + } + + // Extract beams from values set in an LHAinit object. + idA = lhaUpPtr->idBeamA(); + idB = lhaUpPtr->idBeamB(); + eA = lhaUpPtr->eBeamA(); + eB = lhaUpPtr->eBeamB(); + frameType = 2; + + // Now do normal initialization. List info if there. + bool status = initInternal(); + lhaUpPtr->listInit(); + if (status) info.addCounter(2); + else info.errorMsg("Abort from Pythia::init: initialization failed"); + return status; + +} + +//-------------------------------------------------------------------------- + +// Main routine to initialize the generation process. +// (The alternative init forms end up in this one.) + +bool Pythia::initInternal() { + + // Check that constructor worked. + isInit = false; + if (!isConstructed) return false; + + // Reset error counters. + nErrEvent = 0; + info.errorReset(); + info.setTooLowPTmin(false); + info.setSigma( 0, 0, 0, 0., 0.); + + // Initialize data members extracted from database. + doProcessLevel = settings.flag("ProcessLevel:all"); + doPartonLevel = settings.flag("PartonLevel:all") && doProcessLevel; + doHadronLevel = settings.flag("HadronLevel:all"); + doDiffraction = settings.flag("SoftQCD:all") + || settings.flag("SoftQCD:singleDiffractive") + || settings.flag("SoftQCD:doubleDiffractive"); + doMomentumSpread = settings.flag("Beams:allowMomentumSpread"); + doVertexSpread = settings.flag("Beams:allowVertexSpread"); + checkEvent = settings.flag("Check:event"); + nErrList = settings.mode("Check:nErrList"); + epTolErr = settings.parm("Check:epTolErr"); + epTolWarn = settings.parm("Check:epTolWarn"); + + // Initialize the random number generator. + if ( settings.flag("Random:setSeed") ) + rndm.init( settings.mode("Random:seed") ); + + // Initialize tunes to e+e- and pp/ppbar data. + initTunes(); + + // Check that combinations of settings are allowed; change if not. + checkSettings(); + + // Initialize couplings (needed to initialize resonances). + coupSM.init( settings, &rndm); + + // Final setup stage of particle data, notably resonance widths. + particleData.initWidths( resonancePtrs); + + // Set up values related to user hooks. + hasUserHooks = (userHooksPtr > 0); + doVetoProcess = (hasUserHooks) + ? userHooksPtr->canVetoProcessLevel() : false; + doVetoPartons = (hasUserHooks) + ? userHooksPtr->canVetoPartonLevel() : false; + if (hasUserHooks) userHooksPtr->initPtr( &info, &settings, &particleData, + &rndm, &beamA, &beamB, &beamPomA, &beamPomB, &coupSM, &partonSystems, + &sigmaTot); + + // Set up objects for timelike and spacelike showers. + if (timesDecPtr == 0 || timesPtr == 0) { + TimeShower* timesNow = new TimeShower(); + if (timesDecPtr == 0) timesDecPtr = timesNow; + if (timesPtr == 0) timesPtr = timesNow; + useNewTimes = true; + } + if (spacePtr == 0) { + spacePtr = new SpaceShower(); + useNewSpace = true; + } + + // Initialize showers, especially for simple showers in decays. + timesPtr->initPtr( &info, &settings, &particleData, &rndm, &coupSM, + &partonSystems, userHooksPtr); + timesDecPtr->initPtr( &info, &settings, &particleData, &rndm, &coupSM, + &partonSystems, userHooksPtr); + spacePtr->initPtr( &info, &settings, &particleData, &rndm, + &partonSystems, userHooksPtr); + timesDecPtr->init( 0, 0); + + // Set up values related to beam shape. + if (beamShapePtr == 0) { + beamShapePtr = new BeamShape(); + useNewBeamShape = true; + } + beamShapePtr->init( settings, &rndm); + + // Check that beams and beam combination can be handled. + if (!checkBeams()) return false; + + // Do not set up beam kinematics when no process level. + if (!doProcessLevel) frameType = 1; + else { + + // Set up beam kinematics. + if (!initKinematics()) return false; + + // Set up pointers to PDFs. + if (!initPDFs()) return false; + + // Set up the two beams and the common remnant system. + StringFlav* flavSel = hadronLevel.getStringFlavPtr(); + bool isUnresolvedA = ( particleData.isLepton(idA) + && !settings.flag("PDF:lepton") ); + bool isUnresolvedB = ( particleData.isLepton(idB) + && !settings.flag("PDF:lepton") ); + beamA.init( idA, pzAcm, eA, mA, &info, settings, &particleData, &rndm, + pdfAPtr, pdfHardAPtr, isUnresolvedA, flavSel); + beamB.init( idB, pzBcm, eB, mB, &info, settings, &particleData, &rndm, + pdfBPtr, pdfHardBPtr, isUnresolvedB, flavSel); + + // Optionally set up new alternative beams for these Pomerons. + if ( doDiffraction) { + beamPomA.init( 990, 0.5 * eCM, 0.5 * eCM, 0., &info, settings, + &particleData, &rndm, pdfPomAPtr, pdfPomAPtr, false, flavSel); + beamPomB.init( 990, -0.5 * eCM, 0.5 * eCM, 0., &info, settings, + &particleData, &rndm, pdfPomBPtr, pdfPomBPtr, false, flavSel); + } + } + + // Send info/pointers to process level for initialization. + if ( doProcessLevel && !processLevel.init( &info, settings, &particleData, + &rndm, &beamA, &beamB, &coupSM, &sigmaTot, doLHA, &slha, userHooksPtr, + sigmaPtrs) ) return false; + + // Send info/pointers to parton level for initialization. + if ( doPartonLevel && !partonLevel.init( &info, settings, &particleData, + &rndm, &beamA, &beamB, &beamPomA, &beamPomB, &coupSM, &partonSystems, + &sigmaTot, timesDecPtr, timesPtr, spacePtr, userHooksPtr) ) return false; + + // Send info/pointers to hadron level for initialization. + // Note: forceHadronLevel() can come, so we must always initialize. + if ( !hadronLevel.init( &info, settings, particleData, &rndm, timesDecPtr, + decayHandlePtr, handledParticles) ) return false; + + // Optionally check particle data table for inconsistencies. + if ( settings.flag("Check:particleData") ) + particleData.checkTable( settings.mode("Check:levelParticleData") ); + + // Succeeded. + isInit = true; + return true; + +} + +//-------------------------------------------------------------------------- + +// Initialize tunes to e+e- and pp/ppbar data. + +void Pythia::initTunes(int eeTune, int ppTune) { + + // Modes to use. Fast return if all is default. + if (eeTune == 0 && ppTune == 0) { + eeTune = settings.mode("Tune:ee"); + ppTune = settings.mode("Tune:pp"); + } + if (eeTune == 0 && ppTune == 0) return; + + // Old flavour and FSR defaults carried over from very old JETSET tune, + // only with alphaS roughly tuned for "new" pT-ordered shower. + if (eeTune == 1) { + settings.parm("StringFlav:probStoUD", 0.30 ); + settings.parm("StringFlav:probQQtoQ", 0.10 ); + settings.parm("StringFlav:probSQtoQQ", 0.40 ); + settings.parm("StringFlav:probQQ1toQQ0", 0.05 ); + settings.parm("StringFlav:mesonUDvector", 1.00 ); + settings.parm("StringFlav:mesonSvector", 1.50 ); + settings.parm("StringFlav:mesonCvector", 2.50 ); + settings.parm("StringFlav:mesonBvector", 3.00 ); + settings.parm("StringFlav:etaSup", 1.00 ); + settings.parm("StringFlav:etaPrimeSup", 0.40 ); + settings.parm("StringFlav:popcornSpair", 0.50 ); + settings.parm("StringFlav:popcornSmeson", 0.50 ); + settings.parm("StringZ:aLund", 0.30 ); + settings.parm("StringZ:bLund", 0.58 ); + settings.parm("StringZ:rFactB", 1.00 ); + settings.parm("StringPT:sigma", 0.36 ); + settings.parm("TimeShower:alphaSvalue", 0.137 ); + settings.parm("TimeShower:pTmin", 0.5 ); + settings.parm("TimeShower:pTminChgQ", 0.5 ); + } + + // Marc Montull's tune to particle composition at LEP1 (August 2007). + else if (eeTune == 2) { + settings.parm("StringFlav:probStoUD", 0.22 ); + settings.parm("StringFlav:probQQtoQ", 0.08 ); + settings.parm("StringFlav:probSQtoQQ", 0.75 ); + settings.parm("StringFlav:probQQ1toQQ0", 0.025 ); + settings.parm("StringFlav:mesonUDvector", 0.5 ); + settings.parm("StringFlav:mesonSvector", 0.6 ); + settings.parm("StringFlav:mesonCvector", 1.5 ); + settings.parm("StringFlav:mesonBvector", 2.5 ); + settings.parm("StringFlav:etaSup", 0.60 ); + settings.parm("StringFlav:etaPrimeSup", 0.15 ); + settings.parm("StringFlav:popcornSpair", 1.0 ); + settings.parm("StringFlav:popcornSmeson", 1.0 ); + settings.parm("StringZ:aLund", 0.76 ); + settings.parm("StringZ:bLund", 0.58 ); // kept fixed + settings.parm("StringZ:rFactB", 1.00 ); // kept fixed + settings.parm("StringPT:sigma", 0.36 ); // kept fixed + settings.parm("TimeShower:alphaSvalue", 0.137 ); // kept fixed + settings.parm("TimeShower:pTmin", 0.5 ); // kept fixed + settings.parm("TimeShower:pTminChgQ", 0.5 ); // kept fixed + } + + // Full e+e- tune of flavours and FSR to LEP1 data within the + // Rivet + Professor framework, by Hendrik Hoeth (June 2009). + else if (eeTune == 3) { + settings.parm("StringFlav:probStoUD", 0.19 ); + settings.parm("StringFlav:probQQtoQ", 0.09 ); + settings.parm("StringFlav:probSQtoQQ", 1.00 ); + settings.parm("StringFlav:probQQ1toQQ0", 0.027 ); + settings.parm("StringFlav:mesonUDvector", 0.62 ); + settings.parm("StringFlav:mesonSvector", 0.725 ); + settings.parm("StringFlav:mesonCvector", 1.06 ); + settings.parm("StringFlav:mesonBvector", 3.0 ); + settings.parm("StringFlav:etaSup", 0.63 ); + settings.parm("StringFlav:etaPrimeSup", 0.12 ); + settings.parm("StringFlav:popcornSpair", 0.5 ); // kept fixed + settings.parm("StringFlav:popcornSmeson", 0.5 ); // kept fixed + settings.parm("StringZ:aLund", 0.3 ); // kept fixed + settings.parm("StringZ:bLund", 0.8 ); + settings.parm("StringZ:rFactB", 0.67 ); + settings.parm("StringPT:sigma", 0.304 ); + settings.parm("TimeShower:alphaSvalue", 0.1383); + settings.parm("TimeShower:pTmin", 0.4 ); // kept fixed (near limit) + settings.parm("TimeShower:pTminChgQ", 0.4 ); // kept same as pTmin + } + + // Old ISR and MI defaults from early and primitive comparisons with data. + if (ppTune == 1) { + settings.mode("PDF:pSet", 2 ); + settings.parm("SigmaProcess:alphaSvalue", 0.1265); + settings.parm("SigmaDiffractive:dampen", false ); + settings.flag("TimeShower:dampenBeamRecoil", false ); + settings.flag("TimeShower:phiPolAsym", false ); + settings.parm("SpaceShower:alphaSvalue", 0.127 ); + settings.flag("SpaceShower:samePTasMI", true ); + settings.parm("SpaceShower:pT0Ref", 2.2 ); + settings.parm("SpaceShower:ecmRef", 1800.0); + settings.parm("SpaceShower:ecmPow", 0.16 ); + settings.flag("SpaceShower:rapidityOrder", false ); + settings.flag("SpaceShower:phiPolAsym", false ); + settings.flag("SpaceShower:phiIntAsym", false ); + settings.parm("MultipleInteractions:alphaSvalue", 0.127 ); + settings.parm("MultipleInteractions:pT0Ref", 2.15 ); + settings.parm("MultipleInteractions:ecmRef", 1800. ); + settings.parm("MultipleInteractions:ecmPow", 0.16 ); + settings.mode("MultipleInteractions:bProfile", 2 ); + settings.parm("BeamRemnants:primordialKTsoft", 0.4 ); + settings.parm("BeamRemnants:primordialKThard", 2.1 ); + settings.parm("BeamRemnants:halfScaleForKT", 7.0 ); + settings.parm("BeamRemnants:halfMassForKT", 2.0 ); + settings.parm("BeamRemnants:reconnectRange", 2.5 ); + } + + // "Tune 1" simple first tune by Peter Skands to ISR and MI, July 2009. + else if (ppTune == 2) { + settings.mode("PDF:pSet", 2 ); + settings.parm("SigmaProcess:alphaSvalue", 0.1265); + settings.parm("SigmaDiffractive:dampen", false ); + settings.flag("TimeShower:dampenBeamRecoil", false ); + settings.flag("TimeShower:phiPolAsym", false ); + settings.parm("SpaceShower:alphaSvalue", 0.137 ); + settings.flag("SpaceShower:samePTasMI", false ); + settings.parm("SpaceShower:pT0Ref", 2.0 ); + settings.parm("SpaceShower:ecmRef", 1800.0); + settings.parm("SpaceShower:ecmPow", 0.0 ); + settings.flag("SpaceShower:rapidityOrder", false ); + settings.flag("SpaceShower:phiPolAsym", false ); + settings.flag("SpaceShower:phiIntAsym", false ); + settings.parm("MultipleInteractions:alphaSvalue", 0.127 ); + settings.parm("MultipleInteractions:pT0Ref", 2.25 ); + settings.parm("MultipleInteractions:ecmRef", 1800. ); + settings.parm("MultipleInteractions:ecmPow", 0.24 ); + settings.mode("MultipleInteractions:bProfile", 1 ); + settings.parm("BeamRemnants:primordialKTsoft", 0.5 ); + settings.parm("BeamRemnants:primordialKThard", 2.0 ); + settings.parm("BeamRemnants:halfScaleForKT", 1.0 ); + settings.parm("BeamRemnants:halfMassForKT", 1.0 ); + settings.parm("BeamRemnants:reconnectRange", 10.0 ); + } + + // Draft Tune 2C, July 2010. + else if (ppTune == 3) { + settings.mode("PDF:pSet", 8 ); + settings.parm("SigmaProcess:alphaSvalue", 0.135 ); + settings.parm("SigmaDiffractive:dampen", false ); + settings.flag("TimeShower:dampenBeamRecoil", true ); + settings.flag("TimeShower:phiPolAsym", true ); + settings.parm("SpaceShower:alphaSvalue", 0.137 ); + settings.flag("SpaceShower:samePTasMI", false ); + settings.parm("SpaceShower:pT0Ref", 2.0 ); + settings.parm("SpaceShower:ecmRef", 1800.0); + settings.parm("SpaceShower:ecmPow", 0.0 ); + settings.flag("SpaceShower:rapidityOrder", true ); + settings.flag("SpaceShower:phiPolAsym", true ); + settings.flag("SpaceShower:phiIntAsym", true ); + settings.parm("MultipleInteractions:alphaSvalue", 0.135 ); + settings.parm("MultipleInteractions:pT0Ref", 2.32 ); + settings.parm("MultipleInteractions:ecmRef", 1800. ); + settings.parm("MultipleInteractions:ecmPow", 0.21 ); + settings.mode("MultipleInteractions:bProfile", 3 ); + settings.parm("MultipleInteractions:expPow", 1.6 ); + settings.parm("BeamRemnants:primordialKTsoft", 0.5 ); + settings.parm("BeamRemnants:primordialKThard", 2.0 ); + settings.parm("BeamRemnants:halfScaleForKT", 1.0 ); + settings.parm("BeamRemnants:halfMassForKT", 1.0 ); + settings.parm("BeamRemnants:reconnectRange", 3.0 ); + } + + // Draft Tune 2M, July 2010. + else if (ppTune == 4) { + settings.mode("PDF:pSet", 4 ); + settings.parm("SigmaProcess:alphaSvalue", 0.1265); + settings.parm("SigmaDiffractive:dampen", false ); + settings.flag("TimeShower:dampenBeamRecoil", true ); + settings.flag("TimeShower:phiPolAsym", true ); + settings.parm("SpaceShower:alphaSvalue", 0.130 ); + settings.flag("SpaceShower:samePTasMI", false ); + settings.parm("SpaceShower:pT0Ref", 2.0 ); + settings.parm("SpaceShower:ecmRef", 1800.0); + settings.parm("SpaceShower:ecmPow", 0.0 ); + settings.flag("SpaceShower:rapidityOrder", true ); + settings.flag("SpaceShower:phiPolAsym", true ); + settings.flag("SpaceShower:phiIntAsym", true ); + settings.parm("MultipleInteractions:alphaSvalue", 0.127 ); + settings.parm("MultipleInteractions:pT0Ref", 2.455 ); + settings.parm("MultipleInteractions:ecmRef", 1800. ); + settings.parm("MultipleInteractions:ecmPow", 0.26 ); + settings.mode("MultipleInteractions:bProfile", 3 ); + settings.parm("MultipleInteractions:expPow", 1.15 ); + settings.parm("BeamRemnants:primordialKTsoft", 0.5 ); + settings.parm("BeamRemnants:primordialKThard", 2.0 ); + settings.parm("BeamRemnants:halfScaleForKT", 1.0 ); + settings.parm("BeamRemnants:halfMassForKT", 1.0 ); + settings.parm("BeamRemnants:reconnectRange", 3.0 ); + } + + // Draft Tune 3C, July 2010. + else if (ppTune == 5) { + settings.mode("PDF:pSet", 8 ); + settings.parm("SigmaProcess:alphaSvalue", 0.135 ); + settings.parm("SigmaDiffractive:dampen", true ); + settings.flag("TimeShower:dampenBeamRecoil", true ); + settings.flag("TimeShower:phiPolAsym", true ); + settings.parm("SpaceShower:alphaSvalue", 0.130 ); + settings.flag("SpaceShower:samePTasMI", false ); + settings.parm("SpaceShower:pT0Ref", 2.0 ); + settings.parm("SpaceShower:ecmRef", 1800.0); + settings.parm("SpaceShower:ecmPow", 0.0 ); + settings.flag("SpaceShower:rapidityOrder", true ); + settings.flag("SpaceShower:phiPolAsym", true ); + settings.flag("SpaceShower:phiIntAsym", true ); + settings.parm("MultipleInteractions:alphaSvalue", 0.135 ); + settings.parm("MultipleInteractions:pT0Ref", 2.10 ); + settings.parm("MultipleInteractions:ecmRef", 1800. ); + settings.parm("MultipleInteractions:ecmPow", 0.18 ); + settings.mode("MultipleInteractions:bProfile", 3 ); + settings.parm("MultipleInteractions:expPow", 1.6 ); + settings.parm("BeamRemnants:primordialKTsoft", 0.5 ); + settings.parm("BeamRemnants:primordialKThard", 2.0 ); + settings.parm("BeamRemnants:halfScaleForKT", 1.0 ); + settings.parm("BeamRemnants:halfMassForKT", 1.0 ); + settings.parm("BeamRemnants:reconnectRange", 3.0 ); + } + + // Draft Tune 3M, July 2010. + else if (ppTune == 6) { + settings.mode("PDF:pSet", 4 ); + settings.parm("SigmaProcess:alphaSvalue", 0.1265); + settings.parm("SigmaDiffractive:dampen", true ); + settings.flag("TimeShower:dampenBeamRecoil", true ); + settings.flag("TimeShower:phiPolAsym", true ); + settings.parm("SpaceShower:alphaSvalue", 0.130 ); + settings.flag("SpaceShower:samePTasMI", false ); + settings.parm("SpaceShower:pT0Ref", 2.0 ); + settings.parm("SpaceShower:ecmRef", 1800.0); + settings.parm("SpaceShower:ecmPow", 0.0 ); + settings.flag("SpaceShower:rapidityOrder", true ); + settings.flag("SpaceShower:phiPolAsym", true ); + settings.flag("SpaceShower:phiIntAsym", true ); + settings.parm("MultipleInteractions:alphaSvalue", 0.127 ); + settings.parm("MultipleInteractions:pT0Ref", 2.20 ); + settings.parm("MultipleInteractions:ecmRef", 1800. ); + settings.parm("MultipleInteractions:ecmPow", 0.20 ); + settings.mode("MultipleInteractions:bProfile", 3 ); + settings.parm("MultipleInteractions:expPow", 1.15 ); + settings.parm("BeamRemnants:primordialKTsoft", 0.5 ); + settings.parm("BeamRemnants:primordialKThard", 2.0 ); + settings.parm("BeamRemnants:halfScaleForKT", 1.0 ); + settings.parm("BeamRemnants:halfMassForKT", 1.0 ); + settings.parm("BeamRemnants:reconnectRange", 3.0 ); + } +} + +//-------------------------------------------------------------------------- + +// Check that combinations of settings are allowed; change if not. + +void Pythia::checkSettings() { + + // Double rescattering not allowed if ISR or FSR. + if ((settings.flag("PartonLevel:ISR") || settings.flag("PartonLevel:FSR")) + && settings.flag("MultipleInteractions:allowDoubleRescatter")) { + info.errorMsg("Warning in Pythia::checkSettings: " + "double rescattering switched off since showering is on"); + settings.flag("MultipleInteractions:allowDoubleRescatter", false); + } + +} + +//-------------------------------------------------------------------------- + +// Check that beams and beam combination can be handled. + +bool Pythia::checkBeams() { + + // Absolute flavours. If not to do process level then no check needed. + int idAabs = abs(idA); + int idBabs = abs(idB); + if (!doProcessLevel) return true; + + // Hadron-hadron collisions OK. + bool isHadronA = (idAabs == 2212) || (idA == 111) || (idAabs == 211) + || (idA == 990); + bool isHadronB = (idBabs == 2212) || (idA == 111)|| (idBabs == 211) + || (idB == 990); + if (isHadronA && isHadronB) return true; + + // Lepton-lepton collisions OK. + if ( idAabs == idBabs && (idAabs == 11 || idAabs == 13 || idAabs == 15) ) + return true; + + // Only allow neutrinos as beams when leptons unresolved. + if ( idAabs > 10 && idAabs < 17 && idA * idB < 0 + && !settings.flag("PDF:lepton") ) { + if (idAabs == idBabs) return true; + + // Lepton-neutrino only if in same generation. + int idMax = max(idAabs, idBabs); + int idMin = min(idAabs, idBabs); + if (idMax - idMin == 1 && idMax%2 == 0) return true; + } + + // If no case above then failed. + info.errorMsg("Error in Pythia::init: cannot handle this beam combination"); + return false; + +} + +//-------------------------------------------------------------------------- + +// Calculate kinematics at initialization. Store beam four-momenta. + +bool Pythia::initKinematics() { + + // Find masses. Initial guess that we are in CM frame. + mA = particleData.m0(idA); + mB = particleData.m0(idB); + betaZ = 0.; + gammaZ = 1.; + + // Collinear beams not in CM frame: find CM energy. + if (frameType == 2) { + eA = max(eA, mA); + eB = max(eB, mB); + pzA = sqrt(eA*eA - mA*mA); + pzB = -sqrt(eB*eB - mB*mB); + pAinit = Vec4( 0., 0., pzA, eA); + pBinit = Vec4( 0., 0., pzB, eB); + eCM = sqrt( pow2(eA + eB) - pow2(pzA + pzB) ); + + // Find boost to rest frame. + betaZ = (pzA + pzB) / (eA + eB); + gammaZ = (eA + eB) / eCM; + if (abs(betaZ) < 1e-10) frameType = 1; + } + + // Completely general beam directions: find CM energy. + else if (frameType == 3) { + eA = sqrt( pxA*pxA + pyA*pyA + pzA*pzA + mA*mA); + eB = sqrt( pxB*pxB + pyB*pyB + pzB*pzB + mB*mB); + pAinit = Vec4( pxA, pyA, pzA, eA); + pBinit = Vec4( pxB, pyB, pzB, eB); + eCM = (pAinit + pBinit).mCalc(); + + // Find boost+rotation needed to move from/to CM frame. + MfromCM.reset(); + MfromCM.fromCMframe( pAinit, pBinit); + MtoCM = MfromCM; + MtoCM.invert(); + } + + // Fail if CM energy below beam masses. + if (eCM < mA + mB) { + info.errorMsg("Error in Pythia::initKinematics: too low energy"); + return false; + } + + // Set up CM-frame kinematics with beams along +-z axis. + pzAcm = 0.5 * sqrtpos( (eCM + mA + mB) * (eCM - mA - mB) + * (eCM - mA + mB) * (eCM + mA - mB) ) / eCM; + pzBcm = -pzAcm; + eA = sqrt(mA*mA + pzAcm*pzAcm); + eB = sqrt(mB*mB + pzBcm*pzBcm); + + // If in CM frame then store beam four-vectors (else already done above). + if (frameType != 2 && frameType != 3) { + pAinit = Vec4( 0., 0., pzAcm, eA); + pBinit = Vec4( 0., 0., pzBcm, eB); + } + + // Store main info for access in process generation. + info.setBeamA( idA, pzAcm, eA, mA); + info.setBeamB( idB, pzBcm, eB, mB); + info.setECM( eCM); + + // Must allow for generic boost+rotation when beam momentum spread. + if (doMomentumSpread) frameType = 3; + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Set up pointers to PDFs. + +bool Pythia::initPDFs() { + + // Delete any PDF's created in a previous initInternal call. + if (useNewPdfHard) { + if (pdfHardAPtr != pdfAPtr) { + delete pdfHardAPtr; + pdfHardAPtr = 0; + } + if (pdfHardBPtr != pdfBPtr) { + delete pdfHardBPtr; + pdfHardBPtr = 0; + } + useNewPdfHard = false; + } + if (useNewPdfA) { + delete pdfAPtr; + useNewPdfA = false; + pdfAPtr = 0; + } + if (useNewPdfB) { + delete pdfBPtr; + useNewPdfB = false; + pdfBPtr = 0; + } + if (useNewPdfPomA) { + delete pdfPomAPtr; + useNewPdfPomA = false; + pdfPomAPtr = 0; + } + if (useNewPdfPomB) { + delete pdfPomBPtr; + useNewPdfPomB = false; + pdfPomBPtr = 0; + } + + // Set up the PDF's, if not already done. + if (pdfAPtr == 0) { + pdfAPtr = getPDFPtr(idA); + if (pdfAPtr == 0 || !pdfAPtr->isSetup()) { + info.errorMsg("Error in Pythia::init: " + "could not set up PDF for beam A"); + return false; + } + pdfHardAPtr = pdfAPtr; + useNewPdfA = true; + } + if (pdfBPtr == 0) { + pdfBPtr = getPDFPtr(idB); + if (pdfBPtr == 0 || !pdfBPtr->isSetup()) { + info.errorMsg("Error in Pythia::init: " + "could not set up PDF for beam B"); + return false; + } + pdfHardBPtr = pdfBPtr; + useNewPdfB = true; + } + + // Optionally set up separate PDF's for hard process. + if (settings.flag("PDF:useHard") && useNewPdfA && useNewPdfB) { + pdfHardAPtr = getPDFPtr(idA, 2); + if (!pdfHardAPtr->isSetup()) return false; + pdfHardBPtr = getPDFPtr(idB, 2); + if (!pdfHardBPtr->isSetup()) return false; + useNewPdfHard = true; + } + + // Optionally set up Pomeron PDF's for diffractive physics. + if ( doDiffraction) { + if (pdfPomAPtr == 0) { + pdfPomAPtr = getPDFPtr(990); + useNewPdfPomA = true; + } + if (pdfPomBPtr == 0) { + pdfPomBPtr = getPDFPtr(990); + useNewPdfPomB = true; + } + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Main routine to generate the next event, using internal machinery. + +bool Pythia::next() { + + // Set/reset info counters specific to each event. + info.addCounter(3); + for (int i = 10; i < 13; ++i) info.setCounter(i); + + // Simpler option when only HadronLevel to be generated. + if (!doProcessLevel) { + + // Set correct energy for system. + Vec4 pSum = 0.; + for (int i = 1; i < event.size(); ++i) + if (event[i].isFinal()) pSum += event[i].p(); + event[0].p( pSum ); + event[0].m( pSum.mCalc() ); + + // Generate hadronization and decays. + bool status = forceHadronLevel(); + if (status) info.addCounter(4); + return status; + } + + // Reset arrays. + info.clear(); + process.clear(); + event.clear(); + partonSystems.clear(); + beamA.clear(); + beamB.clear(); + beamPomA.clear(); + beamPomB.clear(); + + // Can only generate event if initialization worked. + if (!isInit) { + info.errorMsg("Abort from Pythia::next: " + "not properly initialized so cannot generate events"); + return false; + } + + // Pick beam momentum spread and beam vertex. + if (doMomentumSpread || doVertexSpread) beamShapePtr->pick(); + + // Recalculate kinematics when beam momentum spread. + if (doMomentumSpread) nextKinematics(); + + // Outer loop over hard processes; only relevant for user-set vetoes. + for ( ; ; ) { + info.addCounter(10); + bool hasVetoed = false; + + // Provide the hard process that starts it off. Only one try. + info.clear(); + process.clear(); + if ( !processLevel.next( process) ) { + if (doLHA && info.atEndOfFile()) info.errorMsg("Abort from " + "Pythia::next: reached end of Les Houches Events File"); + else info.errorMsg("Abort from Pythia::next: " + "processLevel failed; giving up"); + return false; + } + info.addCounter(11); + + // Possibility for a user veto of the process-level event. + if (doVetoProcess) { + hasVetoed = userHooksPtr->doVetoProcessLevel( process); + if (hasVetoed) continue; + } + + // Possibility to stop the generation at this stage. + if (!doPartonLevel) { + boostAndVertex( true, true); + processLevel.accumulate(); + info.addCounter(4); + return true; + } + + // Save spare copy of process record in case of problems. + Event processSave = process; + info.addCounter(12); + for (int i = 14; i < 19; ++i) info.setCounter(i); + + // Allow up to ten tries for parton- and hadron-level processing. + bool physical = true; + for (int iTry = 0; iTry < NTRY; ++ iTry) { + info.addCounter(14); + physical = true; + + // Restore original process record if problems. + if (iTry > 0) process = processSave; + + // Reset event record and (extracted partons from) beam remnants. + event.clear(); + beamA.clear(); + beamB.clear(); + beamPomA.clear(); + beamPomB.clear(); + partonSystems.clear(); + + // Parton-level evolution: ISR, FSR, MI. + if ( !partonLevel.next( process, event) ) { + // Skip to next hard process for failure owing to deliberate veto. + hasVetoed = partonLevel.hasVetoed(); + if (hasVetoed) break; + // Else make a new try for other failures. + info.errorMsg("Error in Pythia::next: " + "partonLevel failed; try again"); + physical = false; + continue; + } + info.addCounter(15); + + // Possibility for a user veto of the parton-level event. + if (doVetoPartons) { + hasVetoed = userHooksPtr->doVetoPartonLevel( event); + if (hasVetoed) break; + } + + // Boost to lab frame (before decays, for vertices). + boostAndVertex( true, true); + + // Possibility to stop the generation at this stage. + if (!doHadronLevel) { + processLevel.accumulate(); + partonLevel.accumulate(); + + // Optionally check final event for problems. + if (checkEvent && !check()) { + info.errorMsg("Abort from Pythia::next: " + "check of event revealed problems"); + return false; + } + info.addCounter(4); + return true; + } + + // Hadron-level: hadronization, decays. + info.addCounter(16); + if ( !hadronLevel.next( event) ) { + info.errorMsg("Error in Pythia::next: " + "hadronLevel failed; try again"); + physical = false; + continue; + } + info.addCounter(17); + + // Optionally check final event for problems. + if (checkEvent && !check()) { + info.errorMsg("Error in Pythia::next: " + "check of event revealed problems"); + physical = false; + continue; + } + + // Stop parton- and hadron-level looping if you got this far. + info.addCounter(18); + break; + } + + // If event vetoed then to make a new try. + if (hasVetoed) continue; + + // If event failed any other way (after ten tries) then give up. + if (!physical) { + info.errorMsg("Abort from Pythia::next: " + "parton+hadronLevel failed; giving up"); + return false; + } + + // Process- and parton-level statistics. Event scale. + processLevel.accumulate(); + partonLevel.accumulate(); + event.scale( process.scale() ); + + // End of outer loop over hard processes. Done with normal option. + info.addCounter(13); + break; + } + + // Done. + info.addCounter(4); + return true; + +} + +//-------------------------------------------------------------------------- + +// Generate only the hadronization/decay stage, using internal machinery. +// The "event" instance should already contain a parton-level configuration. + +bool Pythia::forceHadronLevel() { + + // Can only generate event if initialization worked. + if (!isInit) { + info.errorMsg("Abort from Pythia::forceHadronLevel: " + "not properly initialized so cannot generate events"); + return false; + } + + // Check whether any junctions in system. (Normally done in ProcessLevel.) + event.clearJunctions(); + processLevel.findJunctions( event); + + // Save spare copy of event in case of failure. + Event spareEvent = event; + + // Allow up to ten tries for hadron-level processing. + bool physical = true; + for (int iTry = 0; iTry < NTRY; ++ iTry) { + physical = true; + + // Hadron-level: hadronization, decays. + if (hadronLevel.next( event)) break; + + // If failure then warn, restore original configuration and try again. + info.errorMsg("Error in Pythia::forceHadronLevel: " + "hadronLevel failed; try again"); + physical = false; + event = spareEvent; + } + + // Done for simpler option. + if (!physical) { + info.errorMsg("Abort from Pythia::forceHadronLevel: " + "hadronLevel failed; giving up"); + return false; + } + + // Optionally check final event for problems. + if (checkEvent && !check()) { + info.errorMsg("Abort from Pythia::forceHadronLevel: " + "check of event revealed problems"); + return false; + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Recalculate kinematics for each event when beam momentum has a spread. + +void Pythia::nextKinematics() { + + // Read out momentum shift to give current beam momenta. + pAnow = pAinit + beamShapePtr->deltaPA(); + pAnow.e( sqrt(pAnow.pAbs2() + mA * mA) ); + pBnow = pBinit + beamShapePtr->deltaPB(); + pBnow.e( sqrt(pBnow.pAbs2() + mB * mB) ); + + // Construct CM frame kinematics. + eCM = (pAnow + pBnow).mCalc(); + pzAcm = 0.5 * sqrtpos( (eCM + mA + mB) * (eCM - mA - mB) + * (eCM - mA + mB) * (eCM + mA - mB) ) / eCM; + pzBcm = -pzAcm; + eA = sqrt(mA*mA + pzAcm*pzAcm); + eB = sqrt(mB*mB + pzBcm*pzBcm); + + // Set relevant info for other classes to use. + info.setBeamA( idA, pzAcm, eA, mA); + info.setBeamB( idB, pzBcm, eB, mB); + info.setECM( eCM); + beamA.newPzE( pzAcm, eA); + beamB.newPzE( pzBcm, eB); + + // Set boost/rotation matrices from/to CM frame. + MfromCM.reset(); + MfromCM.fromCMframe( pAnow, pBnow); + MtoCM = MfromCM; + MtoCM.invert(); + +} + +//-------------------------------------------------------------------------- + +// Boost from CM frame to lab frame, or inverse. Set production vertex. + +void Pythia::boostAndVertex( bool toLab, bool setVertex) { + + // Boost process from CM frame to lab frame. + if (toLab) { + if (frameType == 2) process.bst(0., 0., betaZ, gammaZ); + else if (frameType == 3) process.rotbst(MfromCM); + + // Boost nonempty event from CM frame to lab frame. + if (event.size() > 0) { + if (frameType == 2) event.bst(0., 0., betaZ, gammaZ); + else if (frameType == 3) event.rotbst(MfromCM); + } + + // Boost process from lab frame to CM frame. + } else { + if (frameType == 2) process.bst(0., 0., -betaZ, gammaZ); + else if (frameType == 3) process.rotbst(MtoCM); + + // Boost nonempty event from lab frame to CM frame. + if (event.size() > 0) { + if (frameType == 2) event.bst(0., 0., -betaZ, gammaZ); + else if (frameType == 3) event.rotbst(MtoCM); + } + } + + // Set production vertex; assumes particles are in lab frame and at origin + if (setVertex && doVertexSpread) { + Vec4 vertex = beamShapePtr->vertex(); + for (int i = 0; i < process.size(); ++i) process[i].vProd( vertex); + for (int i = 0; i < event.size(); ++i) event[i].vProd( vertex); + } + +} + +//-------------------------------------------------------------------------- + +// Print statistics on event generation. + +void Pythia::statistics(bool all, bool reset) { + + // Statistics on cross section and number of events. + if (doProcessLevel) processLevel.statistics(reset); + + // Statistics from other classes, e.g. multiple interactions. + if (all) partonLevel.statistics(reset); + + // Summary of which and how many warnings/errors encountered. + info.errorStatistics(); + if (reset) info.errorReset(); + +} + +//-------------------------------------------------------------------------- + +// Write the Pythia banner, with symbol and version information. + +void Pythia::banner(ostream& os) { + + // Read in version number and last date of change. + double versionNumber = settings.parm("Pythia:versionNumber"); + int versionDate = settings.mode("Pythia:versionDate"); + string month[12] = {"Jan", "Feb", "Mar", "Apr", "May", "Jun", + "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"}; + + // Get date and time. + time_t t = time(0); + char dateNow[12]; + strftime(dateNow,12,"%d %b %Y",localtime(&t)); + char timeNow[9]; + strftime(timeNow,9,"%H:%M:%S",localtime(&t)); + + os << "\n" + << " *-------------------------------------------" + << "-----------------------------------------* \n" + << " | " + << " | \n" + << " | *----------------------------------------" + << "--------------------------------------* | \n" + << " | | " + << " | | \n" + << " | | " + << " | | \n" + << " | | PPP Y Y TTTTT H H III A " + << " Welcome to the Lund Monte Carlo! | | \n" + << " | | P P Y Y T H H I A A " + << " This is PYTHIA version " << fixed << setprecision(3) + << setw(5) << versionNumber << " | | \n" + << " | | PPP Y T HHHHH I AAAAA" + << " Last date of change: " << setw(2) << versionDate%100 + << " " << month[ (versionDate/100)%100 - 1 ] + << " " << setw(4) << versionDate/10000 << " | | \n" + << " | | P Y T H H I A A" + << " | | \n" + << " | | P Y T H H III A A" + << " Now is " << dateNow << " at " << timeNow << " | | \n" + << " | | " + << " | | \n" + << " | | Torbjorn Sjostrand; Department of Th" + << "eoretical Physics, Lund University, | | \n" + << " | | Solvegatan 14A, SE-223 62 Lund, Sw" + << "eden; | | \n" + << " | | phone: + 46 - 46 - 222 48 16; e-ma" + << "il: torbjorn@thep.lu.se | | \n" + << " | | Stefan Ask; School of Physics and As" + << "tronomy, University of Manchester, | | \n" + << " | | Oxford Road, Manchester M13 9PL, U" + << "nited Kingdom; | | \n" + << " | | phone: + 41 - 22 - 767 5670; e-mai" + << "l: Stefan.Ask@cern.ch | | \n" + << " | | Richard Corke; Department of Theoret" + << "ical Physics, Lund University, | | \n" + << " | | Solvegatan 14A, SE-223 62 Lund, Sw" + << "eden; | | \n" + << " | | phone: + 46 - 46 - 222 31 92; e-ma" + << "il: richard.corke@thep.lu.se | | \n" + << " | | Stephen Mrenna; Computing Division, " + << "Simulations Group, | | \n" + << " | | Fermi National Accelerator Laborat" + << "ory, MS 234, Batavia, IL 60510, USA; | | \n" + << " | | phone: + 1 - 630 - 840 - 2556; e-m" + << "ail: mrenna@fnal.gov | | \n" + << " | | Peter Skands; Theoretical Physics, C" + << "ERN, CH-1211 Geneva 23, Switzerland; | | \n" + << " | | phone: + 41 - 22 - 767 2447; e-mai" + << "l: peter.skands@cern.ch | | \n" + << " | | " + << " | | \n" + << " | | The main program reference is the 'Br" + << "ief Introduction to PYTHIA 8.1', | | \n" + << " | | T. Sjostrand, S. Mrenna and P. Skands" + << ", Comput. Phys. Comm. 178 (2008) 85 | | \n" + << " | | [arXiv:0710.3820] " + << " | | \n" + << " | | " + << " | | \n" + << " | | The main physics reference is the 'PY" + << "THIA 6.4 Physics and Manual', | | \n" + << " | | T. Sjostrand, S. Mrenna and P. Skands" + << ", JHEP05 (2006) 026 [hep-ph/0603175]. | | \n" + << " | | " + << " | | \n" + << " | | An archive of program versions and do" + << "cumentation is found on the web: | | \n" + << " | | http://www.thep.lu.se/~torbjorn/Pythi" + << "a.html | | \n" + << " | | " + << " | | \n" + << " | | This program is released under the GN" + << "U General Public Licence version 2. | | \n" + << " | | Please respect the MCnet Guidelines f" + << "or Event Generator Authors and Users. | | \n" + << " | | " + << " | | \n" + << " | | Disclaimer: this program comes withou" + << "t any guarantees. | | \n" + << " | | Beware of errors and use common sense" + << " when interpreting results. | | \n" + << " | | " + << " | | \n" + << " | | Copyright (C) 2010 Torbjorn Sjostrand" + << " | | \n" + << " | | " + << " | | \n" + << " | | " + << " | | \n" + << " | *----------------------------------------" + << "--------------------------------------* | \n" + << " | " + << " | \n" + << " *-------------------------------------------" + << "-----------------------------------------* \n" << endl; + +} + +//-------------------------------------------------------------------------- + +// Check for lines in file that mark the beginning of new subrun. + +int Pythia::readSubrun(string line, bool warn, ostream& os) { + + // If empty line then done. + int subrunLine = SUBRUNDEFAULT; + if (line.find_first_not_of(" \n\t\v\b\r\f\a") == string::npos) return subrunLine; + + // If first character is not a letter, then done. + string lineNow = line; + int firstChar = lineNow.find_first_not_of(" \n\t\v\b\r\f\a"); + if (!isalpha(lineNow[firstChar])) return subrunLine; + + // Replace an equal sign by a blank to make parsing simpler. + while (lineNow.find("=") != string::npos) { + int firstEqual = lineNow.find_first_of("="); + lineNow.replace(firstEqual, 1, " "); + } + + // Get first word of a line. + istringstream splitLine(lineNow); + string name; + splitLine >> name; + + // Replace two colons by one (:: -> :) to allow for such mistakes. + while (name.find("::") != string::npos) { + int firstColonColon = name.find_first_of("::"); + name.replace(firstColonColon, 2, ":"); + } + + // Convert to lowercase. + for (int i = 0; i < int(name.length()); ++i) + name[i] = std::tolower(name[i]); + + // If no match then done. + if (name != "main:subrun") return subrunLine; + + // Else find new subrun number and return it. + splitLine >> subrunLine; + if (!splitLine) { + if (warn) os << "\n PYTHIA Warning: Main:subrun number not" + << " recognized; skip:\n " << line << endl; + subrunLine = SUBRUNDEFAULT; + } + return subrunLine; + +} + +//-------------------------------------------------------------------------- + +// Check that the final event makes sense: no unknown id codes; +// charge and energy-momentum conserved. + +bool Pythia::check(ostream& os) { + + // Reset. + bool physical = true; + bool listVertices = false; + bool listSystems = false; + bool listBeams = false; + iErrId.resize(0); + iErrCol.resize(0); + iErrNan.resize(0); + iErrNanVtx.resize(0); + Vec4 pSum; + double chargeSum = 0.; + + // Incoming beams counted with negative momentum and charge. + if (doProcessLevel) { + pSum = - (event[1].p() + event[2].p()); + chargeSum = - (event[1].charge() + event[2].charge()); + + // If no ProcessLevel then sum final state of process record. + } else if (process.size() > 0) { + pSum = - process[0].p(); + for (int i = 0; i < process.size(); ++i) + if (process[i].isFinal()) chargeSum -= process[i].charge(); + + // If process not filled, then use outgoing primary in event. + } else { + pSum = - event[0].p(); + for (int i = 1; i < event.size(); ++i) + if (event[i].statusAbs() < 10 || event[i].statusAbs() == 23) + chargeSum -= event[i].charge(); + } + double eLab = abs(pSum.e()); + + // Loop over particles in the event. + for (int i = 0; i < event.size(); ++i) { + + // Look for any unrecognized particle codes. + int id = event[i].id(); + if (id == 0 || !particleData.isParticle(id)) { + ostringstream errCode; + errCode << ", id = " << id; + info.errorMsg("Error in Pythia::check: " + "unknown particle code", errCode.str()); + physical = false; + iErrId.push_back(i); + + // Check that colour assignments are the expected ones. + } else { + int colType = event[i].colType(); + int col = event[i].col(); + int acol = event[i].acol(); + if ( (colType == 0 && (col > 0 || acol > 0)) + || (colType == 1 && (col <= 0 || acol > 0)) + || (colType == -1 && (col > 0 || acol <= 0)) + || (colType == 2 && (col <= 0 || acol <= 0)) ) { + ostringstream errCode; + errCode << ", id = " << id << " cols = " << col << " " << acol; + info.errorMsg("Error in Pythia::check: " + "incorrect colours", errCode.str()); + physical = false; + iErrCol.push_back(i); + } + } + + // Look for particles with not-a-number energy/momentum/mass. + if (abs(event[i].px()) >= 0. && abs(event[i].py()) >= 0. + && abs(event[i].pz()) >= 0. && abs(event[i].e()) >= 0. + && abs(event[i].m()) >= 0.) ; + else { + info.errorMsg("Error in Pythia::check: " + "not-a-number energy/momentum/mass"); + physical = false; + iErrNan.push_back(i); + } + + // Look for particles with not-a-number vertex/lifetime. + if (abs(event[i].xProd()) >= 0. && abs(event[i].yProd()) >= 0. + && abs(event[i].zProd()) >= 0. && abs(event[i].tProd()) >= 0. + && abs(event[i].tau()) >= 0.) ; + else { + info.errorMsg("Error in Pythia::check: " + "not-a-number vertex/lifetime"); + physical = false; + listVertices = true; + iErrNanVtx.push_back(i); + } + + // Add final-state four-momentum and charge. + if (event[i].isFinal()) { + pSum += event[i].p(); + chargeSum += event[i].charge(); + } + + // End of particle loop. + } + + // Check energy-momentum/charge conservation. + double epDev = abs(pSum.e()) + abs(pSum.px()) + abs(pSum.py()) + + abs(pSum.pz()); + if (epDev > epTolErr * eLab) { + info.errorMsg("Error in Pythia::check: energy-momentum not conserved"); + physical = false; + } else if (epDev > epTolWarn * eLab) { + info.errorMsg("Warning in Pythia::check: " + "energy-momentum not quite conserved"); + } + if (abs(chargeSum) > 0.1) { + info.errorMsg("Error in Pythia::check: charge not conserved"); + physical = false; + } + + // Check that beams and event records agree on incoming partons. + // Only meaningful for resolved beams. + if (info.isResolved()) + for (int iSys = 0; iSys < beamA.sizeInit(); ++iSys) { + int eventANw = partonSystems.getInA(iSys); + int eventBNw = partonSystems.getInB(iSys); + int beamANw = beamA[iSys].iPos(); + int beamBNw = beamB[iSys].iPos(); + if (eventANw != beamANw || eventBNw != beamBNw) { + info.errorMsg("Error in Pythia::check: " + "event and beams records disagree"); + physical = false; + listSystems = true; + listBeams = true; + } + } + + // Done for sensible events. + if (physical) return true; + + // Print (the first few) flawed events. + if (nErrEvent < nErrList) { + os << " PYTHIA erroneous event info: \n"; + if (iErrId.size() > 0) { + os << " unknown particle codes in lines "; + for (int i = 0; i < int(iErrId.size()); ++i) + os << iErrId[i] << " "; + os << "\n"; + } + if (iErrCol.size() > 0) { + os << " incorrect colour assignments in lines "; + for (int i = 0; i < int(iErrCol.size()); ++i) + os << iErrCol[i] << " "; + os << "\n"; + } + if (iErrNan.size() > 0) { + os << " not-a-number energy/momentum/mass in lines "; + for (int i = 0; i < int(iErrNan.size()); ++i) + os << iErrNan[i] << " "; + os << "\n"; + } + if (iErrNanVtx.size() > 0) { + os << " not-a-number vertex/lifetime in lines "; + for (int i = 0; i < int(iErrNanVtx.size()); ++i) + os << iErrNanVtx[i] << " "; + os << "\n"; + } + if (epDev > epTolErr * eLab) os << scientific << setprecision(3) + << " total energy-momentum non-conservation = " << epDev << "\n"; + if (abs(chargeSum) > 0.1) os << fixed << setprecision(2) + << " total charge non-conservation = " << chargeSum << "\n"; + info.list(); + event.list(listVertices); + if (listSystems) partonSystems.list(); + if (listBeams) beamA.list(); + if (listBeams) beamB.list(); + } + + // Update error counter. Done also for flawed event. + ++nErrEvent; + return false; + +} + +//-------------------------------------------------------------------------- + +// Routine to set up a PDF pointer. + +PDF* Pythia::getPDFPtr(int idIn, int sequence) { + + // Temporary pointer to be returned. + PDF* tempPDFPtr = 0; + + // One option is to treat a Pomeron like a pi0. + if (idIn == 990 && settings.mode("PDF:PomSet") == 2) idIn = 111; + + // Proton beam, normal choice. + if (abs(idIn) == 2212 && sequence == 1) { + int pSet = settings.mode("PDF:pSet"); + bool useLHAPDF = settings.flag("PDF:useLHAPDF"); + + // Use internal sets. + if (!useLHAPDF) { + if (pSet == 1) tempPDFPtr = new GRV94L(idIn); + else if (pSet == 2) tempPDFPtr = new CTEQ5L(idIn); + else if (pSet <= 6) + tempPDFPtr = new MSTWpdf(idIn, pSet - 2, xmlPath, &info); + else tempPDFPtr = new CTEQ6pdf(idIn, pSet - 6, xmlPath, &info); + } + + // Use sets from LHAPDF. + else { + string LHAPDFset = settings.word("PDF:LHAPDFset"); + int LHAPDFmember = settings.mode("PDF:LHAPDFmember"); + tempPDFPtr = new LHAPDF(idIn, LHAPDFset, LHAPDFmember, 1, &info); + + // Optionally allow extrapolation beyond x and Q2 limits. + tempPDFPtr->setExtrapolate( settings.flag("PDF:extrapolateLHAPDF") ); + } + } + + // Proton beam, special choice for the hard process. + else if (abs(idIn) == 2212) { + int pSet = settings.mode("PDF:pHardSet"); + bool useLHAPDF = settings.flag("PDF:useHardLHAPDF"); + + // Use internal sets. + if (!useLHAPDF) { + if (pSet == 1) tempPDFPtr = new GRV94L(idIn); + else if (pSet == 2) tempPDFPtr = new CTEQ5L(idIn); + else if (pSet <= 6) + tempPDFPtr = new MSTWpdf(idIn, pSet - 2, xmlPath, &info); + else tempPDFPtr = new CTEQ6pdf(idIn, pSet - 6, xmlPath, &info); + } + + // Use sets from LHAPDF. + else { + string LHAPDFset = settings.word("PDF:hardLHAPDFset"); + int LHAPDFmember = settings.mode("PDF:hardLHAPDFmember"); + tempPDFPtr = new LHAPDF(idIn, LHAPDFset, LHAPDFmember, 2, &info); + + // Optionally allow extrapolation beyond x and Q2 limits. + tempPDFPtr->setExtrapolate( settings.flag("PDF:extrapolateLHAPDF") ); + } + } + + // Pion beam (or, in one option, Pomeron beam). + else if (abs(idIn) == 211 || idIn == 111) { + bool useLHAPDF = settings.flag("PDF:piUseLHAPDF"); + + // Use internal sets. + if (!useLHAPDF) { + tempPDFPtr = new GRVpiL(idIn); + } + + // Use sets from LHAPDF. + else { + string LHAPDFset = settings.word("PDF:piLHAPDFset"); + int LHAPDFmember = settings.mode("PDF:piLHAPDFmember"); + tempPDFPtr = new LHAPDF(idIn, LHAPDFset, LHAPDFmember, 1, &info); + + // Optionally allow extrapolation beyond x and Q2 limits. + tempPDFPtr->setExtrapolate( settings.flag("PDF:extrapolateLHAPDF") ); + } + } + + // Pomeron beam, if not treated like a pi0 beam. + else if (idIn == 990) { + int pomSet = settings.mode("PDF:PomSet"); + double rescale = settings.parm("PDF:PomRescale"); + + // A generic Q2-independent parametrization. + if (pomSet == 1) { + double gluonA = settings.parm("PDF:PomGluonA"); + double gluonB = settings.parm("PDF:PomGluonB"); + double quarkA = settings.parm("PDF:PomQuarkA"); + double quarkB = settings.parm("PDF:PomQuarkB"); + double quarkFrac = settings.parm("PDF:PomQuarkFrac"); + double strangeSupp = settings.parm("PDF:PomStrangeSupp"); + tempPDFPtr = new PomFix( 990, gluonA, gluonB, quarkA, quarkB, + quarkFrac, strangeSupp); + } + + // The H1 Q2-dependent parametrizations. Initialization requires files. + else if (pomSet == 3 || pomSet == 4) + tempPDFPtr = new PomH1FitAB( 990, pomSet - 2, rescale, xmlPath, &info); + else if (pomSet == 5) + tempPDFPtr = new PomH1Jets( 990, rescale, xmlPath, &info); + else if (pomSet == 6) + tempPDFPtr = new PomH1FitAB( 990, 3, rescale, xmlPath, &info); + } + + // Lepton beam; resolved or not. + else if (abs(idIn) > 10 && abs(idIn) < 17) { + if (settings.flag("PDF:lepton") && abs(idIn)%2 == 1) + tempPDFPtr = new Lepton(idIn); + else tempPDFPtr = new LeptonPoint(idIn); + } + + // Failure for unrecognized particle. + else tempPDFPtr = 0; + + // Done. + return tempPDFPtr; +} + +//-------------------------------------------------------------------------- + +} // end namespace Pythia8 + + diff --git a/PYTHIA8/pythia8140/src/PythiaStdlib.cxx b/PYTHIA8/pythia8140/src/PythiaStdlib.cxx new file mode 100644 index 00000000000..a484c3156c7 --- /dev/null +++ b/PYTHIA8/pythia8140/src/PythiaStdlib.cxx @@ -0,0 +1,41 @@ +// PythiaStdlib.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the Gamma function. + +#include "PythiaStdlib.h" + +namespace Pythia8 { + +//========================================================================== + +// The Gamma function for real arguments, using the Lanczos approximation. +// Code based on http://en.wikipedia.org/wiki/Lanczos_approximation + +double GammaCoef[9] = { + 0.99999999999980993, 676.5203681218851, -1259.1392167224028, + 771.32342877765313, -176.61502916214059, 12.507343278686905, + -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7}; + +double GammaReal(double x) { + + // Reflection formula (recursive!) for x < 0.5. + if (x < 0.5) return M_PI / (sin(M_PI * x) * GammaReal(1 - x)); + + // Iterate through terms. + double z = x - 1.; + double gamma = GammaCoef[0]; + for (int i = 1; i < 9; ++i) gamma += GammaCoef[i] / (z + i); + + // Answer. + double t = z + 7.5; + gamma *= sqrt(2. * M_PI) * pow(t, z + 0.5) * exp(-t); + return gamma; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/ResonanceDecays.cxx b/PYTHIA8/pythia8140/src/ResonanceDecays.cxx new file mode 100644 index 00000000000..50a09235c2e --- /dev/null +++ b/PYTHIA8/pythia8140/src/ResonanceDecays.cxx @@ -0,0 +1,805 @@ +// ResonanceDecays.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for +// the ResonanceDecays class. + +#include "ResonanceDecays.h" + +namespace Pythia8 { + +//========================================================================== + +// The ResonanceDecays class. +// Do all resonance decays sequentially. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of tries to pick a decay channel. +const int ResonanceDecays::NTRYCHANNEL = 10; + +// Number of tries to pick a set of daughter masses. +const int ResonanceDecays::NTRYMASSES = 10000; + +// Mass above threshold for allowed decays. +const double ResonanceDecays::MSAFETY = 0.1; + +// When constrainted kinematics cut high-mass tail of Breit-Wigner. +const double ResonanceDecays::WIDTHCUT = 5.; + +// Small number (relative to 1) to protect against roundoff errors. +const double ResonanceDecays::TINY = 1e-10; + +// Forbid small Breit-Wigner mass range, as mapped onto atan range. +const double ResonanceDecays::TINYBWRANGE = 1e-8; + +// These numbers are hardwired empirical parameters, +// intended to speed up the M-generator. +const double ResonanceDecays::WTCORRECTION[11] = { 1., 1., 1., + 2., 5., 15., 60., 250., 1250., 7000., 50000. }; + +//-------------------------------------------------------------------------- + +bool ResonanceDecays::next( Event& process) { + + // Loop over all entries to find resonances that should decay. + int iDec = 0; + do { + Particle& decayer = process[iDec]; + if (decayer.isFinal() && decayer.canDecay() && decayer.mayDecay() + && decayer.isResonance() ) { + + // Fill the decaying particle in slot 0 of arrays. + id0 = decayer.id(); + m0 = decayer.m(); + idProd.resize(0); + mProd.resize(0); + idProd.push_back( id0 ); + mProd.push_back( m0 ); + + // Mother flavour - relevant for gamma*/Z0 mixing. (Not always??) + int idIn = process[decayer.mother1()].id(); + + // Prepare decay selection. + decayer.particleDataEntry().preparePick(id0, m0, idIn); + + // Pick a decay channel; allow up to ten tries. + bool foundChannel = false; + for (int iTryChannel = 0; iTryChannel < NTRYCHANNEL; ++iTryChannel) { + + // Pick decay channel. Find multiplicity. + DecayChannel& channel = decayer.particleDataEntry().pickChannel(); + mult = channel.multiplicity(); + + // Read out flavours. + idProd.resize(1); + int idNow; + for (int i = 1; i <= mult; ++i) { + idNow = channel.product(i - 1); + if (id0 < 0 && particleDataPtr->hasAnti(idNow)) idNow = -idNow; + idProd.push_back( idNow); + } + + // Pick masses. Pick new channel if fail. + if (!pickMasses()) continue; + foundChannel = true; + break; + } + + // Failed to find acceptable decays. + if (!foundChannel) { + infoPtr->errorMsg("Error in ResonanceDecays::next:" + " failed to find workable decay channel"); + return false; + } + + // Select colours in decay. + if (!pickColours(iDec, process)) return false; + + // Select four-momenta in decay, boosted to lab frame. + pProd.resize(0); + pProd.push_back( decayer.p() ); + if (!pickKinematics()) return false; + + // Append decay products to the process event record. Set lifetimes. + int iFirst = process.size(); + for (int i = 1; i <= mult; ++i) { + int j = process.append( idProd[i], 23, iDec, 0, 0, 0, + cols[i], acols[i], pProd[i], mProd[i], m0); + process[j].tau( process[j].tau0() * rndmPtr->exp() ); + } + int iLast = process.size() - 1; + + // Modify mother status and daughters. + decayer.status(-22); + decayer.daughters(iFirst, iLast); + + // End of loop over all entries. + } + } while (++iDec < process.size()); + + // Done. + return true; + +} + +// Select masses of decay products. + +bool ResonanceDecays::pickMasses() { + + // Arrays with properties of particles. Fill with dummy values for mother. + vector useBW; + vector m0BW, mMinBW, mMaxBW, widthBW; + double mMother = mProd[0]; + double m2Mother = mMother * mMother; + useBW.push_back( false ); + m0BW.push_back( mMother ); + mMinBW.push_back( mMother ); + mMaxBW.push_back( mMother ); + widthBW.push_back( 0. ); + + // Loop throught products for masses and widths. Set nominal mass. + bool useBWNow; + double m0Now, mMinNow, mMaxNow, widthNow; + for (int i = 1; i <= mult; ++i) { + useBWNow = particleDataPtr->useBreitWigner( idProd[i] ); + m0Now = particleDataPtr->m0( idProd[i] ); + mMinNow = particleDataPtr->m0Min( idProd[i] ); + mMaxNow = particleDataPtr->m0Max( idProd[i] ); + if (useBWNow && mMaxNow < mMinNow) mMaxNow = mMother; + widthNow = particleDataPtr->mWidth( idProd[i] ); + useBW.push_back( useBWNow ); + m0BW.push_back( m0Now ); + mMinBW.push_back( mMinNow ); + mMaxBW.push_back( mMaxNow ); + widthBW.push_back( widthNow ); + mProd.push_back( m0Now ); + } + + // Find number of Breit-Wigners and summed (minimal) masses. + int nBW = 0; + double mSum = 0.; + double mSumMin = 0.; + for (int i = 1; i <= mult; ++i) { + if (useBW[i]) ++nBW; + mSum += max( m0BW[i], mMinBW[i]); + mSumMin += mMinBW[i]; + } + + // If sum of minimal masses above mother mass then give up. + if (mSumMin + MSAFETY > mMother) return false; + + // If sum of masses below and no Breit-Wigners then done. + if (mSum + 0.5 * MSAFETY < mMother && nBW == 0) return true; + + // Else if below then retry Breit-Wigners, with simple treshold. + if (mSum + MSAFETY < mMother) { + double wtMax = 2. * sqrtpos(1. - mSum*mSum / m2Mother); + double wt; + for (int iTryMasses = 0; iTryMasses <= NTRYMASSES; ++ iTryMasses) { + if (iTryMasses == NTRYMASSES) return false; + mSum = 0.; + for (int i = 1; i <= mult; ++i) { + if (useBW[i]) mProd[i] = particleDataPtr->mass( idProd[i] ); + mSum += mProd[i]; + } + wt = (mSum + 0.5 * MSAFETY < mMother) + ? sqrtpos(1. - mSum*mSum / m2Mother) : 0.; + if (wt > rndmPtr->flat() * wtMax) break; + } + return true; + } + + // From now on some particles will have to be forced off shell. + + // Order Breit-Wigners in decreasing widths. Sum of other masses. + vector iBW; + double mSum0 = 0.; + for (int i = 1; i <= mult; ++i) { + if (useBW[i]) iBW.push_back(i); + else mSum0 += mProd[i]; + } + for (int i = 1; i < nBW; ++i) { + for (int j = i - 1; j >= 0; --j) { + if (widthBW[iBW[j+1]] > widthBW[iBW[j]]) swap (iBW[j+1], iBW[j]); + else break; + } + } + + // Do all but broadest two in increasing-width order. Includes only one. + if (nBW != 2) { + int iMin = (nBW == 1) ? 0 : 2; + for (int i = nBW - 1; i >= iMin; --i) { + int iBWi = iBW[i]; + + // Find allowed mass range of current resonance. + double mMax = mMother - mSum0 - MSAFETY; + if (nBW != 1) for (int j = 0; j < i; ++j) mMax -= mMinBW[iBW[j]]; + mMax = min( mMaxBW[iBWi], mMax ); + double mMin = min( mMinBW[iBWi], mMax - MSAFETY); + if (mMin < 0.) return false; + + // Parameters for Breit-Wigner choice, with constrained mass range. + double m2Nom = pow2( m0BW[iBWi] ); + double m2Max = mMax * mMax; + double m2Min = mMin * mMin; + double mmWid = m0BW[iBWi] * widthBW[iBWi]; + double atanMin = atan( (m2Min - m2Nom) / mmWid ); + double atanMax = atan( (m2Max - m2Nom) / mmWid ); + double atanDif = atanMax - atanMin; + + // Fail if too narrow mass range; e.g. out in tail of Breit-Wigner. + if (atanDif < TINYBWRANGE) return false; + + // Retry mass according to Breit-Wigner, with simple threshold factor. + double mr1 = mSum0*mSum0 / m2Mother; + double mr2 = m2Min / m2Mother; + double wtMax = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + double m2Now, wt; + for (int iTryMasses = 0; iTryMasses <= NTRYMASSES; ++ iTryMasses) { + if (iTryMasses == NTRYMASSES) return false; + m2Now = m2Nom + mmWid * tan(atanMin + rndmPtr->flat() * atanDif); + mr2 = m2Now / m2Mother; + wt = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + if (wt > rndmPtr->flat() * wtMax) break; + } + + // Prepare to iterate for more. Done for one Breit-Wigner. + mProd[iBWi] = sqrt(m2Now); + mSum0 += mProd[iBWi]; + } + if (nBW == 1) return true; + } + + // Left to do two broadest Breit-Wigners correlated, i.e. more realistic. + int iBW1 = iBW[0]; + int iBW2 = iBW[1]; + int idMother = abs(idProd[0]); + int idDau1 = abs(idProd[iBW1]); + int idDau2 = abs(idProd[iBW2]); + + // In some cases known phase-space behaviour; else simple beta factor. + int psMode = 1 ; + if ( (idMother == 25 || idMother == 35) && idDau1 < 19 + && idDau2 == idDau1 ) psMode = 3; + if ( (idMother == 25 || idMother == 35 || idMother == 36) + && (idDau1 == 23 || idDau1 == 24) && idDau2 == idDau1 ) psMode = 5; + + // Find allowed mass ranges + double mRem = mMother - mSum0 - MSAFETY; + double mMax1 = min( mMaxBW[iBW1], mRem - mMinBW[iBW2] ); + double mMin1 = min( mMinBW[iBW1], mMax1 - MSAFETY); + double mMax2 = min( mMaxBW[iBW2], mRem - mMinBW[iBW1] ); + double mMin2 = min( mMinBW[iBW2], mMax2 - MSAFETY); + + // At least one range must extend below half remaining mass. + double mMid = 0.5 * mRem; + bool hasMid1 = (mMin1 < 0.5 * mRem); + bool hasMid2 = (mMin2 < 0.5 * mRem); + if (!hasMid1 && !hasMid2) return false; + + // Parameters for Breit-Wigner choice, with constrained mass range. + double m2Nom1 = pow2( m0BW[iBW1] ); + double m2Max1 = mMax1 * mMax1; + double m2Min1 = mMin1 * mMin1; + double mmWid1 = m0BW[iBW1] * widthBW[iBW1]; + double atanMin1 = atan( (m2Min1 - m2Nom1) / mmWid1 ); + double atanMax1 = atan( (m2Max1 - m2Nom1) / mmWid1 ); + double atanMid1 = (hasMid1) ? atan( (mMid*mMid - m2Nom1) / mmWid1 ) : 0.; + double m2Nom2 = pow2( m0BW[iBW2] ); + double m2Max2 = mMax1 * mMax2; + double m2Min2 = mMin1 * mMin2; + double mmWid2 = m0BW[iBW2] * widthBW[iBW2]; + double atanMin2 = atan( (m2Min2 - m2Nom2) / mmWid2 ); + double atanMax2 = atan( (m2Max2 - m2Nom2) / mmWid2 ); + double atanMid2 = (hasMid2) ? atan( (mMid*mMid - m2Nom2) / mmWid2 ) : 0.; + + // Relative weight to pick either below half remaining mass. + double probLow1 = (hasMid1) ? 1. : 0.; + if (hasMid1 && hasMid2) probLow1 = (atanMid1 - atanMin1) + / ( (atanMid1 - atanMin1) + (atanMid2 - atanMin1) ); + + // Maximum matrix element times phase space weight. + double m2Rem = mRem * mRem; + double mr1 = m2Min1 / m2Rem; + double mr2 = m2Min2 / m2Rem; + double psMax = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + double wtMax = 1.; + if (psMode == 1) wtMax = psMax; + else if (psMode == 2) wtMax = psMax * psMax; + else if (psMode == 3) wtMax = pow3(psMax); + else if (psMode == 5) wtMax = psMax + * (pow2(1. - mr1 - mr2) + 8. * mr1 * mr2); + + // Retry mass according to Breit-Wigners, with simple threshold factor. + double atanDif1, atanDif2, m2Now1, m2Now2, mNow1, mNow2, ps, wt; + for (int iTryMasses = 0; iTryMasses <= NTRYMASSES; ++ iTryMasses) { + if (iTryMasses == NTRYMASSES) return false; + + // Pick either below half remaining mass. + if (rndmPtr->flat() < probLow1) { + atanDif1 = atanMid1 - atanMin1; + atanDif2 = atanMax2 - atanMin2; + } else { + atanDif1 = atanMax1 - atanMin1; + atanDif2 = atanMid2 - atanMin2; + } + m2Now1 = m2Nom1 + mmWid1 * tan(atanMin1 + rndmPtr->flat() * atanDif1); + m2Now2 = m2Nom2 + mmWid2 * tan(atanMin2 + rndmPtr->flat() * atanDif2); + mNow1 = sqrt(m2Now1); + mNow2 = sqrt(m2Now2); + + // Threshold weight. + mr1 = m2Now1 / m2Rem; + mr2 = m2Now2 / m2Rem; + wt = 0.; + if (mNow1 + mNow2 + MSAFETY < mMother) { + ps = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + wt = 1.; + if (psMode == 1) wt = ps; + else if (psMode == 2) wt = ps * ps; + else if (psMode == 3) wt = pow3(ps); + else if (psMode == 5) wt = ps + * (pow2(1. - mr1 - mr2) + 8. * mr1 * mr2); + } + if (wt > rndmPtr->flat() * wtMax) break; + } + mProd[iBW1] = mNow1; + mProd[iBW2] = mNow2; + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Select colours of decay products. + +bool ResonanceDecays::pickColours(int iDec, Event& process) { + + // Reset or create arrays with colour info. + cols.resize(0); + acols.resize(0); + vector iTriplet, iAtriplet, iOctet, iDipCol, iDipAcol; + + // Mother colours already known. + int col0 = process[iDec].col(); + int acol0 = process[iDec].acol(); + cols.push_back( col0); + acols.push_back(acol0); + + // Loop through all daughters. + int colTypeNow; + for (int i = 1; i <= mult; ++i) { + // Daughter colours initially empty, so that all is set for singlet. + cols.push_back(0); + acols.push_back(0); + // Find character (singlet, triplet, antitriplet, octet) of daughters. + colTypeNow = particleDataPtr->colType( idProd[i] ); + if (colTypeNow == 0); + else if (colTypeNow == 1) iTriplet.push_back(i); + else if (colTypeNow == -1) iAtriplet.push_back(i); + else if (colTypeNow == 2) iOctet.push_back(i); + else { + infoPtr->errorMsg("Error in ResonanceDecays::pickColours:" + " unknown colour type encountered"); + return false; + } + } + + // Check excess of colours and anticolours in final over initial state. + int nCol = iTriplet.size(); + if (col0 != 0) --nCol; + int nAcol = iAtriplet.size(); + if (acol0 != 0) --nAcol; + + // If net creation of three colours then find junction kind: + // mother is 1 = singlet, 3 = antitriplet, 5 = octet. + if (nCol - nAcol == 3) { + int kindJun = (col0 == 0) ? ((acol0 == 0) ? 1 : 3) : 5; + + // Set colours in three junction legs and store junction. + int colJun[3]; + colJun[0] = (kindJun == 1) ? process.nextColTag() : acol0; + colJun[1] = process.nextColTag(); + colJun[2] = process.nextColTag(); + process.appendJunction( kindJun, colJun[0], colJun[1], colJun[2]); + + // Loop over three legs. Remove an incoming anticolour on first leg. + for (int leg = 0; leg < 3; ++leg) { + if (leg == 0 && kindJun != 1) acol0 = 0; + + // Pick final-state triplets to carry these new colours. + else { + int pickT = (iTriplet.size() == 1) ? 0 + : int( TINY + rndmPtr->flat() * (iTriplet.size() - TINY) ); + int iPickT = iTriplet[pickT]; + cols[iPickT] = colJun[leg]; + + // Remove matched triplet and store new colour dipole ends. + iTriplet[pickT] = iTriplet.back(); + iTriplet.pop_back(); + iDipCol.push_back(iPickT); + iDipAcol.push_back(0); + } + } + + // Update colour counter. Done with junction. + nCol -= 3; + } + + // If net creation of three anticolours then find antijunction kind: + // mother is 2 = singlet, 4 = triplet, 6 = octet. + if (nAcol - nCol == 3) { + int kindJun = (acol0 == 0) ? ((col0 == 0) ? 2 : 4) : 6; + + // Set anticolours in three antijunction legs and store antijunction. + int acolJun[3]; + acolJun[0] = (kindJun == 2) ? process.nextColTag() : col0; + acolJun[1] = process.nextColTag(); + acolJun[2] = process.nextColTag(); + process.appendJunction( kindJun, acolJun[0], acolJun[1], acolJun[2]); + + // Loop over three legs. Remove an incoming colour on first leg. + for (int leg = 0; leg < 3; ++leg) { + if (leg == 0 && kindJun != 2) col0 = 0; + + // Pick final-state antitriplets to carry these new anticolours. + else { + int pickA = (iAtriplet.size() == 1) ? 0 + : int( TINY + rndmPtr->flat() * (iAtriplet.size() - TINY) ); + int iPickA = iAtriplet[pickA]; + acols[iPickA] = acolJun[leg]; + + // Remove matched antitriplet and store new colour dipole ends. + iAtriplet[pickA] = iAtriplet.back(); + iAtriplet.pop_back(); + iDipCol.push_back(0); + iDipAcol.push_back(iPickA); + } + } + + // Update anticolour counter. Done with antijunction. + nAcol -= 3; + } + + // If colours and anticolours do not match now then unphysical. + if (nCol != nAcol) { + infoPtr->errorMsg("Error in ResonanceDecays::pickColours:" + " inconsistent colour tags"); + return false; + } + + // Pick final-state triplet (if any) to carry initial colour. + if (col0 != 0 && iTriplet.size() > 0) { + int pickT = (iTriplet.size() == 1) ? 0 + : int( TINY + rndmPtr->flat() * (iTriplet.size() - TINY) ); + int iPickT = iTriplet[pickT]; + cols[iPickT] = col0; + + // Remove matched triplet and store new colour dipole ends. + col0 = 0; + iTriplet[pickT] = iTriplet.back(); + iTriplet.pop_back(); + iDipCol.push_back(iPickT); + iDipAcol.push_back(0); + } + + // Pick final-state antitriplet (if any) to carry initial anticolour. + if (acol0 != 0 && iAtriplet.size() > 0) { + int pickA = (iAtriplet.size() == 1) ? 0 + : int( TINY + rndmPtr->flat() * (iAtriplet.size() - TINY) ); + int iPickA = iAtriplet[pickA]; + acols[iPickA] = acol0; + + // Remove matched antitriplet and store new colour dipole ends. + acol0 = 0; + iAtriplet[pickA] = iAtriplet.back(); + iAtriplet.pop_back(); + iDipCol.push_back(0); + iDipAcol.push_back(iPickA); + } + + // Error checks that amount of leftover colours and anticolours match. + if ( (iTriplet.size() != iAtriplet.size()) + || (col0 != 0 && acol0 == 0) || (col0 == 0 && acol0 != 0) ) { + infoPtr->errorMsg("Error in ResonanceDecays::pickColours:" + " inconsistent colour tags"); + return false; + } + + // Match triplets to antitriplets in the final state. + for (int pickT = 0; pickT < int(iTriplet.size()); ++pickT) { + int iPickT = iTriplet[pickT]; + int pickA = (iAtriplet.size() == 1) ? 0 + : int( TINY + rndmPtr->flat() * (iAtriplet.size() - TINY) ); + int iPickA = iAtriplet[pickA]; + + // Connect pair with new colour tag. + cols[iPickT] = process.nextColTag(); + acols[iPickA] = cols[iPickT]; + + // Remove matched antitriplet and store new colour dipole ends. + iAtriplet[pickT] = iAtriplet.back(); + iAtriplet.pop_back(); + iDipCol.push_back(iPickT); + iDipAcol.push_back(iPickA); + } + + // If no octets are around then matching is done. + if (col0 == 0 && acol0 == 0 && iOctet.size() == 0) return true; + + // If initial-state octet remains then store as (first!) new dipole. + if (col0 != 0) { + iDipCol.push_back(0); + iDipAcol.push_back(0); + } + + // Now attach all final-state octets at random to existing dipoles. + for (int i = 0; i < int(iOctet.size()); ++i) { + int iOct = iOctet[i]; + + // If no dipole then start new one. (Happens for singlet -> octets.) + if (iDipCol.size() == 0) { + cols[iOct] = process.nextColTag(); + acols[iOct] = cols[iOct] ; + iDipCol.push_back(iOct); + iDipAcol.push_back(iOct); + } + + // Else attach to existing dipole picked at random. + else { + int pickDip = (iDipCol.size() == 1) ? 0 + : int( TINY + rndmPtr->flat() * (iDipCol.size() - TINY) ); + + // Case with dipole in initial state: reattach existing colours. + if (iDipCol[pickDip] == 0 && iDipAcol[pickDip] == 0) { + cols[iOct] = col0; + acols[iOct] = acol0; + iDipAcol[pickDip] = iOct; + iDipCol.push_back(iOct); + iDipAcol.push_back(0); + + // Case with dipole from colour in initial state: also new colour. + } else if (iDipAcol[pickDip] == 0) { + int iPickCol = iDipCol[pickDip]; + cols[iOct] = cols[iPickCol]; + acols[iOct] = process.nextColTag(); + cols[iPickCol] = acols[iOct]; + iDipCol[pickDip] = iOct; + iDipCol.push_back(iPickCol); + iDipAcol.push_back(iOct); + + // Remaining cases with dipole from anticolour in initial state + // or dipole inside final state: also new colour. + } else { + int iPickAcol = iDipAcol[pickDip]; + acols[iOct] = acols[iPickAcol]; + cols[iOct] = process.nextColTag(); + acols[iPickAcol] = cols[iOct]; + iDipAcol[pickDip] = iOct; + iDipCol.push_back(iOct); + iDipAcol.push_back(iPickAcol); + } + } + } + + // Must now have at least two dipoles (no 1 -> 8 or 8 -> 1). + if (iDipCol.size() < 2) { + infoPtr->errorMsg("Error in ResonanceDecays::pickColours:" + " inconsistent colour tags"); + return false; + } + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Select decay products momenta isotropically in phase space. +// Process-dependent angular distributions may be imposed in SigmaProcess. + +bool ResonanceDecays::pickKinematics() { + + // Description of two-body decays as simple special case. + if (mult == 2) { + + // Masses. + m0 = mProd[0]; + double m1 = mProd[1]; + double m2 = mProd[2]; + + // Energies and absolute momentum in the rest frame. + double e1 = 0.5 * (m0*m0 + m1*m1 - m2*m2) / m0; + double e2 = 0.5 * (m0*m0 + m2*m2 - m1*m1) / m0; + double pAbs = 0.5 * sqrtpos( (m0 - m1 - m2) * (m0 + m1 + m2) + * (m0 + m1 - m2) * (m0 - m1 + m2) ) / m0; + + // Pick isotropic angles to give three-momentum. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi = 2. * M_PI * rndmPtr->flat(); + double pX = pAbs * sinTheta * cos(phi); + double pY = pAbs * sinTheta * sin(phi); + double pZ = pAbs * cosTheta; + + // Fill four-momenta in mother rest frame and then boost to lab frame. + pProd.push_back( Vec4( pX, pY, pZ, e1) ); + pProd.push_back( Vec4( -pX, -pY, -pZ, e2) ); + pProd[1].bst( pProd[0] ); + pProd[2].bst( pProd[0] ); + + // Done for two-body decay. + return true; + } + + // Description of three-body decays as semi-simple special case. + if (mult == 3) { + + // Masses. + m0 = mProd[0]; + double m1 = mProd[1]; + double m2 = mProd[2]; + double m3 = mProd[3]; + double mDiff = m0 - (m1 + m2 + m3); + + // Kinematical limits for 2+3 mass. Maximum phase-space weight. + double m23Min = m2 + m3; + double m23Max = m0 - m1; + double p1Max = 0.5 * sqrtpos( (m0 - m1 - m23Min) * (m0 + m1 + m23Min) + * (m0 + m1 - m23Min) * (m0 - m1 + m23Min) ) / m0; + double p23Max = 0.5 * sqrtpos( (m23Max - m2 - m3) * (m23Max + m2 + m3) + * (m23Max + m2 - m3) * (m23Max - m2 + m3) ) / m23Max; + double wtPSmax = 0.5 * p1Max * p23Max; + + // Pick an intermediate mass m23 flat in the allowed range. + double wtPS, m23, p1Abs, p23Abs; + do { + m23 = m23Min + rndmPtr->flat() * mDiff; + + // Translate into relative momenta and find phase-space weight. + p1Abs = 0.5 * sqrtpos( (m0 - m1 - m23) * (m0 + m1 + m23) + * (m0 + m1 - m23) * (m0 - m1 + m23) ) / m0; + p23Abs = 0.5 * sqrtpos( (m23 - m2 - m3) * (m23 + m2 + m3) + * (m23 + m2 - m3) * (m23 - m2 + m3) ) / m23; + wtPS = p1Abs * p23Abs; + + // If rejected, try again with new invariant masses. + } while ( wtPS < rndmPtr->flat() * wtPSmax ); + + // Set up m23 -> m2 + m3 isotropic in its rest frame. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi = 2. * M_PI * rndmPtr->flat(); + double pX = p23Abs * sinTheta * cos(phi); + double pY = p23Abs * sinTheta * sin(phi); + double pZ = p23Abs * cosTheta; + double e2 = sqrt( m2*m2 + p23Abs*p23Abs); + double e3 = sqrt( m3*m3 + p23Abs*p23Abs); + Vec4 p2( pX, pY, pZ, e2); + Vec4 p3( -pX, -pY, -pZ, e3); + + // Set up 0 -> 1 + 23 isotropic in its rest frame. + cosTheta = 2. * rndmPtr->flat() - 1.; + sinTheta = sqrt(1. - cosTheta*cosTheta); + phi = 2. * M_PI * rndmPtr->flat(); + pX = p1Abs * sinTheta * cos(phi); + pY = p1Abs * sinTheta * sin(phi); + pZ = p1Abs * cosTheta; + double e1 = sqrt( m1*m1 + p1Abs*p1Abs); + double e23 = sqrt( m23*m23 + p1Abs*p1Abs); + pProd.push_back( Vec4( pX, pY, pZ, e1) ); + + // Boost 2 + 3 to the 0 rest frame and then boost to lab frame. + Vec4 p23( -pX, -pY, -pZ, e23); + p2.bst( p23 ); + p3.bst( p23 ); + pProd.push_back( p2 ); + pProd.push_back( p3 ); + pProd[1].bst( pProd[0] ); + pProd[2].bst( pProd[0] ); + pProd[3].bst( pProd[0] ); + + // Done for three-body decay. + return true; + } + + // Do a multibody decay using the M-generator algorithm. + + // Mother and sum daughter masses. + m0 = mProd[0]; + double mSum = mProd[1]; + for (int i = 2; i <= mult; ++i) mSum += mProd[i]; + double mDiff = m0 - mSum; + + // Begin setup of intermediate invariant masses. + vector mInv; + for (int i = 0; i <= mult; ++i) mInv.push_back( mProd[i]); + + // Calculate the maximum weight in the decay. + double wtPSmax = 1. / WTCORRECTION[mult]; + double mMax = mDiff + mProd[mult]; + double mMin = 0.; + for (int i = mult - 1; i > 0; --i) { + mMax += mProd[i]; + mMin += mProd[i+1]; + double mNow = mProd[i]; + wtPSmax *= 0.5 * sqrtpos( (mMax - mMin - mNow) * (mMax + mMin + mNow) + * (mMax + mMin - mNow) * (mMax - mMin + mNow) ) / mMax; + } + + // Begin loop to find the set of intermediate invariant masses. + vector rndmOrd; + double wtPS; + do { + wtPS = 1.; + + // Find and order random numbers in descending order. + rndmOrd.resize(0); + rndmOrd.push_back(1.); + for (int i = 1; i < mult - 1; ++i) { + double rndm = rndmPtr->flat(); + rndmOrd.push_back(rndm); + for (int j = i - 1; j > 0; --j) { + if (rndm > rndmOrd[j]) swap( rndmOrd[j], rndmOrd[j+1] ); + else break; + } + } + rndmOrd.push_back(0.); + + // Translate into intermediate masses and find weight. + for (int i = mult - 1; i > 0; --i) { + mInv[i] = mInv[i+1] + mProd[i] + (rndmOrd[i-1] - rndmOrd[i]) * mDiff; + wtPS *= 0.5 * sqrtpos( (mInv[i] - mInv[i+1] - mProd[i]) + * (mInv[i] + mInv[i+1] + mProd[i]) * (mInv[i] + mInv[i+1] - mProd[i]) + * (mInv[i] - mInv[i+1] + mProd[i]) ) / mInv[i]; + } + + // If rejected, try again with new invariant masses. + } while ( wtPS < rndmPtr->flat() * wtPSmax ); + + // Perform two-particle decays in the respective rest frame. + vector pInv; + pInv.resize(mult + 1); + for (int i = 1; i < mult; ++i) { + double pAbs = 0.5 * sqrtpos( (mInv[i] - mInv[i+1] - mProd[i]) + * (mInv[i] + mInv[i+1] + mProd[i]) * (mInv[i] + mInv[i+1] - mProd[i]) + * (mInv[i] - mInv[i+1] + mProd[i]) ) / mInv[i]; + + // Isotropic angles give three-momentum. + double cosTheta = 2. * rndmPtr->flat() - 1.; + double sinTheta = sqrt(1. - cosTheta*cosTheta); + double phi = 2. * M_PI * rndmPtr->flat(); + double pX = pAbs * sinTheta * cos(phi); + double pY = pAbs * sinTheta * sin(phi); + double pZ = pAbs * cosTheta; + + // Calculate energies, fill four-momenta. + double eHad = sqrt( mProd[i]*mProd[i] + pAbs*pAbs); + double eInv = sqrt( mInv[i+1]*mInv[i+1] + pAbs*pAbs); + pProd.push_back( Vec4( pX, pY, pZ, eHad) ); + pInv[i+1].p( -pX, -pY, -pZ, eInv); + } + pProd.push_back( pInv[mult] ); + + // Boost decay products to the mother rest frame and on to lab frame. + pInv[1] = pProd[0]; + for (int iFrame = mult - 1; iFrame > 0; --iFrame) + for (int i = iFrame; i <= mult; ++i) pProd[i].bst(pInv[iFrame]); + + // Done for multibody decay. + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/ResonanceWidths.cxx b/PYTHIA8/pythia8140/src/ResonanceWidths.cxx new file mode 100644 index 00000000000..57081551783 --- /dev/null +++ b/PYTHIA8/pythia8140/src/ResonanceWidths.cxx @@ -0,0 +1,2129 @@ +// ResonanceWidths.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for +// the ResonanceWidths class and classes derived from it. + +#include "ResonanceWidths.h" +#include "PythiaComplex.h" + +namespace Pythia8 { + +//========================================================================== + +// The ResonanceWidths class. +// Base class for the various resonances. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of points in integration direction for numInt routines. +const int ResonanceWidths::NPOINT = 100; + +// The sum of product masses must not be too close to the resonance mass. +const double ResonanceWidths::MASSMARGIN = 0.1; + +//-------------------------------------------------------------------------- + +// Initialize data members. +// Calculate and store partial and total widths at the nominal mass. + +bool ResonanceWidths::init(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, CoupSM* coupSMPtrIn) { + + // Save pointers. + infoPtr = infoPtrIn; + settingsPtr = settingsPtrIn; + particleDataPtr = particleDataPtrIn; + coupSMPtr = coupSMPtrIn; + + // Minimal decaying-resonance width. Minimal phase space for meMode = 103. + minWidth = settingsPtr->parm("ResonanceWidths:minWidth"); + minThreshold = settingsPtr->parm("ResonanceWidths:minThreshold"); + + // Pointer to particle species. + particlePtr = particleDataPtr->particleDataEntryPtr(idRes); + if (particlePtr == 0) { + infoPtr->errorMsg("Error in ResonanceWidths::init:" + " unknown resonance identity code"); + return false; + } + + // Generic particles should not have meMode < 100, but allow + // some exceptions: not used Higgses and not used Technicolor. + if (idRes == 35 || idRes == 36 || idRes == 37 + || idRes/1000000 == 3) isGeneric = false; + + // Resonance properties: antiparticle, mass, width + hasAntiRes = particlePtr->hasAnti(); + mRes = particlePtr->m0(); + GammaRes = particlePtr->mWidth(); + m2Res = mRes*mRes; + + // For very narrow resonances assign fictitious small width. + if (GammaRes < minWidth) GammaRes = 0.1 * minWidth; + GamMRat = GammaRes / mRes; + + // Secondary decay chains by default all on. + openPos = 1.; + openNeg = 1.; + + // Allow option where on-shell width is forced to current value. + doForceWidth = particlePtr->doForceWidth(); + forceFactor = 1.; + + // Check that resonance OK. + if (particlePtr == 0) infoPtr->errorMsg("Error in ResonanceWidths::init:" + " unknown resonance identity code"); + + // Initialize constants used for a resonance. + initConstants(); + + // Calculate various common prefactors for the current mass. + mHat = mRes; + calcPreFac(true); + + // Reset quantities to sum. Declare variables inside loop. + double widTot = 0.; + double widPos = 0.; + double widNeg = 0.; + int idNow, idAnti; + double openSecPos, openSecNeg; + + // Loop over all decay channels. Basic properties of channel. + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + iChannel = i; + onMode = particlePtr->channel(i).onMode(); + meMode = particlePtr->channel(i).meMode(); + mult = particlePtr->channel(i).multiplicity(); + widNow = 0.; + + // Warn if not relevant meMode. + if ( meMode < 0 || meMode > 103 || (isGeneric && meMode < 100) ) { + infoPtr->errorMsg("Error in ResonanceWidths::init:" + " resonance meMode not acceptable"); + } + + // Channels with meMode < 100 must be implemented in derived classes. + if (meMode < 100) { + + // Read out information on channel: primarily use first two. + id1 = particlePtr->channel(i).product(0); + id2 = particlePtr->channel(i).product(1); + id1Abs = abs(id1); + id2Abs = abs(id2); + + // Order first two in descending order of absolute values. + if (id2Abs > id1Abs) {swap( id1, id2); swap( id1Abs, id2Abs);} + + // Allow for third product to be treated in derived classes. + if (mult > 2) { + id3 = particlePtr->channel(i).product(2); + id3Abs = abs(id3); + + // Also order third into descending order of absolute values. + if (id3Abs > id2Abs) {swap( id2, id3); swap( id2Abs, id3Abs);} + if (id2Abs > id1Abs) {swap( id1, id2); swap( id1Abs, id2Abs);} + } + + // Read out masses. Calculate two-body phase space. + mf1 = particleDataPtr->m0(id1Abs); + mf2 = particleDataPtr->m0(id2Abs); + mr1 = pow2(mf1 / mHat); + mr2 = pow2(mf2 / mHat); + ps = (mHat < mf1 + mf2 + MASSMARGIN) ? 0. + : sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + if (mult > 2) { + mf3 = particleDataPtr->m0(id3Abs); + mr3 = pow2(mf3 / mHat); + } + + // Let derived class calculate width for channel provided. + calcWidth(true); + } + + // Channels with meMode >= 100 are calculated based on stored values. + else widNow = GammaRes * particlePtr->channel(i).bRatio(); + + // Find secondary open fractions of partial width. + openSecPos = 1.; + openSecNeg = 1.; + if (widNow > 0.) for (int j = 0; j < mult; ++j) { + idNow = particlePtr->channel(i).product(j); + idAnti = (particleDataPtr->hasAnti(idNow)) ? -idNow : idNow; + // Secondary widths not yet initialized for heavier states, + // so have to assume unit open fraction there. + if (idNow == 23 || abs(idNow) == 24 + || particleDataPtr->m0(abs(idNow)) < mRes) { + openSecPos *= particleDataPtr->resOpenFrac(idNow); + openSecNeg *= particleDataPtr->resOpenFrac(idAnti); + } + } + + // Store partial widths and secondary open fractions. + particlePtr->channel(i).onShellWidth(widNow); + particlePtr->channel(i).openSec( idRes, openSecPos); + particlePtr->channel(i).openSec(-idRes, openSecNeg); + + // Update sum over all channnels and over open channels only. + widTot += widNow; + if (onMode == 1 || onMode == 2) widPos += widNow * openSecPos; + if (onMode == 1 || onMode == 3) widNeg += widNow * openSecNeg; + } + + // If no decay channels are open then set particle stable and done. + if (widTot < minWidth) { + particlePtr->setMayDecay(false, false); + particlePtr->setMWidth(0., false); + for (int i = 0; i < particlePtr->sizeChannels(); ++i) + particlePtr->channel(i).bRatio( 0., false); + return true; + } + + // Normalize branching ratios to unity. + double bRatio; + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + bRatio = particlePtr->channel(i).onShellWidth() / widTot; + particlePtr->channel(i).bRatio( bRatio, false); + } + + // Optionally force total width by rescaling of all partial ones. + if (doForceWidth) { + forceFactor = GammaRes / widTot; + for (int i = 0; i < particlePtr->sizeChannels(); ++i) + particlePtr->channel(i).onShellWidthFactor( forceFactor); + } + + // Else update newly calculated partial width. + else { + particlePtr->setMWidth(widTot, false); + GammaRes = widTot; + } + + // Updated width-to-mass ratio. Secondary widths for open. + GamMRat = GammaRes / mRes; + openPos = widPos / widTot; + openNeg = widNeg / widTot; + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Calculate the total width and store phase-space-weighted coupling sums. + +double ResonanceWidths::width(int idSgn, double mHatIn, int idInFlavIn, + bool openOnly, bool setBR, int idOutFlav1, int idOutFlav2) { + + // Calculate various prefactors for the current mass. + mHat = mHatIn; + idInFlav = idInFlavIn; + calcPreFac(false); + + // Reset quantities to sum. Declare variables inside loop. + double widSum = 0.; + double mfSum, psOnShell; + + // Loop over all decay channels. Basic properties of channel. + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + iChannel = i; + onMode = particlePtr->channel(i).onMode(); + meMode = particlePtr->channel(i).meMode(); + mult = particlePtr->channel(i).multiplicity(); + + // Initially assume vanishing branching ratio. + widNow = 0.; + if (setBR) particlePtr->channel(i).currentBR(widNow); + + // Optionally only consider specific (two-body) decay channel. + // Currently only used for Higgs -> q qbar, g g or gamma gamma. + if (idOutFlav1 > 0 || idOutFlav2 > 0) { + if (mult > 2) continue; + if (particlePtr->channel(i).product(0) != idOutFlav1) continue; + if (particlePtr->channel(i).product(1) != idOutFlav2) continue; + } + + // Optionally only consider open channels. + if (openOnly) { + if (idSgn > 0 && onMode !=1 && onMode != 2) continue; + if (idSgn < 0 && onMode !=1 && onMode != 3) continue; + } + + // Channels with meMode < 100 must be implemented in derived classes. + if (meMode < 100) { + + // Read out information on channel: primarily use first two. + id1 = particlePtr->channel(i).product(0); + id2 = particlePtr->channel(i).product(1); + id1Abs = abs(id1); + id2Abs = abs(id2); + + // Order first two in descending order of absolute values. + if (id2Abs > id1Abs) {swap( id1, id2); swap( id1Abs, id2Abs);} + + // Allow for third product to be treated in derived classes. + if (mult > 2) { + id3 = particlePtr->channel(i).product(2); + id3Abs = abs(id3); + + // Also order third into descending order of absolute values. + if (id3Abs > id2Abs) {swap( id2, id3); swap( id2Abs, id3Abs);} + if (id2Abs > id1Abs) {swap( id1, id2); swap( id1Abs, id2Abs);} + } + + // Read out masses. Calculate two-body phase space. + mf1 = particleDataPtr->m0(id1Abs); + mf2 = particleDataPtr->m0(id2Abs); + mr1 = pow2(mf1 / mHat); + mr2 = pow2(mf2 / mHat); + ps = (mHat < mf1 + mf2 + MASSMARGIN) ? 0. + : sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + if (mult > 2) { + mf3 = particleDataPtr->m0(id3Abs); + mr3 = pow2(mf3 / mHat); + } + + // Let derived class calculate width for channel provided. + calcWidth(false); + } + + // Now on to meMode >= 100. First case: no correction at all. + else if (meMode == 100) + widNow = GammaRes * particlePtr->channel(i).bRatio(); + + // Correction by step at threshold. + else if (meMode == 101) { + mfSum = 0.; + for (int j = 0; j < mult; ++j) mfSum + += particleDataPtr->m0( particlePtr->channel(i).product(j) ); + if (mfSum + MASSMARGIN < mHat) + widNow = GammaRes * particlePtr->channel(i).bRatio(); + } + + // Correction by a phase space factor for two-body decays. + else if ( (meMode == 102 || meMode == 103) && mult == 2) { + mf1 = particleDataPtr->m0( particlePtr->channel(i).product(0) ); + mf2 = particleDataPtr->m0( particlePtr->channel(i).product(1) ); + mr1 = pow2(mf1 / mHat); + mr2 = pow2(mf2 / mHat); + ps = (mHat < mf1 + mf2 + MASSMARGIN) ? 0. + : sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + mr1 = pow2(mf1 / mRes); + mr2 = pow2(mf2 / mRes); + psOnShell = (meMode == 102) ? 1. : max( minThreshold, + sqrtpos( pow2(1.- mr1 - mr2) - 4. * mr1 * mr2) ); + widNow = GammaRes * particlePtr->channel(i).bRatio() * ps / psOnShell; + } + + // Correction by simple threshold factor for multibody decay. + else if (meMode == 102 || meMode == 103) { + mfSum = 0.; + for (int j = 0; j < mult; ++j) mfSum + += particleDataPtr->m0( particlePtr->channel(i).product(j) ); + ps = sqrtpos(1. - mfSum / mHat); + psOnShell = (meMode == 102) ? 1. : max( minThreshold, + sqrtpos(1. - mfSum / mRes) ); + widNow = GammaRes * particlePtr->channel(i).bRatio() * ps / psOnShell; + } + + // Optionally multiply by secondary widths. + if (openOnly) widNow *= particlePtr->channel(i).openSec(idSgn); + + // Optionally include factor to force to fixed width?? + // Optionally multiply by current/nominal resonance mass?? + + // Sum back up. + widSum += widNow; + + // Optionally store partial widths for later decay channel choice. + if (setBR) particlePtr->channel(i).currentBR(widNow); + } + + // Done. + return widSum; + +} + +//-------------------------------------------------------------------------- + +// Numerical integration of matrix-element in two-body decay, +// where one particle is described by a Breit-Wigner mass distribution. +// Normalization to unit integral if matrix element is unity +// and there are no phase-space restrictions. + +double ResonanceWidths::numInt1BW(double mHatIn, double m1, double Gamma1, + double mMin1, double m2, int psMode) { + + // Check that phase space is open for integration. + if (mMin1 + m2 > mHatIn) return 0.; + + // Precalculate coefficients for Breit-Wigner selection. + double s1 = m1 * m1; + double mG1 = m1 * Gamma1; + double mMax1 = mHatIn - m2; + double atanMin1 = atan( (mMin1 * mMin1 - s1) / mG1 ); + double atanMax1 = atan( (mMax1 * mMax1 - s1) / mG1 ); + double atanDif1 = atanMax1 - atanMin1; + double wtDif1 = atanDif1 / (M_PI * NPOINT); + + // Step size in atan-mapped variable. + double xStep = 1. / NPOINT; + + // Variables used in loop over integration points. + double sum = 0.; + double mrNow2 = pow2(m2 / mHatIn); + double xNow1, sNow1, mNow1, mrNow1, psNow, value; + + // Loop with first-particle mass selection. + for (int ip1 = 0; ip1 < NPOINT; ++ip1) { + xNow1 = xStep * (ip1 + 0.5); + sNow1 = s1 + mG1 * tan(atanMin1 + xNow1 * atanDif1); + mNow1 = min( mMax1, max( mMin1, sqrtpos(sNow1) ) ); + mrNow1 = pow2(mNow1 / mHatIn); + + // Evaluate value and add to sum. Different matrix elements. + psNow = sqrtpos( pow2(1. - mrNow1 - mrNow2) + - 4. * mrNow1 * mrNow2); + value = 1.; + if (psMode == 1) value = psNow; + if (psMode == 2) value = psNow * psNow; + if (psMode == 3) value = pow3(psNow); + if (psMode == 5) value = psNow * + (pow2(1. - mrNow1 - mrNow2) + 8. * mrNow1 * mrNow2); + sum += value; + + // End of loop over integration points. Overall normalization. + } + sum *= wtDif1; + + // Done. + return sum; +} + +//-------------------------------------------------------------------------- + +// Numerical integration of matrix-element in two-body decay, +// where both particles are described by Breit-Wigner mass distributions. +// Normalization to unit integral if matrix element is unity +// and there are no phase-space restrictions. + +double ResonanceWidths::numInt2BW(double mHatIn, double m1, double Gamma1, + double mMin1, double m2, double Gamma2, double mMin2, int psMode) { + + // Check that phase space is open for integration. + if (mMin1 + mMin2 > mHatIn) return 0.; + + // Precalculate coefficients for Breit-Wigner selection. + double s1 = m1 * m1; + double mG1 = m1 * Gamma1; + double mMax1 = mHatIn - mMin2; + double atanMin1 = atan( (mMin1 * mMin1 - s1) / mG1 ); + double atanMax1 = atan( (mMax1 * mMax1 - s1) / mG1 ); + double atanDif1 = atanMax1 - atanMin1; + double wtDif1 = atanDif1 / (M_PI * NPOINT); + double s2 = m2 * m2; + double mG2 = m2 * Gamma2; + double mMax2 = mHatIn - mMin1; + double atanMin2 = atan( (mMin2 * mMin2 - s2) / mG2 ); + double atanMax2 = atan( (mMax2 * mMax2 - s2) / mG2 ); + double atanDif2 = atanMax2 - atanMin2; + double wtDif2 = atanDif2 / (M_PI * NPOINT); + + // If on-shell decay forbidden then split integration range + // to ensure that low-mass region is not forgotten. + bool mustDiv = false; + double mDiv1 = 0.; + double atanDiv1 = 0.; + double atanDLo1 = 0.; + double atanDHi1 = 0.; + double wtDLo1 = 0.; + double wtDHi1 = 0.; + double mDiv2 = 0.; + double atanDiv2 = 0.; + double atanDLo2 = 0.; + double atanDHi2 = 0.; + double wtDLo2 = 0.; + double wtDHi2 = 0.; + if (m1 + m2 > mHatIn) { + mustDiv = true; + double tmpDiv = (mHatIn - m1 - m2) / (Gamma1 + Gamma2); + mDiv1 = m1 + Gamma1 * tmpDiv; + atanDiv1 = atan( (mDiv1 * mDiv1 - s1) / mG1 ); + atanDLo1 = atanDiv1 - atanMin1; + atanDHi1 = atanMax1 - atanDiv1; + wtDLo1 = atanDLo1 / (M_PI * NPOINT); + wtDHi1 = atanDHi1 / (M_PI * NPOINT); + mDiv2 = m2 + Gamma2 * tmpDiv; + atanDiv2 = atan( (mDiv2 * mDiv2 - s2) / mG2 ); + atanDLo2 = atanDiv2 - atanMin2; + atanDHi2 = atanMax2 - atanDiv2; + wtDLo2 = atanDLo2 / (M_PI * NPOINT); + wtDHi2 = atanDHi2 / (M_PI * NPOINT); + } + + // Step size in atan-mapped variable. + double xStep = 1. / NPOINT; + int nIter = (mustDiv) ? 2 * NPOINT : NPOINT; + + // Variables used in loop over integration points. + double sum = 0.; + double xNow1, sNow1, mNow1, mrNow1, xNow2, sNow2, mNow2, mrNow2, psNow, + value; + double wtNow1 = wtDif1; + double wtNow2 = wtDif2; + + // Outer loop with first-particle mass selection. + for (int ip1 = 0; ip1 < nIter; ++ip1) { + if (!mustDiv) { + xNow1 = xStep * (ip1 + 0.5); + sNow1 = s1 + mG1 * tan(atanMin1 + xNow1 * atanDif1); + } else if (ip1 < NPOINT) { + xNow1 = xStep * (ip1 + 0.5); + sNow1 = s1 + mG1 * tan(atanMin1 + xNow1 * atanDLo1); + wtNow1 = wtDLo1; + } else { + xNow1 = xStep * (ip1 - NPOINT + 0.5); + sNow1 = s1 + mG1 * tan(atanDiv1 + xNow1 * atanDHi1); + wtNow1 = wtDHi1; + } + mNow1 = min( mMax1, max( mMin1, sqrtpos(sNow1) ) ); + mrNow1 = pow2(mNow1 / mHatIn); + + // Inner loop with second-particle mass selection. + for (int ip2 = 0; ip2 < nIter; ++ip2) { + if (!mustDiv) { + xNow2 = xStep * (ip2 + 0.5); + sNow2 = s2 + mG2 * tan(atanMin2 + xNow2 * atanDif2); + } else if (ip2 < NPOINT) { + xNow2 = xStep * (ip2 + 0.5); + sNow2 = s2 + mG2 * tan(atanMin2 + xNow2 * atanDLo2); + wtNow2 = wtDLo2; + } else { + xNow2 = xStep * (ip2 - NPOINT + 0.5); + sNow2 = s2 + mG2 * tan(atanDiv2 + xNow2 * atanDHi2); + wtNow2 = wtDHi2; + } + mNow2 = min( mMax2, max( mMin2, sqrtpos(sNow2) ) ); + mrNow2 = pow2(mNow2 / mHatIn); + + // Check that point is inside phase space. + if (mNow1 + mNow2 > mHatIn) break; + + // Evaluate value and add to sum. Different matrix elements. + psNow = sqrtpos( pow2(1. - mrNow1 - mrNow2) + - 4. * mrNow1 * mrNow2); + value = 1.; + if (psMode == 1) value = psNow; + else if (psMode == 2) value = psNow * psNow; + else if (psMode == 3) value = pow3(psNow); + else if (psMode == 5) value = psNow + * (pow2(1. - mrNow1 - mrNow2) + 8. * mrNow1 * mrNow2); + sum += value * wtNow1 * wtNow2; + + // End of second and first loop over integration points. + } + } + + // Done. + return sum; +} + +//========================================================================== + +// The ResonanceGmZ class. +// Derived class for gamma*/Z0 properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceGmZ::initConstants() { + + // Locally stored properties and couplings. + gmZmode = settingsPtr->mode("WeakZ0:gmZmode"); + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() + * coupSMPtr->cos2thetaW()); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceGmZ::calcPreFac(bool calledFromInit) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * mHat / 3.; + + // When call for incoming flavour need to consider gamma*/Z0 mix. + if (!calledFromInit) { + + // Couplings when an incoming fermion is specified; elso only pure Z0. + ei2 = 0.; + eivi = 0.; + vi2ai2 = 1.; + int idInFlavAbs = abs(idInFlav); + if (idInFlavAbs > 0 && idInFlavAbs < 19) { + ei2 = coupSMPtr->ef2(idInFlavAbs); + eivi = coupSMPtr->efvf(idInFlavAbs); + vi2ai2 = coupSMPtr->vf2af2(idInFlavAbs); + } + + // Calculate prefactors for gamma/interference/Z0 terms. + double sH = mHat * mHat; + gamNorm = ei2; + intNorm = 2. * eivi * thetaWRat * sH * (sH - m2Res) + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + resNorm = vi2ai2 * pow2(thetaWRat * sH) + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + + // Rescale Z0 height normalization to compensate for a width one?? + //if (doForceWidth) { + // intNorm *= forceFactor; + // resNorm *= forceFactor; + //} + + // Optionally only keep gamma* or Z0 term. + if (gmZmode == 1) {intNorm = 0.; resNorm = 0.;} + if (gmZmode == 2) {gamNorm = 0.; intNorm = 0.;} + } + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceGmZ::calcWidth(bool calledFromInit) { + + // Check that above threshold. + if (ps == 0.) return; + + // Only contributions from three fermion generations, except top. + if ( (id1Abs > 5 && id1Abs < 11) || id1Abs > 16 ) return; + + // At initialization only the pure Z0 should be considered. + if (calledFromInit) { + + // Combine kinematics with colour factor and couplings. + widNow = preFac * ps * (coupSMPtr->vf2(id1Abs) * (1. + 2. * mr1) + + coupSMPtr->af2(id1Abs) * ps*ps); + if (id1Abs < 6) widNow *= colQ; + } + + // When call for incoming flavour need to consider gamma*/Z0 mix. + else { + + // Kinematical factors and couplings. + double kinFacV = ps * (1. + 2. * mr1); + double ef2 = coupSMPtr->ef2(id1Abs) * kinFacV; + double efvf = coupSMPtr->efvf(id1Abs) * kinFacV; + double vf2af2 = coupSMPtr->vf2(id1Abs) * kinFacV + + coupSMPtr->af2(id1Abs) * pow3(ps); + + // Relative outwidths: combine instate, propagator and outstate. + widNow = gamNorm * ef2 + intNorm * efvf + resNorm * vf2af2; + + // Colour factor. + if (id1Abs < 6) widNow *= colQ; + } + +} + +//========================================================================== + +// The ResonanceW class. +// Derived class for W+- properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceW::initConstants() { + + // Locally stored properties and couplings. + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceW::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * mHat; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceW::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // Only contributions from three fermion generations, except top. + if ( (id1Abs > 5 && id1Abs < 11) || id1Abs > 16 ) return; + + + // Combine kinematics with colour factor and couplings. + widNow = preFac * ps + * (1. - 0.5 * (mr1 + mr2) - 0.5 * pow2(mr1 - mr2)); + if (id1Abs < 6) widNow *= colQ * coupSMPtr->V2CKMid(id1Abs, id2Abs); + +} + +//========================================================================== + +// The ResonanceTop class. +// Derived class for top/antitop properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceTop::initConstants() { + + // Locally stored properties and couplings. + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW()); + m2W = pow2(particleDataPtr->m0(24)); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceTop::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 1. - 2.5 * alpS / M_PI; + preFac = alpEM * thetaWRat * pow3(mHat) / m2W; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceTop::calcWidth(bool) { + + // Only contributions from W + quark. + if (id1Abs != 24 || id2Abs > 5) return; + + // Check that above threshold. Kinematical factor. + if (ps == 0.) return; + widNow = preFac * ps + * ( pow2(1. - mr2) + (1. + mr2) * mr1 - 2. * mr1 * mr1 ); + + // Combine with colour factor and CKM couplings. + widNow *= colQ * coupSMPtr->V2CKMid(6, id2Abs); + +} + +//========================================================================== + +// The ResonanceFour class. +// Derived class for fourth-generation properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceFour::initConstants() { + + // Locally stored properties and couplings. + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW()); + m2W = pow2(particleDataPtr->m0(24)); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceFour::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = (idRes < 9) ? 1. - 2.5 * alpS / M_PI : 1.; + preFac = alpEM * thetaWRat * pow3(mHat) / m2W; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceFour::calcWidth(bool) { + + // Only contributions from W + fermion. + if (id1Abs != 24 || id2Abs > 18) return; + + // Check that above threshold. Kinematical factor. + if (ps == 0.) return; + widNow = preFac * ps + * ( pow2(1. - mr2) + (1. + mr2) * mr1 - 2. * mr1 * mr1 ); + + // Combine with colour factor and CKM couplings. + if (idRes < 9) widNow *= colQ * coupSMPtr->V2CKMid(idRes, id2Abs); + +} + +//========================================================================== + +// The ResonanceH class. +// Derived class for SM and BSM Higgs properties. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Minimal mass for W, Z, top in integration over respective Breit-Wigner. +const double ResonanceH::MASSMIN = 10.; + +// Number of widths above threshold where B-W integration not needed. +const double ResonanceH::GAMMAMARGIN = 10.; + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceH::initConstants() { + + // Locally stored properties and couplings. + useCubicWidth = settingsPtr->flag("Higgs:cubicWidth"); + useRunLoopMass = settingsPtr->flag("Higgs:runningLoopMass"); + sin2tW = coupSMPtr->sin2thetaW(); + cos2tW = 1. - sin2tW; + mT = particleDataPtr->m0(6); + mZ = particleDataPtr->m0(23); + mW = particleDataPtr->m0(24); + mHchg = particleDataPtr->m0(37); + GammaT = particleDataPtr->mWidth(6); + GammaZ = particleDataPtr->mWidth(23); + GammaW = particleDataPtr->mWidth(24); + + // Couplings to fermions, Z and W, depending on Higgs type. + coup2d = 1.; + coup2u = 1.; + coup2l = 1.; + coup2Z = 1.; + coup2W = 1.; + coup2Hchg = 0.; + coup2H1H1 = 0.; + coup2A3A3 = 0.; + coup2H1Z = 0.; + coup2A3Z = 0.; + coup2A3H1 = 0.; + coup2HchgW = 0.; + if (higgsType == 1) { + coup2d = settingsPtr->parm("HiggsH1:coup2d"); + coup2u = settingsPtr->parm("HiggsH1:coup2u"); + coup2l = settingsPtr->parm("HiggsH1:coup2l"); + coup2Z = settingsPtr->parm("HiggsH1:coup2Z"); + coup2W = settingsPtr->parm("HiggsH1:coup2W"); + coup2Hchg = settingsPtr->parm("HiggsH1:coup2Hchg"); + } else if (higgsType == 2) { + coup2d = settingsPtr->parm("HiggsH2:coup2d"); + coup2u = settingsPtr->parm("HiggsH2:coup2u"); + coup2l = settingsPtr->parm("HiggsH2:coup2l"); + coup2Z = settingsPtr->parm("HiggsH2:coup2Z"); + coup2W = settingsPtr->parm("HiggsH2:coup2W"); + coup2Hchg = settingsPtr->parm("HiggsH2:coup2Hchg"); + coup2H1H1 = settingsPtr->parm("HiggsH2:coup2H1H1"); + coup2A3A3 = settingsPtr->parm("HiggsH2:coup2A3A3"); + coup2H1Z = settingsPtr->parm("HiggsH2:coup2H1Z"); + coup2A3Z = settingsPtr->parm("HiggsA3:coup2H2Z"); + coup2A3H1 = settingsPtr->parm("HiggsH2:coup2A3H1"); + coup2HchgW = settingsPtr->parm("HiggsH2:coup2HchgW"); + } else if (higgsType == 3) { + coup2d = settingsPtr->parm("HiggsA3:coup2d"); + coup2u = settingsPtr->parm("HiggsA3:coup2u"); + coup2l = settingsPtr->parm("HiggsA3:coup2l"); + coup2Z = settingsPtr->parm("HiggsA3:coup2Z"); + coup2W = settingsPtr->parm("HiggsA3:coup2W"); + coup2Hchg = settingsPtr->parm("HiggsA3:coup2Hchg"); + coup2H1H1 = settingsPtr->parm("HiggsA3:coup2H1H1"); + coup2H1Z = settingsPtr->parm("HiggsA3:coup2H1Z"); + coup2HchgW = settingsPtr->parm("HiggsA3:coup2Hchg"); + } + + // Initialization of threshold kinematical factor by stepwise + // numerical integration of H -> t tbar, Z0 Z0 and W+ W-. + int psMode = (higgsType < 3) ? 3 : 1; + for (int i = 0; i <= 100; ++i) { + kinFacT[i] = numInt2BW( (0.5 + 0.025 * i) * mT, + mT, GammaT, MASSMIN, mT, GammaT, MASSMIN, psMode); + kinFacZ[i] = numInt2BW( (0.5 + 0.025 * i) * mZ, + mZ, GammaZ, MASSMIN, mZ, GammaZ, MASSMIN, 5); + kinFacW[i] = numInt2BW( (0.5 + 0.025 * i) * mW, + mW, GammaW, MASSMIN, mW, GammaW, MASSMIN, 5); + } + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceH::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = (alpEM / (8. * sin2tW)) * pow3(mHat) / pow2(mW); +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceH::calcWidth(bool) { + + // Widths of decays Higgs -> f + fbar. + if ( id2Abs == id1Abs && ( (id1Abs > 0 && id1Abs < 7) + || (id1Abs > 10 && id1Abs < 17) ) ) { + kinFac = 0.; + + // Check that above threshold (well above for top). Kinematical factor. + if ( (id1Abs != 6 && mHat > 2. * mf1 + MASSMARGIN) + || (id1Abs == 6 && mHat > 3. * mT ) ) { + // A0 behaves like beta, h0 and H0 like beta**3. + kinFac = (higgsType < 3) ? pow3(ps) : ps; + } + + // Top near or below threshold: interpolate in table or extrapolate below. + else if (id1Abs == 6 && mHat > 0.5 * mT) { + double xTab = 40. * (mHat / mT - 0.5); + int iTab = max( 0, min( 99, int(xTab) ) ); + kinFac = kinFacT[iTab] + * pow( kinFacT[iTab + 1] / kinFacT[iTab], xTab - iTab); + } + else if (id1Abs == 6) kinFac = kinFacT[0] + * 2. / (1. + pow6(0.5 * mT / mHat)); + + // Coupling from mass and from BSM deviation from SM. + double coupFac = pow2(particleDataPtr->mRun(id1Abs, mHat) / mHat); + if (id1Abs < 7 && id1Abs%2 == 1) coupFac *= coup2d * coup2d; + else if (id1Abs < 7) coupFac *= coup2u * coup2u; + else coupFac *= coup2l * coup2l; + + // Combine couplings and phase space with colour factor. + widNow = preFac * coupFac * kinFac; + if (id1Abs < 7) widNow *= colQ; + } + + // Widths of decays Higgs -> g + g. + else if (id1Abs == 21 && id2Abs == 21) + widNow = preFac * pow2(alpS / M_PI) * eta2gg(); + + // Widths of decays Higgs -> gamma + gamma. + else if (id1Abs == 22 && id2Abs == 22) + widNow = preFac * pow2(alpEM / M_PI) * 0.5 * eta2gaga(); + + // Widths of decays Higgs -> Z0 + gamma0. + else if (id1Abs == 23 && id2Abs == 22) + widNow = preFac * pow2(alpEM / M_PI) * pow3(ps) * eta2gaZ(); + + // Widths of decays Higgs (h0, H0) -> Z0 + Z0. + else if (id1Abs == 23 && id2Abs == 23) { + // If Higgs heavy use on-shell expression, else interpolation in table + if (mHat > 3. * mZ) kinFac = (1. - 4. * mr1 + 12. * mr1 * mr1) * ps; + else if (mHat > 0.5 * mZ) { + double xTab = 40. * (mHat / mZ - 0.5); + int iTab = max( 0, min( 99, int(xTab) ) ); + kinFac = kinFacZ[iTab] + * pow( kinFacZ[iTab + 1] / kinFacZ[iTab], xTab - iTab ); + } + else kinFac = kinFacZ[0] * 2. / (1. + pow6(0.5 * mZ / mHat)); + // Prefactor, normally rescaled to mRes^2 * mHat rather than mHat^3. + widNow = 0.25 * preFac * pow2(coup2Z) * kinFac; + if (!useCubicWidth) widNow *= pow2(mRes / mHat); + } + + // Widths of decays Higgs (h0, H0) -> W+ + W-. + else if (id1Abs == 24 && id2Abs == 24) { + // If Higgs heavy use on-shell expression, else interpolation in table. + if (mHat > 3. * mW) kinFac = (1. - 4. * mr1 + 12. * mr1 * mr1) * ps; + else if (mHat > 0.5 * mW) { + double xTab = 40. * (mHat / mW - 0.5); + int iTab = max( 0, min( 99, int(xTab) ) ); + kinFac = kinFacW[iTab] + * pow( kinFacW[iTab + 1] / kinFacW[iTab], xTab - iTab); + } + else kinFac = kinFacW[0] * 2. / (1. + pow6(0.5 * mW / mHat)); + // Prefactor, normally rescaled to mRes^2 * mHat rather than mHat^3. + widNow = 0.5 * preFac * pow2(coup2W) * kinFac; + if (!useCubicWidth) widNow *= pow2(mRes / mHat); + } + + // Widths of decays Higgs (H0) -> h0 + h0. + else if (id1Abs == 25 && id2Abs == 25) + widNow = 0.25 * preFac * pow4(mZ / mHat) * ps * pow2(coup2H1H1); + + // Widths of decays Higgs (H0) -> A0 + A0. + else if (id1Abs == 36 && id2Abs == 36) + widNow = 0.5 * preFac * pow4(mZ / mHat) * ps * pow2(coup2A3A3); + + // Widths of decays Higgs (A0) -> h0 + Z0. + else if (id1Abs == 25 && id2Abs == 23) + widNow = 0.5 * preFac * pow3(ps) * pow2(coup2H1Z); + + // Widths of decays Higgs (H0) -> A0 + Z0. + else if (id1Abs == 36 && id2Abs == 23) + widNow = 0.5 * preFac * pow3(ps) * pow2(coup2A3Z); + + // Widths of decays Higgs (H0) -> A0 + h0. + else if (id1Abs == 36 && id2Abs == 25) + widNow = 0.25 * preFac * pow4(mZ / mHat) * ps * pow2(coup2A3H1); + + // Widths of decays Higgs -> H+- + W-+. + else if (id1Abs == 37 && id2Abs == 24) + widNow = 0.5 * preFac * pow3(ps) * pow2(coup2HchgW); + +} + +//-------------------------------------------------------------------------- + +// Sum up quark loop contributions in Higgs -> g + g. +// Note: running quark masses are used, unlike Pythia6 (not negligible shift). + +double ResonanceH::eta2gg() { + + // Initial values. + complex eta = complex(0., 0.); + double mLoop, epsilon, root, rootLog; + complex phi, etaNow; + + // Loop over s, c, b, t quark flavours. + for (int idNow = 3; idNow < 7; ++idNow) { + mLoop = (useRunLoopMass) ? particleDataPtr->mRun(idNow, mHat) + : particleDataPtr->m0(idNow); + epsilon = pow2(2. * mLoop / mHat); + + // Value of loop integral. + if (epsilon <= 1.) { + root = sqrt(1. - epsilon); + rootLog = (epsilon < 1e-4) ? log(4. / epsilon - 2.) + : log( (1. + root) / (1. - root) ); + phi = complex( -0.25 * (pow2(rootLog) - pow2(M_PI)), + 0.5 * M_PI * rootLog ); + } + else phi = complex( pow2( asin(1. / sqrt(epsilon)) ), 0.); + + // Factors that depend on Higgs and flavour type. + if (higgsType < 3) etaNow = -0.5 * epsilon + * (complex(1., 0.) + (1. - epsilon) * phi); + else etaNow = -0.5 * epsilon * phi; + if (idNow%2 == 1) etaNow *= coup2d; + else etaNow *= coup2u; + + // Sum up contribution and return square of absolute value. + eta += etaNow; + } + return (pow2(eta.real()) + pow2(eta.imag())); + +} + +//-------------------------------------------------------------------------- + +// Sum up quark, lepton, W+- and (for BSM) H+- loop contributions +// in Higgs -> gamma + gamma. + +double ResonanceH::eta2gaga() { + + // Initial values. + complex eta = complex(0., 0.); + int idNow; + double ef, mLoop, epsilon, root, rootLog; + complex phi, etaNow; + + // Loop over s, c, b, t, mu, tau, W+-, H+- flavours. + for (int idLoop = 0; idLoop < 8; ++idLoop) { + if (idLoop < 4) idNow = idLoop + 3; + else if (idLoop < 6) idNow = 2 * idLoop + 5; + else if (idLoop < 7) idNow = 24; + else idNow = 37; + if (idNow == 37 && higgsType == 0) continue; + + // Charge and loop integral parameter. + ef = (idNow < 20) ? coupSMPtr->ef(idNow) : 1.; + mLoop = (useRunLoopMass) ? particleDataPtr->mRun(idNow, mHat) + : particleDataPtr->m0(idNow); + epsilon = pow2(2. * mLoop / mHat); + + // Value of loop integral. + if (epsilon <= 1.) { + root = sqrt(1. - epsilon); + rootLog = (epsilon < 1e-4) ? log(4. / epsilon - 2.) + : log( (1. + root) / (1. - root) ); + phi = complex( -0.25 * (pow2(rootLog) - pow2(M_PI)), + 0.5 * M_PI * rootLog ); + } + else phi = complex( pow2( asin(1. / sqrt(epsilon)) ), 0.); + + // Expressions for quarks and leptons that depend on Higgs type. + if (idNow < 17) { + if (higgsType < 3) etaNow = -0.5 * epsilon + * (complex(1., 0.) + (1. - epsilon) * phi); + else etaNow = -0.5 * epsilon * phi; + if (idNow < 7 && idNow%2 == 1) etaNow *= 3. * pow2(ef) * coup2d; + else if (idNow < 7 ) etaNow *= 3. * pow2(ef) * coup2u; + else etaNow *= pow2(ef) * coup2l; + } + + // Expression for W+-. + else if (idNow == 24) etaNow = (complex(0.5 + 0.75 * epsilon, 0.) + + 0.75 * epsilon * (2. - epsilon) * phi) * coup2W; + + // Expression for H+-. + else etaNow = (complex(epsilon, 0.) - epsilon * epsilon * phi) + * pow2(mW / mHchg) * coup2Hchg; + + // Sum up contribution and return square of absolute value. + eta += etaNow; + } + return (pow2(eta.real()) + pow2(eta.imag())); + +} + +//-------------------------------------------------------------------------- + +// Sum up quark, lepton, W+- and (for BSM) H+- loop contributions +// in Higgs -> gamma + Z0. + +double ResonanceH::eta2gaZ() { + + // Initial values. + complex eta = complex(0., 0.); + int idNow; + double ef, vf, mLoop, epsilon, epsPrime, root, rootLog, asinEps; + complex phi, psi, phiPrime, psiPrime, fXY, f1, etaNow; + + // Loop over s, c, b, t, mu , tau, W+-, H+- flavours. + for (int idLoop = 0; idLoop < 7; ++idLoop) { + if (idLoop < 4) idNow = idLoop + 3; + else if (idLoop < 6) idNow = 2 * idLoop + 5; + else if (idLoop < 7) idNow = 24; + else idNow = 37; + + // Electroweak charges and loop integral parameters. + ef = (idNow < 20) ? coupSMPtr->ef(idNow) : 1.; + vf = (idNow < 20) ? coupSMPtr->vf(idNow) : 0.; + mLoop = (useRunLoopMass) ? particleDataPtr->mRun(idNow, mHat) + : particleDataPtr->m0(idNow); + epsilon = pow2(2. * mLoop / mHat); + epsPrime = pow2(2. * mLoop / mZ); + + // Value of loop integral for epsilon = 4 m^2 / sHat. + if (epsilon <= 1.) { + root = sqrt(1. - epsilon); + rootLog = (epsilon < 1e-4) ? log(4. / epsilon - 2.) + : log( (1. + root) / (1. - root) ); + phi = complex( -0.25 * (pow2(rootLog) - pow2(M_PI)), + 0.5 * M_PI * rootLog ); + psi = 0.5 * root * complex( rootLog, -M_PI); + } else { + asinEps = asin(1. / sqrt(epsilon)); + phi = complex( pow2(asinEps), 0.); + psi = complex( sqrt(epsilon - 1.) * asinEps, 0.); + } + + // Value of loop integral for epsilonPrime = 4 m^2 / m_Z^2. + if (epsPrime <= 1.) { + root = sqrt(1. - epsPrime); + rootLog = (epsPrime < 1e-4) ? log(4. / epsPrime - 2.) + : log( (1. + root) / (1. - root) ); + phiPrime = complex( -0.25 * (pow2(rootLog) - pow2(M_PI)), + 0.5 * M_PI * rootLog ); + psiPrime = 0.5 * root * complex( rootLog, -M_PI); + } else { + asinEps = asin(1. / sqrt(epsPrime)); + phiPrime = complex( pow2(asinEps), 0.); + psiPrime = complex( sqrt(epsPrime - 1.) * asinEps, 0.); + } + + // Combine the two loop integrals. + fXY = (epsilon * epsPrime / (8. * pow2(epsilon - epsPrime))) + * ( complex(epsilon - epsPrime, 0) + + epsilon * epsPrime * (phi - phiPrime) + + 2. * epsilon * (psi - psiPrime) ); + f1 = - (epsilon * epsPrime / (2. * (epsilon - epsPrime))) + * (phi - phiPrime); + + // Expressions for quarks and leptons that depend on Higgs type. + if (idNow < 17) { + etaNow = (higgsType < 3) ? -fXY + 0.25 * f1 : 0.25 * f1; + if (idNow < 7 && idNow%2 == 1) etaNow *= 3. * ef * vf * coup2d; + else if (idNow < 7) etaNow *= 3. * ef * vf * coup2u; + else etaNow *= ef * vf * coup2l; + + // Expression for W+-. + } else if (idNow == 24) { + double coef1 = 3. - sin2tW / cos2tW; + double coefXY = (1. + 2. / epsilon) * sin2tW / cos2tW + - (5. + 2. / epsilon); + etaNow = -cos2tW * (coef1 * f1 + coefXY * fXY) * coup2W; + + // Expression for H+-. + } else etaNow = (1. - 2. * sin2tW) * fXY * pow2(mW / mHchg) + * coup2Hchg; + + // Sum up contribution and return square of absolute value. + eta += etaNow; + } + return ( (pow2(eta.real()) + pow2(eta.imag())) / (sin2tW * cos2tW) ); + +} + +//========================================================================== + +// The ResonanceHchg class. +// Derived class for H+- properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceHchg::initConstants() { + + // Locally stored properties and couplings. + useCubicWidth = settingsPtr->flag("Higgs:cubicWidth"); + thetaWRat = 1. / (8. * coupSMPtr->sin2thetaW()); + mW = particleDataPtr->m0(24); + tanBeta = settingsPtr->parm("HiggsHchg:tanBeta"); + tan2Beta = tanBeta * tanBeta; + coup2H1W = settingsPtr->parm("HiggsHchg:coup2H1W"); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceHchg::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * pow3(mHat) / pow2(mW); + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceHchg::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // H+- decay to fermions involves running masses. + if (id1Abs < 17 && (id1Abs < 7 || id1Abs > 10)) { + double mRun1 = particleDataPtr->mRun(id1Abs, mHat); + double mRun2 = particleDataPtr->mRun(id2Abs, mHat); + double mrRunDn = pow2(mRun1 / mHat); + double mrRunUp = pow2(mRun2 / mHat); + if (id1Abs%2 == 0) swap( mrRunDn, mrRunUp); + + // Width to fermions: couplings, kinematics, colour factor. + widNow = preFac * max( 0., (mrRunDn * tan2Beta + mrRunUp / tan2Beta) + * (1. - mrRunDn - mrRunUp) - 4. *mrRunDn * mrRunUp ) * ps; + if (id1Abs < 7) widNow *= colQ; + } + + // H+- decay to h0 + W+-. + else if (id1Abs == 25 && id2Abs == 24) + widNow = 0.5 * preFac * pow3(ps) * pow2(coup2H1W); + +} + +//========================================================================== + +// The ResonanceZprime class. +// Derived class for gamma*/Z0/Z'^0 properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceZprime::initConstants() { + + // Locally stored properties and couplings. + gmZmode = settingsPtr->mode("Zprime:gmZmode"); + sin2tW = coupSMPtr->sin2thetaW(); + cos2tW = 1. - sin2tW; + thetaWRat = 1. / (16. * sin2tW * cos2tW); + + // Properties of Z resonance. + mZ = particleDataPtr->m0(23); + GammaZ = particleDataPtr->mWidth(23); + m2Z = mZ*mZ; + GamMRatZ = GammaZ / mZ; + + // Ensure that arrays initially empty. + for (int i = 0; i < 20; ++i) afZp[i] = 0.; + for (int i = 0; i < 20; ++i) vfZp[i] = 0.; + + // Store first-generation axial and vector couplings. + afZp[1] = settingsPtr->parm("Zprime:ad"); + afZp[2] = settingsPtr->parm("Zprime:au"); + afZp[11] = settingsPtr->parm("Zprime:ae"); + afZp[12] = settingsPtr->parm("Zprime:anue"); + vfZp[1] = settingsPtr->parm("Zprime:vd"); + vfZp[2] = settingsPtr->parm("Zprime:vu"); + vfZp[11] = settingsPtr->parm("Zprime:ve"); + vfZp[12] = settingsPtr->parm("Zprime:vnue"); + + // Second and third generation could be carbon copy of this... + if (settingsPtr->flag("Zprime:universality")) { + for (int i = 3; i <= 6; ++i) { + afZp[i] = afZp[i-2]; + vfZp[i] = vfZp[i-2]; + afZp[i+10] = afZp[i+8]; + vfZp[i+10] = vfZp[i+8]; + } + + // ... or could have different couplings. + } else { + afZp[3] = settingsPtr->parm("Zprime:as"); + afZp[4] = settingsPtr->parm("Zprime:ac"); + afZp[5] = settingsPtr->parm("Zprime:ab"); + afZp[6] = settingsPtr->parm("Zprime:at"); + afZp[13] = settingsPtr->parm("Zprime:amu"); + afZp[14] = settingsPtr->parm("Zprime:anumu"); + afZp[15] = settingsPtr->parm("Zprime:atau"); + afZp[16] = settingsPtr->parm("Zprime:anutau"); + vfZp[3] = settingsPtr->parm("Zprime:vs"); + vfZp[4] = settingsPtr->parm("Zprime:vc"); + vfZp[5] = settingsPtr->parm("Zprime:vb"); + vfZp[6] = settingsPtr->parm("Zprime:vt"); + vfZp[13] = settingsPtr->parm("Zprime:vmu"); + vfZp[14] = settingsPtr->parm("Zprime:vnumu"); + vfZp[15] = settingsPtr->parm("Zprime:vtau"); + vfZp[16] = settingsPtr->parm("Zprime:vnutau"); + } + + // Coupling for Z' -> W+ W-. + coupZpWW = settingsPtr->parm("Zprime:coup2WW"); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceZprime::calcPreFac(bool calledFromInit) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * mHat / 3.; + + // When call for incoming flavour need to consider gamma*/Z0 mix. + if (!calledFromInit) { + + // Couplings when an incoming fermion is specified; elso only pure Z'0. + ei2 = 0.; + eivi = 0.; + vai2 = 0.; + eivpi = 0.; + vaivapi = 0., + vapi2 = 1.; + int idInFlavAbs = abs(idInFlav); + if (idInFlavAbs > 0 && idInFlavAbs < 19) { + double ei = coupSMPtr->ef(idInFlavAbs); + double ai = coupSMPtr->af(idInFlavAbs); + double vi = coupSMPtr->vf(idInFlavAbs); + double api = afZp[idInFlavAbs]; + double vpi = vfZp[idInFlavAbs]; + ei2 = ei * ei; + eivi = ei * vi; + vai2 = vi * vi + ai * ai; + eivpi = ei * vpi; + vaivapi = vi * vpi + ai * api;; + vapi2 = vpi * vpi + api * api; + } + + // Calculate prefactors for gamma/interference/Z0 terms. + double sH = mHat * mHat; + double propZ = sH / ( pow2(sH - m2Z) + pow2(sH * GamMRatZ) ); + double propZp = sH / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + gamNorm = ei2; + gamZNorm = 2. * eivi * thetaWRat * (sH - m2Z) * propZ; + ZNorm = vai2 * pow2(thetaWRat) * sH * propZ; + gamZpNorm = 2. * eivpi * thetaWRat * (sH - m2Res) * propZp; + ZZpNorm = 2. * vaivapi * pow2(thetaWRat) * ((sH - m2Res) * (sH - m2Z) + + sH * GamMRat * sH * GamMRatZ) * propZ * propZp; + ZpNorm = vapi2 * pow2(thetaWRat) * sH * propZp; + + // Rescale Z0 height normalization to compensate for a width one?? + //if (doForceWidth) { + // intNorm *= forceFactor; + // resNorm *= forceFactor; + //} + + // Optionally only keep some of gamma*, Z0 and Z' terms. + if (gmZmode == 1) {gamZNorm = 0; ZNorm = 0.; gamZpNorm = 0.; + ZZpNorm = 0.; ZpNorm = 0.;} + if (gmZmode == 2) {gamNorm = 0.; gamZNorm = 0.; gamZpNorm = 0.; + ZZpNorm = 0.; ZpNorm = 0.;} + if (gmZmode == 3) {gamNorm = 0.; gamZNorm = 0.; ZNorm = 0.; + gamZpNorm = 0.; ZZpNorm = 0.;} + if (gmZmode == 4) {gamZpNorm = 0.; ZZpNorm = 0.; ZpNorm = 0.;} + if (gmZmode == 5) {gamZNorm = 0.; ZNorm = 0.; ZZpNorm = 0.;} + if (gmZmode == 6) {gamNorm = 0.; gamZNorm = 0.; gamZpNorm = 0.;} + } + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceZprime::calcWidth(bool calledFromInit) { + + // Check that above threshold. + if (ps == 0.) return; + + // At initialization only the pure Z'0 should be considered. + if (calledFromInit) { + + // Contributions from three fermion generations. + if ( id1Abs < 7 || (id1Abs > 10 && id1Abs < 17) ) { + double apf = afZp[id1Abs]; + double vpf = vfZp[id1Abs]; + widNow = preFac * ps * (vpf*vpf * (1. + 2. * mr1) + + apf*apf * ps*ps); + if (id1Abs < 7) widNow *= colQ; + + // Contribution from Z'0 -> W^+ W^-. + } else if (id1Abs == 24) { + widNow = preFac * pow2(coupZpWW * cos2tW) * pow3(ps) + * (1. + mr1*mr1 + mr2*mr2 + 10. * (mr1 + mr2 + mr1 * mr2)); + } + } + + // When call for incoming flavour need to consider full mix. + else { + + // Contributions from three fermion generations. + if ( id1Abs < 7 || (id1Abs > 10 && id1Abs < 17) ) { + + // Couplings of gamma^*/Z^0/Z'^0 to final flavour + double ef = coupSMPtr->ef(id1Abs); + double af = coupSMPtr->af(id1Abs); + double vf = coupSMPtr->vf(id1Abs); + double apf = afZp[id1Abs]; + double vpf = vfZp[id1Abs]; + + // Combine couplings with kinematical factors. + double kinFacA = pow3(ps); + double kinFacV = ps * (1. + 2. * mr1); + double ef2 = ef * ef * kinFacV; + double efvf = ef * vf * kinFacV; + double vaf2 = vf * vf * kinFacV + af * af * kinFacA; + double efvpf = ef * vpf * kinFacV; + double vafvapf = vf * vpf * kinFacV + af * apf * kinFacA; + double vapf2 = vpf * vpf * kinFacV + apf * apf * kinFacA; + + // Relative outwidths: combine instate, propagator and outstate. + widNow = gamNorm * ef2 + gamZNorm * efvf + ZNorm * vaf2 + + gamZpNorm * efvpf + ZZpNorm * vafvapf + ZpNorm * vapf2; + if (id1Abs < 7) widNow *= colQ; + + // Contribution from Z'0 -> W^+ W^-. + } else if (id1Abs == 24) { + widNow = ZpNorm * pow2(coupZpWW * cos2tW) * pow3(ps) + * (1. + mr1*mr1 + mr2*mr2 + 10. * (mr1 + mr2 + mr1 * mr2)); + } + } + +} + +//========================================================================== + +// The ResonanceWprime class. +// Derived class for W'+- properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceWprime::initConstants() { + + // Locally stored properties and couplings. + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + cos2tW = coupSMPtr->cos2thetaW(); + + // Axial and vector couplings of fermions. + aqWp = settingsPtr->parm("Wprime:aq"); + vqWp = settingsPtr->parm("Wprime:vq"); + alWp = settingsPtr->parm("Wprime:al"); + vlWp = settingsPtr->parm("Wprime:vl"); + + // Coupling for W' -> W Z. + coupWpWZ = settingsPtr->parm("Wprime:coup2WZ"); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceWprime::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * mHat; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceWprime::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // Decay to quarks involves colour factor and CKM matrix. + if (id1Abs > 0 && id1Abs < 7) widNow + = preFac * ps * 0.5 * (aqWp*aqWp + vqWp * vqWp) + * (1. - 0.5 * (mr1 + mr2) - 0.5 * pow2(mr1 - mr2)) + * colQ * coupSMPtr->V2CKMid(id1Abs, id2Abs); + + // Decay to leptons simpler. + else if (id1Abs > 10 && id1Abs < 17) widNow + = preFac * ps * 0.5 * (alWp*aqWp + vlWp * vqWp) + * (1. - 0.5 * (mr1 + mr2) - 0.5 * pow2(mr1 - mr2)); + + // Decay to W^+- Z^0. + else if (id1Abs == 24 && id2Abs == 23) widNow + = preFac * 0.25 * pow2(coupWpWZ) * cos2tW * (mr1 / mr2) * pow3(ps) + * (1. + mr1*mr1 + mr2*mr2 + 10. * (mr1 + mr2 + mr1 * mr2)); + +} + +//========================================================================== + +// The ResonanceRhorizontal class. +// Derived class for R^0 (horizontal gauge boson) properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceRhorizontal::initConstants() { + + // Locally stored properties and couplings. + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceRhorizontal::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * mHat; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceRhorizontal::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // R -> f fbar. Colour factor for quarks. + widNow = preFac * ps * (2. - mr1 - mr2 - pow2(mr1 - mr2)); + if (id1Abs < 9) widNow *= colQ; + +} + +//========================================================================== + +// The ResonanceExcited class. +// Derived class for excited-fermion properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceExcited::initConstants() { + + // Locally stored properties and couplings. + Lambda = settingsPtr->parm("ExcitedFermion:Lambda"); + coupF = settingsPtr->parm("ExcitedFermion:coupF"); + coupFprime = settingsPtr->parm("ExcitedFermion:coupFprime"); + coupFcol = settingsPtr->parm("ExcitedFermion:coupFcol"); + sin2tW = coupSMPtr->sin2thetaW(); + cos2tW = 1. - sin2tW; + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceExcited::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + preFac = pow3(mHat) / pow2(Lambda); + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceExcited::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // f^* -> f g. + if (id1Abs == 21) widNow = preFac * alpS * pow2(coupFcol) / 3.; + + // f^* -> f gamma. + else if (id1Abs == 22) { + double chgI3 = (id2Abs%2 == 0) ? 0.5 : -0.5; + double chgY = (id2Abs < 9) ? 1. / 6. : -0.5; + double chg = chgI3 * coupF + chgY * coupFprime; + widNow = preFac * alpEM * pow2(chg) / 4.; + } + + // f^* -> f Z^0. + else if (id1Abs == 23) { + double chgI3 = (id2Abs%2 == 0) ? 0.5 : -0.5; + double chgY = (id2Abs < 9) ? 1. / 6. : -0.5; + double chg = chgI3 * cos2tW * coupF - chgY * sin2tW * coupFprime; + widNow = preFac * (alpEM * pow2(chg) / (8. * sin2tW * cos2tW)) + * ps*ps * (2. + mr1); + } + + // f^* -> f' W^+-. + else if (id1Abs == 24) widNow = preFac * (alpEM * pow2(coupF) + / (16. * sin2tW)) * ps*ps * (2. + mr1); + +} + +//========================================================================== + +// The ResonanceGraviton class. +// Derived class for excited Graviton properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceGraviton::initConstants() { + + // SMinBulk = off/on, use universal coupling (kappaMG) + // or individual (Gxx) between graviton and SM particles. + m_smbulk = settingsPtr->flag("ExtraDimensionsG*:SMinBulk"); + kappaMG = settingsPtr->parm("ExtraDimensionsG*:kappaMG"); + for (int i = 0; i < 26; ++i) m_coupling[i] = 0.; + double tmp_coup = settingsPtr->parm("ExtraDimensionsG*:Gqq"); + for (int i = 1; i <= 4; ++i) m_coupling[i] = tmp_coup; + m_coupling[5] = settingsPtr->parm("ExtraDimensionsG*:Gbb"); + m_coupling[6] = settingsPtr->parm("ExtraDimensionsG*:Gtt"); + tmp_coup = settingsPtr->parm("ExtraDimensionsG*:Gll"); + for (int i = 11; i <= 16; ++i) m_coupling[i] = tmp_coup; + tmp_coup = settingsPtr->parm("ExtraDimensionsG*:GVV"); + for (int i = 21; i <= 24; ++i) m_coupling[i] = tmp_coup; + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceGraviton::calcPreFac(bool) { + + // Common coupling factors. + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = mHat / M_PI; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceGraviton::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // Widths to fermion pairs. + if (id1Abs < 19) { + widNow = preFac * pow3(ps) * (1. + 8. * mr1 / 3.) / 320.; + if (id1Abs < 9) widNow *= colQ; + } + + // Widths to gluon and photon pair. + else if (id1Abs == 21) widNow = preFac / 20.; + else if (id1Abs == 22) widNow = preFac / 160.; + + // Widths to Z0 Z0 and W+ W- pair. + else if (id1Abs == 23 || id1Abs == 24) { + widNow = preFac * ps * (13. / 12. + 14. * mr1 / 3. + 4. * mr1 * mr1) + / 80.; + if (id1Abs == 23) widNow *= 0.5; + } + + // RS graviton coupling + if (m_smbulk) widNow *= 2. * pow2(m_coupling[min( id1Abs, 25)] * mHat); + else widNow *= pow2(kappaMG); + +} + +//========================================================================== + +// The ResonanceKKgluon class. +// Derived class for excited kk-gluon properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceKKgluon::initConstants() { + + // KK-gluon couplings. + for (int i = 0; i < 10; ++i) m_coupling[i] = 0.; + double tmp_coup = settingsPtr->parm("ExtraDimensionsG*:KKgqq"); + for (int i = 1; i <= 4; ++i) m_coupling[i] = tmp_coup; + m_coupling[5] = settingsPtr->parm("ExtraDimensionsG*:KKgbb"); + m_coupling[6] = settingsPtr->parm("ExtraDimensionsG*:KKgtt"); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceKKgluon::calcPreFac(bool) { + + // Common coupling factors. + alpS = coupSMPtr->alphaS(mHat * mHat); + preFac = alpS * mHat / 6; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceKKgluon::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // Widths to quark pairs. + if (id1Abs < 9) widNow = preFac * ps * (1. + 2. * mr1) + * pow2(m_coupling[id1Abs]); + +} + +//========================================================================== + +// The ResonanceLeptoquark class. +// Derived class for leptoquark properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceLeptoquark::initConstants() { + + // Locally stored properties and couplings. + kCoup = settingsPtr->parm("LeptoQuark:kCoup"); + + // Check that flavour info in decay channel is correctly set. + int id1Now = particlePtr->channel(0).product(0); + int id2Now = particlePtr->channel(0).product(1); + if (id1Now < 1 || id1Now > 5) { + infoPtr->errorMsg("Error in ResonanceLeptoquark::init:" + " unallowed input quark flavour reset to u"); + id1Now = 2; + particlePtr->channel(0).product(0, id1Now); + } + if (abs(id2Now) < 11 || abs(id2Now) > 16) { + infoPtr->errorMsg("Error in ResonanceLeptoquark::init:" + " unallowed input lepton flavour reset to e-"); + id2Now = 11; + particlePtr->channel(0).product(1, id2Now); + } + + // Set/overwrite charge and name of particle. + bool changed = particlePtr->hasChanged(); + int chargeLQ = particleDataPtr->chargeType(id1Now) + + particleDataPtr->chargeType(id2Now); + particlePtr->setChargeType(chargeLQ); + string nameLQ = "LQ_" + particleDataPtr->name(id1Now) + "," + + particleDataPtr->name(id2Now); + particlePtr->setNames(nameLQ, nameLQ + "bar"); + if (!changed) particlePtr->setHasChanged(false); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceLeptoquark::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + preFac = 0.25 * alpEM * kCoup * mHat; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceLeptoquark::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // Width into lepton plus quark. + if (id1Abs > 10 && id1Abs < 17 && id2Abs < 7) widNow = preFac * pow3(ps); + +} + +//========================================================================== + +// The ResonanceNuRight class. +// Derived class for righthanded Majorana neutrino properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceNuRight::initConstants() { + + // Locally stored properties and couplings: righthanded W mass. + thetaWRat = 1. / (768. * M_PI * pow2(coupSMPtr->sin2thetaW())); + mWR = particleDataPtr->m0(9900024); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceNuRight::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = pow2(alpEM) * thetaWRat * pow5(mHat) / pow4(max(mHat, mWR)); + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceNuRight::calcWidth(bool) { + + // Check that above threshold. + if (mHat < mf1 + mf2 + mf3 + MASSMARGIN) return; + + // Coupling part of widths to l- q qbar', l- l'+ nu_lR' and c.c. + widNow = (id2Abs < 9 && id3Abs < 9) + ? preFac * colQ * coupSMPtr->V2CKMid(id2, id3) : preFac; + + // Phase space corrections in decay. Must have y < 1. + double x = (mf1 + mf2 + mf3) / mHat; + double x2 = x * x; + double fx = 1. - 8. * x2 + 8. * pow3(x2) - pow4(x2) + - 24. * pow2(x2) * log(x); + double y = min( 0.999, pow2(mHat / mWR) ); + double fy = ( 12. * (1. - y) * log(1. - y) + 12. * y - 6. * y*y + - 2.* pow3(y) ) / pow4(y); + widNow *= fx * fy; + +} + +//========================================================================== + +// The ResonanceZRight class. +// Derived class for Z_R^0 properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceZRight::initConstants() { + + // Locally stored properties and couplings: righthanded W mass. + sin2tW = coupSMPtr->sin2thetaW(); + thetaWRat = 1. / (48. * sin2tW * (1. - sin2tW) * (1. - 2. * sin2tW) ); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceZRight::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * mHat; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceZRight::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // Couplings to q qbar and l+ l-. + double vf = 0.; + double af = 0.; + double symMaj = 1.; + if (id1Abs < 9 && id1Abs%2 == 1) { + af = -1. + 2. * sin2tW; + vf = -1. + 4. * sin2tW / 3.; + } else if (id1Abs < 9) { + af = 1. - 2. * sin2tW; + vf = 1. - 8. * sin2tW / 3.; + } else if (id1Abs < 19 && id1Abs%2 == 1) { + af = -1. + 2. * sin2tW; + vf = -1. + 4. * sin2tW; + + // Couplings to nu_L nu_Lbar and nu_R nu_Rbar, both assumed Majoranas. + } else if (id1Abs < 19) { + af = -2. * sin2tW; + vf = 0.; + symMaj = 0.5; + } else { + af = 2. * (1. - sin2tW); + vf = 0.; + symMaj = 0.5; + } + + // Width expression, including phase space and colour factor. + widNow = preFac * (vf*vf * (1. + 2. * mr1) + af*af * ps*ps) * ps + * symMaj; + if (id1Abs < 9) widNow *= colQ; + +} + +//========================================================================== + +// The ResonanceWRight class. +// Derived class for W_R+- properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceWRight::initConstants() { + + // Locally stored properties and couplings. + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceWRight::calcPreFac(bool) { + + // Common coupling factors. + alpEM = coupSMPtr->alphaEM(mHat * mHat); + alpS = coupSMPtr->alphaS(mHat * mHat); + colQ = 3. * (1. + alpS / M_PI); + preFac = alpEM * thetaWRat * mHat; + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceWRight::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // Combine kinematics with colour factor and CKM couplings. + widNow = preFac * (1. - 0.5 * (mr1 + mr2) - 0.5 * pow2(mr1 - mr2)) + * ps; + if (id1Abs < 9) widNow *= colQ * coupSMPtr->V2CKMid(id1Abs, id2Abs); + +} + +//========================================================================== + +// The ResonanceHchgchgLeft class. +// Derived class for H++/H-- (left) properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceHchgchgLeft::initConstants() { + + // Read in Yukawa matrix for couplings to a lepton pair. + yukawa[1][1] = settingsPtr->parm("LeftRightSymmmetry:coupHee"); + yukawa[2][1] = settingsPtr->parm("LeftRightSymmmetry:coupHmue"); + yukawa[2][2] = settingsPtr->parm("LeftRightSymmmetry:coupHmumu"); + yukawa[3][1] = settingsPtr->parm("LeftRightSymmmetry:coupHtaue"); + yukawa[3][2] = settingsPtr->parm("LeftRightSymmmetry:coupHtaumu"); + yukawa[3][3] = settingsPtr->parm("LeftRightSymmmetry:coupHtautau"); + + // Locally stored properties and couplings. + gL = settingsPtr->parm("LeftRightSymmmetry:gL"); + vL = settingsPtr->parm("LeftRightSymmmetry:vL"); + mW = particleDataPtr->m0(24); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceHchgchgLeft::calcPreFac(bool) { + + // Common coupling factors. + preFac = mHat / (8. * M_PI); + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceHchgchgLeft::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // H++-- width to a pair of leptons. Combinatorial factor of 2. + if (id1Abs < 17 && id2Abs < 17) { + widNow = preFac * pow2(yukawa[(id1Abs-9)/2][(id2Abs-9)/2]) * ps; + if (id2Abs != id1Abs) widNow *= 2.; + } + + // H++-- width to a pair of lefthanded W's. + else if (id1Abs == 24 && id2Abs == 24) + widNow = preFac * 0.5 * pow2(gL*gL * vL / mW) + * (3. * mr1 + 0.25 / mr1 - 1.) * ps; + +} + +//========================================================================== + +// The ResonanceHchgchgRight class. +// Derived class for H++/H-- (right) properties. + +//-------------------------------------------------------------------------- + +// Initialize constants. + +void ResonanceHchgchgRight::initConstants() { + + // Read in Yukawa matrix for couplings to a lepton pair. + yukawa[1][1] = settingsPtr->parm("LeftRightSymmmetry:coupHee"); + yukawa[2][1] = settingsPtr->parm("LeftRightSymmmetry:coupHmue"); + yukawa[2][2] = settingsPtr->parm("LeftRightSymmmetry:coupHmumu"); + yukawa[3][1] = settingsPtr->parm("LeftRightSymmmetry:coupHtaue"); + yukawa[3][2] = settingsPtr->parm("LeftRightSymmmetry:coupHtaumu"); + yukawa[3][3] = settingsPtr->parm("LeftRightSymmmetry:coupHtautau"); + + // Locally stored properties and couplings. + idWR = 9000024; + gR = settingsPtr->parm("LeftRightSymmmetry:gR"); + +} + +//-------------------------------------------------------------------------- + +// Calculate various common prefactors for the current mass. + +void ResonanceHchgchgRight::calcPreFac(bool) { + + // Common coupling factors. + preFac = mHat / (8. * M_PI); + +} + +//-------------------------------------------------------------------------- + +// Calculate width for currently considered channel. + +void ResonanceHchgchgRight::calcWidth(bool) { + + // Check that above threshold. + if (ps == 0.) return; + + // H++-- width to a pair of leptons. Combinatorial factor of 2. + if (id1Abs < 17 && id2Abs < 17) { + widNow = preFac * pow2(yukawa[(id1Abs-9)/2][(id2Abs-9)/2]) * ps; + if (id2Abs != id1Abs) widNow *= 2.; + } + + // H++-- width to a pair of lefthanded W's. + else if (id1Abs == idWR && id2Abs == idWR) + widNow = preFac * pow2(yukawa[(id1Abs-9)/2][(id2Abs-9)/2]) * ps; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/Settings.cxx b/PYTHIA8/pythia8140/src/Settings.cxx new file mode 100644 index 00000000000..d3046753dc5 --- /dev/null +++ b/PYTHIA8/pythia8140/src/Settings.cxx @@ -0,0 +1,677 @@ +// Settings.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the Settings class. + +#include "Settings.h" + +// Allow string and character manipulation. +#include + +namespace Pythia8 { + +//========================================================================== + +// Settings class. +// This class contains flags, modes, parms and words used in generation. + +//-------------------------------------------------------------------------- + +// Read in database from specific file. + +bool Settings::init(string startFile, bool append, ostream& os) { + + // Don't initialize if it has already been done and not in append mode. + if (isInit && !append) return true; + int nError = 0; + + // List of files to be checked. Start with input file. + vector files; + files.push_back(startFile); + + // If nontrivial startfile path, then use that for other files as well. + string pathName = ""; + if (startFile.rfind("/") != string::npos) + pathName = startFile.substr(0, startFile.rfind("/") + 1); + + // Loop over files. Open them for read. + for (int i = 0; i < int(files.size()); ++i) { + const char* cstring = files[i].c_str(); + ifstream is(cstring); + + // Check that instream is OK. + if (!is.good()) { + os << "\n PYTHIA Error: settings file " << files[i] + << " not found" << endl; + return false; + } + + // Read in one line at a time. + string line; + while ( getline(is, line) ) { + + // Get first word of a line, to interpret it as tag. + istringstream getfirst(line); + string tag; + getfirst >> tag; + + // Skip ahead if not interesting. Only look for new files in startfile. + if (tag != ". + while (line.find(">") == string::npos) { + string addLine; + getline(is, addLine); + line += " " + addLine; + } + + // Remove extra blanks before an = sign. + while (line.find(" =") != string::npos) line.erase( line.find(" ="), 1); + + // Add file also to be read. + if (tag == "> name; + + // Replace two colons by one (:: -> :) to allow for such mistakes. + while (name.find("::") != string::npos) { + int firstColonColon = name.find_first_of("::"); + name.replace(firstColonColon, 2, ":"); + } + + // Check whether this is in the database. Done if not. + int inDataBase = 0; + if (isFlag(name)) inDataBase = 1; + else if (isMode(name)) inDataBase = 2; + else if (isParm(name)) inDataBase = 3; + else if (isWord(name)) inDataBase = 4; + if (inDataBase == 0) { + if (warn) os << "\n PYTHIA Warning: input string not found in settings" + << " databases; skip:\n " << line << endl; + return false; + } + + // Find value. Warn if none found. + string valueString; + splitLine >> valueString; + if (!splitLine) { + if (warn) os << "\n PYTHIA Warning: variable recognized, but its value" + << " not meaningful; skip:\n " << line << endl; + return false; + } + + // Update flag map; allow many ways to say yes. + if (inDataBase == 1) { + bool value = boolString(valueString); + flag(name, value); + + // Update mode map. + } else if (inDataBase == 2) { + istringstream modeData(valueString); + int value; + modeData >> value; + if (!modeData) { + if (warn) os << "\n PYTHIA Warning: variable recognized, but its value" + << " not meaningful; skip:\n " << line << endl; + return false; + } + mode(name, value); + + // Update parm map. + } else if (inDataBase == 3) { + istringstream parmData(valueString); + double value; + parmData >> value; + if (!parmData) { + if (warn) os << "\n PYTHIA Warning: variable recognized, but its value" + << " not meaningful; skip:\n " << line << endl; + return false; + } + parm(name, value); + + // Update word map. + } else { + word(name, valueString); + } + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Write updates or everything to user-defined file. + +bool Settings::writeFile(string toFile, bool writeAll) { + + // Open file for writing. + const char* cstring = toFile.c_str(); + ofstream os(cstring); + if (!os) { + infoPtr->errorMsg("Error in Settings::writeFile:" + " could not open file", toFile); + return false; + } + + // Hand over real work to next method. + return writeFile( os, writeAll); + +} + +//-------------------------------------------------------------------------- + +// Write updates or everything to user-defined stream (or file). + +bool Settings::writeFile(ostream& os, bool writeAll) { + + // Write simple header as comment. + if (writeAll) os << "! List of all current PYTHIA "; + else os << "! List of all modified PYTHIA "; + os << fixed << setprecision(3) << parm("Pythia:versionNumber") + << " settings.\n"; + + // Iterators for the flag, mode and parm tables. + map::iterator flagEntry = flags.begin(); + map::iterator modeEntry = modes.begin(); + map::iterator parmEntry = parms.begin(); + map::iterator wordEntry = words.begin(); + + // Loop while there is something left to do. + while (flagEntry != flags.end() || modeEntry != modes.end() + || parmEntry != parms.end() || wordEntry != words.end()) { + + // Check if a flag is next in lexigraphical order; if so print it. + if ( flagEntry != flags.end() + && ( modeEntry == modes.end() || flagEntry->first < modeEntry->first ) + && ( parmEntry == parms.end() || flagEntry->first < parmEntry->first ) + && ( wordEntry == words.end() || flagEntry->first < wordEntry->first ) + ) { + string state[2] = {"off", "on"}; + bool valNow = flagEntry->second.valNow; + bool valDefault = flagEntry->second.valDefault; + if ( writeAll || valNow != valDefault ) + os << flagEntry->second.name << " = " << state[valNow] << "\n"; + ++flagEntry; + + // Else check if mode is next, and if so print it. + } else if ( modeEntry != modes.end() + && ( parmEntry == parms.end() || modeEntry->first < parmEntry->first ) + && ( wordEntry == words.end() || modeEntry->first < wordEntry->first ) + ) { + int valNow = modeEntry->second.valNow; + int valDefault = modeEntry->second.valDefault; + if ( writeAll || valNow != valDefault ) + os << modeEntry->second.name << " = " << valNow << "\n"; + ++modeEntry; + + // Else check if parm is next, and if so print it; + // fixed or scientific depending on value. + } else if ( parmEntry != parms.end() + && ( wordEntry == words.end() || parmEntry->first < wordEntry->first ) + ) { + double valNow = parmEntry->second.valNow; + double valDefault = parmEntry->second.valDefault; + if ( writeAll || valNow != valDefault ) { + os << parmEntry->second.name << " = "; + if ( valNow == 0. ) os << fixed << setprecision(1); + else if ( abs(valNow) < 0.001 ) os << scientific << setprecision(4); + else if ( abs(valNow) < 0.1 ) os << fixed << setprecision(7); + else if ( abs(valNow) < 1000. ) os << fixed << setprecision(5); + else if ( abs(valNow) < 1000000. ) os << fixed << setprecision(3); + else os << scientific << setprecision(4); + os << valNow << "\n"; + } + ++parmEntry; + + // Else print word. + } else { + string valNow = wordEntry->second.valNow; + string valDefault = wordEntry->second.valDefault; + if ( writeAll || valNow != valDefault ) + os << wordEntry->second.name << " = " << valNow << "\n"; + ++wordEntry; + } + } ; + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Print out table of database in lexigraphical order. + +void Settings::list(bool doListAll, bool doListString, string match, + ostream& os) { + + // Table header; output for bool as off/on. + if (doListAll) + os << "\n *------- PYTHIA Flag + Mode + Parm + Word Settings (all) " + << " -------------------------------------------------------* \n"; + else if (!doListString) + os << "\n *------- PYTHIA Flag + Mode + Parm + Word Settings (chang" + << "es only) ----------------------------------------------* \n" ; + else + os << "\n *------- PYTHIA Flag + Mode + Parm + Word Settings (with " + << "requested string) -------------------------------------* \n" ; + os << " | " + << " | \n" + << " | Name | " + << " Now | Default Min Max | \n" + << " | | " + << " | | \n"; + + // Convert input string to lowercase for match. + match = toLower(match); + if (match == "") match = " "; + + // Iterators for the flag, mode and parm tables. + map::iterator flagEntry = flags.begin(); + map::iterator modeEntry = modes.begin(); + map::iterator parmEntry = parms.begin(); + map::iterator wordEntry = words.begin(); + + // Loop while there is something left to do. + while (flagEntry != flags.end() || modeEntry != modes.end() + || parmEntry != parms.end() || wordEntry != words.end()) { + + // Check if a flag is next in lexigraphical order; if so print it. + if ( flagEntry != flags.end() + && ( modeEntry == modes.end() || flagEntry->first < modeEntry->first ) + && ( parmEntry == parms.end() || flagEntry->first < parmEntry->first ) + && ( wordEntry == words.end() || flagEntry->first < wordEntry->first ) + ) { + string state[2] = {"off", "on"}; + bool valNow = flagEntry->second.valNow; + bool valDefault = flagEntry->second.valDefault; + if ( doListAll || (!doListString && valNow != valDefault) + || (doListString && flagEntry->first.find(match) != string::npos) ) + os << " | " << setw(45) << left + << flagEntry->second.name << " | " << setw(24) << right + << state[valNow] << " | " << setw(12) << state[valDefault] + << " | \n"; + ++flagEntry; + + // Else check if mode is next, and if so print it. + } else if ( modeEntry != modes.end() + && ( parmEntry == parms.end() || modeEntry->first < parmEntry->first ) + && ( wordEntry == words.end() || modeEntry->first < wordEntry->first ) + ) { + int valNow = modeEntry->second.valNow; + int valDefault = modeEntry->second.valDefault; + if ( doListAll || (!doListString && valNow != valDefault) + || (doListString && modeEntry->first.find(match) != string::npos) ) { + os << " | " << setw(45) << left + << modeEntry->second.name << " | " << setw(24) << right + << valNow << " | " << setw(12) << valDefault; + if (modeEntry->second.hasMin) + os << setw(12) << modeEntry->second.valMin; + else os << " "; + if (modeEntry->second.hasMax) + os << setw(12) << modeEntry->second.valMax; + else os << " "; + os << " | \n"; + } + ++modeEntry; + + // Else check if parm is next, and if so print it; + // fixed or scientific depending on value. + } else if ( parmEntry != parms.end() + && ( wordEntry == words.end() || parmEntry->first < wordEntry->first ) + ) { + double valNow = parmEntry->second.valNow; + double valDefault = parmEntry->second.valDefault; + if ( doListAll || (!doListString && valNow != valDefault ) + || (doListString && parmEntry->first.find(match) != string::npos) ) { + os << " | " << setw(45) << left + << parmEntry->second.name << right << " | "; + for (int i = 0; i < 4; ++i) { + if (i == 1) valNow = valDefault; + if (i == 2) valNow = parmEntry->second.valMin; + if (i == 3) valNow = parmEntry->second.valMax; + if ( (i == 2 && !parmEntry->second.hasMin) + || (i == 3 && !parmEntry->second.hasMax) ) + os << " "; + else if ( valNow == 0. ) + os << fixed << setprecision(1) << setw(12) << valNow; + else if ( abs(valNow) < 0.001 ) + os << scientific << setprecision(4) << setw(12) << valNow; + else if ( abs(valNow) < 0.1 ) + os << fixed << setprecision(7) << setw(12) << valNow; + else if ( abs(valNow) < 1000. ) + os << fixed << setprecision(5) << setw(12) << valNow; + else if ( abs(valNow) < 1000000. ) + os << fixed << setprecision(3) << setw(12) << valNow; + else + os << scientific << setprecision(4) << setw(12) << valNow; + if (i == 0) os << " | "; + } + os << " | \n"; + } + ++parmEntry; + + // Else print word. + } else { + string valNow = wordEntry->second.valNow; + string valDefault = wordEntry->second.valDefault; + int blankLeft = max(0, 60 - max(24, int(valNow.length()) ) + - max(12, int(valDefault.length()) ) ); + string blankPad( blankLeft, ' '); + if ( doListAll || (!doListString && valNow != valDefault) + || (doListString && wordEntry->first.find(match) != string::npos) ) + os << " | " << setw(45) << left + << wordEntry->second.name << " | " << setw(24) << right + << valNow << " | " << setw(12) << valDefault << blankPad + << " | \n"; + ++wordEntry; + } + } ; + + // End of loop over database contents. + os << " | " + << " | \n" + << " *------- End PYTHIA Flag + Mode + Parm + Word Settings ---" + << "------------------------------------------------------* " << endl; + +} + +//-------------------------------------------------------------------------- + +// Reset all values to their defaults. + +void Settings::resetAll() { + + // Loop through the flags table, resetting all entries. + for (map::iterator flagEntry = flags.begin(); + flagEntry != flags.end(); ++flagEntry) { + string name = flagEntry->first; + resetFlag(name); + } + + // Loop through the modes table, resetting all entries. + for (map::iterator modeEntry = modes.begin(); + modeEntry != modes.end(); ++modeEntry) { + string name = modeEntry->first; + resetMode(name); + } + + // Loop through the parms table, resetting all entries. + for (map::iterator parmEntry = parms.begin(); + parmEntry != parms.end(); ++parmEntry) { + string name = parmEntry->first; + resetParm(name); + } + + // Loop through the words table, resetting all entries. + for (map::iterator wordEntry = words.begin(); + wordEntry != words.end(); ++wordEntry) { + string name = wordEntry->first; + resetWord(name); + } + +} + +//-------------------------------------------------------------------------- + +// Give back current value, with check that key exists. + +bool Settings::flag(string keyIn) { + if (isFlag(keyIn)) return flags[toLower(keyIn)].valNow; + infoPtr->errorMsg("Error in Settings::flag: unknown key", keyIn); + return false; +} + +int Settings::mode(string keyIn) { + if (isMode(keyIn)) return modes[toLower(keyIn)].valNow; + infoPtr->errorMsg("Error in Settings::mode: unknown key", keyIn); + return 0; +} + +double Settings::parm(string keyIn) { + if (isParm(keyIn)) return parms[toLower(keyIn)].valNow; + infoPtr->errorMsg("Error in Settings::parm: unknown key", keyIn); + return 0.; +} + +string Settings::word(string keyIn) { + if (isWord(keyIn)) return words[toLower(keyIn)].valNow; + infoPtr->errorMsg("Error in Settings::word: unknown key", keyIn); + return " "; +} + +//-------------------------------------------------------------------------- + +// Change current value, respecting limits. + +void Settings::flag(string keyIn, bool nowIn) { + if (isFlag(keyIn)) flags[toLower(keyIn)].valNow = nowIn; +} + +void Settings:: mode(string keyIn, int nowIn) { + if (isMode(keyIn)) { + Mode& modeNow = modes[toLower(keyIn)]; + if (modeNow.hasMin && nowIn < modeNow.valMin) + modeNow.valNow = modeNow.valMin; + else if (modeNow.hasMax && nowIn > modeNow.valMax) + modeNow.valNow = modeNow.valMax; + else modeNow.valNow = nowIn; + } +} + +void Settings::parm(string keyIn, double nowIn) { + if (isParm(keyIn)) { + Parm& parmNow = parms[toLower(keyIn)]; + if (parmNow.hasMin && nowIn < parmNow.valMin) + parmNow.valNow = parmNow.valMin; + else if (parmNow.hasMax && nowIn > parmNow.valMax) + parmNow.valNow = parmNow.valMax; + else parmNow.valNow = nowIn; + } +} + +void Settings::word(string keyIn, string nowIn) { + if (isWord(keyIn)) words[toLower(keyIn)].valNow = nowIn; +} + +//-------------------------------------------------------------------------- + +// Convert string to lowercase for case-insensitive comparisons. +// Also remove initial and trailing blanks, if any. + +string Settings::toLower(const string& name) { + + // Copy string without initial and trailing blanks. + if (name.find_first_not_of(" \n\t\v\b\r\f\a") == string::npos) return ""; + int firstChar = name.find_first_not_of(" \n\t\v\b\r\f\a"); + int lastChar = name.find_last_not_of(" \n\t\v\b\r\f\a"); + string temp = name.substr( firstChar, lastChar + 1 - firstChar); + + // Convert to lowercase letter by letter. + for (int i = 0; i < int(temp.length()); ++i) + temp[i] = std::tolower(temp[i]); + return temp; + +} + +//-------------------------------------------------------------------------- + +// Allow several alternative inputs for true/false. + +bool Settings::boolString(string tag) { + + string tagLow = toLower(tag); + return ( tagLow == "true" || tagLow == "1" || tagLow == "on" + || tagLow == "yes" || tagLow == "ok" ); + +} + +//-------------------------------------------------------------------------- + +// Extract XML value string following XML attribute. + +string Settings::attributeValue(string line, string attribute) { + + if (line.find(attribute) == string::npos) return ""; + int iBegAttri = line.find(attribute); + int iBegQuote = line.find("\"", iBegAttri + 1); + int iEndQuote = line.find("\"", iBegQuote + 1); + return line.substr(iBegQuote + 1, iEndQuote - iBegQuote - 1); + +} + +//-------------------------------------------------------------------------- + +// Extract XML bool value following XML attribute. + +bool Settings::boolAttributeValue(string line, string attribute) { + + string valString = attributeValue(line, attribute); + if (valString == "") return false; + return boolString(valString); + +} + +//-------------------------------------------------------------------------- + +// Extract XML int value following XML attribute. + +int Settings::intAttributeValue(string line, string attribute) { + string valString = attributeValue(line, attribute); + if (valString == "") return 0; + istringstream valStream(valString); + int intVal; + valStream >> intVal; + return intVal; + +} + +//-------------------------------------------------------------------------- + +// Extract XML double value following XML attribute. + +double Settings::doubleAttributeValue(string line, string attribute) { + string valString = attributeValue(line, attribute); + if (valString == "") return 0.; + istringstream valStream(valString); + double doubleVal; + valStream >> doubleVal; + return doubleVal; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaCompositeness.cxx b/PYTHIA8/pythia8140/src/SigmaCompositeness.cxx new file mode 100644 index 00000000000..45472e6871e --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaCompositeness.cxx @@ -0,0 +1,616 @@ +// SigmaCompositeness.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// compositeness simulation classes. + +#include "SigmaCompositeness.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma1qg2qStar class. +// Cross section for q g -> q^* (excited quark state). +// Note: for simplicity decay is assumed isotropic. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1qg2qStar::initProc() { + + // Set up process properties from the chosen quark flavour. + idRes = 4000000 + idq; + codeSave = 4000 + idq; + if (idq == 1) nameSave = "d g -> d^*"; + else if (idq == 2) nameSave = "u g -> u^*"; + else if (idq == 3) nameSave = "s g -> s^*"; + else if (idq == 4) nameSave = "c g -> c^*"; + else nameSave = "b g -> b^*"; + + // Store q* mass and width for propagator. + mRes = particleDataPtr->m0(idRes); + GammaRes = particleDataPtr->mWidth(idRes); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Locally stored properties and couplings. + Lambda = settingsPtr->parm("ExcitedFermion:Lambda"); + coupFcol = settingsPtr->parm("ExcitedFermion:coupFcol"); + + // Set pointer to particle properties and decay table. + qStarPtr = particleDataPtr->particleDataEntryPtr(idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1qg2qStar::sigmaKin() { + + // Incoming width for correct quark. + widthIn = pow3(mH) * alpS * pow2(coupFcol) / (3. * pow2(Lambda)); + + // Set up Breit-Wigner. + sigBW = M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat) for specific incoming flavours. + +double Sigma1qg2qStar::sigmaHat() { + + // Identify whether correct incoming flavours. + int idqNow = (id2 == 21) ? id1 : id2; + if (abs(idqNow) != idq) return 0.; + + // Outgoing width and total sigma. Done. + return widthIn * sigBW * qStarPtr->resWidthOpen(idqNow, mH); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1qg2qStar::setIdColAcol() { + + // Flavours. + int idqNow = (id2 == 21) ? id1 : id2; + int idqStar = (idqNow > 0) ? idRes : -idRes; + setId( id1, id2, idqStar); + + // Colour flow topology. + if (id1 == idqNow) setColAcol( 1, 0, 2, 1, 2, 0); + else setColAcol( 2, 1, 1, 0, 2, 0); + if (idqNow < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for q* decay angle. + +double Sigma1qg2qStar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // q* should sit in entry 5. Sequential Z/W decay assumed isotropic. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Sign of asymmetry. + int sideIn = (process[3].idAbs() < 20) ? 1 : 2; + int sideOut = (process[6].idAbs() < 20) ? 1 : 2; + double eps = (sideIn == sideOut) ? 1. : -1.; + + // Phase space factors. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + + // Reconstruct decay angle. Default isotropic decay. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + double wt = 1.; + double wtMax = 1.; + + // Decay q* -> q (g/gamma) or q (Z^0/W^+-). + int idBoson = (sideOut == 1) ? process[7].idAbs() : process[6].idAbs(); + if (idBoson == 21 || idBoson == 22) { + wt = 1. + eps * cosThe; + wtMax = 2.; + } else if (idBoson == 23 || idBoson == 24) { + double mrB = (sideOut == 1) ? mr2 : mr1; + double ratB = (1. - 0.5 * mrB) / (1 + 0.5 * mrB); + wt = 1. + eps * cosThe * ratB; + wtMax = 1. + ratB; + } + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma1lgm2lStar class. +// Cross section for l gamma -> l^* (excited lepton state). +// Note: for simplicity decay is assumed isotropic. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1lgm2lStar::initProc() { + + // Set up process properties from the chosen lepton flavour. + idRes = 4000000 + idl; + codeSave = 4000 + idl; + if (idl == 11) nameSave = "e gamma -> e^*"; + else if (idl == 13) nameSave = "mu gamma -> mu^*"; + else nameSave = "tau gamma -> tau^*"; + + // Store l* mass and width for propagator. + mRes = particleDataPtr->m0(idRes); + GammaRes = particleDataPtr->mWidth(idRes); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Locally stored properties and couplings. + Lambda = settingsPtr->parm("ExcitedFermion:Lambda"); + double coupF = settingsPtr->parm("ExcitedFermion:coupF"); + double coupFp = settingsPtr->parm("ExcitedFermion:coupFprime"); + coupChg = -0.5 * coupF - 0.5 * coupFp; + + // Set pointer to particle properties and decay table. + qStarPtr = particleDataPtr->particleDataEntryPtr(idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1lgm2lStar::sigmaKin() { + + // Incoming width for correct lepton. + widthIn = pow3(mH) * alpEM * pow2(coupChg) / pow2(Lambda); + + // Set up Breit-Wigner. + sigBW = M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat) for specific incoming flavours. + +double Sigma1lgm2lStar::sigmaHat() { + + // Identify whether correct incoming flavours. + int idlNow = (id2 == 22) ? id1 : id2; + if (abs(idlNow) != idl) return 0.; + + // Outgoing width and total sigma. Done. + return widthIn * sigBW * qStarPtr->resWidthOpen(idlNow, mH); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1lgm2lStar::setIdColAcol() { + + // Flavours. + int idlNow = (id2 == 22) ? id1 : id2; + int idlStar = (idlNow > 0) ? idRes : -idRes; + setId( id1, id2, idlStar); + + // No colour flow. + setColAcol( 0, 0, 0, 0, 0, 0); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for l* decay angle. + +double Sigma1lgm2lStar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // l* should sit in entry 5. Sequential Z/W decay assumed isotropic. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Sign of asymmetry. + int sideIn = (process[3].idAbs() < 20) ? 1 : 2; + int sideOut = (process[6].idAbs() < 20) ? 1 : 2; + double eps = (sideIn == sideOut) ? 1. : -1.; + + // Phase space factors. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + + // Reconstruct decay angle. Default isotropic decay. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + double wt = 1.; + double wtMax = 1.; + + // Decay l* -> l gamma or l (Z^0/W^+-). + int idBoson = (sideOut == 1) ? process[7].idAbs() : process[6].idAbs(); + if (idBoson == 22) { + wt = 1. + eps * cosThe; + wtMax = 2.; + } else if (idBoson == 23 || idBoson == 24) { + double mrB = (sideOut == 1) ? mr2 : mr1; + double ratB = (1. - 0.5 * mrB) / (1 + 0.5 * mrB); + wt = 1. + eps * cosThe * ratB; + wtMax = 1. + ratB; + } + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma2qq2qStarq class. +// Cross section for q q' -> q^* q' (excited quark state). +// Note: for simplicity decay is assumed isotropic. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qq2qStarq::initProc() { + + // Set up process properties from the chosen quark flavour. + idRes = 4000000 + idq; + codeSave = 4020 + idq; + if (idq == 1) nameSave = "q q -> d^* q"; + else if (idq == 2) nameSave = "q q -> u^* q"; + else if (idq == 3) nameSave = "q q -> s^* q"; + else if (idq == 4) nameSave = "q q -> c^* q"; + else nameSave = "q q -> b^* q"; + + // Locally stored properties and couplings. + Lambda = settingsPtr->parm("ExcitedFermion:Lambda"); + preFac = M_PI / pow4(Lambda); + + // Secondary open width fractions. + openFracPos = particleDataPtr->resOpenFrac( idRes); + openFracNeg = particleDataPtr->resOpenFrac(-idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qq2qStarq::sigmaKin() { + + // Two possible expressions, for like or unlike sign. + sigmaA = preFac * (1. - s3 / sH); + sigmaB = preFac * (-uH) * (sH + tH) / sH2; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat) for specific incoming flavours. + +double Sigma2qq2qStarq::sigmaHat() { + + // Identify different allowed incoming flavour combinations. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + double open1 = (id1 > 0) ? openFracPos : openFracNeg; + double open2 = (id2 > 0) ? openFracPos : openFracNeg; + double sigma = 0.; + if (id1 * id2 > 0) { + if (id1Abs == idq) sigma += (4./3.) * sigmaA * open1; + if (id2Abs == idq) sigma += (4./3.) * sigmaA * open2; + } else if (id1Abs == idq && id2 == -id1) + sigma = (8./3.) * sigmaB * (open1 + open2); + else if (id2 == -id1) sigma = sigmaB * (open1 + open2); + else if (id1Abs == idq) sigma = sigmaB * open1; + else if (id2Abs == idq) sigma = sigmaB * open2; + + // Done. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qq2qStarq::setIdColAcol() { + + // Flavours: either side may have been excited. + double open1 = 0.; + double open2 = 0.; + if (abs(id1) == idq) open1 = (id1 > 0) ? openFracPos : openFracNeg; + if (abs(id2) == idq) open2 = (id2 > 0) ? openFracPos : openFracNeg; + if (open1 == 0. && open2 == 0.) { + open1 = (id1 > 0) ? openFracPos : openFracNeg; + open2 = (id2 > 0) ? openFracPos : openFracNeg; + } + bool excite1 = (open1 > 0.); + if (open1 > 0. && open2 > 0.) excite1 + = (rndmPtr->flat() * (open1 + open2) < open1); + + // Always excited quark in slot 3 so colour flow flipped or not. + if (excite1) { + id3 = (id1 > 0) ? idq : -idq; + id4 = id2; + if (id1 * id2 > 0) setColAcol( 1, 0, 2, 0, 1, 0, 2, 0); + else setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + if (id1 < 0) swapColAcol(); + } else { + id3 = (id2 > 0) ? idq : -idq; + id4 = id1; + swapTU = true; + if (id1 * id2 > 0) setColAcol( 1, 0, 2, 0, 2, 0, 1, 0); + else setColAcol( 1, 0, 0, 2, 0, 2, 1, 0); + if (id1 < 0) swapColAcol(); + } + setId( id1, id2, id3, id4); + +} + +//========================================================================== + +// Sigma2qqbar2lStarlbar class. +// Cross section for q qbar -> l^* lbar (excited lepton state). +// Note: for simplicity decay is assumed isotropic. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2lStarlbar::initProc() { + + // Set up process properties from the chosen lepton flavour. + idRes = 4000000 + idl; + codeSave = 4020 + idl; + if (idl == 11) nameSave = "q qbar -> e^*+- e^-+"; + else if (idl == 12) nameSave = "q qbar -> nu_e^* nu_ebar"; + else if (idl == 13) nameSave = "q qbar -> mu^*+- mu^-+"; + else if (idl == 14) nameSave = "q qbar -> nu_mu^* nu_mubar"; + else if (idl == 15) nameSave = "q qbar -> tau^*+- tau^-+"; + else nameSave = "q qbar -> nu_tau^* nu_taubar"; + + // Secondary open width fractions. + openFracPos = particleDataPtr->resOpenFrac( idRes); + openFracNeg = particleDataPtr->resOpenFrac(-idRes); + + // Locally stored properties and couplings. + Lambda = settingsPtr->parm("ExcitedFermion:Lambda"); + preFac = (M_PI / pow4(Lambda)) * (openFracPos + openFracNeg) / 3.; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qqbar2lStarlbar::sigmaKin() { + + // Only one possible expressions + sigma = preFac * (-uH) * (sH + tH) / sH2; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2lStarlbar::setIdColAcol() { + + // Flavours: either lepton or antilepton may be excited. + if (rndmPtr->flat() * (openFracPos + openFracNeg) < openFracPos) { + setId( id1, id2, idRes, -idl); + if (id1 < 0) swapTU = true; + } else { + setId( id1, id2, -idRes, idl); + if (id1 > 0) swapTU = true; + } + + // Colour flow trivial. + if (id1 > 0) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 1, 1, 0, 0, 0, 0, 0); + +} + +//========================================================================== + +// Sigma2QCqq2qq class. +// Cross section for q q -> q q (quark contact interactions). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2QCqq2qq::initProc() { + + m_Lambda2 = settingsPtr->parm("ContactInteractions:Lambda"); + m_etaLL = settingsPtr->mode("ContactInteractions:etaLL");; + m_etaRR = settingsPtr->mode("ContactInteractions:etaRR");; + m_etaLR = settingsPtr->mode("ContactInteractions:etaLR");; + m_Lambda2 *= m_Lambda2; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2QCqq2qq::sigmaKin() { + + // Calculate kinematics dependence for different terms. + sigT = (4./9.) * (sH2 + uH2) / tH2; + sigU = (4./9.) * (sH2 + tH2) / uH2; + sigTU = - (8./27.) * sH2 / (tH * uH); + sigST = - (8./27.) * uH2 / (sH * tH); + + sigQCSTU = sH2 * (1 / tH + 1 / uH); + sigQCUTS = uH2 * (1 / tH + 1 / sH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2QCqq2qq::sigmaHat() { + + // Terms from QC contact interactions. + double sigQCLL = 0; + double sigQCRR = 0; + double sigQCLR = 0; + + // Combine cross section terms; factor 1/2 when identical quarks. + // q q -> q q + if (id2 == id1) { + + sigSum = 0.5 * (sigT + sigU + sigTU); // SM terms. + + // Contact terms. + sigQCLL = (8./9.) * alpS * (m_etaLL/m_Lambda2) * sigQCSTU + + (8./3.) * pow2(m_etaLL/m_Lambda2) * sH2; + sigQCRR = (8./9.) * alpS * (m_etaRR/m_Lambda2) * sigQCSTU + + (8./3.) * pow2(m_etaRR/m_Lambda2) * sH2; + sigQCLR = 2. * (uH2 + tH2) * pow2(m_etaLR/m_Lambda2); + + sigQCLL /= 2; + sigQCRR /= 2; + sigQCLR /= 2; + + // q qbar -> q qbar, without pure s-channel term. + } else if (id2 == -id1) { + + sigSum = sigT + sigST; // SM terms. + + // Contact terms, minus the terms included in qqbar2qqbar. + sigQCLL = (8./9.) * alpS * (m_etaLL/m_Lambda2) * sigQCUTS + + (5./3.) * pow2(m_etaLL/m_Lambda2) * uH2; + sigQCRR = (8./9.) * alpS * (m_etaRR/m_Lambda2) * sigQCUTS + + (5./3.) * pow2(m_etaRR/m_Lambda2) * uH2; + sigQCLR = 2. * sH2 * pow2(m_etaLR/m_Lambda2); + + // q q' -> q q' or q qbar' -> q qbar' + } else { + + sigSum = sigT; // SM terms. + + // Contact terms. + if (id1 * id2 > 0) { + sigQCLL = pow2(m_etaLL/m_Lambda2) * sH2; + sigQCRR = pow2(m_etaRR/m_Lambda2) * sH2; + sigQCLR = 2 * pow2(m_etaLR/m_Lambda2) * uH2; + } else { + sigQCLL = pow2(m_etaLL/m_Lambda2) * uH2; + sigQCRR = pow2(m_etaRR/m_Lambda2) * uH2; + sigQCLR = 2 * pow2(m_etaLR/m_Lambda2) * sH2; + } + } + + // Answer. + double sigma = (M_PI/sH2) * ( pow2(alpS) * sigSum + + sigQCLL + sigQCRR + sigQCLR ); + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2QCqq2qq::setIdColAcol() { + + // Outgoing = incoming flavours. + setId( id1, id2, id1, id2); + + // Colour flow topologies. Swap when antiquarks. + if (id1 * id2 > 0) setColAcol( 1, 0, 2, 0, 2, 0, 1, 0); + else setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + if (id2 == id1 && (sigT + sigU) * rndmPtr->flat() > sigT) + setColAcol( 1, 0, 2, 0, 1, 0, 2, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2QCqqbar2qqbar class. +// Cross section for q qbar -> q' qbar' (quark contact interactions). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2QCqqbar2qqbar::initProc() { + + m_nQuarkNew = settingsPtr->mode("ContactInteractions:nQuarkNew"); + m_Lambda2 = settingsPtr->parm("ContactInteractions:Lambda"); + m_etaLL = settingsPtr->mode("ContactInteractions:etaLL"); + m_etaRR = settingsPtr->mode("ContactInteractions:etaRR"); + m_etaLR = settingsPtr->mode("ContactInteractions:etaLR"); + m_Lambda2 *= m_Lambda2; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2QCqqbar2qqbar::sigmaKin() { + + // Pick new flavour. + idNew = 1 + int( m_nQuarkNew * rndmPtr->flat() ); + mNew = particleDataPtr->m0(idNew); + m2New = mNew*mNew; + + // Calculate kinematics dependence. + double sigQC = 0.; + sigS = 0.; + if (sH > 4. * m2New) { + sigS = (4./9.) * (tH2 + uH2) / sH2; + sigQC = pow2(m_etaLL/m_Lambda2) * uH2 + + pow2(m_etaRR/m_Lambda2) * uH2 + + 2 * pow2(m_etaLR/m_Lambda2) * tH2; + } + + // Answer is proportional to number of outgoing flavours. + sigma = (M_PI / sH2) * m_nQuarkNew * ( pow2(alpS) * sigS + sigQC); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2QCqqbar2qqbar::setIdColAcol() { + + // Set outgoing flavours ones. + id3 = (id1 > 0) ? idNew : -idNew; + setId( id1, id2, id3, -id3); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaEW.cxx b/PYTHIA8/pythia8140/src/SigmaEW.cxx new file mode 100644 index 00000000000..09b0356f710 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaEW.cxx @@ -0,0 +1,2851 @@ +// SigmaEW.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// electroweak simulation classes (including photon processes). + +#include "SigmaEW.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma2qg2qgamma class. +// Cross section for q g -> q gamma. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qg2qgamma::sigmaKin() { + + // Calculate kinematics dependence. + sigUS = (1./3.) * (sH2 + uH2) / (-sH * uH); + + // Answer. + sigma0 = (M_PI/sH2) * alpS * alpEM * sigUS; + + } + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qg2qgamma::sigmaHat() { + + // Incoming flavour gives charge factor. + int idNow = (id2 == 21) ? id1 : id2; + double eNow = coupSMPtr->ef( abs(idNow) ); + return sigma0 * pow2(eNow); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2qgamma::setIdColAcol() { + + // Construct outgoing flavours. + id3 = (id1 == 21) ? 22 : id1; + id4 = (id2 == 21) ? 22 : id2; + setId( id1, id2, id3, id4); + + // Colour flow topology. Swap if first is gluon, or when antiquark. + setColAcol( 1, 0, 2, 1, 2, 0, 0, 0); + if (id1 == 21) swapCol1234(); + if (id1 < 0 || id2 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2ggamma class. +// Cross section for q qbar -> g gamma. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2ggamma::sigmaKin() { + + // Calculate kinematics dependence. + double sigTU = (8./9.) * (tH2 + uH2) / (tH * uH); + + // Answer. + sigma0 = (M_PI/sH2) * alpS * alpEM * sigTU; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2ggamma::sigmaHat() { + + // Incoming flavour gives charge factor. + double eNow = coupSMPtr->ef( abs(id1) ); + return sigma0 * pow2(eNow); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2ggamma::setIdColAcol() { + + // Outgoing flavours trivial. + setId( id1, id2, 21, 22); + + // One colour flow topology. Swap if first is antiquark. + setColAcol( 1, 0, 0, 2, 1, 2, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2ggamma class. +// Cross section for g g -> g gamma. +// Proceeds through a quark box, by default using 5 massless quarks. + +//-------------------------------------------------------------------------- + +// Initialize process, especially parton-flux object. + +void Sigma2gg2ggamma::initProc() { + + // Maximum quark flavour in loop. + int nQuarkLoop = settingsPtr->mode("PromptPhoton:nQuarkLoop"); + + // Calculate charge factor from the allowed quarks in the box. + chargeSum = - 1./3. + 2./3. - 1./3.; + if (nQuarkLoop >= 4) chargeSum += 2./3.; + if (nQuarkLoop >= 5) chargeSum -= 1./3.; + if (nQuarkLoop >= 6) chargeSum += 2./3.; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat). + +void Sigma2gg2ggamma::sigmaKin() { + + // Logarithms of Mandelstam variable ratios. + double logST = log( -sH / tH ); + double logSU = log( -sH / uH ); + double logTU = log( tH / uH ); + + // Real and imaginary parts of separate amplitudes. + double b0stuRe = 1. + (tH - uH) / sH * logTU + + 0.5 * (tH2 + uH2) / sH2 * (pow2(logTU) + pow2(M_PI)); + double b0stuIm = 0.; + double b0tsuRe = 1. + (sH - uH) / tH * logSU + + 0.5 * (sH2 + uH2) / tH2 * pow2(logSU); + double b0tsuIm = -M_PI * ( (sH - uH) / tH + (sH2 + uH2) / tH2 * logSU); + double b0utsRe = 1. + (sH - tH) / uH * logST + + 0.5 * (sH2 + tH2) / uH2 * pow2(logST); + double b0utsIm = -M_PI * ( (sH - tH) / uH + (sH2 + tH2) / uH2 * logST); + double b1stuRe = -1.; + double b1stuIm = 0.; + double b2stuRe = -1.; + double b2stuIm = 0.; + + // Calculate kinematics dependence. + double sigBox = pow2(b0stuRe) + pow2(b0stuIm) + pow2(b0tsuRe) + + pow2(b0tsuIm) + pow2(b0utsRe) + pow2(b0utsIm) + 4. * pow2(b1stuRe) + + 4. * pow2(b1stuIm) + pow2(b2stuRe) + pow2(b2stuIm); + + // Answer. + sigma = (5. / (192. * M_PI * sH2)) * pow2(chargeSum) + * pow3(alpS) * alpEM * sigBox; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2ggamma::setIdColAcol() { + + // Flavours and colours are trivial. + setId( id1, id2, 21, 22); + setColAcol( 1, 2, 2, 3, 1, 3, 0, 0); + if (rndmPtr->flat() > 0.5) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbar2gammagamma class. +// Cross section for q qbar -> gamma gamma. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2gammagamma::sigmaKin() { + + // Calculate kinematics dependence. + sigTU = 2. * (tH2 + uH2) / (tH * uH); + + // Answer contains factor 1/2 from identical photons. + sigma0 = (M_PI/sH2) * pow2(alpEM) * 0.5 * sigTU; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2gammagamma::sigmaHat() { + + // Incoming flavour gives charge and colour factors. + double eNow = coupSMPtr->ef( abs(id1) ); + double colFac = (abs(id1) < 9) ? 1. / 3. : 1.; + return sigma0 * pow4(eNow) * colFac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2gammagamma::setIdColAcol() { + + // Outgoing flavours trivial. + setId( id1, id2, 22, 22); + + // No colours at all or one flow topology. Swap if first is antiquark. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2gammagamma class. +// Cross section for g g -> gamma gamma. +// Proceeds through a quark box, by default using 5 massless quarks. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2gammagamma::initProc() { + + // Maximum quark flavour in loop. + int nQuarkLoop = settingsPtr->mode("PromptPhoton:nQuarkLoop"); + + // Calculate charge factor from the allowed quarks in the box. + charge2Sum = 1./9. + 4./9. + 1./9.; + if (nQuarkLoop >= 4) charge2Sum += 4./9.; + if (nQuarkLoop >= 5) charge2Sum += 1./9.; + if (nQuarkLoop >= 6) charge2Sum += 4./9.; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat). + +void Sigma2gg2gammagamma::sigmaKin() { + + // Logarithms of Mandelstam variable ratios. + double logST = log( -sH / tH ); + double logSU = log( -sH / uH ); + double logTU = log( tH / uH ); + + // Real and imaginary parts of separate amplitudes. + double b0stuRe = 1. + (tH - uH) / sH * logTU + + 0.5 * (tH2 + uH2) / sH2 * (pow2(logTU) + pow2(M_PI)); + double b0stuIm = 0.; + double b0tsuRe = 1. + (sH - uH) / tH * logSU + + 0.5 * (sH2 + uH2) / tH2 * pow2(logSU); + double b0tsuIm = -M_PI * ( (sH - uH) / tH + (sH2 + uH2) / tH2 * logSU); + double b0utsRe = 1. + (sH - tH) / uH * logST + + 0.5 * (sH2 + tH2) / uH2 * pow2(logST); + double b0utsIm = -M_PI * ( (sH - tH) / uH + (sH2 + tH2) / uH2 * logST); + double b1stuRe = -1.; + double b1stuIm = 0.; + double b2stuRe = -1.; + double b2stuIm = 0.; + + // Calculate kinematics dependence. + double sigBox = pow2(b0stuRe) + pow2(b0stuIm) + pow2(b0tsuRe) + + pow2(b0tsuIm) + pow2(b0utsRe) + pow2(b0utsIm) + 4. * pow2(b1stuRe) + + 4. * pow2(b1stuIm) + pow2(b2stuRe) + pow2(b2stuIm); + + // Answer contains factor 1/2 from identical photons. + sigma = (0.5 / (16. * M_PI * sH2)) * pow2(charge2Sum) + * pow2(alpS) * pow2(alpEM) * sigBox; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2gammagamma::setIdColAcol() { + + // Flavours and colours are trivial. + setId( id1, id2, 22, 22); + setColAcol( 1, 2, 2, 1, 0, 0, 0, 0); + +} + +//========================================================================== + +// Sigma2ff2fftgmZ class. +// Cross section for f f' -> f f' via t-channel gamma*/Z0 exchange +// (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ff2fftgmZ::initProc() { + + // Store Z0 mass for propagator. Common coupling factor. + gmZmode = settingsPtr->mode("WeakZ0:gmZmode"); + mZ = particleDataPtr->m0(23); + mZS = mZ*mZ; + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ff2fftgmZ::sigmaKin() { + + // Cross section part common for all incoming flavours. + double sigma0 = (M_PI / sH2) * pow2(alpEM); + + // Kinematical functions for gamma-gamma, gamma-Z and Z-Z parts. + sigmagmgm = sigma0 * 2. * (sH2 + uH2) / tH2; + sigmagmZ = sigma0 * 4. * thetaWRat * sH2 / (tH * (tH - mZS)); + sigmaZZ = sigma0 * 2. * pow2(thetaWRat) * sH2 / pow2(tH - mZS); + if (gmZmode == 1) {sigmagmZ = 0.; sigmaZZ = 0.;} + if (gmZmode == 2) {sigmagmgm = 0.; sigmagmZ = 0.;} + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ff2fftgmZ::sigmaHat() { + + // Couplings for current flavour combination. + int id1Abs = abs(id1); + double e1 = coupSMPtr->ef(id1Abs); + double v1 = coupSMPtr->vf(id1Abs); + double a1 = coupSMPtr->af(id1Abs); + int id2Abs = abs(id2); + double e2 = coupSMPtr->ef(id2Abs); + double v2 = coupSMPtr->vf(id2Abs); + double a2 = coupSMPtr->af(id2Abs); + + // Distinguish same-sign and opposite-sign fermions. + double epsi = (id1 * id2 > 0) ? 1. : -1.; + + // Flavour-dependent cross section. + double sigma = sigmagmgm * pow2(e1 * e2) + + sigmagmZ * e1 * e2 * (v1 * v2 * (1. + uH2 / sH2) + + a1 * a2 * epsi * (1. - uH2 / sH2)) + + sigmaZZ * ((v1*v1 + a1*a1) * (v2*v2 + a2*a2) * (1. + uH2 / sH2) + + 4. * v1 * a1 * v2 * a2 * epsi * (1. - uH2 / sH2)); + + // Spin-state extra factor 2 per incoming neutrino. + if (id1Abs == 12 || id1Abs == 14 || id1Abs == 16) sigma *= 2.; + if (id2Abs == 12 || id2Abs == 14 || id2Abs == 16) sigma *= 2.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ff2fftgmZ::setIdColAcol() { + + // Trivial flavours: out = in. + setId( id1, id2, id1, id2); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && abs(id2) < 9 && id1*id2 > 0) + setColAcol( 1, 0, 2, 0, 1, 0, 2, 0); + else if (abs(id1) < 9 && abs(id2) < 9) + setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 0, 1, 0, 0, 0); + else if (abs(id2) < 9) setColAcol( 0, 0, 1, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if ( (abs(id1) < 9 && id1 < 0) || (abs(id1) > 10 && id2 < 0) ) + swapColAcol(); + +} + +//========================================================================== + +// Sigma2ff2fftW class. +// Cross section for f_1 f_2 -> f_3 f_4 via t-channel W+- exchange +// (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ff2fftW::initProc() { + + // Store W+- mass for propagator. Common coupling factor. + mW = particleDataPtr->m0(24); + mWS = mW*mW; + thetaWRat = 1. / (4. * coupSMPtr->sin2thetaW()); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ff2fftW::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * pow2(alpEM * thetaWRat) + * 4. * sH2 / pow2(tH - mWS); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ff2fftW::sigmaHat() { + + // Some flavour combinations not possible. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + if ( (id1Abs%2 == id2Abs%2 && id1 * id2 > 0) + || (id1Abs%2 != id2Abs%2 && id1 * id2 < 0) ) return 0.; + + // Basic cross section. + double sigma = sigma0; + if (id1 * id2 < 0) sigma *= uH2 / sH2; + + // CKM factors for final states. + sigma *= coupSMPtr->V2CKMsum(id1Abs) * coupSMPtr->V2CKMsum(id2Abs); + + // Spin-state extra factor 2 per incoming neutrino. + if (id1Abs == 12 || id1Abs == 14 || id1Abs == 16) sigma *= 2.; + if (id2Abs == 12 || id2Abs == 14 || id2Abs == 16) sigma *= 2.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ff2fftW::setIdColAcol() { + + // Pick out-flavours by relative CKM weights. + id3 = coupSMPtr->V2CKMpick(id1); + id4 = coupSMPtr->V2CKMpick(id2); + setId( id1, id2, id3, id4); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && abs(id2) < 9 && id1*id2 > 0) + setColAcol( 1, 0, 2, 0, 1, 0, 2, 0); + else if (abs(id1) < 9 && abs(id2) < 9) + setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 0, 1, 0, 0, 0); + else if (abs(id2) < 9) setColAcol( 0, 0, 1, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if ( (abs(id1) < 9 && id1 < 0) || (abs(id1) > 10 && id2 < 0) ) + swapColAcol(); + +} + + +//========================================================================== + +// Sigma2qq2QqtW class. +// Cross section for q q' -> Q q" via t-channel W+- exchange. +// Related to Sigma2ff2ffViaW class, but with massive matrix elements. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qq2QqtW::initProc() { + + // Process name. + nameSave = "q q -> Q q (t-channel W+-)"; + if (idNew == 4) nameSave = "q q -> c q (t-channel W+-)"; + if (idNew == 5) nameSave = "q q -> b q (t-channel W+-)"; + if (idNew == 6) nameSave = "q q -> t q (t-channel W+-)"; + if (idNew == 7) nameSave = "q q -> b' q (t-channel W+-)"; + if (idNew == 8) nameSave = "q q -> t' q (t-channel W+-)"; + + // Store W+- mass for propagator. Common coupling factor. + mW = particleDataPtr->m0(24); + mWS = mW*mW; + thetaWRat = 1. / (4. * coupSMPtr->sin2thetaW()); + + // Secondary open width fractions, relevant for top (or heavier). + openFracPos = particleDataPtr->resOpenFrac(idNew); + openFracNeg = particleDataPtr->resOpenFrac(-idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qq2QqtW::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * pow2(alpEM * thetaWRat) * 4. / pow2(tH - mWS); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qq2QqtW::sigmaHat() { + + // Some flavour combinations not possible. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + bool diff12 = (id1Abs%2 != id2Abs%2); + if ( (!diff12 && id1 * id2 > 0) + || ( diff12 && id1 * id2 < 0) ) return 0.; + + // Basic cross section. + double sigma = sigma0; + sigma *= (id1 * id2 > 0) ? sH * (sH - s3) : uH * (uH - s3); + + // Secondary width if t or tbar produced on either side. + double openFrac1 = (id1 > 0) ? openFracPos : openFracNeg; + double openFrac2 = (id2 > 0) ? openFracPos : openFracNeg; + + // CKM factors for final states; further impossible case. + bool diff1N = (id1Abs%2 != idNew%2); + bool diff2N = (id2Abs%2 != idNew%2); + if (diff1N && diff2N) + sigma *= ( coupSMPtr->V2CKMid(id1Abs, idNew) * openFrac1 + * coupSMPtr->V2CKMsum(id2Abs) + coupSMPtr->V2CKMsum(id1Abs) + * coupSMPtr->V2CKMid(id2Abs, idNew) * openFrac2 ); + else if (diff1N) + sigma *= coupSMPtr->V2CKMid(id1Abs, idNew) * openFrac1 + * coupSMPtr->V2CKMsum(id2Abs); + else if (diff2N) + sigma *= coupSMPtr->V2CKMsum(id1Abs) + * coupSMPtr->V2CKMid(id2Abs, idNew) * openFrac2; + else sigma = 0.; + + // Spin-state extra factor 2 per incoming neutrino. + if (id1Abs == 12 || id1Abs == 14 || id1Abs == 16) sigma *= 2.; + if (id2Abs == 12 || id2Abs == 14 || id2Abs == 16) sigma *= 2.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qq2QqtW::setIdColAcol() { + + // For topologies like d dbar -> (t/c/u) (t/c/u)bar pick side. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + int side = 1; + if ( (id1Abs + idNew)%2 == 1 && (id2Abs + idNew)%2 == 1 ) { + double prob1 = coupSMPtr->V2CKMid(id1Abs, idNew) + * coupSMPtr->V2CKMsum(id2Abs); + prob1 *= (id1 > 0) ? openFracPos : openFracNeg; + double prob2 = coupSMPtr->V2CKMid(id2Abs, idNew) + * coupSMPtr->V2CKMsum(id1Abs); + prob2 *= (id2 > 0) ? openFracPos : openFracNeg; + if (prob2 > rndmPtr->flat() * (prob1 + prob2)) side = 2; + } + else if ((id2Abs + idNew)%2 == 1) side = 2; + + // Pick out-flavours by relative CKM weights. + if (side == 1) { + // q q' -> t q" : correct order from start. + id3 = (id1 > 0) ? idNew : -idNew; + id4 = coupSMPtr->V2CKMpick(id2); + setId( id1, id2, id3, id4); + } else { + // q q' -> q" t : stored as t q" so swap tHat <-> uHat. + swapTU = true; + id3 = coupSMPtr->V2CKMpick(id1); + id4 = (id2 > 0) ? idNew : -idNew; + setId( id1, id2, id4, id3); + } + + // Colour flow topologies. Swap when antiquarks on side 1. + if (side == 1 && id1 * id2 > 0) setColAcol( 1, 0, 2, 0, 1, 0, 2, 0); + else if (id1 * id2 > 0) setColAcol( 1, 0, 2, 0, 2, 0, 1, 0); + else if (side == 1) setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + else setColAcol( 1, 0, 0, 2, 0, 2, 1, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles of W in top decay. + +double Sigma2qq2QqtW::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // For top decay hand over to standard routine, else done. + if (idNew == 6 && process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + else return 1.; + +} + +//========================================================================== + +// Sigma1ffbar2gmZ class. +// Cross section for f fbar -> gamma*/Z0 (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2gmZ::initProc() { + + // Allow to pick only gamma* or Z0 part of full gamma*/Z0 expression. + gmZmode = settingsPtr->mode("WeakZ0:gmZmode"); + + // Store Z0 mass and width for propagator. + mRes = particleDataPtr->m0(23); + GammaRes = particleDataPtr->mWidth(23); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(23); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2gmZ::sigmaKin() { + + // Common coupling factors. + double colQ = 3. * (1. + alpS / M_PI); + + // Reset quantities to sum. Declare variables in loop. + gamSum = 0.; + intSum = 0.; + resSum = 0.; + int idAbs, onMode; + double mf, mr, psvec, psaxi, betaf, ef2, efvf, vf2af2, colf; + + // Loop over all Z0 decay channels. + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + idAbs = abs( particlePtr->channel(i).product(0) ); + + // Only contributions from three fermion generations, except top. + if ( (idAbs > 0 && idAbs < 6) || ( idAbs > 10 && idAbs < 17)) { + mf = particleDataPtr->m0(idAbs); + + // Check that above threshold. Phase space. + if (mH > 2. * mf + MASSMARGIN) { + mr = pow2(mf / mH); + betaf = sqrtpos(1. - 4. * mr); + psvec = betaf * (1. + 2. * mr); + psaxi = pow3(betaf); + + // Combine phase space with couplings. + ef2 = coupSMPtr->ef2(idAbs) * psvec; + efvf = coupSMPtr->efvf(idAbs) * psvec; + vf2af2 = coupSMPtr->vf2(idAbs) * psvec + + coupSMPtr->af2(idAbs) * psaxi; + colf = (idAbs < 6) ? colQ : 1.; + + // Store sum of combinations. For outstate only open channels. + onMode = particlePtr->channel(i).onMode(); + if (onMode == 1 || onMode == 2) { + gamSum += colf * ef2; + intSum += colf * efvf; + resSum += colf * vf2af2; + } + + // End loop over fermions. + } + } + } + + // Calculate prefactors for gamma/interference/Z0 cross section terms. + gamProp = 4. * M_PI * pow2(alpEM) / (3. * sH); + intProp = gamProp * 2. * thetaWRat * sH * (sH - m2Res) + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + resProp = gamProp * pow2(thetaWRat * sH) + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + + // Optionally only keep gamma* or Z0 term. + if (gmZmode == 1) {intProp = 0.; resProp = 0.;} + if (gmZmode == 2) {gamProp = 0.; intProp = 0.;} + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2gmZ::sigmaHat() { + + // Combine gamma, interference and Z0 parts. + int idAbs = abs(id1); + double sigma = coupSMPtr->ef2(idAbs) * gamProp * gamSum + + coupSMPtr->efvf(idAbs) * intProp * intSum + + coupSMPtr->vf2af2(idAbs) * resProp * resSum; + + // Colour factor. Answer. + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2gmZ::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, 23); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for gamma*/Z0 decay angle. + +double Sigma1ffbar2gmZ::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Z should sit in entry 5. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Couplings for in- and out-flavours. + int idInAbs = process[3].idAbs(); + double ei = coupSMPtr->ef(idInAbs); + double vi = coupSMPtr->vf(idInAbs); + double ai = coupSMPtr->af(idInAbs); + int idOutAbs = process[6].idAbs(); + double ef = coupSMPtr->ef(idOutAbs); + double vf = coupSMPtr->vf(idOutAbs); + double af = coupSMPtr->af(idOutAbs); + + // Phase space factors. (One power of beta left out in formulae.) + double mf = process[6].m(); + double mr = mf*mf / sH; + double betaf = sqrtpos(1. - 4. * mr); + + // Coefficients of angular expression. + double coefTran = ei*ei * gamProp * ef*ef + ei * vi * intProp * ef * vf + + (vi*vi + ai*ai) * resProp * (vf*vf + pow2(betaf) * af*af); + double coefLong = 4. * mr * ( ei*ei * gamProp * ef*ef + + ei * vi * intProp * ef * vf + (vi*vi + ai*ai) * resProp * vf*vf ); + double coefAsym = betaf * ( ei * ai * intProp * ef * af + + 4. * vi * ai * resProp * vf * af ); + + // Flip asymmetry for in-fermion + out-antifermion. + if (process[3].id() * process[6].id() < 0) coefAsym = -coefAsym; + + // Reconstruct decay angle and weight for it. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + double wtMax = 2. * (coefTran + abs(coefAsym)); + double wt = coefTran * (1. + pow2(cosThe)) + + coefLong * (1. - pow2(cosThe)) + 2. * coefAsym * cosThe; + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma1ffbar2W class. +// Cross section for f fbar' -> W+- (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2W::initProc() { + + // Store W+- mass and width for propagator. + mRes = particleDataPtr->m0(24); + GammaRes = particleDataPtr->mWidth(24); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2W::sigmaKin() { + + // Set up Breit-Wigner. Cross section for W+ and W- separately. + double sigBW = 12. * M_PI / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double preFac = alpEM * thetaWRat * mH; + sigma0Pos = preFac * sigBW * particlePtr->resWidthOpen(24, mH); + sigma0Neg = preFac * sigBW * particlePtr->resWidthOpen(-24, mH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2W::sigmaHat() { + + // Secondary width for W+ or W-. CKM and colour factors. + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + double sigma = (idUp > 0) ? sigma0Pos : sigma0Neg; + if (abs(id1) < 9) sigma *= coupSMPtr->V2CKMid(abs(id1), abs(id2)) / 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2W::setIdColAcol() { + + // Sign of outgoing W. + int sign = 1 - 2 * (abs(id1)%2); + if (id1 < 0) sign = -sign; + setId( id1, id2, 24 * sign); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for W decay angle. + +double Sigma1ffbar2W::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // W should sit in entry 5. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Phase space factors. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + + // Sign of asymmetry. + double eps = (process[3].id() * process[6].id() > 0) ? 1. : -1.; + + // Reconstruct decay angle and weight for it. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + double wtMax = 4.; + double wt = pow2(1. + betaf * eps * cosThe) - pow2(mr1 - mr2); + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma2ffbar2ffbarsgm class. +// Cross section f fbar -> gamma* -> f' fbar', for multiple interactions. + + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2ffbarsgm::sigmaKin() { + + // Pick new flavour. Allow three leptons and five quarks. + double colQ = 1. + (alpS / M_PI); + double flavWt = 3. + colQ * 11. / 3.; + double flavRndm = rndmPtr->flat() * flavWt; + if (flavRndm < 3.) { + if (flavRndm < 1.) idNew = 11; + else if (flavRndm < 2.) idNew = 13; + else idNew = 15; + } else { + flavRndm = 3. * (flavWt - 3.) / colQ; + if (flavRndm < 4.) idNew = 2; + else if (flavRndm < 8.) idNew = 4; + else if (flavRndm < 9.) idNew = 1; + else if (flavRndm < 10.) idNew = 3; + else idNew = 5; + } + double mNew = particleDataPtr->m0(idNew); + double m2New = mNew*mNew; + + // Calculate kinematics dependence. Give correct mass factors for + // tHat, uHat defined as if massless kinematics, d(sigma)/d(Omega) + // = beta (1 + cos^2(theta) + (1 - beta^2) sin^2(theta)). + // Special case related to phase space form in multiple interactions. + double sigS = 0.; + if (sH > 4. * m2New) { + double beta = sqrt(1. - 4. * m2New / sH); + sigS = beta * (2.* (tH2 + uH2) + 4. * (1. - beta * beta) * tH * uH) + / sH2; + } + + // Answer is proportional to number of outgoing flavours. + sigma0 = (M_PI/sH2) * pow2(alpEM) * sigS * flavWt; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2ffbarsgm::sigmaHat() { + + // Charge and colour factors. + double eNow = coupSMPtr->ef( abs(id1) ); + double sigma = sigma0 * pow2(eNow); + if (abs(id1) < 9) sigma /= 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2ffbarsgm::setIdColAcol() { + + // Set outgoing flavours. + id3 = (id1 > 0) ? idNew : -idNew; + setId( id1, id2, id3, -id3); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && idNew < 9) setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else if (idNew < 9) setColAcol( 0, 0, 0, 0, 1, 0, 0, 1); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbar2FFbarsgmZ class. +// Cross section f fbar -> gamma*/Z0 -> F Fbar. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2FFbarsgmZ::initProc() { + + // Process name. + nameSave = "f fbar -> F Fbar (s-channel gamma*/Z0)"; + if (idNew == 4) nameSave = "f fbar -> c cbar (s-channel gamma*/Z0)"; + if (idNew == 5) nameSave = "f fbar -> b bbar (s-channel gamma*/Z0)"; + if (idNew == 6) nameSave = "f fbar -> t tbar (s-channel gamma*/Z0)"; + if (idNew == 7) nameSave = "f fbar -> b' b'bar (s-channel gamma*/Z0)"; + if (idNew == 8) nameSave = "f fbar -> t' t'bar (s-channel gamma*/Z0)"; + if (idNew == 15) nameSave = "f fbar -> tau+ tau- (s-channel gamma*/Z0)"; + if (idNew == 17) nameSave = "f fbar -> tau'+ tau'- (s-channel gamma*/Z0)"; + if (idNew == 18) + nameSave = "f fbar -> nu'_tau nu'bar_tau (s-channel gamma*/Z0)"; + + // Allow to pick only gamma* or Z0 part of full gamma*/Z0 expression. + gmZmode = settingsPtr->mode("WeakZ0:gmZmode"); + + // Store Z0 mass and width for propagator. + mRes = particleDataPtr->m0(23); + GammaRes = particleDataPtr->mWidth(23); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() + * coupSMPtr->cos2thetaW()); + + // Store couplings of F. + ef = coupSMPtr->ef(idNew); + vf = coupSMPtr->vf(idNew); + af = coupSMPtr->af(idNew); + + // Secondary open width fraction, relevant for top (or heavier). + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2FFbarsgmZ::sigmaKin() { + + // Check that above threshold. + isPhysical = true; + if (mH < m3 + m4 + MASSMARGIN) { + isPhysical = false; + return; + } + + // Define average F, Fbar mass so same beta. Phase space. + double s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + mr = s34Avg / sH; + betaf = sqrtpos(1. - 4. * mr); + + // Final-state colour factor. + double colF = (idNew < 9) ? 3. * (1. + alpS / M_PI) : 1.; + + // Reconstruct decay angle so can reuse 2 -> 1 cross section. + cosThe = (tH - uH) / (betaf * sH); + + // Calculate prefactors for gamma/interference/Z0 cross section terms. + gamProp = colF * M_PI * pow2(alpEM) / sH2; + intProp = gamProp * 2. * thetaWRat * sH * (sH - m2Res) + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + resProp = gamProp * pow2(thetaWRat * sH) + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + + // Optionally only keep gamma* or Z0 term. + if (gmZmode == 1) {intProp = 0.; resProp = 0.;} + if (gmZmode == 2) {gamProp = 0.; intProp = 0.;} + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2FFbarsgmZ::sigmaHat() { + + // Fail if below threshold. + if (!isPhysical) return 0.; + + // Couplings for in-flavours. + int idAbs = abs(id1); + double ei = coupSMPtr->ef(idAbs); + double vi = coupSMPtr->vf(idAbs); + double ai = coupSMPtr->af(idAbs); + + // Coefficients of angular expression. + double coefTran = ei*ei * gamProp * ef*ef + ei * vi * intProp * ef * vf + + (vi*vi + ai*ai) * resProp * (vf*vf + pow2(betaf) * af*af); + double coefLong = 4. * mr * ( ei*ei * gamProp * ef*ef + + ei * vi * intProp * ef * vf + (vi*vi + ai*ai) * resProp * vf*vf ); + double coefAsym = betaf * ( ei * ai * intProp * ef * af + + 4. * vi * ai * resProp * vf * af ); + + // Combine gamma, interference and Z0 parts. + double sigma = coefTran * (1. + pow2(cosThe)) + + coefLong * (1. - pow2(cosThe)) + 2. * coefAsym * cosThe; + + // Top: corrections for closed decay channels. + sigma *= openFracPair; + + // Initial-state colour factor. Answer. + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2FFbarsgmZ::setIdColAcol() { + + // Set outgoing flavours. + id3 = (id1 > 0) ? idNew : -idNew; + setId( id1, id2, id3, -id3); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && idNew < 9) setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else if (idNew < 9) setColAcol( 0, 0, 0, 0, 1, 0, 0, 1); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles of W in top decay. + +double Sigma2ffbar2FFbarsgmZ::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // For top decay hand over to standard routine, else done. + if (idNew == 6 && process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + else return 1.; + +} + +//========================================================================== + +// Sigma2ffbar2FfbarsW class. +// Cross section f fbar' -> W+- -> F fbar". + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2FfbarsW::initProc() { + + // Process name. + nameSave = "f fbar -> F fbar (s-channel W+-)"; + if (idNew == 4) nameSave = "f fbar -> c qbar (s-channel W+-)"; + if (idNew == 5) nameSave = "f fbar -> b qbar (s-channel W+-)"; + if (idNew == 6) nameSave = "f fbar -> t qbar (s-channel W+-)"; + if (idNew == 7) nameSave = "f fbar -> b' qbar (s-channel W+-)"; + if (idNew == 8) nameSave = "f fbar -> t' qbar (s-channel W+-)"; + if (idNew == 7 && idNew2 == 6) + nameSave = "f fbar -> b' tbar (s-channel W+-)"; + if (idNew == 8 && idNew2 == 7) + nameSave = "f fbar -> t' b'bar (s-channel W+-)"; + if (idNew == 15 || idNew == 16) + nameSave = "f fbar -> tau nu_taubar (s-channel W+-)"; + if (idNew == 17 || idNew == 18) + nameSave = "f fbar -> tau' nu'_taubar (s-channel W+-)"; + + // Store W+- mass and width for propagator. + mRes = particleDataPtr->m0(24); + GammaRes = particleDataPtr->mWidth(24); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + + // For t/t' want to use at least b mass. + idPartner = idNew2; + if ( (idNew == 6 || idNew == 8) && idNew2 == 0 ) idPartner = 5; + + // Sum of CKM weights for quarks. + V2New = (idNew < 9) ? coupSMPtr->V2CKMsum(idNew) : 1.; + if (idNew2 != 0) V2New = coupSMPtr->V2CKMid(idNew, idNew2); + + // Secondary open width fractions, relevant for top or heavier. + openFracPos = particleDataPtr->resOpenFrac( idNew, -idNew2); + openFracNeg = particleDataPtr->resOpenFrac(-idNew, idNew2); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2FfbarsW::sigmaKin() { + + // Check that above threshold. + isPhysical = true; + if (mH < m3 + m4 + MASSMARGIN) { + isPhysical = false; + return; + } + + // Phase space factors. + double mr1 = s3 / sH; + double mr2 = s4 / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + + // Reconstruct decay angle so can reuse 2 -> 1 cross section. + double cosThe = (tH - uH) / (betaf * sH); + + // Set up Breit-Wigner and in- and out-widths. + double sigBW = 9. * M_PI * pow2(alpEM * thetaWRat) + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + + // Initial-state colour factor. + double colF = (idNew < 9) ? 3. * (1. + alpS / M_PI) * V2New : 1.; + + // Angular dependence. + double wt = pow2(1. + betaf * cosThe) - pow2(mr1 - mr2); + + // Temporary answer. + sigma0 = sigBW * colF * wt; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2FfbarsW::sigmaHat() { + + // Fail if below threshold. + if (!isPhysical) return 0.; + + // CKM and colour factors. + double sigma = sigma0; + if (abs(id1) < 9) sigma *= coupSMPtr->V2CKMid(abs(id1), abs(id2)) / 3.; + + // Correction for secondary width in top (or heavier) decay. + int idSame = ((abs(id1) + idNew)%2 == 0) ? id1 : id2; + sigma *= (idSame > 0) ? openFracPos : openFracNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2FfbarsW::setIdColAcol() { + + // Set outgoing flavours. + id3 = idNew; + id4 = (idNew2 != 0) ? idNew2 : coupSMPtr->V2CKMpick(idNew); + if (idNew%2 == 0) { + int idInUp = (abs(id1)%2 == 0) ? id1 : id2; + if (idInUp > 0) id4 = -id4; + else id3 = -id3; + } else { + int idInDn = (abs(id1)%2 == 1) ? id1 : id2; + if (idInDn > 0) id4 = -id4; + else id3 = -id3; + } + setId( id1, id2, id3, id4); + + // Swap tHat and uHat for fbar' f -> F f". + if (id1 * id3 < 0) swapTU = true; + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && idNew < 9) setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else if (idNew < 9) setColAcol( 0, 0, 0, 0, 1, 0, 0, 1); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapCol12(); + if (id3 < 0) swapCol34(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles of W in top decay. + +double Sigma2ffbar2FfbarsW::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // For top decay hand over to standard routine, else done. + if (idNew == 6 && process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + else return 1.; + +} + +//========================================================================== + +// Sigma2ffbargmZWgmZW class. +// Collects common methods for f fbar -> gamma*/Z0/W+- gamma*/Z0/W-+. + +//-------------------------------------------------------------------------- + +// Calculate and store internal products. + +void Sigma2ffbargmZWgmZW::setupProd( Event& process, int i1, int i2, + int i3, int i4, int i5, int i6) { + + // Store incoming and outgoing momenta, + pRot[1] = process[i1].p(); + pRot[2] = process[i2].p(); + pRot[3] = process[i3].p(); + pRot[4] = process[i4].p(); + pRot[5] = process[i5].p(); + pRot[6] = process[i6].p(); + + // Do random rotation to avoid accidental zeroes in HA expressions. + bool smallPT = false; + do { + smallPT = false; + double thetaNow = acos(2. * rndmPtr->flat() - 1.); + double phiNow = 2. * M_PI * rndmPtr->flat(); + for (int i = 1; i <= 6; ++i) { + pRot[i].rot( thetaNow, phiNow); + if (pRot[i].pT2() < 1e-4 * pRot[i].pAbs2()) smallPT = true; + } + } while (smallPT); + + // Calculate internal products. + for (int i = 1; i < 6; ++i) { + for (int j = i + 1; j <= 6; ++j) { + hA[i][j] = + sqrt( (pRot[i].e() - pRot[i].pz()) * (pRot[j].e() + pRot[j].pz()) + / pRot[i].pT2() ) * complex( pRot[i].px(), pRot[i].py() ) + - sqrt( (pRot[i].e() + pRot[i].pz()) * (pRot[j].e() - pRot[j].pz()) + / pRot[j].pT2() ) * complex( pRot[j].px(), pRot[j].py() ); + hC[i][j] = conj( hA[i][j] ); + if (i <= 2) { + hA[i][j] *= complex( 0., 1.); + hC[i][j] *= complex( 0., 1.); + } + hA[j][i] = - hA[i][j]; + hC[j][i] = - hC[i][j]; + } + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate the F function of Gunion and Kunszt. + +complex Sigma2ffbargmZWgmZW::fGK(int j1, int j2, int j3, int j4, int j5, + int j6) { + + return 4. * hA[j1][j3] * hC[j2][j6] + * ( hA[j1][j5] * hC[j1][j4] + hA[j3][j5] * hC[j3][j4] ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate the Xi function of Gunion and Kunszt. + +double Sigma2ffbargmZWgmZW::xiGK( double tHnow, double uHnow) { + + return - 4. * s3 * s4 + tHnow * (3. * tHnow + 4. * uHnow) + + tHnow * tHnow * ( tHnow * uHnow / (s3 * s4) + - 2. * (1. / s3 + 1./s4) * (tHnow + uHnow) + + 2. * (s3 / s4 + s4 / s3) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate the Xj function of Gunion and Kunszt. + +double Sigma2ffbargmZWgmZW::xjGK( double tHnow, double uHnow) { + + return 8. * pow2(s3 + s4) - 8. * (s3 + s4) * (tHnow + uHnow) + - 6. * tHnow * uHnow - 2. * tHnow * uHnow * ( tHnow * uHnow + / (s3 * s4) - 2. * (1. / s3 + 1. / s4) * (tHnow + uHnow) + + 2. * (s3 / s4 + s4 / s3) ); + +} + +//========================================================================== + +// Sigma2ffbar2gmZgmZ class. +// Cross section for f fbar -> gamma*/Z0 gamma*/Z0 (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2gmZgmZ::initProc() { + + // Allow to pick only gamma* or Z0 part of full gamma*/Z0 expression. + gmZmode = settingsPtr->mode("WeakZ0:gmZmode"); + + // Store Z0 mass and width for propagator. + mRes = particleDataPtr->m0(23); + GammaRes = particleDataPtr->mWidth(23); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() + * coupSMPtr->cos2thetaW()); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(23); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2gmZgmZ::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * pow2(alpEM) * 0.5 + * ( (tH2 + uH2 + 2. * (s3 + s4) * sH) / (tH * uH) + - s3 * s4 * (1./tH2 + 1./uH2) ); + + // Common coupling factors at the resonance masses + double alpEM3 = coupSMPtr->alphaEM(s3); + double alpS3 = coupSMPtr->alphaS(s3); + double colQ3 = 3. * (1. + alpS3 / M_PI); + double alpEM4 = coupSMPtr->alphaEM(s4); + double alpS4 = coupSMPtr->alphaS(s4); + double colQ4 = 3. * (1. + alpS4 / M_PI); + + // Reset quantities to sum. Declare variables in loop. + gamSum3 = 0.; + intSum3 = 0.; + resSum3 = 0.; + gamSum4 = 0.; + intSum4 = 0.; + resSum4 = 0.; + int onMode; + double mf, mr, psvec, psaxi, betaf, ef2, efvf, vf2af2, colf; + + // Loop over all Z0 decay channels. + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + int idAbs = abs( particlePtr->channel(i).product(0) ); + + // Only contributions from three fermion generations, except top. + if ( (idAbs > 0 && idAbs < 6) || ( idAbs > 10 && idAbs < 17)) { + mf = particleDataPtr->m0(idAbs); + onMode = particlePtr->channel(i).onMode(); + + // First Z0: check that above threshold. Phase space. + if (m3 > 2. * mf + MASSMARGIN) { + mr = pow2(mf / m3); + betaf = sqrtpos(1. - 4. * mr); + psvec = betaf * (1. + 2. * mr); + psaxi = pow3(betaf); + + // First Z0: combine phase space with couplings. + ef2 = coupSMPtr->ef2(idAbs) * psvec; + efvf = coupSMPtr->efvf(idAbs) * psvec; + vf2af2 = coupSMPtr->vf2(idAbs) * psvec + + coupSMPtr->af2(idAbs) * psaxi; + colf = (idAbs < 6) ? colQ3 : 1.; + + // First Z0: store sum of combinations for open outstate channels. + if (onMode == 1 || onMode == 2) { + gamSum3 += colf * ef2; + intSum3 += colf * efvf; + resSum3 += colf * vf2af2; + } + } + + // Second Z0: check that above threshold. Phase space. + if (m4 > 2. * mf + MASSMARGIN) { + mr = pow2(mf / m4); + betaf = sqrtpos(1. - 4. * mr); + psvec = betaf * (1. + 2. * mr); + psaxi = pow3(betaf); + + // Second Z0: combine phase space with couplings. + ef2 = coupSMPtr->ef2(idAbs) * psvec; + efvf = coupSMPtr->efvf(idAbs) * psvec; + vf2af2 = coupSMPtr->vf2(idAbs) * psvec + + coupSMPtr->af2(idAbs) * psaxi; + colf = (idAbs < 6) ? colQ4 : 1.; + + // Second Z0: store sum of combinations for open outstate channels. + if (onMode == 1 || onMode == 2) { + gamSum4 += colf * ef2; + intSum4 += colf * efvf; + resSum4 += colf * vf2af2; + } + } + + // End loop over fermions. + } + } + + // First Z0: calculate prefactors for gamma/interference/Z0 terms. + gamProp3 = 4. * alpEM3 / (3. * M_PI * s3); + intProp3 = gamProp3 * 2. * thetaWRat * s3 * (s3 - m2Res) + / ( pow2(s3 - m2Res) + pow2(s3 * GamMRat) ); + resProp3 = gamProp3 * pow2(thetaWRat * s3) + / ( pow2(s3 - m2Res) + pow2(s3 * GamMRat) ); + + // First Z0: optionally only keep gamma* or Z0 term. + if (gmZmode == 1) {intProp3 = 0.; resProp3 = 0.;} + if (gmZmode == 2) {gamProp3 = 0.; intProp3 = 0.;} + + // Second Z0: calculate prefactors for gamma/interference/Z0 terms. + gamProp4 = 4. * alpEM4 / (3. * M_PI * s4); + intProp4 = gamProp4 * 2. * thetaWRat * s4 * (s4 - m2Res) + / ( pow2(s4 - m2Res) + pow2(s4 * GamMRat) ); + resProp4 = gamProp4 * pow2(thetaWRat * s4) + / ( pow2(s4 - m2Res) + pow2(s4 * GamMRat) ); + + // Second Z0: optionally only keep gamma* or Z0 term. + if (gmZmode == 1) {intProp4 = 0.; resProp4 = 0.;} + if (gmZmode == 2) {gamProp4 = 0.; intProp4 = 0.;} + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2gmZgmZ::sigmaHat() { + + // Charge/2, left- and righthanded couplings for in-fermion. + int idAbs = abs(id1); + double ei = 0.5 * coupSMPtr->ef(idAbs); + double li = coupSMPtr->lf(idAbs); + double ri = coupSMPtr->rf(idAbs); + + // Combine left/right gamma, interference and Z0 parts for each Z0. + double left3 = ei * ei * gamProp3 * gamSum3 + + ei * li * intProp3 * intSum3 + + li * li * resProp3 * resSum3; + double right3 = ei * ei * gamProp3 * gamSum3 + + ei * ri * intProp3 * intSum3 + + ri * ri * resProp3 * resSum3; + double left4 = ei * ei * gamProp4 * gamSum4 + + ei * li * intProp4 * intSum4 + + li * li * resProp4 * resSum4; + double right4 = ei * ei * gamProp4 * gamSum4 + + ei * ri * intProp4 * intSum4 + + ri * ri * resProp4 * resSum4; + + // Combine left- and right-handed couplings for the two Z0's. + double sigma = sigma0 * (left3 * left4 + right3 * right4); + + // Correct for the running-width Z0 propagators weight in PhaseSpace. + sigma /= (runBW3 * runBW4); + + // Initial-state colour factor. Answer. + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2gmZgmZ::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, 23, 23); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate correlated decay flavours of the two gamma*/Z0. +// Unique complication, caused by gamma*/Z0 mix different left/right. + +double Sigma2ffbar2gmZgmZ::weightDecayFlav( Event& process) { + + // Order so that fbar(1) f(2) -> f'(3) fbar'(4) f"(5) fbar"(6). + i1 = (process[3].id() < 0) ? 3 : 4; + i2 = 7 - i1; + i3 = (process[7].id() > 0) ? 7 : 8; + i4 = 15 - i3; + i5 = (process[9].id() > 0) ? 9 : 10; + i6 = 19 - i5; + + // Charge/2, left- and righthanded couplings for in- and out-fermions. + int idAbs = process[i1].idAbs(); + double ei = 0.5 * coupSMPtr->ef(idAbs); + double li = coupSMPtr->lf(idAbs); + double ri = coupSMPtr->rf(idAbs); + idAbs = process[i3].idAbs(); + double e3 = 0.5 * coupSMPtr->ef(idAbs); + double l3 = coupSMPtr->lf(idAbs); + double r3 = coupSMPtr->rf(idAbs); + idAbs = process[i5].idAbs(); + double e4 = 0.5 * coupSMPtr->ef(idAbs); + double l4 = coupSMPtr->lf(idAbs); + double r4 = coupSMPtr->rf(idAbs); + + // Left- and righthanded couplings combined with propagators. + c3LL = ei * ei * gamProp3 * e3 * e3 + + ei * li * intProp3 * e3 * l3 + + li * li * resProp3 * l3 * l3; + c3LR = ei * ei * gamProp3 * e3 * e3 + + ei * li * intProp3 * e3 * r3 + + li * li * resProp3 * r3 * r3; + c3RL = ei * ei * gamProp3 * e3 * e3 + + ei * ri * intProp3 * e3 * l3 + + ri * ri * resProp3 * l3 * l3; + c3RR = ei * ei * gamProp3 * e3 * e3 + + ei * ri * intProp3 * e3 * r3 + + ri * ri * resProp3 * r3 * r3; + c4LL = ei * ei * gamProp4 * e4 * e4 + + ei * li * intProp4 * e4 * l4 + + li * li * resProp4 * l4 * l4; + c4LR = ei * ei * gamProp4 * e4 * e4 + + ei * li * intProp4 * e4 * r4 + + li * li * resProp4 * r4 * r4; + c4RL = ei * ei * gamProp4 * e4 * e4 + + ei * ri * intProp4 * e4 * l4 + + ri * ri * resProp4 * l4 * l4; + c4RR = ei * ei * gamProp4 * e4 * e4 + + ei * ri * intProp4 * e4 * r4 + + ri * ri * resProp4 * r4 * r4; + + // Flavour weight and maximum. + flavWt = (c3LL + c3LR) * (c4LL + c4LR) + (c3RL + c3RR) * (c4RL + c4RR); + double flavWtMax = (c3LL + c3LR + c3RL + c3RR) * (c4LL + c4LR + c4RL + c4RR); + + // Done. + return flavWt / flavWtMax; + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles of the two gamma*/Z0. + +double Sigma2ffbar2gmZgmZ::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Two resonance decays, but with common weight. + if (iResBeg != 5 || iResEnd != 6) return 1.; + + // Set up four-products and internal products. + setupProd( process, i1, i2, i3, i4, i5, i6); + + // Flip tHat and uHat if first incoming is fermion. + double tHres = tH; + double uHres = uH; + if (process[3].id() > 0) swap( tHres, uHres); + + // Kinematics factors (norm(x) = |x|^2). + double fGK135 = norm( fGK( 1, 2, 3, 4, 5, 6) / tHres + + fGK( 1, 2, 5, 6, 3, 4) / uHres ); + double fGK145 = norm( fGK( 1, 2, 4, 3, 5, 6) / tHres + + fGK( 1, 2, 5, 6, 4, 3) / uHres ); + double fGK136 = norm( fGK( 1, 2, 3, 4, 6, 5) / tHres + + fGK( 1, 2, 6, 5, 3, 4) / uHres ); + double fGK146 = norm( fGK( 1, 2, 4, 3, 6, 5) / tHres + + fGK( 1, 2, 6, 5, 4, 3) / uHres ); + double fGK253 = norm( fGK( 2, 1, 5, 6, 3, 4) / tHres + + fGK( 2, 1, 3, 4, 5, 6) / uHres ); + double fGK263 = norm( fGK( 2, 1, 6, 5, 3, 4) / tHres + + fGK( 2, 1, 3, 4, 6, 5) / uHres ); + double fGK254 = norm( fGK( 2, 1, 5, 6, 4, 3) / tHres + + fGK( 2, 1, 4, 3, 5, 6) / uHres ); + double fGK264 = norm( fGK( 2, 1, 6, 5, 4, 3) / tHres + + fGK( 2, 1, 4, 3, 6, 5) / uHres ); + + // Weight and maximum. + double wt = c3LL * c4LL * fGK135 + c3LR * c4LL * fGK145 + + c3LL * c4LR * fGK136 + c3LR * c4LR * fGK146 + + c3RL * c4RL * fGK253 + c3RR * c4RL * fGK263 + + c3RL * c4RR * fGK254 + c3RR * c4RR * fGK264; + double wtMax = 16. * s3 * s4 * flavWt + * ( (tHres*tHres + uHres*uHres + 2. * sH * (s3 + s4)) / (tHres * uHres) + - s3 * s4 * (1. / (tHres*tHres) + 1. / (uHres*uHres)) ); + + // Done. + return wt / wtMax; + +} + +//========================================================================== + +// Sigma2ffbar2ZW class. +// Cross section for f fbar' -> Z0 W+- (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2ZW::initProc() { + + // Store W+- mass and width for propagator. + mW = particleDataPtr->m0(24); + widW = particleDataPtr->mWidth(24); + mWS = mW*mW; + mwWS = pow2(mW * widW); + + // Left-handed couplings for up/nu- and down/e-type quarks. + lun = (hasLeptonBeams) ? coupSMPtr->lf(12) : coupSMPtr->lf(2); + lde = (hasLeptonBeams) ? coupSMPtr->lf(11) : coupSMPtr->lf(1); + + // Common weak coupling factor. + sin2thetaW = coupSMPtr->sin2thetaW(); + cos2thetaW = coupSMPtr->cos2thetaW(); + thetaWRat = 1. / (4. * cos2thetaW); + cotT = sqrt(cos2thetaW / sin2thetaW); + thetaWpt = (9. - 8. * sin2thetaW) / 4.; + thetaWmm = (8. * sin2thetaW - 6.) / 4.; + + // Secondary open width fractions. + openFracPos = particleDataPtr->resOpenFrac(23, 24); + openFracNeg = particleDataPtr->resOpenFrac(23, -24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2ffbar2ZW::sigmaKin() { + + // Evaluate cross section, as programmed by Merlin Kole (after tidying), + // based on Brown, Sahdev, Mikaelian, Phys Rev. D20 (1979) 1069. + double resBW = 1. / (pow2(sH - mWS) + mwWS); + double prefac = 12.0 * M_PI * pow2(alpEM) / (sH2 * 8. * sin2thetaW); + double temp1 = tH * uH - s3 * s4; + double temp2 = temp1 / (s3 * s4); + double temp3 = (s3 + s4) / sH; + double temp4 = s3 * s4 / sH; + double partA = temp2 * (0.25 - 0.5 * temp3 + + (pow2(s3 + s4) + 8. * s3 * s4)/(4. * sH2) ) + + (s3 + s4)/(s3 * s4) * (sH/2. - s3 - s4 + pow2(s3 - s4)/(2. * sH)); + double partB1 = lun * (0.25 * temp2 * (1. - temp3 - 4. * temp4 / tH) + + ((s3 + s4)/(2. * s3 * s4)) * (sH - s3 - s4 + 2. * s3 * s4 / tH) ); + double partB2 = lde * ( 0.25 * temp2 * (1.- temp3 - 4. * temp4 / uH) + + ((s3 + s4)/(2. * s3 * s4)) * (sH - s3 - s4 + 2. * s3 * s4 / uH) ); + double partE = 0.25 * temp2 + 0.5 *(s3 + s4) / temp4; + sigma0 = prefac * (pow2(cotT) * sH2 * resBW * partA + + 2.* sH * cotT * resBW * (sH - mWS) * (partB2 - partB1) + + pow2(lun - lde) * partE + pow2(lde) * temp1/uH2 + + pow2(lun) * temp1/tH2 + 2. * lun * lde * sH * (s3 + s4) / (uH * tH)); + + // Evaluate cross section. Expression from EHLQ, with bug fix, + // but can still give negative cross section so suspect. + //sigma0 = (M_PI / sH2) * 0.5 * pow2(alpEM / sin2thetaW); + //sigma0 *= sH * resBW * (thetaWpt * pT2 + thetaWmm * (s3 + s4)) + // + (sH - mWS) * resBW * sH * (pT2 - s3 - s4) * (lun / tH - lde / uH) + // + thetaWRat * sH * pT2 * ( lun*lun / tH2 + lde*lde / uH2 ) + // + 2. * thetaWRat * sH * (s3 + s4) * lun * lde / (tH * uH); + // Need to protect against negative cross sections at times. + //sigma0 = max(0., sigma0); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2ZW::sigmaHat() { + + // CKM and colour factors. + double sigma = sigma0; + if (abs(id1) < 9) sigma *= coupSMPtr->V2CKMid(abs(id1), abs(id2)) / 3.; + + // Corrections for secondary widths in Z0 and W+- decays. + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + sigma *= (idUp > 0) ? openFracPos : openFracNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2ZW::setIdColAcol() { + + // Sign of outgoing W. + int sign = 1 - 2 * (abs(id1)%2); + if (id1 < 0) sign = -sign; + setId( id1, id2, 23, 24 * sign); + + // tHat is defined between (f, W-) or (fbar, W+), + // so OK for u/ubar on side 1, but must swap tHat <-> uHat if d/dbar. + if (abs(id1)%2 == 1) swapTU = true; + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for Z0 and W+- decay angles. + +double Sigma2ffbar2ZW::weightDecay( Event& process, int iResBeg, int iResEnd) { + + // Two resonance decays, but with common weight. + if (iResBeg != 5 || iResEnd != 6) return 1.; + + // Order so that fbar(1) f(2) -> f'(3) fbar'(4) f"(5) fbar"(6) + // with f' fbar' from W+- and f" fbar" from Z0 (note flip Z0 <-> W+-). + int i1 = (process[3].id() < 0) ? 3 : 4; + int i2 = 7 - i1; + int i3 = (process[9].id() > 0) ? 9 : 10; + int i4 = 19 - i3; + int i5 = (process[7].id() > 0) ? 7 : 8; + int i6 = 15 - i5; + + // Set up four-products and internal products. + setupProd( process, i1, i2, i3, i4, i5, i6); + + // Swap tHat and uHat if incoming fermion is downtype. + double tHres = tH; + double uHres = uH; + if (process[i2].id()%2 == 1) swap( tHres, uHres); + + // Couplings of incoming (anti)fermions and outgoing from Z0. + int idAbs = process[i1].idAbs(); + double ai = coupSMPtr->af(idAbs); + double li1 = coupSMPtr->lf(idAbs); + idAbs = process[i2].idAbs(); + double li2 = coupSMPtr->lf(idAbs); + idAbs = process[i5].idAbs(); + double l4 = coupSMPtr->lf(idAbs); + double r4 = coupSMPtr->rf(idAbs); + + // W propagator/interference factor. + double Wint = cos2thetaW * (sH - mWS) / (pow2(sH - mWS) + mwWS); + + // Combinations of couplings and kinematics (norm(x) = |x|^2). + double aWZ = li2 / tHres - 2. * Wint * ai; + double bWZ = li1 / uHres + 2. * Wint * ai; + double fGK135 = norm( aWZ * fGK( 1, 2, 3, 4, 5, 6) + + bWZ * fGK( 1, 2, 5, 6, 3, 4) ); + double fGK136 = norm( aWZ * fGK( 1, 2, 3, 4, 6, 5) + + bWZ * fGK( 1, 2, 6, 5, 3, 4) ); + double xiT = xiGK( tHres, uHres); + double xiU = xiGK( uHres, tHres); + double xjTU = xjGK( tHres, uHres); + + // Weight and maximum weight. + double wt = l4*l4 * fGK135 + r4*r4 * fGK136; + double wtMax = 4. * s3 * s4 * (l4*l4 + r4*r4) + * (aWZ * aWZ * xiT + bWZ * bWZ * xiU + aWZ * bWZ * xjTU); + + // Done. + return wt / wtMax; + +} + +//========================================================================== + +// Sigma2ffbar2WW class. +// Cross section for f fbar -> W- W+ (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2WW::initProc() { + + // Store Z0 mass and width for propagator. Common coupling factor. + mZ = particleDataPtr->m0(23); + widZ = particleDataPtr->mWidth(23); + mZS = mZ*mZ; + mwZS = pow2(mZ * widZ); + thetaWRat = 1. / (4. * coupSMPtr->sin2thetaW()); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(24, -24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2ffbar2WW::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * pow2(alpEM); + + // Z0 propagator and gamma*/Z0 interference. + double Zprop = sH2 / (pow2(sH - mZS) + mwZS); + double Zint = Zprop * (1. - mZS / sH); + + // Common coupling factors (g = gamma*, Z = Z0, f = t-channel fermion). + cgg = 0.5; + cgZ = thetaWRat * Zint; + cZZ = 0.5 * pow2(thetaWRat) * Zprop; + cfg = thetaWRat; + cfZ = pow2(thetaWRat) * Zint; + cff = pow2(thetaWRat); + + // Kinematical functions. + double rat34 = sH * (2. * (s3 + s4) + pT2) / (s3 * s4); + double lambdaS = pow2(sH - s3 - s4) - 4. * s3 * s4; + double intA = (sH - s3 - s4) * rat34 / sH; + double intB = 4. * (s3 + s4 - pT2); + gSS = (lambdaS * rat34 + 12. * sH * pT2) / sH2; + gTT = rat34 + 4. * sH * pT2 / tH2; + gST = intA + intB / tH; + gUU = rat34 + 4. * sH * pT2 / uH2; + gSU = intA + intB / uH; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2WW::sigmaHat() { + + // Flavour-specific couplings. + int idAbs = abs(id1); + double ei = coupSMPtr->ef(idAbs); + double vi = coupSMPtr->vf(idAbs); + double ai = coupSMPtr->af(idAbs); + + // Combine, with different cases for up- and down-type in-flavours. + double sigma = sigma0; + sigma *= (idAbs%2 == 1) + ? (cgg * ei*ei + cgZ * ei * vi + cZZ * (vi*vi + ai*ai)) * gSS + + (cfg * ei + cfZ * (vi + ai)) * gST + cff * gTT + : (cgg * ei*ei + cgZ * ei * vi + cZZ * (vi*vi + ai*ai)) * gSS + - (cfg * ei + cfZ * (vi + ai)) * gSU + cff * gUU; + + // Initial-state colour factor. Correction for secondary widths. Answer. + if (idAbs < 9) sigma /= 3.; + sigma *= openFracPair; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2WW::setIdColAcol() { + + // Always order W- W+, i.e. W- first. + setId( id1, id2, -24, 24); + + // tHat is defined between (f, W-) or (fbar, W+), + if (id1 < 0) swapTU = true; + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for W+ and W- decay angles. + +double Sigma2ffbar2WW::weightDecay( Event& process, int iResBeg, int iResEnd) { + + // Two resonance decays, but with common weight. + if (iResBeg != 5 || iResEnd != 6) return 1.; + + // Order so that fbar(1) f(2) -> f'(3) fbar'(4) f"(5) fbar"(6). + // with f' fbar' from W- and f" fbar" from W+. + int i1 = (process[3].id() < 0) ? 3 : 4; + int i2 = 7 - i1; + int i3 = (process[7].id() > 0) ? 7 : 8; + int i4 = 15 - i3; + int i5 = (process[9].id() > 0) ? 9 : 10; + int i6 = 19 - i5; + + // Set up four-products and internal products. + setupProd( process, i1, i2, i3, i4, i5, i6); + + // tHat and uHat of fbar f -> W- W+ opposite to previous convention. + double tHres = uH; + double uHres = tH; + + // Couplings of incoming (anti)fermion. + int idAbs = process[i1].idAbs(); + double ai = coupSMPtr->af(idAbs); + double li = coupSMPtr->lf(idAbs); + double ri = coupSMPtr->rf(idAbs); + + // gamma*/Z0 propagator/interference factor. + double Zint = mZS * (sH - mZS) / (pow2(sH - mZS) + mwZS); + + // Combinations of couplings and kinematics (norm(x) = |x|^2). + double dWW = (li * Zint + ai) / sH; + double aWW = dWW + 0.5 * (ai + 1.) / tHres; + double bWW = dWW + 0.5 * (ai - 1.) / uHres; + double cWW = ri * Zint / sH; + double fGK135 = norm( aWW * fGK( 1, 2, 3, 4, 5, 6) + - bWW * fGK( 1, 2, 5, 6, 3, 4) ); + double fGK253 = norm( cWW * ( fGK( 2, 1, 5, 6, 3, 4) + - fGK( 2, 1, 3, 4, 5, 6) ) ); + double xiT = xiGK( tHres, uHres); + double xiU = xiGK( uHres, tHres); + double xjTU = xjGK( tHres, uHres); + + // Weight and maximum weight. + double wt = fGK135 + fGK253; + double wtMax = 4. * s3 * s4 + * ( aWW * aWW * xiT + bWW * bWW * xiU - aWW * bWW * xjTU + + cWW * cWW * (xiT + xiU - xjTU) ); + + // Done. + return wt / wtMax; +} + +//========================================================================== + +// Sigma2ffbargmZggm class. +// Collects common methods for f fbar -> gamma*/Z0 g/gamma and permutations. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbargmZggm::initProc() { + + // Allow to pick only gamma* or Z0 part of full gamma*/Z0 expression. + gmZmode = settingsPtr->mode("WeakZ0:gmZmode"); + + // Store Z0 mass and width for propagator. + mRes = particleDataPtr->m0(23); + GammaRes = particleDataPtr->mWidth(23); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() + * coupSMPtr->cos2thetaW()); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(23); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sum of flavour couplings times phase space. + +void Sigma2ffbargmZggm::flavSum() { + + // Coupling factors for Z0 subsystem. + double alpSZ = coupSMPtr->alphaS(s3); + double colQZ = 3. * (1. + alpSZ / M_PI); + + // Reset quantities to sum. Declare variables in loop. + gamSum = 0.; + intSum = 0.; + resSum = 0.; + int onMode; + double mf, mr, psvec, psaxi, betaf, ef2, efvf, vf2af2, colf; + + // Loop over all Z0 decay channels. + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + int idAbs = abs( particlePtr->channel(i).product(0) ); + + // Only contributions from three fermion generations, except top. + if ( (idAbs > 0 && idAbs < 6) || ( idAbs > 10 && idAbs < 17)) { + mf = particleDataPtr->m0(idAbs); + + // Check that above threshold. Phase space. + if (m3 > 2. * mf + MASSMARGIN) { + mr = pow2(mf / m3); + betaf = sqrtpos(1. - 4. * mr); + psvec = betaf * (1. + 2. * mr); + psaxi = pow3(betaf); + + // Combine phase space with couplings. + ef2 = coupSMPtr->ef2(idAbs) * psvec; + efvf = coupSMPtr->efvf(idAbs) * psvec; + vf2af2 = coupSMPtr->vf2(idAbs) * psvec + + coupSMPtr->af2(idAbs) * psaxi; + colf = (idAbs < 6) ? colQZ : 1.; + + // Store sum of combinations. For outstate only open channels. + onMode = particlePtr->channel(i).onMode(); + if (onMode == 1 || onMode == 2) { + gamSum += colf * ef2; + intSum += colf * efvf; + resSum += colf * vf2af2; + } + + // End loop over fermions. + } + } + } + + // Done. Return values in gamSum, intSum and resSum. + +} + +//-------------------------------------------------------------------------- + +// Calculate common parts of gamma/interference/Z0 propagator terms. + +void Sigma2ffbargmZggm::propTerm() { + + // Calculate prefactors for gamma/interference/Z0 cross section terms. + gamProp = 4. * alpEM / (3. * M_PI * s3); + intProp = gamProp * 2. * thetaWRat * s3 * (s3 - m2Res) + / ( pow2(s3 - m2Res) + pow2(s3 * GamMRat) ); + resProp = gamProp * pow2(thetaWRat * s3) + / ( pow2(s3 - m2Res) + pow2(s3 * GamMRat) ); + + // Optionally only keep gamma* or Z0 term. + if (gmZmode == 1) {intProp = 0.; resProp = 0.;} + if (gmZmode == 2) {gamProp = 0.; intProp = 0.;} + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for gamma*/Z0 decay angle. + +double Sigma2ffbargmZggm::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Z should sit in entry 5 and one more parton in entry 6. + if (iResBeg != 5 || iResEnd != 6) return 1.; + + // In an outgoing sense fermions are labelled f(1) fbar(2) f'(3) fbar'(4) + // where f' fbar' come from gamma*/Z0 decay. + int i1, i2; + int i3 = (process[7].id() > 0) ? 7 : 8; + int i4 = 15 - i3; + + // Order so that fbar(1) f(2) -> gamma*/Z0 g/gamma. + if (process[3].idAbs() < 20 && process[4].idAbs() < 20) { + i1 = (process[3].id() < 0) ? 3 : 4; + i2 = 7 - i1; + + // Order so that f(2)/fbar(1) g/gamma -> f(1)/fbar(2) f'(3) gamma*/Z0. + } else if (process[3].idAbs() < 20) { + i1 = (process[3].id() < 0) ? 3 : 6; + i2 = 9 - i1; + } else { + i1 = (process[4].id() < 0) ? 4 : 6; + i2 = 10 - i1; + } + + // Charge/2, left- and righthanded couplings for in- and out-fermion. + int id1Abs = process[i1].idAbs(); + double ei = 0.5 * coupSMPtr->ef(id1Abs); + double li = coupSMPtr->lf(id1Abs); + double ri = coupSMPtr->rf(id1Abs); + int id3Abs = process[i3].idAbs(); + double ef = 0.5 * coupSMPtr->ef(id3Abs); + double lf = coupSMPtr->lf(id3Abs); + double rf = coupSMPtr->rf(id3Abs); + + // Combinations of left/right for in/out, gamma*/interference/Z0. + double clilf = ei*ei * gamProp * ef*ef + ei*li * intProp * ef*lf + + li*li * resProp * lf*lf; + double clirf = ei*ei * gamProp * ef*ef + ei*li * intProp * ef*rf + + li*li * resProp * rf*rf; + double crilf = ei*ei * gamProp * ef*ef + ei*ri * intProp * ef*lf + + ri*ri * resProp * lf*lf; + double crirf = ei*ei * gamProp * ef*ef + ei*ri * intProp * ef*rf + + ri*ri * resProp * rf*rf; + + // Evaluate four-vector products. + double p13 = process[i1].p() * process[i3].p(); + double p14 = process[i1].p() * process[i4].p(); + double p23 = process[i2].p() * process[i3].p(); + double p24 = process[i2].p() * process[i4].p(); + + // Calculate weight and its maximum. + double wt = (clilf + crirf) * (p13*p13 + p24*p24) + + (clirf + crilf) * (p14*p14 + p23*p23) ; + double wtMax = (clilf + clirf + crilf + crirf) + * (pow2(p13 + p14) + pow2(p23 + p24)); + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma2qqbar2gmZg class. +// Cross section for q qbar -> gamma*/Z0 g. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2gmZg::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM * alpS) + * (2./9.) * (tH2 + uH2 + 2. * sH * s3) / (tH * uH); + + // Calculate flavour sums for final state. + flavSum(); + + // Calculate prefactors for gamma/interference/Z0 cross section terms. + propTerm(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2gmZg::sigmaHat() { + + // Combine gamma, interference and Z0 parts. + int idAbs = abs(id1); + double sigma = sigma0 + * ( coupSMPtr->ef2(idAbs) * gamProp * gamSum + + coupSMPtr->efvf(idAbs) * intProp * intSum + + coupSMPtr->vf2af2(idAbs) * resProp * resSum); + + // Correct for the running-width Z0 propagater weight in PhaseSpace. + sigma /= runBW3; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2gmZg::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, 23, 21); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 0, 0, 1, 2); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qg2gmZq class. +// Cross section for q g -> gamma*/Z0 q. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qg2gmZq::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM * alpS) + * (1./12.) * (sH2 + uH2 + 2. * tH * s3) / (-sH * uH); + + // Calculate flavour sums for final state. + flavSum(); + + // Calculate prefactors for gamma/interference/Z0 cross section terms. + propTerm(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qg2gmZq::sigmaHat() { + + // Combine gamma, interference and Z0 parts. + int idAbs = (id2 == 21) ? abs(id1) : abs(id2); + double sigma = sigma0 + * ( coupSMPtr->ef2(idAbs) * gamProp * gamSum + + coupSMPtr->efvf(idAbs) * intProp * intSum + + coupSMPtr->vf2af2(idAbs) * resProp * resSum); + + // Correct for the running-width Z0 propagater weight in PhaseSpace. + sigma /= runBW3; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2gmZq::setIdColAcol() { + + // Flavour set up for q g -> gamma*/Z0 q. + int idq = (id2 == 21) ? id1 : id2; + setId( id1, id2, 23, idq); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbar2gmZgm class. +// Cross section for f fbar -> gamma*/Z0 gamma. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2gmZgm::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM*alpEM) + * 0.5 * (tH2 + uH2 + 2. * sH * s3) / (tH * uH); + + // Calculate flavour sums for final state. + flavSum(); + + // Calculate prefactors for gamma/interference/Z0 cross section terms. + propTerm(); + + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2gmZgm::sigmaHat() { + + // Combine gamma, interference and Z0 parts. + int idAbs = abs(id1); + double sigma = sigma0 * coupSMPtr->ef2(idAbs) + * ( coupSMPtr->ef2(idAbs) * gamProp * gamSum + + coupSMPtr->efvf(idAbs) * intProp * intSum + + coupSMPtr->vf2af2(idAbs) * resProp * resSum); + + // Correct for the running-width Z0 propagater weight in PhaseSpace. + sigma /= runBW3; + + // Colour factor. Answer. + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2gmZgm::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, 23, 22); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2fgm2gmZf class. +// Cross section for f gamma -> gamma*/Z0 f'. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2fgm2gmZf::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM*alpEM) + * 0.5 * (sH2 + uH2 + 2. * tH * s3) / (- sH * uH); + + // Calculate flavour sums for final state. + flavSum(); + + // Calculate prefactors for gamma/interference/Z0 cross section terms. + propTerm(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2fgm2gmZf::sigmaHat() { + + // Combine gamma, interference and Z0 parts. + int idAbs = (id2 == 22) ? abs(id1) : abs(id2); + double sigma = sigma0 * coupSMPtr->ef2(idAbs) + * ( coupSMPtr->ef2(idAbs) * gamProp * gamSum + + coupSMPtr->efvf(idAbs) * intProp * intSum + + coupSMPtr->vf2af2(idAbs) * resProp * resSum); + + // Correct for the running-width Z0 propagater weight in PhaseSpace. + sigma /= runBW3; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2fgm2gmZf::setIdColAcol() { + + // Flavour set up for q gamma -> gamma*/Z0 q. + int idq = (id2 == 22) ? id1 : id2; + setId( id1, id2, 23, idq); + + // tH defined between f and f': must swap tHat <-> uHat if q gamma in. + swapTU = (id2 == 22); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 0, 0, 0, 1, 0); + else if (abs(id2) < 9) setColAcol( 0, 0, 1, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbarWggm class. +// Collects common methods for f fbar -> W+- g/gamma and permutations. + +//-------------------------------------------------------------------------- + +// Evaluate weight for W+- decay angle. + +double Sigma2ffbarWggm::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // W should sit in entry 5 and one more parton in entry 6. + if (iResBeg != 5 || iResEnd != 6) return 1.; + + // In an outgoing sense fermions are labelled f(1) fbar(2) f'(3) fbar'(4) + // where f' fbar' come from W+- decay. + int i1, i2; + int i3 = (process[7].id() > 0) ? 7 : 8; + int i4 = 15 - i3; + + // Order so that fbar(1) f(2) -> W+- g/gamma. + if (process[3].idAbs() < 20 && process[4].idAbs() < 20) { + i1 = (process[3].id() < 0) ? 3 : 4; + i2 = 7 - i1; + + // Order so that f(2)/fbar(1) g/gamma -> f(1)/fbar(2) f'(3) W+-. + } else if (process[3].idAbs() < 20) { + i1 = (process[3].id() < 0) ? 3 : 6; + i2 = 9 - i1; + } else { + i1 = (process[4].id() < 0) ? 4 : 6; + i2 = 10 - i1; + } + + // Evaluate four-vector products. + double p13 = process[i1].p() * process[i3].p(); + double p14 = process[i1].p() * process[i4].p(); + double p23 = process[i2].p() * process[i3].p(); + double p24 = process[i2].p() * process[i4].p(); + + // Calculate weight and its maximum. + double wt = pow2(p13) + pow2(p24); + double wtMax = pow2(p13 + p14) + pow2(p23 + p24); + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma2qqbar2Wg class. +// Cross section for q qbar' -> W+- g. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2Wg::initProc() { + + // Secondary open width fractions, relevant for top (or heavier). + openFracPos = particleDataPtr->resOpenFrac(24); + openFracNeg = particleDataPtr->resOpenFrac(-24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2Wg::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM * alpS / coupSMPtr->sin2thetaW()) + * (2./9.) * (tH2 + uH2 + 2. * sH * s3) / (tH * uH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2Wg::sigmaHat() { + + // CKM factor. Secondary width for W+ or W-. + double sigma = sigma0 * coupSMPtr->V2CKMid(abs(id1), abs(id2)); + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + sigma *= (idUp > 0) ? openFracPos : openFracNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2Wg::setIdColAcol() { + + // Sign of outgoing W. + int sign = 1 - 2 * (abs(id1)%2); + if (id1 < 0) sign = -sign; + setId( id1, id2, 24 * sign, 21); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 0, 0, 1, 2); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qg2Wq class. +// Cross section for q g -> W+- q'. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2Wq::initProc() { + + // Secondary open width fractions, relevant for top (or heavier). + openFracPos = particleDataPtr->resOpenFrac(24); + openFracNeg = particleDataPtr->resOpenFrac(-24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qg2Wq::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM * alpS / coupSMPtr->sin2thetaW()) + * (1./12.) * (sH2 + uH2 + 2. * tH * s3) / (-sH * uH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qg2Wq::sigmaHat() { + + // CKM factor. Secondary width for W+ or W-. + int idAbs = (id2 == 21) ? abs(id1) : abs(id2); + double sigma = sigma0 * coupSMPtr->V2CKMsum(idAbs); + int idUp = (id2 == 21) ? id1 : id2; + if (idAbs%2 == 1) idUp = -idUp; + sigma *= (idUp > 0) ? openFracPos : openFracNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2Wq::setIdColAcol() { + + // Sign of outgoing W. Flavour of outgoing quark. + int idq = (id2 == 21) ? id1 : id2; + int sign = 1 - 2 * (abs(idq)%2); + if (idq < 0) sign = -sign; + id4 = coupSMPtr->V2CKMpick(idq); + + // Flavour set up for q g -> W q. + setId( id1, id2, 24 * sign, id4); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbar2Wgm class. +// Cross section for f fbar' -> W+- gamma. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2Wgm::initProc() { + + // Secondary open width fractions, relevant for top (or heavier). + openFracPos = particleDataPtr->resOpenFrac(24); + openFracNeg = particleDataPtr->resOpenFrac(-24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2Wgm::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM*alpEM / coupSMPtr->sin2thetaW()) + * 0.5 * (tH2 + uH2 + 2. * sH * s3) / (tH * uH); +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2Wgm::sigmaHat() { + + // Extrafactor different for e nu and q qbar' instate. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + double chgUp = (id1Abs > 10) ? 0. : 2./3.; + double sigma = sigma0 * pow2( chgUp - tH / (tH + uH) ); + + // CKM and colour factors. Secondary width for W+ or W-. + if (id1Abs < 9) sigma *= coupSMPtr->V2CKMid(id1Abs, id2Abs) / 3.; + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + sigma *= (idUp > 0) ? openFracPos : openFracNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2Wgm::setIdColAcol() { + + // Sign of outgoing W. + int sign = 1 - 2 * (abs(id1)%2); + if (id1 < 0) sign = -sign; + setId( id1, id2, 24 * sign, 22); + + // tH defined between (f,W-) or (fbar',W+). + swapTU = (sign * id1 > 0); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2fgm2Wf class. +// Cross section for f gamma -> W+- f'. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2fgm2Wf::initProc() { + + // Secondary open width fractions, relevant for top (or heavier). + openFracPos = particleDataPtr->resOpenFrac(24); + openFracNeg = particleDataPtr->resOpenFrac(-24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2fgm2Wf::sigmaKin() { + + // Cross section part common for all incoming flavours. + sigma0 = (M_PI / sH2) * (alpEM*alpEM / coupSMPtr->sin2thetaW()) + * 0.5 * (sH2 + uH2 + 2. * tH * s3) / (pT2 * s3 - sH * uH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2fgm2Wf::sigmaHat() { + + // Extrafactor dependent on charge of incoming fermion. + int idAbs = (id2 == 22) ? abs(id1) : abs(id2); + double charge = (idAbs > 10) ? 1. : ( (idAbs%2 == 1) ? 1./3. : 2./3. ); + double sigma = sigma0 * pow2( charge - sH / (sH + uH) ); + + // CKM factor. Secondary width for W+ or W-. + sigma *= coupSMPtr->V2CKMsum(idAbs); + int idUp = (id2 == 22) ? id1 : id2; + if (idAbs%2 == 1) idUp = -idUp; + sigma *= (idUp > 0) ? openFracPos : openFracNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2fgm2Wf::setIdColAcol() { + + // Sign of outgoing W. Flavour of outgoing fermion. + int idq = (id2 == 22) ? id1 : id2; + int sign = 1 - 2 * (abs(idq)%2); + if (idq < 0) sign = -sign; + id4 = coupSMPtr->V2CKMpick(idq); + + // Flavour set up for q gamma -> W q. + setId( id1, id2, 24 * sign, id4); + + // tH defined between f and f': must swap tHat <-> uHat if q gamma in. + swapTU = (id2 == 22); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 0, 0, 0, 1, 0); + else if (abs(id2) < 9) setColAcol( 0, 0, 1, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gmgm2ffbar class. +// Cross section for gamma gamma -> l lbar. + +//-------------------------------------------------------------------------- + +// Initialize process wrt flavour. + +void Sigma2gmgm2ffbar::initProc() { + + // Process name. + nameSave = "gamma gamma -> f fbar"; + if (idNew == 1) nameSave = "gamma gamma -> q qbar (uds)"; + if (idNew == 4) nameSave = "gamma gamma -> c cbar"; + if (idNew == 5) nameSave = "gamma gamma -> b bbar"; + if (idNew == 6) nameSave = "gamma gamma -> t tbar"; + if (idNew == 11) nameSave = "gamma gamma -> e+ e-"; + if (idNew == 13) nameSave = "gamma gamma -> mu+ mu-"; + if (idNew == 15) nameSave = "gamma gamma -> tau+ tau-"; + + // Generate massive phase space, except for u+d+s. + idMass = 0; + if (idNew > 3) idMass = idNew; + + // Charge and colour factor. + ef4 = 1.; + if (idNew == 1) ef4 = 3. * (pow4(2./3.) + 2. * pow4(1./3.)); + if (idNew == 4 || idNew == 6) ef4 = 3. * pow4(2./3.); + if (idNew == 5) ef4 = 3. * pow4(1./3.); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2gmgm2ffbar::sigmaKin() { + + // Pick current flavour for u+d+s mix by e_q^4 weights. + if (idNew == 1) { + double rId = 18. * rndmPtr->flat(); + idNow = 1; + if (rId > 1.) idNow = 2; + if (rId > 17.) idNow = 3; + s34Avg = pow2(particleDataPtr->m0(idNow)); + } else { + idNow = idNew; + s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + } + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + double tHQ = -0.5 * (sH - tH + uH); + double uHQ = -0.5 * (sH + tH - uH); + double tHQ2 = tHQ * tHQ; + double uHQ2 = uHQ * uHQ; + + // Calculate kinematics dependence. + if (sH < 4. * s34Avg) sigTU = 0.; + else sigTU = 2. * (tHQ * uHQ - s34Avg * sH) + * (tHQ2 + uHQ2 + 2. * s34Avg * sH) / (tHQ2 * uHQ2); + + // Answer. + sigma = (M_PI / sH2) * pow2(alpEM) * ef4 * sigTU * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gmgm2ffbar::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idNow, -idNow); + + // Colour flow in singlet state. + if (idNow < 10) setColAcol( 0, 0, 0, 0, 1, 0, 0, 1); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaExtraDim.cxx b/PYTHIA8/pythia8140/src/SigmaExtraDim.cxx new file mode 100644 index 00000000000..30ef2324f2c --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaExtraDim.cxx @@ -0,0 +1,2490 @@ +// SigmaExtraDim.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// Copyright (C) 2010 Stefan Ask for the *LED* routines. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// extra-dimensional simulation classes. + +#include "SigmaExtraDim.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma1gg2GravitonStar class. +// Cross section for g g -> G* (excited graviton state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1gg2GravitonStar::initProc() { + + // Store G* mass and width for propagator. + idGstar = 5100039; + mRes = particleDataPtr->m0(idGstar); + GammaRes = particleDataPtr->mWidth(idGstar); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // SMinBulk = off/on, use universal coupling (kappaMG) + // or individual (Gxx) between graviton and SM particles. + m_smbulk = settingsPtr->flag("ExtraDimensionsG*:SMinBulk"); + kappaMG = settingsPtr->parm("ExtraDimensionsG*:kappaMG"); + for (int i = 0; i < 26; ++i) m_coupling[i] = 0.; + double tmp_coup = settingsPtr->parm("ExtraDimensionsG*:Gqq"); + for (int i = 1; i <= 4; ++i) m_coupling[i] = tmp_coup; + m_coupling[5] = settingsPtr->parm("ExtraDimensionsG*:Gbb"); + m_coupling[6] = settingsPtr->parm("ExtraDimensionsG*:Gtt"); + tmp_coup = settingsPtr->parm("ExtraDimensionsG*:Gll"); + for (int i = 11; i <= 16; ++i) m_coupling[i] = tmp_coup; + tmp_coup = settingsPtr->parm("ExtraDimensionsG*:GVV"); + for (int i = 21; i <= 24; ++i) m_coupling[i] = tmp_coup; + + // Set pointer to particle properties and decay table. + gStarPtr = particleDataPtr->particleDataEntryPtr(idGstar); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1gg2GravitonStar::sigmaKin() { + + // Incoming width for gluons. + double widthIn = mH / (160. * M_PI); + + // RS graviton coupling + if (m_smbulk) widthIn *= 2. * pow2(m_coupling[21] * mH); + else widthIn *= pow2(kappaMG); + + // Set up Breit-Wigner. Width out only includes open channels. + double sigBW = 5. * M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double widthOut = gStarPtr->resWidthOpen(idGstar, mH); + + // Modify cross section in wings of peak. Done. + sigma = widthIn * sigBW * widthOut * pow2(sH / m2Res); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1gg2GravitonStar::setIdColAcol() { + + // Flavours trivial. + setId( 21, 21, idGstar); + + // Colour flow topology. + setColAcol( 1, 2, 2, 1, 0, 0); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for G* decay angle. + +double Sigma1gg2GravitonStar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // G* should sit in entry 5. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Phase space factors. Reconstruct decay angle. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + + // Default is isotropic decay. + double wt = 1.; + + // Angular weight for g + g -> G* -> f + fbar. + if (process[6].idAbs() < 19) wt = 1. - pow4(cosThe); + + // Angular weight for g + g -> G* -> g + g or gamma + gamma. + else if (process[6].id() == 21 || process[6].id() == 22) + wt = (1. + 6. * pow2(cosThe) + pow4(cosThe)) / 8.; + + // Done. + return wt; + +} + +//========================================================================== + +// Sigma1ffbar2GravitonStar class. +// Cross section for f fbar -> G* (excited graviton state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2GravitonStar::initProc() { + + // Store G* mass and width for propagator. + idGstar = 5100039; + mRes = particleDataPtr->m0(idGstar); + GammaRes = particleDataPtr->mWidth(idGstar); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // SMinBulk = off/on, use universal coupling (kappaMG) + // or individual (Gxx) between graviton and SM particles. + m_smbulk = settingsPtr->flag("ExtraDimensionsG*:SMinBulk"); + kappaMG = settingsPtr->parm("ExtraDimensionsG*:kappaMG"); + for (int i = 0; i < 26; ++i) m_coupling[i] = 0.; + double tmp_coup = settingsPtr->parm("ExtraDimensionsG*:Gqq"); + for (int i = 1; i <= 4; ++i) m_coupling[i] = tmp_coup; + m_coupling[5] = settingsPtr->parm("ExtraDimensionsG*:Gbb"); + m_coupling[6] = settingsPtr->parm("ExtraDimensionsG*:Gtt"); + tmp_coup = settingsPtr->parm("ExtraDimensionsG*:Gll"); + for (int i = 11; i <= 16; ++i) m_coupling[i] = tmp_coup; + tmp_coup = settingsPtr->parm("ExtraDimensionsG*:GVV"); + for (int i = 21; i <= 24; ++i) m_coupling[i] = tmp_coup; + + // Set pointer to particle properties and decay table. + gStarPtr = particleDataPtr->particleDataEntryPtr(idGstar); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2GravitonStar::sigmaKin() { + + // Incoming width for fermions, disregarding colour factor. + double widthIn = mH / (80. * M_PI); + + // Set up Breit-Wigner. Width out only includes open channels. + double sigBW = 5. * M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double widthOut = gStarPtr->resWidthOpen(idGstar, mH); + + // Modify cross section in wings of peak. Done. + sigma0 = widthIn * sigBW * widthOut * pow2(sH / m2Res); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part dependent of incoming flavour. + +double Sigma1ffbar2GravitonStar::sigmaHat() { + + double sigma = sigma0; + + // RS graviton coupling + if (m_smbulk) sigma *= 2. * pow2(m_coupling[min( abs(id1), 25)] * mH); + else sigma *= pow2(kappaMG); + + // If initial quarks, 1/N_C + if (abs(id1) < 9) sigma /= 3.; + + return sigma; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2GravitonStar::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idGstar); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for G* decay angle. + +double Sigma1ffbar2GravitonStar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // G* should sit in entry 5. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Phase space factors. Reconstruct decay angle. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + + // Default is isotropic decay. + double wt = 1.; + + // Angular weight for f + fbar -> G* -> f + fbar. + if (process[6].idAbs() < 19) + wt = (1. - 3. * pow2(cosThe) + 4. * pow4(cosThe)) / 2.; + + // Angular weight for f + fbar -> G* -> g + g or gamma + gamma. + else if (process[6].id() == 21 || process[6].id() == 22) + wt = 1. - pow4(cosThe); + + // Done. + return wt; + +} + +//========================================================================== + +// Sigma1qqbar2KKgluonStar class. +// Cross section for q qbar -> KK-gluon^* (excited KK-gluon state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1qqbar2KKgluonStar::initProc() { + + // Store kk-gluon* mass and width for propagator. + idKKgluon = 5100021; + mRes = particleDataPtr->m0(idKKgluon); + GammaRes = particleDataPtr->mWidth(idKKgluon); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // KK-gluon couplings. + for (int i = 0; i < 10; ++i) m_coupling[i] = 0.; + double tmp_coup = settingsPtr->parm("ExtraDimensionsG*:KKgqq"); + for (int i = 1; i <= 4; ++i) m_coupling[i] = tmp_coup; + m_coupling[5] = settingsPtr->parm("ExtraDimensionsG*:KKgbb"); + m_coupling[6] = settingsPtr->parm("ExtraDimensionsG*:KKgtt"); + + // Set pointer to particle properties and decay table. + gStarPtr = particleDataPtr->particleDataEntryPtr(idKKgluon); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1qqbar2KKgluonStar::sigmaKin() { + + // Incoming width for fermions, disregarding colour factor. + double widthIn = alpS * mH * 4 / 27; + + // Set up Breit-Wigner. Width out only includes open channels. + double sigBW = 12. * M_PI / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double widthOut = gStarPtr->resWidthOpen(idKKgluon, mH); + + // Do not modify cross section in wings of peak, to be understood! + sigma0 = widthIn * sigBW * widthOut; // * pow2(sH / m2Res); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part dependent of incoming flavour. + +double Sigma1qqbar2KKgluonStar::sigmaHat() { + + // RS graviton coupling. + double sigma = sigma0 * pow2(m_coupling[min(abs(id1), 9)]); + + return sigma; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1qqbar2KKgluonStar::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idKKgluon); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 1, 2); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for KK-gluon* decay angle. + +double Sigma1qqbar2KKgluonStar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // G* should sit in entry 5. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Phase space factors. Reconstruct decay angle. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + + // Default is isotropic decay. + double wt = 1.; + + // Angular weight for f + fbar -> g* -> f + fbar. + if (process[6].idAbs() < 19) + wt = (1. + pow2(cosThe) + (1 - pow2(betaf)) * (1 - pow2(cosThe))) / 2.; + + // Done. + return wt; + +} + +//========================================================================== + +// Sigma2gg2GravitonStarg class. +// Cross section for g g -> G* g (excited graviton state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2GravitonStarg::initProc() { + + // Store G* mass and width for propagator. + idGstar = 5100039; + mRes = particleDataPtr->m0(idGstar); + GammaRes = particleDataPtr->mWidth(idGstar); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Overall coupling strength kappa * m_G*. + kappaMG = settingsPtr->parm("ExtraDimensionsG*:kappaMG"); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idGstar); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2gg2GravitonStarg::sigmaKin() { + + // Evaluate cross section. Secondary width for G*. + sigma = (3. * pow2(kappaMG) * alpS) / (32. * sH * s3) + * ( pow2(tH2 + tH * uH + uH2) / (sH2 * tH * uH) + + 2. * (tH2 / uH + uH2 / tH) / sH + 3. * (tH / uH + uH / tH) + + 2. * (sH / uH + sH/tH) + sH2 / (tH * uH) ); + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2GravitonStarg::setIdColAcol() { + + // Flavours trivial. + setId( 21, 21, idGstar, 21); + + // Colour flow topologies: random choice between two mirrors. + if (rndmPtr->flat() < 0.5) setColAcol( 1, 2, 2, 3, 0, 0, 1, 3); + else setColAcol( 1, 2, 3, 1, 0, 0, 3, 2); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles: currently G* assumed isotropic. + +double Sigma2gg2GravitonStarg::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // No equations for G* decay so assume isotropic. + return 1.; + +} + +//========================================================================== + +// Sigma2qg2GravitonStarq class. +// Cross section for q g -> G* q (excited graviton state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2GravitonStarq::initProc() { + + // Store G* mass and width for propagator. + idGstar = 5100039; + mRes = particleDataPtr->m0(idGstar); + GammaRes = particleDataPtr->mWidth(idGstar); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Overall coupling strength kappa * m_G*. + kappaMG = settingsPtr->parm("ExtraDimensionsG*:kappaMG"); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idGstar); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qg2GravitonStarq::sigmaKin() { + + // Evaluate cross section. Secondary width for G*. + sigma = -(pow2(kappaMG) * alpS) / (192. * sH * s3) + * ( 4. * (sH2 + uH2) / (tH * sH) + 9. * (sH + uH) / sH + sH / uH + + uH2 / sH2 + 3. * tH * (4. + sH / uH + uH / sH) / sH + + 4. * tH2 * (1. / uH + 1. / sH) / sH + 2. * tH2 * tH / (uH * sH2) ); + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2GravitonStarq::setIdColAcol() { + + // Flavour set up for q g -> H q. + int idq = (id2 == 21) ? id1 : id2; + setId( id1, id2, idGstar, idq); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles: currently G* assumed isotropic. + +double Sigma2qg2GravitonStarq::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // No equations for G* decay so assume isotropic. + return 1.; + +} + +//========================================================================== + +// Sigma2qqbar2GravitonStarg class. +// Cross section for q qbar -> G* g (excited graviton state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2GravitonStarg::initProc() { + + // Store G* mass and width for propagator. + idGstar = 5100039; + mRes = particleDataPtr->m0(idGstar); + GammaRes = particleDataPtr->mWidth(idGstar); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Overall coupling strength kappa * m_G*. + kappaMG = settingsPtr->parm("ExtraDimensionsG*:kappaMG"); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idGstar); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qqbar2GravitonStarg::sigmaKin() { + + // Evaluate cross section. Secondary width for G*. + sigma = (pow2(kappaMG) * alpS) / (72. * sH * s3) + * ( 4. * (tH2 + uH2) / sH2 + 9. * (tH + uH) / sH + + (tH2 / uH + uH2 / tH) / sH + 3. * (4. + tH / uH + uH/ tH) + + 4. * (sH / uH + sH / tH) + 2. * sH2 / (tH * uH) ); + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2GravitonStarg::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idGstar, 21); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 0, 0, 1, 2); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles: currently G* assumed isotropic. + +double Sigma2qqbar2GravitonStarg::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // No equations for G* decay so assume isotropic. + return 1.; + +} + +//========================================================================== + +// NOAM: Sigma2ffbar2TEVffbar class. +// Cross section for, f fbar -> gammaKK/ZKK -> F Fbar. +// Process provided by N. Hod et al. and is described in arXiv:XXXX.YYYY + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2TEVffbar::initProc() { + + // Process name. + nameSave = "f fbar -> F Fbar (s-channel gamma_KK/Z_KK)"; + if (idNew == 4) nameSave = "f fbar -> c cbar (s-channel gamma_KK/Z_KK)"; + if (idNew == 5) nameSave = "f fbar -> b bbar (s-channel gamma_KK/Z_KK)"; + if (idNew == 6) nameSave = "f fbar -> t tbar (s-channel gamma_KK/Z_KK)"; + if (idNew == 7) nameSave = "f fbar -> b' b'bar (s-channel gamma_KK/Z_KK)"; + if (idNew == 8) nameSave = "f fbar -> t' t'bar (s-channel gamma_KK/Z_KK)"; + if (idNew == 15) + nameSave = "f fbar -> tau+ tau- (s-channel gamma_KK/Z_KK)"; + if (idNew == 17) + nameSave = "f fbar -> tau'+ tau'- (s-channel gamma_KK/Z_KK)"; + if (idNew == 18) + nameSave = "f fbar -> nu'_tau nu'bar_tau (s-channel gamma_KK/Z_KK)"; + + // Allow to pick only gamma* or Z0 part of full gamma*/Z0 expression. + gmZmode = settingsPtr->mode("ExtraDimensionsTEV:gmZmode"); + + // Pick number of KK excitations + n_excitation_max = (int)settingsPtr->parm("ExtraDimensionsTEV:nMax"); + + // Initialize the widths of the KK propogators. + wgmKKFactor = 0.; // partial width of the KK photon + wgmKKn = 0.; // total width of the KK photon + wZKKn = 0.; // will be proportional to "wZ0" + ttbar addition + + // Store Z0 mass and width for propagator. + wZ0 = particleDataPtr->mWidth(23); + mRes = particleDataPtr->m0(23); + m2Res = mRes*mRes; + + // Store the top mass for the ttbar width calculations + mTop = particleDataPtr->m0(6); + m2Top = mTop*mTop; + + // Store the KK mass parameter, equivalent to the mass of the first KK + // excitation: particleDataPtr->m0(5000023); + mStar = (double)settingsPtr->parm("ExtraDimensionsTEV:mStar"); + + // Get alphaEM - relevant for the calculation of the widths + alphaem_fixed = settingsPtr->parm("StandardModel:alphaEM0"); + + // initialize imaginari number + M_I = complex(0.,1.); + + // Sum all partial widths of the KK photon except for the ttbar channel + // which is handeled afterwards seperately + if (gmZmode>=0 && gmZmode<=5) { + for (int i=1 ; i<17 ; i++) { + if (i==7) { i=11; } + if (i==6) { continue; } // skip the ttbar decay and add its contribution later + if (i<9) { + wgmKKFactor += ( (alphaem_fixed / 6.) * 4. + * coupSMPtr->ef(i) * coupSMPtr->ef(i) * 3. ); + } + else { + wgmKKFactor += (alphaem_fixed / 6.) * 4. + * coupSMPtr->ef(i) * coupSMPtr->ef(i); + } + } + } + + // Get the helicity-couplings of the Z0 to all the fermions except top + gMinusF = ( coupSMPtr->t3f(idNew) - coupSMPtr->ef(idNew) + * coupSMPtr->sin2thetaW() ) + / sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() ); + gPlusF = -1. * coupSMPtr->ef(idNew) * coupSMPtr->sin2thetaW() + / sqrt( coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW() ); + // Get the helicity-couplings of the Z0 to the top quark + gMinusTop = ( coupSMPtr->t3f(6) - coupSMPtr->ef(6) + * coupSMPtr->sin2thetaW() ) + / sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() ); + + gPlusTop = -1. * coupSMPtr->ef(6) * coupSMPtr->sin2thetaW() + / sqrt( coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW() ); + // calculate the constant factor of the unique ttbar decay width + ttbar_wFactorA = pow2(gMinusTop) + pow2(gPlusTop); + ttbar_wFactorB = 6.*gMinusTop*gPlusTop - pow2(gMinusTop) - pow2(gPlusTop); + + // Secondary open width fraction, relevant for top (or heavier). + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); +} + +//-------------------------------------------------------------------------- + +// For improving the phase-space sampling (there can be 2 resonances) + +int Sigma2ffbar2TEVffbar::resonanceB() { + + return 23; + +} + +//-------------------------------------------------------------------------- + +// For improving the phase-space sampling (there can be 2 resonances) + +int Sigma2ffbar2TEVffbar::resonanceA() { + + if (gmZmode>=3) { + phaseSpace_mHatMin = settingsPtr->parm("PhaseSpace:mHatMin"); + phaseSpace_mHatMax = settingsPtr->parm("PhaseSpace:mHatMax"); + double mResFirstKKMode = sqrt(pow2(particleDataPtr->m0(23)) + pow2(mStar)); + if (mResFirstKKMode/2. <= phaseSpace_mHatMax + || 3*mResFirstKKMode/2. >= phaseSpace_mHatMin) { return 5000023; } + else { return 23; } + } + else { return 23; } // no KK terms at all + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2TEVffbar::sigmaKin() { + + // Check that above threshold. + isPhysical = true; + if (mH < m3 + m4 + MASSMARGIN) { + isPhysical = false; + return; + } + + // Define average F, Fbar mass so same beta. Phase space. + double s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + mr = s34Avg / sH; + betaf = sqrtpos(1. - 4. * mr); + + // Reconstruct decay angle so can reuse 2 -> 1 cross section. + cosThe = (tH - uH) / (betaf * sH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2TEVffbar::sigmaHat() { + + // Fail if below threshold. + if (!isPhysical) return 0.; + + // Couplings for in/out-flavours. + int idAbs = abs(id1); + + // The couplings of the Z0 to the fermions for in/out flavors + gMinusf = ( coupSMPtr->t3f(idAbs) - coupSMPtr->ef(idAbs) + * coupSMPtr->sin2thetaW() ) + / sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() ); + gPlusf = -1. * coupSMPtr->ef(idAbs)*coupSMPtr->sin2thetaW() + / sqrt( coupSMPtr->sin2thetaW()*coupSMPtr->cos2thetaW() ); + + // Initialize the some values + helicityME2 = 0.; + coefAngular = 0.; + gf=0.; + gF=0.; + gammaProp = complex(0.,0.); + resProp = complex(0.,0.); + gmPropKK = complex(0.,0.); + ZPropKK = complex(0.,0.); + totalProp = complex(0.,0.); + + // Sum all initial and final helicity states this corresponds to an + // unpolarized beams and unmeasured polarization final-state + for (double helicityf=-0.5 ; helicityf<=0.5 ; helicityf++) { + for (double helicityF=-0.5 ; helicityF<=0.5 ; helicityF++) { + // the couplings for the initial-final helicity configuration + gF = (helicityF == +0.5) ? gMinusF : gPlusF; + gf = (helicityf == +0.5) ? gMinusf : gPlusf; + // 0=SM gmZ, 1=SM gm, 2=SM Z, 3=SM+KK gmZ, 4=KK gm, 5=KK Z + switch(gmZmode) { + case 0: // SM photon and Z0 only + gammaProp = coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)/sH; + resProp = gf*gF/( sH - m2Res + M_I*sH*(wZ0/mRes) ); + break; + case 1: // SM photon only + gammaProp = coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)/sH; + break; + case 2: // SM Z0 only + resProp = gf*gF/( sH - m2Res + M_I*sH*(wZ0/mRes) ); + break; + case 3: // KK photon and Z + gammaProp = coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)/sH; + resProp = gf*gF/( sH - m2Res + M_I*sH*(wZ0/mRes) ); + ZPropKK = complex(0.,0.); + gmPropKK = complex(0.,0.); + // Sum all KK excitations contributions + for(int n_excitation = 1; n_excitation <= n_excitation_max; + n_excitation++) { + mZKKn = sqrt(m2Res + pow2(mStar * n_excitation)); + m2ZKKn = m2Res + pow2(mStar * n_excitation); + mgmKKn = mStar * n_excitation; + m2gmKKn = (mStar*n_excitation)*(mStar*n_excitation); + // calculate the width of the n'th excitation of the KK Z + // (proportional to the Z0 width + ttbar partial width) + ttbar_wZKKn = 2.*(alphaem_fixed*3./6.)*mZKKn + * sqrt(1.-4.*m2Top/m2ZKKn) + * (ttbar_wFactorA+(m2Top/m2ZKKn)*ttbar_wFactorB); + wZKKn = 2.*wZ0*mZKKn/mRes+ttbar_wZKKn; + // calculate the width of the n'th excitation of the + // KK photon + ttbar_wgmKKn = 2.*(alphaem_fixed*3./6.)*mgmKKn + * sqrt(1.-4.*m2Top/m2gmKKn) + * 2.*pow2(coupSMPtr->ef(6))*(1.+2.*(m2Top/m2gmKKn)); + wgmKKn = wgmKKFactor*mgmKKn+ttbar_wgmKKn; + // the propogators + gmPropKK += (2.*coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)) + / (sH-m2gmKKn+M_I*sH*wgmKKn/mgmKKn); + ZPropKK += (2.*gf*gF)/(sH-m2ZKKn+M_I*sH*wZKKn/mZKKn ); + } + break; + case 4: // SM photon and Z0 with KK photon only + gammaProp = coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)/sH; + resProp = gf*gF/( sH - m2Res + M_I*sH*(wZ0/mRes) ); + gmPropKK = complex(0.,0.); + for (int n_excitation = 1; n_excitation <= n_excitation_max; + n_excitation++ ) { + mgmKKn = mStar * n_excitation; + m2gmKKn = (mStar*n_excitation)*(mStar*n_excitation); + + ttbar_wgmKKn = 2.*(alphaem_fixed*3./6.)*mgmKKn + * sqrt(1.-4.*m2Top/m2gmKKn) + * 2.*pow2(coupSMPtr->ef(6))*(1.+2.*(m2Top/m2gmKKn)); + wgmKKn = wgmKKFactor*mgmKKn+ttbar_wgmKKn; + gmPropKK += (2.*coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)) + / (sH-m2gmKKn+M_I*sH*wgmKKn/mgmKKn); + } + break; + case 5: // SM photon and Z0 with KK Z only + gammaProp = coupSMPtr->ef(idAbs)*coupSMPtr->ef(idNew)/sH; + resProp = gf*gF/( sH - m2Res + M_I*sH*(wZ0/mRes) ); + ZPropKK = complex(0.,0.); + for (int n_excitation = 1; n_excitation <= n_excitation_max; + n_excitation++ ) { + mZKKn = sqrt(m2Res + pow2(mStar * n_excitation)); + m2ZKKn = m2Res + pow2(mStar * n_excitation); + + ttbar_wZKKn = 2.*(alphaem_fixed*3./6.)*mZKKn + * sqrt(1.-4.*m2Top/m2ZKKn) + * (ttbar_wFactorA+(m2Top/m2ZKKn)*ttbar_wFactorB); + wZKKn = 2.*wZ0*mZKKn/mRes+ttbar_wZKKn; + ZPropKK += (2.*gf*gF)/(sH-m2ZKKn+M_I*sH*wZKKn/mZKKn ); + } + break; + default: break; + } // end run over initial and final helicity states + + // sum all contributing amplitudes + totalProp = gammaProp + resProp + ZPropKK + gmPropKK; + + // angular distribution for the helicity configuration + coefAngular = 1. + 4. * helicityF * helicityf * cosThe; + + // the squared helicity matrix element + helicityME2 += real(totalProp*conj(totalProp))*pow2(coefAngular); + } + } + + // calculate the coefficient of the squared helicity matrix element. + coefTot = (2./sH) * 2*M_PI * pow2(alpEM)/(4.*sH) * pow2(sH)/4.; + + // the full squared helicity matrix element. + double sigma = helicityME2 * coefTot; + + // Top: corrections for closed decay channels. + sigma *= openFracPair; + + // Initial-state colour factor. Answer. + if (idAbs < 9) sigma /= 3.; + return sigma; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2TEVffbar::setIdColAcol() { + + // Set outgoing flavours. + id3 = (id1 > 0) ? idNew : -idNew; + setId( id1, id2, id3, -id3); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && idNew < 9) setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else if (idNew < 9) setColAcol( 0, 0, 0, 0, 1, 0, 0, 1); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles of W in top decay. + +double Sigma2ffbar2TEVffbar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // For top decay hand over to standard routine, else done. + if (idNew == 6 && process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + else return 1.; + +} + +//========================================================================== + +// Sigma2gg2LEDUnparticleg class. +// Cross section for g g -> U/G g (real graviton emission in +// large extra dimensions or unparticle emission). + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDUnparticleg::initProc() { + + // Init model parameters. + m_idG = 5000039; + if (m_graviton) { + m_spin = (settingsPtr->flag("ExtraDimensionsLED:GravScalar")) ? 0 : 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 0.5 * m_nGrav + 1; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:MD"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + m_cf = settingsPtr->parm("ExtraDimensionsLED:c"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + m_cutoff = settingsPtr->mode("ExtraDimensionsUnpart:CutOffMode"); + } + + // The A(dU) or S'(n) value. + double tmpAdU = 0; + if (m_graviton) { + tmpAdU = 2 * M_PI * sqrt( pow(M_PI, double(m_nGrav)) ) + / GammaReal(0.5 * m_nGrav); + if (m_spin == 0) { // Scalar graviton + tmpAdU *= sqrt( pow(2., double(m_nGrav)) ); + m_cf *= m_cf; + } + } else { + tmpAdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + } + + // Cross section related constants + // and ME dependent powers of lambda / LambdaU. + double tmpExp = m_dU - 2; + double tmpLS = pow2(m_LambdaU); + m_constantTerm = tmpAdU / (2 * 16 * pow2(M_PI) * tmpLS * pow(tmpLS,tmpExp)); + if (m_graviton) { + m_constantTerm /= tmpLS; + } else if (m_spin == 0) { + m_constantTerm *= pow2(m_lambda) / tmpLS; + } else { + m_constantTerm = 0; + infoPtr->errorMsg("Error in Sigma2gg2LEDUnparticleg::initProc: " + "Incorrect spin value (turn process off)!"); + } + +} + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDUnparticleg::sigmaKin() { + + // Set graviton mass. + mG = m3; + mGS = mG*mG; + + // Set mandelstam variables and ME expressions. + if (m_graviton) { + + double A0 = 1/sH; + if (m_spin == 0) { // Scalar graviton + double tmpTerm1 = uH + tH; + double tmpTerm2 = uH + sH; + double tmpTerm3 = tH + sH; + double T0 = pow(tmpTerm1,4) + pow(tmpTerm2,4) + pow(tmpTerm3,4) + + 12. * sH * tH * uH * mGS; + m_sigma0 = m_cf * A0 * T0 / (sH2 * tH * uH); + } else { + double xH = tH/sH; + double yH = mGS/sH; + double xHS = pow2(xH); + double yHS = pow2(yH); + double xHC = pow(xH,3); + double yHC = pow(yH,3); + double xHQ = pow(xH,4); + double yHQ = pow(yH,4); + + double T0 = 1/(xH*(yH-1-xH)); + double T1 = 1 + 2*xH + 3*xHS + 2*xHC + xHQ; + double T2 = -2*yH*(1 + xHC); + double T3 = 3*yHS*(1 + xHS); + double T4 = -2*yHC*(1 + xH); + double T5 = yHQ; + + m_sigma0 = A0 * T0 *( T1 + T2 + T3 + T4 + T5 ); + } + + } else if (m_spin == 0) { + + double A0 = 1/pow2(sH); + double sHQ = pow(sH,4); + double tHQ = pow(tH,4); + double uHQ = pow(uH,4); + + m_sigma0 = A0 * (pow(mGS,4) + sHQ + tHQ + uHQ) / (sH * tH * uH); + + } + + // Mass measure, (m^2)^(d-2). + double tmpExp = m_dU - 2; + m_sigma0 *= pow(mGS, tmpExp); + + // Constants. + m_sigma0 *= m_constantTerm; + +} + +//-------------------------------------------------------------------------- + +double Sigma2gg2LEDUnparticleg::sigmaHat() { + + // Mass spectrum weighting. + double sigma = m_sigma0 / runBW3; + + // SM couplings... + if (m_graviton) { + sigma *= 16 * M_PI * alpS * 3 / 16; + } else if (m_spin == 0) { + sigma *= 6 * M_PI * alpS; + } + + // Truncate sH region or use form factor. + // Form factor uses either pythia8 renormScale2 + // or E_jet in cms. + if (m_cutoff == 1) { + if (sH > pow2(m_LambdaU) ) { sigma *= pow(m_LambdaU,4)/pow2(sH); } + } else if ( (m_graviton && (m_spin == 2)) + && ((m_cutoff == 2) || (m_cutoff == 3)) ) { + double tmp_mu = sqrt(Q2RenSave); + if (m_cutoff == 3) tmp_mu = (sH + s4 - s3) / (2 * mH); + double tmp_formfact = tmp_mu / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + sigma *= 1 / (1 + pow(tmp_formfact, tmp_exp)); + } + + return sigma; +} + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDUnparticleg::setIdColAcol() { + + // Flavours trivial. + setId( 21, 21, m_idG, 21); + + // Colour flow topologies: random choice between two mirrors. + if (rndmPtr->flat() < 0.5) setColAcol( 1, 2, 2, 3, 0, 0, 1, 3); + else setColAcol( 1, 2, 3, 1, 0, 0, 3, 2); + +} + +//========================================================================== + +// Sigma2qg2LEDUnparticleq class. +// Cross section for q g -> U/G q (real graviton emission in +// large extra dimensions or unparticle emission). + +//-------------------------------------------------------------------------- + +void Sigma2qg2LEDUnparticleq::initProc() { + + // Init model parameters. + m_idG = 5000039; + if (m_graviton) { + m_spin = (settingsPtr->flag("ExtraDimensionsLED:GravScalar")) ? 0 : 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 0.5 * m_nGrav + 1; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:MD"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + m_gf = settingsPtr->parm("ExtraDimensionsLED:g"); + m_cf = settingsPtr->parm("ExtraDimensionsLED:c"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + m_cutoff = settingsPtr->mode("ExtraDimensionsUnpart:CutOffMode"); + } + + // The A(dU) or S'(n) value. + double tmpAdU = 0; + if (m_graviton) { + tmpAdU = 2 * M_PI * sqrt( pow(M_PI, double(m_nGrav)) ) + / GammaReal(0.5 * m_nGrav); + if (m_spin == 0) { // Scalar graviton + tmpAdU *= 2. * sqrt( pow(2., double(m_nGrav)) ); + m_cf *= 4. * m_cf / pow2(m_LambdaU); + double tmpExp = 2. * double(m_nGrav) / (double(m_nGrav) + 2.); + m_gf *= m_gf / pow(2. * M_PI, tmpExp); + } + } else { + tmpAdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + } + + // Cross section related constants + // and ME dependent powers of lambda / LambdaU. + double tmpExp = m_dU - 2; + double tmpLS = pow2(m_LambdaU); + m_constantTerm = tmpAdU / (2 * 16 * pow2(M_PI) * tmpLS * pow(tmpLS,tmpExp)); + if (m_graviton && (m_spin == 2)) { + m_constantTerm /= tmpLS; + } else if (m_spin == 1) { + m_constantTerm *= pow2(m_lambda); + } else if (m_spin == 0) { + m_constantTerm *= pow2(m_lambda); + } else { + m_constantTerm = 0; + infoPtr->errorMsg("Error in Sigma2qg2LEDUnparticleq::initProc: " + "Incorrect spin value (turn process off)!"); + } + + +} + +//-------------------------------------------------------------------------- + +void Sigma2qg2LEDUnparticleq::sigmaKin() { + + // Set graviton mass. + mG = m3; + mGS = mG*mG; + + // Set mandelstam variables and ME expressions. + if (m_graviton) { + + double A0 = 1/sH; + if (m_spin == 0) { // Scalar graviton + A0 /= sH; + double T0 = -(uH2 + pow2(mGS)) / (sH * tH); + double T1 = -(tH2 + sH2)/ uH; + m_sigma0 = A0 * (m_gf * T0 + m_cf * T1); + } else { + double xH = tH/sH; + double yH = mGS/sH; + double x2H = xH/(yH - 1 - xH); + double y2H = yH/(yH - 1 - xH); + double x2HS = pow2(x2H); + double y2HS = pow2(y2H); + double x2HC = pow(x2H,3); + double y2HC = pow(y2H,3); + + double T0 = -(yH - 1 - xH); + double T20 = 1/(x2H*(y2H-1-x2H)); + double T21 = -4*x2H*(1 + x2H)*(1 + 2*x2H + 2*x2HS); + double T22 = y2H*(1 + 6*x2H + 18*x2HS + 16*x2HC); + double T23 = -6*y2HS*x2H*(1+2*x2H); + double T24 = y2HC*(1 + 4*x2H); + + m_sigma0 = A0 * T0 * T20 * ( T21 + T22 + T23 + T24 ); + } + + } else if (m_spin == 1) { + + double A0 = 1/pow2(sH); + double tmpTerm1 = tH - mGS; + double tmpTerm2 = sH - mGS; + + m_sigma0 = A0 * (pow2(tmpTerm1) + pow2(tmpTerm2)) / (sH*tH); + + } else if (m_spin == 0) { + + double A0 = 1/pow2(sH); + + m_sigma0 = A0 * (pow2(tH) + pow2(mGS)) / (sH*uH); // Sign correction by Tom + + } + + // Mass measure, (m^2)^(d-2). + double tmpExp = m_dU - 2; + m_sigma0 *= pow(mGS, tmpExp); + + // Constants. + m_sigma0 *= m_constantTerm; + +} + +//-------------------------------------------------------------------------- + +double Sigma2qg2LEDUnparticleq::sigmaHat() { + + // Mass spactrum weighting. + double sigma = m_sigma0 /runBW3; + + // SM couplings... + if (m_graviton) { + sigma *= 16 * M_PI * alpS / 96; + } else if (m_spin == 1) { + sigma *= - 4 * M_PI * alpS / 3; + } else if (m_spin == 0) { + sigma *= - 2 * M_PI * alpS / 3; + } + + // Truncate sH region or use form factor. + // Form factor uses either pythia8 renormScale2 + // or E_jet in cms. + if (m_cutoff == 1) { + if (sH > pow2(m_LambdaU) ) { sigma *= pow(m_LambdaU,4)/pow2(sH); } + } else if ( (m_graviton && (m_spin == 2)) + && ((m_cutoff == 2) || (m_cutoff == 3)) ) { + double tmp_mu = sqrt(Q2RenSave); + if (m_cutoff == 3) tmp_mu = (sH + s4 - s3) / (2 * mH); + double tmp_formfact = tmp_mu / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + sigma *= 1 / (1 + pow(tmp_formfact, tmp_exp)); + } + + return sigma; +} + +//-------------------------------------------------------------------------- + +void Sigma2qg2LEDUnparticleq::setIdColAcol() { + + // Flavour set up for q g -> G* q. + int idq = (id2 == 21) ? id1 : id2; + setId( id1, id2, m_idG, idq); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2LEDUnparticleg class. +// Cross section for q qbar -> U/G g (real graviton emission in +// large extra dimensions or unparticle emission). + +//-------------------------------------------------------------------------- + +void Sigma2qqbar2LEDUnparticleg::initProc() { + + // Init model parameters. + m_idG = 5000039; + if (m_graviton) { + m_spin = (settingsPtr->flag("ExtraDimensionsLED:GravScalar")) ? 0 : 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 0.5 * m_nGrav + 1; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:MD"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + m_gf = settingsPtr->parm("ExtraDimensionsLED:g"); + m_cf = settingsPtr->parm("ExtraDimensionsLED:c"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + m_cutoff = settingsPtr->mode("ExtraDimensionsUnpart:CutOffMode"); + } + + // The A(dU) or S'(n) value. + double tmpAdU = 0; + if (m_graviton) { + tmpAdU = 2 * M_PI * sqrt( pow(M_PI, double(m_nGrav)) ) + / GammaReal(0.5 * m_nGrav); + if (m_spin == 0) { // Scalar graviton + tmpAdU *= 2. * sqrt( pow(2., double(m_nGrav)) ); + m_cf *= 4. * m_cf / pow2(m_LambdaU); + double tmpExp = 2. * double(m_nGrav) / (double(m_nGrav) + 2.); + m_gf *= m_gf / pow(2. * M_PI, tmpExp); + } + } else { + tmpAdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + } + + // Cross section related constants + // and ME dependent powers of lambda / LambdaU. + double tmpExp = m_dU - 2; + double tmpLS = pow2(m_LambdaU); + m_constantTerm = tmpAdU / (2 * 16 * pow2(M_PI) * tmpLS * pow(tmpLS,tmpExp)); + if (m_graviton && (m_spin == 2)) { + m_constantTerm /= tmpLS; + } else if (m_spin == 1) { + m_constantTerm *= pow2(m_lambda); + } else if (m_spin == 0) { + m_constantTerm *= pow2(m_lambda); + } else { + m_constantTerm = 0; + infoPtr->errorMsg("Error in Sigma2qqbar2LEDUnparticleg::initProc: " + "Incorrect spin value (turn process off)!"); + } + +} + +//-------------------------------------------------------------------------- + +void Sigma2qqbar2LEDUnparticleg::sigmaKin() { + + // Set graviton mass. + mG = m3; + mGS = mG*mG; + + // Set mandelstam variables and ME expressions. + if (m_graviton) { + + double A0 = 1/sH; + if (m_spin == 0) { // Scalar graviton + A0 /= sH; + double tmpTerm1 = uH + tH; + double T0 = (2. * mGS * sH + pow2(tmpTerm1)) / (uH * tH); + double T1 = (tH2 + uH2) / sH; + m_sigma0 = A0 * (m_gf * T0 + m_cf * T1); + } else { + double xH = tH/sH; + double yH = mGS/sH; + double xHS = pow2(xH); + double yHS = pow2(yH); + double xHC = pow(xH,3); + double yHC = pow(yH,3); + + double T0 = 1/(xH*(yH-1-xH)); + double T1 = -4*xH*(1 + xH)*(1 + 2*xH + 2*xHS); + double T2 = yH*(1 + 6*xH + 18*xHS + 16*xHC); + double T3 = -6*yHS*xH*(1+2*xH); + double T4 = yHC*(1 + 4*xH); + + m_sigma0 = A0 * T0 *( T1 + T2 + T3 + T4 ); + } + + } else if (m_spin == 1) { + + double A0 = 1/pow2(sH); + double tmpTerm1 = tH - mGS; + double tmpTerm2 = uH - mGS; + + m_sigma0 = A0 * (pow2(tmpTerm1) + pow2(tmpTerm2)) / (tH * uH); + + } else if (m_spin == 0) { + + double A0 = 1/pow2(sH); + + m_sigma0 = A0 * (pow2(sH) - pow2(mGS)) / (tH * uH); + + } + + // Mass measure, (m^2)^(d-2). + double tmpExp = m_dU - 2; + m_sigma0 *= pow(mGS, tmpExp); + + // Constants. + m_sigma0 *= m_constantTerm; + +} + +//-------------------------------------------------------------------------- + +double Sigma2qqbar2LEDUnparticleg::sigmaHat() { + + // Mass spactrum weighting. + double sigma = m_sigma0 /runBW3; + + // SM couplings... + if (m_graviton) { + sigma *= 16 * M_PI * alpS / 36; + } else if (m_spin == 1) { + sigma *= 4 * M_PI * 8 * alpS / 9; + } else if (m_spin == 0) { + sigma *= 4 * M_PI * 4 * alpS / 9; + } + + // Truncate sH region or use form factor. + // Form factor uses either pythia8 renormScale2 + // or E_jet in cms. + if (m_cutoff == 1) { + if (sH > pow2(m_LambdaU) ) { sigma *= pow(m_LambdaU,4)/pow2(sH); } + } else if ( (m_graviton && (m_spin == 2)) + && ((m_cutoff == 2) || (m_cutoff == 3)) ) { + double tmp_mu = sqrt(Q2RenSave); + if (m_cutoff == 3) tmp_mu = (sH + s4 - s3) / (2 * mH); + double tmp_formfact = tmp_mu / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + sigma *= 1 / (1 + pow(tmp_formfact, tmp_exp)); + } + + return sigma; +} + +//-------------------------------------------------------------------------- + +void Sigma2qqbar2LEDUnparticleg::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, m_idG, 21); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 2, 0, 0, 1, 2); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbar2LEDUnparticleZ class. +// Cross section for f fbar -> U/G Z (real LED graviton or unparticle +// emission). + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// FIXRATIO: +// Ratio between the two possible coupling constants of the spin-2 ME. +// A value different from one give rise to an IR divergence which makes +// the event generation very slow, so this values is fixed to 1 until +// investigated further. +const double Sigma2ffbar2LEDUnparticleZ::FIXRATIO = 1.; + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDUnparticleZ::initProc() { + + // Init model parameters. + m_idG = 5000039; + if (m_graviton) { + m_spin = 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 0.5 * m_nGrav + 1; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:MD"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + m_ratio = FIXRATIO; + // = settingsPtr->parm("ExtraDimensionsUnpart:ratio"); + m_cutoff = settingsPtr->mode("ExtraDimensionsUnpart:CutOffMode"); + } + + // Store Z0 mass and width for propagator. + mZ = particleDataPtr->m0(23); + widZ = particleDataPtr->mWidth(23); + mZS = mZ*mZ; + mwZS = pow2(mZ * widZ); + + // Init spin-2 parameters + if ( m_spin != 2 ){ + m_graviton = false; + m_lambdaPrime = 0; + } else if (m_graviton) { + m_lambda = 1; + m_ratio = 1; + m_lambdaPrime = m_lambda; + } else { + m_lambdaPrime = m_ratio * m_lambda; + } + + // The A(dU) or S'(n) value + double tmpAdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + + if (m_graviton) { + tmpAdU = 2 * M_PI * sqrt( pow(M_PI, double(m_nGrav)) ) + / GammaReal(0.5 * m_nGrav); + } + + // Standard 2 to 2 cross section related constants + double tmpTerm1 = 1/(2 * 16 * pow2(M_PI)); + double tmpLS = pow2(m_LambdaU); + + // Spin dependent constants from ME. + double tmpTerm2 = 0; + if ( m_spin == 0 ) { + tmpTerm2 = 2 * pow2(m_lambda); + } else if (m_spin == 1) { + tmpTerm2 = 4 * pow2(m_lambda); + } else if (m_spin == 2) { + tmpTerm2 = pow2(m_lambda)/(4 * 3 * tmpLS); + } + + // Unparticle phase space related + double tmpExp2 = m_dU - 2; + double tmpTerm3 = tmpAdU / (tmpLS * pow(tmpLS, tmpExp2)); + + // All in total + m_constantTerm = tmpTerm1 * tmpTerm2 * tmpTerm3; + +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDUnparticleZ::sigmaKin() { + + // Set graviton mass and some powers of mandelstam variables + mU = m3; + mUS = mU*mU; + + sHS = pow2(sH); + tHS = pow2(tH); + uHS = pow2(uH); + tHC = pow(tH,3); + uHC = pow(uH,3); + tHQ = pow(tH,4); + uHQ = pow(uH,4); + tHuH = tH+uH; + + // Evaluate (m**2, t, u) part of differential cross section. + // Extra 1/sHS comes from standard 2 to 2 cross section + // phase space factors. + + if ( m_spin == 0 ) { + + double A0 = 1/sHS; + double T1 = - sH/tH - sH/uH; + double T2 = - (1 - mZS/tH)*(1 - mUS/tH); + double T3 = - (1 - mZS/uH)*(1 - mUS/uH); + double T4 = 2*(1 - mUS/tH)*(1 - mUS/uH); + + m_sigma0 = A0 * ( T1 + T2 + T3 + T4); + + } else if ( m_spin == 1 ) { + + double A0 = 1/sHS; + double T1 = 0.5 * (tH/uH + uH/tH); + double T2 = pow2(mZS + mUS)/(tH * uH); + double T3 = - 0.5 * mUS * (mZS/tHS + mZS/uHS) ; + double T4 = - (mZS+mUS)*(1/tH + 1/uH); + + m_sigma0 = A0 * ( T1 + T2 + T3 + T4 ); + + } else if ( m_spin == 2 ) { + + double A0 = 1 / ( sHS * uHS * tHS * pow2(sH-mZS) ); + double F0 = 2*tHS*uHS*( 16*pow(mZS,3) + mUS*(7*tHS + 12*tH*uH + 7*uHS) + - 3*(3*tHC + 11*tHS*uH + 11*tH*uHS + 3*uHC) + + 6*pow(mZS,2)*(7*mUS - 2*tHuH) + mZS*(14*pow(mUS,2) + - 15*tHS - 44*tH*uH - 15*uHS + 2*mUS*tHuH) ); + double F2 = 2*tHS*uHS*tHuH*( -8*pow(mZS,2)*tHuH + + 4*mZS*(tHS + 3*tH*uH + uHS) + + 3*(tHC + 5*tHS*uH + 5*tH*uHS + uHC) ); + double F4 = -2*tHS*uHS*pow(tHuH,3)*(tHS + uHS - mZS*tHuH); + + double G0 = 4*tH*uH*( 6*pow(mZS,3)*(mUS - tH - uH)*tHuH + + pow(mZS,2)*( 9*tHC + 7*tHS*uH + 7*tH*uHS + 9*uHC + + 15*pow2(mUS)*tHuH - 2*mUS*(12*tHS + 19*tH*uH + 12*uHS) ) + + tH*uH*( 6*pow(mUS,3) - 9*pow(mUS,2)*tHuH - mUS*(tHS + + 12*tH*uH + uHS) + 6*(tHC + 6*tHS*uH + 6*tH*uHS + uHC) ) + + mZS*(-3*tHQ + 25*tHC*uH + 58*tHS*uHS + 25*tH*uHC + - 3*uHQ + 6*pow(mUS,3)*tHuH + - pow(mUS,2)*(15*tHS + 2*tH*uH + 15*uHS) + 2*mUS*(6*tHC + - 11*tHS*uH - 11*tH*uHS + 6*uHC)) ); + double G2 = -4*tHS*uHS*tHuH*( -10*pow2(mZS)*tHuH + 2*mZS*(3*tHS + + 7*tH*uH + 3*uHS) + 3*(tHC + 5*tHS*uH + 5*tH*uHS + uHC) ); + double G4 = -2*F4; + + double H0 = 24*pow(mZS,3)*tH*uH*pow2(-mUS + tHuH) + - 6*pow(mZS,2)*tH*uH*( -9*pow(mUS,3) + 24*pow(mUS,2)*tHuH + - mUS*(21*tHS + 38*tH*uH + 21*uHS) + + 2*(3*tHC + 5*tHS*uH + 5*tH*uHS + 3*uHC) ) + - mZS*( 3*pow(mUS,4)*(tHS - 12*tH*uH + uHS) + - 2*tH*uH*pow2(tHuH)*(6*tHS - 29*tH*uH + 6*uHS) + - 6*pow(mUS,3)*(tHC - 16*tHS*uH - 16*tH*uHS + uHC) + + 54*mUS*tH*uH*(tHC + tHS*uH + tH*uHS + uHC) + + pow2(mUS)*(3*tHQ - 102*tHC*uH - 166*tHS*uHS + - 102*tH*uHC + 3*uHQ) ) + + tH*uH*( 6*pow(mUS,5) - 18*pow(mUS,4)*tHuH + - 12*pow(mUS,2)*pow(tHuH,3) + + 3*pow(mUS,3)*(7*tHS + 12*tH*uH + 7*uHS) + - 18*tH*uH*(tHC + 5*tHS*uH + 5*tH*uHS + uHC) + + mUS*(3*tHQ + 32*tHC*uH + 78*tHS*uHS + 32*tH*uHC + 3*uHQ) ); + double H2 = 2*tHS*uHS*pow2(tHuH)*( -12*pow2(mZS) + 8*mZS*tHuH + + 3*(tHS + 4*tH*uH + uHS) ); + double H4 = F4; + + m_sigma0 = A0*( F0 + 1/mUS*F2 + 1/pow2(mUS)*F4 + + m_ratio*(G0 + 1/mUS*G2 + 1/pow2(mUS)*G4) + + pow2(m_ratio)*(H0 + 1/mUS*H2 + 1/pow2(mUS)*H4) ); + + } else { + + m_sigma0 = 0; + + } + +} + +//-------------------------------------------------------------------------- + +double Sigma2ffbar2LEDUnparticleZ::sigmaHat() { + + // Electroweak couplings. + int idAbs = abs(id1); + // Note: 1/2 * (g_L^2 + g_R^2) = (g_v^2 + g_a^2) + double facEWS = 4 * M_PI * alpEM + / (coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()) + * ( 0.25 * 0.25 * coupSMPtr->vf2af2(idAbs) ); + + // Mass Spectrum, (m^2)^(d-2) + double tmpExp = m_dU - 2; + double facSpect = pow(mUS, tmpExp); + + // Total cross section + double sigma = m_constantTerm * facEWS * facSpect * m_sigma0; + + // If f fbar are quarks (1/N_c) + if (idAbs < 9) sigma /= 3.; + + // Related to mass spactrum weighting. + sigma /= runBW3; + + // Truncate sH region or use form factor. + // Form factor uses either pythia8 renormScale2 + // or E_jet in cms. + if (m_cutoff == 1) { + if (sH > pow2(m_LambdaU) ) { sigma *= pow(m_LambdaU,4)/pow2(sH); } + } else if (m_graviton && ((m_cutoff == 2) || (m_cutoff == 3))) { + double tmp_mu = sqrt(Q2RenSave); + if (m_cutoff == 3) tmp_mu = (sH + s4 - s3) / (2 * mH); + double tmp_formfact = tmp_mu / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + sigma *= 1 / (1 + pow(tmp_formfact, tmp_exp)); + } + + return sigma; + +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDUnparticleZ::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, m_idG, 23); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbar2LEDUnparticlegamma class. +// Cross section for f fbar -> U/G gamma (real LED graviton or unparticle +// emission). + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// FIXRATIO: +// Ratio between the two possible coupling constants of the spin-2 ME. +// A value different from one give rise to an IR divergence which makes +// the event generation very slow, so this values is fixed to 1 until +// investigated further. +const double Sigma2ffbar2LEDUnparticlegamma::FIXRATIO = 1.; + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDUnparticlegamma::initProc() { + + // WARNING: Keep in mind that this class uses the photon limit + // of the Z+G/U ME code. This might give rise to some + // confusing things, e.g. mZ = particleDataPtr->m0(22); + + // Init model parameters. + m_idG = 5000039; + if (m_graviton) { + m_spin = 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 0.5 * m_nGrav + 1; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:MD"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + m_ratio = FIXRATIO; + // = settingsPtr->parm("ExtraDimensionsUnpart:ratio"); + m_cutoff = settingsPtr->mode("ExtraDimensionsUnpart:CutOffMode"); + } + + // Store Z0 mass. + mZ = particleDataPtr->m0(22); + mZS = mZ*mZ; + + // Init spin-2 parameters + if ( m_spin != 2 ){ + m_graviton = false; + m_lambdaPrime = 0; + } else if (m_graviton) { + m_lambda = 1; + m_ratio = 1; + m_lambdaPrime = m_lambda; + } else { + m_lambdaPrime = m_ratio * m_lambda; + } + + // The A(dU) or S'(n) value + double tmpAdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + + if (m_graviton) { + tmpAdU = 2 * M_PI * sqrt( pow(M_PI, double(m_nGrav)) ) + / GammaReal(0.5 * m_nGrav); + } + + // Standard 2 to 2 cross section related constants + double tmpTerm1 = 1/(2 * 16 * pow2(M_PI)); + double tmpLS = pow2(m_LambdaU); + + // Spin dependent constants from ME. + double tmpTerm2 = 0; + if ( m_spin == 0 ) { + tmpTerm2 = 2 * pow2(m_lambda); + } else if (m_spin == 1) { + tmpTerm2 = 4 * pow2(m_lambda); + } else if (m_spin == 2) { + tmpTerm2 = pow2(m_lambda)/(4 * 3 * tmpLS); + } + + // Unparticle phase space related + double tmpExp2 = m_dU - 2; + double tmpTerm3 = tmpAdU / (tmpLS * pow(tmpLS, tmpExp2)); + + // All in total + m_constantTerm = tmpTerm1 * tmpTerm2 * tmpTerm3; + +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDUnparticlegamma::sigmaKin() { + + // Set graviton mass and some powers of mandelstam variables + mU = m3; + mUS = mU*mU; + + sHS = pow2(sH); + tHS = pow2(tH); + uHS = pow2(uH); + tHC = pow(tH,3); + uHC = pow(uH,3); + tHQ = pow(tH,4); + uHQ = pow(uH,4); + tHuH = tH+uH; + + // Evaluate (m**2, t, u) part of differential cross section. + // Extra 1/sHS comes from standard 2 to 2 cross section + // phase space factors. + + if ( m_spin == 0 ) { + + double A0 = 1/sHS; + double T1 = - sH/tH - sH/uH; + double T2 = - (1 - mZS/tH)*(1 - mUS/tH); + double T3 = - (1 - mZS/uH)*(1 - mUS/uH); + double T4 = 2*(1 - mUS/tH)*(1 - mUS/uH); + + m_sigma0 = A0 * ( T1 + T2 + T3 + T4); + + } else if ( m_spin == 1 ) { + + double A0 = 1/sHS; + double T1 = 0.5 * (tH/uH + uH/tH); + double T2 = pow2(mZS + mUS)/(tH * uH); + double T3 = - 0.5 * mUS * (mZS/tHS + mZS/uHS) ; + double T4 = - (mZS+mUS)*(1/tH + 1/uH); + + m_sigma0 = A0 * ( T1 + T2 + T3 + T4 ); + + } else if ( m_spin == 2 ) { + + double A0 = 1 / ( sHS * uHS * tHS * pow2(sH-mZS) ); + double F0 = 2*tHS*uHS*( 16*pow(mZS,3) + mUS*(7*tHS + 12*tH*uH + 7*uHS) + - 3*(3*tHC + 11*tHS*uH + 11*tH*uHS + 3*uHC) + + 6*pow(mZS,2)*(7*mUS - 2*tHuH) + mZS*(14*pow(mUS,2) + - 15*tHS - 44*tH*uH - 15*uHS + 2*mUS*tHuH) ); + double F2 = 2*tHS*uHS*tHuH*( -8*pow(mZS,2)*tHuH + + 4*mZS*(tHS + 3*tH*uH + uHS) + + 3*(tHC + 5*tHS*uH + 5*tH*uHS + uHC) ); + double F4 = -2*tHS*uHS*pow(tHuH,3)*(tHS + uHS - mZS*tHuH); + + double G0 = 4*tH*uH*( 6*pow(mZS,3)*(mUS - tH - uH)*tHuH + + pow(mZS,2)*( 9*tHC + 7*tHS*uH + 7*tH*uHS + 9*uHC + + 15*pow2(mUS)*tHuH - 2*mUS*(12*tHS + 19*tH*uH + 12*uHS) ) + + tH*uH*( 6*pow(mUS,3) - 9*pow(mUS,2)*tHuH + - mUS*(tHS + 12*tH*uH + uHS) + + 6*(tHC + 6*tHS*uH + 6*tH*uHS + uHC) ) + + mZS*(-3*tHQ + 25*tHC*uH + 58*tHS*uHS + 25*tH*uHC + - 3*uHQ + 6*pow(mUS,3)*tHuH + - pow(mUS,2)*(15*tHS + 2*tH*uH + 15*uHS) + + 2*mUS*(6*tHC - 11*tHS*uH - 11*tH*uHS + 6*uHC)) ); + double G2 = -4*tHS*uHS*tHuH*( -10*pow2(mZS)*tHuH + + 2*mZS*(3*tHS + 7*tH*uH + 3*uHS) + + 3*(tHC + 5*tHS*uH + 5*tH*uHS + uHC) ); + double G4 = -2*F4; + + double H0 = 24*pow(mZS,3)*tH*uH*pow2(-mUS + tHuH) + - 6*pow(mZS,2)*tH*uH*( -9*pow(mUS,3) + 24*pow(mUS,2)*tHuH + - mUS*(21*tHS + 38*tH*uH + 21*uHS) + + 2*(3*tHC + 5*tHS*uH + 5*tH*uHS + 3*uHC) ) + - mZS*( 3*pow(mUS,4)*(tHS - 12*tH*uH + uHS) + - 2*tH*uH*pow2(tHuH)*(6*tHS - 29*tH*uH + 6*uHS) + - 6*pow(mUS,3)*(tHC - 16*tHS*uH - 16*tH*uHS + uHC) + + 54*mUS*tH*uH*(tHC + tHS*uH + tH*uHS + uHC) + + pow2(mUS)*(3*tHQ - 102*tHC*uH - 166*tHS*uHS + - 102*tH*uHC + 3*uHQ) ) + + tH*uH*( 6*pow(mUS,5) - 18*pow(mUS,4)*tHuH + - 12*pow(mUS,2)*pow(tHuH,3) + + 3*pow(mUS,3)*(7*tHS + 12*tH*uH + 7*uHS) + - 18*tH*uH*(tHC + 5*tHS*uH + 5*tH*uHS + uHC) + + mUS*(3*tHQ + 32*tHC*uH + 78*tHS*uHS + 32*tH*uHC + 3*uHQ) ); + double H2 = 2*tHS*uHS*pow2(tHuH)*( -12*pow2(mZS) + 8*mZS*tHuH + + 3*(tHS + 4*tH*uH + uHS) ); + double H4 = F4; + + m_sigma0 = A0*( F0 + 1/mUS*F2 + 1/pow2(mUS)*F4 + + m_ratio*(G0 + 1/mUS*G2 + 1/pow2(mUS)*G4) + + pow2(m_ratio)*(H0 + 1/mUS*H2 + 1/pow2(mUS)*H4) ); + + } else { + + m_sigma0 = 0; + + } + +} + +//-------------------------------------------------------------------------- + +double Sigma2ffbar2LEDUnparticlegamma::sigmaHat() { + + // Electroweak couplings.. + int idAbs = abs(id1); + double facEWS = 4 * M_PI * alpEM * coupSMPtr->ef2(idAbs); + + // Mass Spectrum, (m^2)^(d-2) + double tmpExp = m_dU - 2; + double facSpect = pow(mUS, tmpExp); + + // Total cross section + double sigma = m_constantTerm * facEWS * facSpect * m_sigma0; + + // If f fbar are quarks + if (idAbs < 9) sigma /= 3.; + + // Related to mass spactrum weighting. + sigma /= runBW3; + + // Truncate sH region or use form factor. + // Form factor uses either pythia8 renormScale2 + // or E_jet in cms. + if (m_cutoff == 1) { + if (sH > pow2(m_LambdaU) ) { sigma *= pow(m_LambdaU,4)/pow2(sH); } + } else if (m_graviton && ((m_cutoff == 2) || (m_cutoff == 3))) { + double tmp_mu = sqrt(Q2RenSave); + if (m_cutoff == 3) tmp_mu = (sH + s4 - s3) / (2 * mH); + double tmp_formfact = tmp_mu / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + sigma *= 1 / (1 + pow(tmp_formfact, tmp_exp)); + } + + return sigma; + +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDUnparticlegamma::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, m_idG, 22); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2ffbar2LEDgammagamma class. +// Cross section for f fbar -> (LED G*/U*) -> gamma gamma +// (virtual graviton/unparticle exchange). + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDgammagamma::initProc() { + + // Init model parameters. + if (m_graviton) { + m_spin = 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 2; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:LambdaT"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + } + + // Model dependent constants. + if (m_graviton) { + m_lambda2chi = 4*M_PI; + } else { + double tmp_AdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + double tmp_dUpi = m_dU * M_PI; + m_lambda2chi = pow2(m_lambda) * tmp_AdU / (2 * sin(tmp_dUpi)); + } + + // Model parameter check (if not applicable, sigma = 0). + // Note: SM contribution still generated. + if ( !(m_spin==0 || m_spin==2) ) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2ffbar2LEDgammagamma::initProc: " + "Incorrect spin value (turn process off)!"); + } else if ( !m_graviton && (m_dU >= 2)) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2ffbar2LEDgammagamma::initProc: " + "This process requires dU < 2 (turn process off)!"); + } + +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDgammagamma::sigmaKin() { + + // Mandelstam variables. + double sHS = pow2(sH); + double sHQ = pow(sH, 4); + double tHS = pow2(tH); + double uHS = pow2(uH); + + // Form factor. + double tmp_effLambdaU = m_LambdaU; + if (m_graviton && ((m_cutoff == 2) || (m_cutoff == 3))) { + double tmp_ffterm = sqrt(Q2RenSave) / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + double tmp_formfact = 1 + pow(tmp_ffterm, tmp_exp); + tmp_effLambdaU *= pow(tmp_formfact,0.25); + } + + // ME from spin-0 and spin-2 unparticles + // including extra 1/sHS from 2-to-2 phase space. + if (m_spin == 0) { + double tmp_sLambda2 = sH / pow2(tmp_effLambdaU); + double tmp_exp = 2 * m_dU - 1; + m_term1 = pow(tmp_sLambda2,tmp_exp); + m_term1 /= sHS; + } else { + m_term1 = (uH / tH + tH / uH); + m_term1 /= sHS; + double tmp_sLambda2 = sH / pow2(tmp_effLambdaU); + double tmp_exp = m_dU; + m_term2 = pow(tmp_sLambda2,tmp_exp) * (uHS + tHS) / sHS; + m_term2 /= sHS; + tmp_exp = 2 * m_dU; + m_term3 = pow(tmp_sLambda2,tmp_exp) * tH * uH * (uHS + tHS) / sHQ; + m_term3 /= sHS; + } + +} + +//-------------------------------------------------------------------------- + +double Sigma2ffbar2LEDgammagamma::sigmaHat() { + + // Incoming fermion flavor. + int idAbs = abs(id1); + + // Couplings and constants. + // Note: ME already contain 1/2 for identical + // particles in the final state. + double sigma = 0; + if (m_spin == 0) { + sigma = pow2(m_lambda2chi) * m_term1 / 8; + } else { + double tmp_e2Q2 = 4 * M_PI * alpEM * coupSMPtr->ef2(idAbs); + double tmp_dUpi = m_dU * M_PI; + sigma = pow2(tmp_e2Q2) * m_term1 + - tmp_e2Q2 * m_lambda2chi * cos(tmp_dUpi) * m_term2 + + pow2(m_lambda2chi) * m_term3 / 4; + } + + // dsigma/dt, 2-to-2 phase space factors. + sigma /= 16 * M_PI; + + // If f fbar are quarks. + if (idAbs < 9) sigma /= 3.; + + return sigma; +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDgammagamma::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, 22, 22); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2LEDgammagamma class. +// Cross section for g g -> (LED G*/U*) -> gamma gamma +// (virtual graviton/unparticle exchange). + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDgammagamma::initProc() { + + // Init model parameters. + if (m_graviton) { + m_spin = 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 2; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:LambdaT"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + } + + // Model dependent constants. + if (m_graviton) { + m_lambda2chi = 4 * M_PI; + + } else { + double tmp_AdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + double tmp_dUpi = m_dU * M_PI; + m_lambda2chi = pow2(m_lambda) * tmp_AdU / (2 * sin(tmp_dUpi)); + } + + // Model parameter check (if not applicable, sigma = 0). + if ( !(m_spin==0 || m_spin==2) ) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2gg2LEDgammagamma::initProc: " + "Incorrect spin value (turn process off)!"); + } else if ( !m_graviton && (m_dU >= 2)) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2gg2LEDgammagamma::initProc: " + "This process requires dU < 2 (turn process off)!"); + } + +} + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDgammagamma::sigmaKin() { + + // Mandelstam variables. + double sHS = pow2(sH); + double sHQ = pow(sH, 4); + double tHQ = pow(tH, 4); + double uHQ = pow(uH, 4); + + // Form factor. + double tmp_effLambdaU = m_LambdaU; + if (m_graviton && ((m_cutoff == 2) || (m_cutoff == 3))) { + double tmp_ffterm = sqrt(Q2RenSave) / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + double tmp_formfact = 1 + pow(tmp_ffterm, tmp_exp); + tmp_effLambdaU *= pow(tmp_formfact,0.25); + } + + // ME from spin-0 and spin-2 unparticles. + if (m_spin == 0) { + double tmp_sLambda2 = sH / pow2(tmp_effLambdaU); + double tmp_exp = 2 * m_dU; + m_sigma0 = pow(tmp_sLambda2,tmp_exp); + } else { + double tmp_sLambda2 = sH / pow2(tmp_effLambdaU); + double tmp_exp = 2 * m_dU; + m_sigma0 = pow(tmp_sLambda2,tmp_exp) * (uHQ + tHQ) / sHQ; + } + + // extra 1/sHS from 2-to-2 phase space. + m_sigma0 /= sHS; + +} + +//-------------------------------------------------------------------------- + +double Sigma2gg2LEDgammagamma::sigmaHat() { + + // Couplings and constants. + // Note: ME already contain 1/2 for identical + // particles in the final state. + double sigma = m_sigma0; + if (m_spin == 0) { + sigma *= pow2(m_lambda2chi) / 256; + } else { + sigma *= pow2(m_lambda2chi) / 32; + } + + // dsigma/dt, 2-to-2 phase space factors. + sigma /= 16 * M_PI; + + return sigma; +} + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDgammagamma::setIdColAcol() { + + // Flavours trivial. + setId( 21, 21, 22, 22); + + // Colour flow topologies. + setColAcol( 1, 2, 2, 1, 0, 0, 0, 0); + +} + +//========================================================================== + +// Sigma2ffbar2LEDllbar class. +// Cross section for f fbar -> (LED G*/U*) -> l lbar +// (virtual graviton/unparticle exchange). +// Does not include t-channel contributions relevant for e^+e^- to e^+e^- + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDllbar::initProc() { + + // Init model parameters. + if (m_graviton) { + m_spin = 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 2; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:LambdaT"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + m_nxx = settingsPtr->mode("ExtraDimensionsUnpart:gXX"); + m_nxy = settingsPtr->mode("ExtraDimensionsUnpart:gXY"); + } + + m_mZ = particleDataPtr->m0(23); + m_mZS = m_mZ * m_mZ; + m_GZ = particleDataPtr->mWidth(23); + m_GZS = m_GZ * m_GZ; + + // Model dependent constants. + if (m_graviton) { + m_lambda2chi = 4*M_PI; + } else { + double tmp_AdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + double tmp_dUpi = m_dU * M_PI; + m_lambda2chi = pow2(m_lambda) * tmp_AdU / (2 * sin(tmp_dUpi)); + } + + // Model parameter check (if not applicable, sigma = 0). + // Note: SM contribution still generated. + if ( !(m_spin==1 || m_spin==2) ) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2ffbar2LEDllbar::initProc: " + "Incorrect spin value (turn process off)!"); + } else if ( !m_graviton && (m_dU >= 2)) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2ffbar2LEDllbar::initProc: " + "This process requires dU < 2 (turn process off)!"); + } + +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDllbar::sigmaKin() { + + // Mandelstam variables. + double tHS = pow2(tH); + double uHS = pow2(uH); + double tHC = pow(tH,3); + double uHC = pow(uH,3); + double tHQ = pow(tH,4); + double uHQ = pow(uH,4); + + // Form factor. + double tmp_effLambdaU = m_LambdaU; + if (m_graviton && ((m_cutoff == 2) || (m_cutoff == 3))) { + double tmp_ffterm = sqrt(Q2RenSave) / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + double tmp_formfact = 1 + pow(tmp_ffterm, tmp_exp); + tmp_effLambdaU *= pow(tmp_formfact,0.25); + } + + // ME from spin-1 and spin-2 unparticles + m_denomPropZ = pow2(sH - m_mZS) + m_mZS * m_GZS; + m_rePropZ = (sH - m_mZS) / m_denomPropZ; + m_imPropZ = -m_mZ * m_GZ / m_denomPropZ; + m_rePropGamma = 1 / sH; + if (m_spin == 1) { + double tmp_sLambda2 = sH / pow2(tmp_effLambdaU); + double tmp_exp = m_dU - 2; + m_absMeU = m_lambda2chi * pow(tmp_sLambda2,tmp_exp) + / pow2(tmp_effLambdaU); + } else { + double tmp_sLambda2 = sH / pow2(tmp_effLambdaU); + double tmp_exp = m_dU - 2; + double tmp_A = -m_lambda2chi * pow(tmp_sLambda2,tmp_exp) + / (8 * pow(tmp_effLambdaU,4)); + m_absAS = pow2(tmp_A); + m_reA = tmp_A * cos(M_PI * m_dU); + m_reABW = tmp_A * ((sH - m_mZS) * cos(M_PI * m_dU) + m_mZ * m_GZ + * sin(M_PI * m_dU)) / m_denomPropZ; + m_poly1 = tHQ + uHQ - 6*tHC*uH - 6*tH*uHC + 18*tHS*uHS; + double tmp_diffUT = uH - tH; + m_poly2 = pow(tmp_diffUT,3); + m_poly3 = tHC - 3*tHS*uH - 3*tH*uHS + uHC; + } + +} + +//-------------------------------------------------------------------------- + +double Sigma2ffbar2LEDllbar::sigmaHat() { + + // Incoming fermion flavor. + int idAbs = abs(id1); + + // Couplings and constants. + // Qq = coupSMPtr->ef(idAbs), quark, i.e. id > 0. + // Ql = coupSMPtr->ef(11), electron. + double tmp_e2QfQl = 4 * M_PI * alpEM * coupSMPtr->ef(idAbs) + * coupSMPtr->ef(11); + double tmp_gvq = 0.25 * coupSMPtr->vf(idAbs); + double tmp_gaq = 0.25 * coupSMPtr->af(idAbs); + double tmp_gLq = tmp_gvq + tmp_gaq; + double tmp_gRq = tmp_gvq - tmp_gaq; + double tmp_gvl = 0.25 * coupSMPtr->vf(11); + double tmp_gal = 0.25 * coupSMPtr->af(11); + double tmp_gLl = tmp_gvl + tmp_gal; + double tmp_gRl = tmp_gvl - tmp_gal; + double tmp_e2s2c2 = 4 * M_PI * alpEM + / (coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()); + + // LL, RR, LR, RL couplings. + vector tmp_coupZ; + tmp_coupZ.push_back(tmp_e2s2c2 * tmp_gLq * tmp_gLl); + tmp_coupZ.push_back(tmp_e2s2c2 * tmp_gRq * tmp_gRl); + tmp_coupZ.push_back(tmp_e2s2c2 * tmp_gRq * tmp_gLl); + tmp_coupZ.push_back(tmp_e2s2c2 * tmp_gLq * tmp_gRl); + vector tmp_coupU; + if (m_nxx == 1) { + tmp_coupU.push_back(-1); // LL + tmp_coupU.push_back(-1); // RR + } else if (m_nxx == 2) { + tmp_coupU.push_back(0); // LL + tmp_coupU.push_back(0); // RR + } else { + tmp_coupU.push_back(1); // LL + tmp_coupU.push_back(1); // RR + } + if (m_nxy == 1) { + tmp_coupU.push_back(-1); // RL + tmp_coupU.push_back(-1); // LR + } else if (m_nxy == 2) { + tmp_coupU.push_back(0); // RL + tmp_coupU.push_back(0); // LR + } else { + tmp_coupU.push_back(1); // RL + tmp_coupU.push_back(1); // LR + } + + // Matrix elements + double tmp_MES = 0; + if (m_spin == 1) { + + for (unsigned int i = 0; illbar) = 3 * sigma(ffbar->eebar) + sigma *= 3.; + + return sigma; +} + +//-------------------------------------------------------------------------- + +void Sigma2ffbar2LEDllbar::setIdColAcol() { + + double tmp_rand = rndmPtr->flat(); + // Flavours trivial. + if (tmp_rand < 0.33333333) { setId( id1, id2, 11, -11); } + else if (tmp_rand < 0.66666667) { setId( id1, id2, 13, -13); } + else { setId( id1, id2, 15, -15); } + + // tH defined between f and f': must swap tHat <-> uHat if id1 is fbar. + swapTU = (id2 > 0); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2LEDllbar class. +// Cross section for g g -> (LED G*/U*) -> l lbar +// (virtual graviton/unparticle exchange). + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDllbar::initProc() { + + // Init model parameters. + if (m_graviton) { + m_spin = 2; + m_nGrav = settingsPtr->mode("ExtraDimensionsLED:n"); + m_dU = 2; + m_LambdaU = settingsPtr->parm("ExtraDimensionsLED:LambdaT"); + m_lambda = 1; + m_cutoff = settingsPtr->mode("ExtraDimensionsLED:CutOffMode"); + m_tff = settingsPtr->parm("ExtraDimensionsLED:t"); + } else { + m_spin = settingsPtr->mode("ExtraDimensionsUnpart:spinU"); + m_dU = settingsPtr->parm("ExtraDimensionsUnpart:dU"); + m_LambdaU = settingsPtr->parm("ExtraDimensionsUnpart:LambdaU"); + m_lambda = settingsPtr->parm("ExtraDimensionsUnpart:lambda"); + } + + // Model dependent constants. + if (m_graviton) { + m_lambda2chi = 4 * M_PI; + + } else { + double tmp_AdU = 16 * pow2(M_PI) * sqrt(M_PI) / pow(2. * M_PI, 2. * m_dU) + * GammaReal(m_dU + 0.5) / (GammaReal(m_dU - 1.) * GammaReal(2. * m_dU)); + double tmp_dUpi = m_dU * M_PI; + m_lambda2chi = pow2(m_lambda) * tmp_AdU / (2 * sin(tmp_dUpi)); + } + + // Model parameter check (if not applicable, sigma = 0). + if ( !(m_spin==2) ) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2gg2LEDllbar::initProc: " + "Incorrect spin value (turn process off)!"); + } else if ( !m_graviton && (m_dU >= 2)) { + m_lambda2chi = 0; + infoPtr->errorMsg("Error in Sigma2gg2LEDllbar::initProc: " + "This process requires dU < 2 (turn process off)!"); + } + +} + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDllbar::sigmaKin() { + + // Form factor. + double tmp_effLambdaU = m_LambdaU; + if (m_graviton && ((m_cutoff == 2) || (m_cutoff == 3))) { + double tmp_ffterm = sqrt(Q2RenSave) / (m_tff * m_LambdaU); + double tmp_exp = double(m_nGrav) + 2; + double tmp_formfact = 1 + pow(tmp_ffterm, tmp_exp); + tmp_effLambdaU *= pow(tmp_formfact,0.25); + } + + // ME from spin-2 unparticle. + double tmp_sLambda2 = sH / pow2(tmp_effLambdaU); + double tmp_exp = m_dU - 2; + double tmp_A = -m_lambda2chi * pow(tmp_sLambda2,tmp_exp) + / (8 * pow(tmp_effLambdaU,4)); + m_sigma0 = 4 * pow2(tmp_A) * uH * tH * (pow2(uH) + pow2(tH)); + + // extra 1/sHS from 2-to-2 phase space. + m_sigma0 /= 16 * M_PI * pow2(sH); + + // sigma(ffbar->llbar) = 3 * sigma(ffbar->eebar) + m_sigma0 *= 3.; + +} + +//-------------------------------------------------------------------------- + +void Sigma2gg2LEDllbar::setIdColAcol() { + + double tmp_rand = rndmPtr->flat(); + // Flavours trivial. + if (tmp_rand < 0.33333333) { setId( 21, 21, 11, -11); } + else if (tmp_rand < 0.66666667) { setId( 21, 21, 13, -13); } + else { setId( 21, 21, 15, -15); } + + // Colour flow topologies. + setColAcol( 1, 2, 2, 1, 0, 0, 0, 0); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaGeneric.cxx b/PYTHIA8/pythia8140/src/SigmaGeneric.cxx new file mode 100644 index 00000000000..855f811bb92 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaGeneric.cxx @@ -0,0 +1,333 @@ +// SigmaGeneric.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Johan Bijnens, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for various generic +// production processes, to be used as building blocks for some BSM processes. +// Currently represented by QCD pair production of colour triplet objects, +// with spin either 0, 1/2 or 1. + +// Cross sections are only provided for fixed m3 = m4, so do some gymnastics: +// i) s34Avg picked so that beta34 same when s3, s4 -> s34Avg. +// ii) tHQ = tH - mQ^2 = -0.5 sH (1 - beta34 cos(thetaH)) for m3 = m4 = mQ, +// but tH - uH = sH beta34 cos(thetaH) also for m3 != m4, so use +// tH, uH selected for m3 != m4 to derive tHQ, uHQ valid for m3 = m4. + +#include "SigmaGeneric.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma2gg2qGqGbar class. +// Cross section for g g -> qG qGbar (generic quark of spin 0, 1/2 or 1). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2qGqGbar::initProc() { + + // Number of colours. Anomalous coupling kappa - 1 used for vector state. + nCHV = settingsPtr->mode("HiddenValley:Ngauge"); + kappam1 = settingsPtr->parm("HiddenValley:kappa") - 1.; + hasKappa = (abs(kappam1) > 1e-8); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2gg2qGqGbar::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + double delta = 0.25 * pow2(s3 - s4) / sH; + double s34Avg = 0.5 * (s3 + s4) - delta; + double tHavg = tH - delta; + double uHavg = uH - delta; + double tHQ = -0.5 * (sH - tH + uH); + double uHQ = -0.5 * (sH + tH - uH); + double tHQ2 = tHQ * tHQ; + double uHQ2 = uHQ * uHQ; + + // Evaluate cross section for spin 0 colour triplet. + if (spinSave == 0) { + sigSum = 0.5 * ( 7. / 48. + 3. * pow2(uHavg - tHavg) / (16. * sH2) ) + * ( 1. + 2. * s34Avg * tHavg / pow2(tHavg - s34Avg) + + 2. * s34Avg * uHavg / pow2(uHavg - s34Avg) + + 4. * pow2(s34Avg) / ((tHavg - s34Avg) * (uHavg - s34Avg)) ); + + // Equal probability for two possible colour flows. + sigTS = 0.5 * sigSum; + sigUS = sigTS; + } + + // Evaluate cross section for spin 1/2 colour triplet. + else if (spinSave == 1) { + double tumHQ = tHQ * uHQ - s34Avg * sH; + sigTS = ( uHQ / tHQ - 2.25 * uHQ2 / sH2 + 4.5 * s34Avg * tumHQ + / ( sH * tHQ2) + 0.5 * s34Avg * (tHQ + s34Avg) / tHQ2 + - s34Avg*s34Avg / (sH * tHQ) ) / 6.; + sigUS = ( tHQ / uHQ - 2.25 * tHQ2 / sH2 + 4.5 * s34Avg * tumHQ + / ( sH * uHQ2) + 0.5 * s34Avg * (uHQ + s34Avg) / uHQ2 + - s34Avg*s34Avg / (sH * uHQ) ) / 6.; + sigSum = sigTS + sigUS; + } + + // Evaluate cross section for spin 1 colour triplet. + else { + double tmu = tHavg - uHavg; + double s34Pos = s34Avg / sH; + double s34Pos2 = s34Pos * s34Pos; + double s34Neg = sH / s34Avg; + double s34Neg2 = s34Neg * s34Neg; + sigSum = pow2(tmu) * sH2 * (241./1536. - 1./32. * s34Pos + + 9./16. * s34Pos2) + + pow4(tmu) * (37./512. + 9./64. * s34Pos) + + pow6(tmu) * (9./512. / sH2) + + sH2 * sH2 * (133./1536. - 7./64. * s34Pos + 7./16. * s34Pos2); + + // Anomalous coupling. + if (hasKappa) + sigSum += pow2(tmu) * sH2 * (kappam1 * (143./384. - 7./3072 * s34Neg) + + pow2(kappam1) * (- 1./768. * s34Neg + 185./768.) + + pow3(kappam1) * (- 7./3072. * s34Neg2 + - 25./3072. * s34Neg + 67./1536.) + + pow4(kappam1) * (- 37./49152. * s34Neg2 + - 25./6144. * s34Neg + 5./1536.) ) + + pow4(tmu) * (kappam1 * 3./32. + + pow2(kappam1) * (7./6144. * s34Neg2 - 7./768. * s34Neg + 3./128.) + + pow3(kappam1) * (7./6144. * s34Neg2 - 7./1536. * s34Neg) + + pow4(kappam1) * (- 1./49152. * s34Neg2 + 5./6144. * s34Neg) ) + + pow6(tmu) * pow4(kappam1) * 13./49152. / pow2(s34Avg) + + sH2 * sH2 * ( kappam1 * 77./384. + + pow2(kappam1) * (7./6144. * s34Neg2 + 1./96.* s34Neg + 39./256.) + + pow3(kappam1) * (7./6144. * s34Neg2 + 13./1024. * s34Neg + 61./1536.) + + pow4(kappam1) * (25./49152. * s34Neg2 + 5./1536. * s34Neg + 1./512.) + ); + + // Equal probability for two possible colour flows. + sigSum /= pow2( (uHavg-s34Avg) * (tHavg-s34Avg) ); + sigTS = 0.5 * sigSum; + sigUS = sigTS; + } + + // Final answer, with common factors. + sigma = (M_PI / sH2) * pow2(alpS) * sigSum * nCHV * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2qGqGbar::setIdColAcol() { + + // Flavours trivial. + setId( 21, 21, idNew, -idNew); + + // Two colour flow topologies. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 2, 2, 3, 1, 0, 0, 3); + else setColAcol( 1, 2, 3, 1, 3, 0, 0, 2); + +} + +//========================================================================== + +// Sigma2qqbar2qGqGbar class. +// Cross section for q qbar -> qG qGbar (generic quark of spin 0, 1/2 or 1). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2qGqGbar::initProc() { + + // Number of colours. Coupling kappa used for vector state. + nCHV = settingsPtr->mode("HiddenValley:Ngauge"); + kappa = settingsPtr->parm("HiddenValley:kappa"); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2qGqGbar::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + double delta = 0.25 * pow2(s3 - s4) / sH; + double s34Avg = 0.5 * (s3 + s4) - delta; + double tHavg = tH - delta; + double uHavg = uH - delta; + double tHQ = -0.5 * (sH - tH + uH); + double uHQ = -0.5 * (sH + tH - uH); + double tHQ2 = tHQ * tHQ; + double uHQ2 = uHQ * uHQ; + + // Evaluate cross section for spin 0 colour triplet. + if (spinSave == 0) { + sigSum = (1./9.) * (sH * (sH - 4. * s34Avg) + - pow2(uHavg - tHavg)) / sH2; + } + + // Evaluate cross section for spin 1/2 colour triplet. + else if (spinSave == 1) { + sigSum = (4./9.) * ((tHQ2 + uHQ2) / sH2 + 2. * s34Avg / sH); + } + + // Evaluate cross section for spin 1 colour triplet. + else { + double tuH34 = (tHavg + uHavg) / s34Avg; + sigSum = (1./9.) * ( + pow2(1. + kappa) * sH * s34Avg * (pow2(tuH34) - 4.) + + (tHavg * uHavg - pow2(s34Avg)) * (8. + 2. * (1. - pow2(kappa)) * tuH34 + + pow2(kappa) * pow2(tuH34)) ) / sH2; + } + + // Final answer, with common factors. + sigma = (M_PI / sH2) * pow2(alpS) * sigSum * nCHV * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2qGqGbar::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idNew, -idNew); + + // tH defined between f and qG: must swap tHat <-> uHat if qbar q in. + swapTU = (id1 < 0); + + // Colour flow topologies. + if (id1 > 0) setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + else setColAcol( 0, 2, 1, 0, 1, 0, 0, 2); + +} + + +//========================================================================== + +// Sigma2ffbar2fGfGbar class. +// Cross section for f fbar -> qG qGbar (generic quark of spin 0, 1/2 or 1) +// via gamma^*/Z^* s-channel exchange. Still under development!! ?? + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2fGfGbar::initProc() { + + // Charge and number of colours. Coupling kappa used for vector state. + eQHV2 = pow2( particleDataPtr->charge(idNew) ); + nCHV = settingsPtr->mode("HiddenValley:Ngauge"); + kappa = settingsPtr->parm("HiddenValley:kappa"); + + // Coloured or uncoloured particle. + hasColour = (particleDataPtr->colType(idNew) != 0); + colFac = (hasColour) ? 3. : 1.; + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2fGfGbar::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + double delta = 0.25 * pow2(s3 - s4) / sH; + double s34Avg = 0.5 * (s3 + s4) - delta; + double tHavg = tH - delta; + double uHavg = uH - delta; + double tHQ = -0.5 * (sH - tH + uH); + double uHQ = -0.5 * (sH + tH - uH); + double tHQ2 = tHQ * tHQ; + double uHQ2 = uHQ * uHQ; + + // Evaluate cross section for spin 0 colour triplet. + if (spinSave == 0) { + sigSum = 0.5 * (sH * (sH - 4. * s34Avg) - pow2(uHavg - tHavg)) / sH2; + } + + // Evaluate cross section for spin 1/2 colour triplet. + else if (spinSave == 1) { + sigSum = 2. * ((tHQ2 + uHQ2) / sH2 + 2. * s34Avg / sH); + } + + // Evaluate cross section for spin 1 colour triplet. + else { + double tuH34 = (tHavg + uHavg) / s34Avg; + sigSum = 0.5 * ( pow2(1. + kappa) * sH * s34Avg * (pow2(tuH34) - 4.) + + (tHavg * uHavg - pow2(s34Avg)) * (8. + 2. * (1. - pow2(kappa)) * tuH34 + + pow2(kappa) * pow2(tuH34)) ) / sH2; + } + + // Final-state charge factors. + sigSum *= colFac * eQHV2 * (1. + alpS / M_PI); + + // Final answer, except for initial-state weight + sigma0 = (M_PI / sH2) * pow2(alpEM) * sigSum * nCHV * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2fGfGbar::sigmaHat() { + + // Charge and colour factors. + double eNow = coupSMPtr->ef( abs(id1) ); + double sigma = sigma0 * pow2(eNow); + if (abs(id1) < 9) sigma /= 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2fGfGbar::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idNew, -idNew); + + // tH defined between f and qG: must swap tHat <-> uHat if fbar f in. + swapTU = (id1 < 0); + + // Colour flow topologies. + if (hasColour) { + if (id1 > 0 && id1 < 7) setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + else if (id1 > -7 && id1 < 0) setColAcol( 0, 1, 1, 0, 2, 0, 0, 2); + else setColAcol( 0, 0, 0, 0, 1, 0, 0, 1); + } else { + if (id1 > 0 && id1 < 7) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else if (id1 > -7 && id1 < 0) setColAcol( 0, 1, 1, 0, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + } + +} + + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaHiggs.cxx b/PYTHIA8/pythia8140/src/SigmaHiggs.cxx new file mode 100644 index 00000000000..d2be4a3a689 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaHiggs.cxx @@ -0,0 +1,2531 @@ +// SigmaHiggs.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// Part of code written by Marc Montull, CERN summer student 2007. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. +// Function definitions (not found in the header) for the +// Higgs simulation classes. + +#include "SigmaHiggs.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma1ffbar2H class. +// Cross section for f fbar -> H0 , H1, H2 or A3. +// (f is quark or lepton, H0 SM Higgs and H1, H2, A3 BSM Higgses ). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2H::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "f fbar -> H (SM)"; + codeSave = 901; + idRes = 25; + } + else if (higgsType == 1) { + nameSave = "f fbar -> h0(H1)"; + codeSave = 1001; + idRes = 25; + } + else if (higgsType == 2) { + nameSave = "f fbar -> H0(H2)"; + codeSave = 1021; + idRes = 35; + } + else if (higgsType == 3) { + nameSave = "f fbar -> A0(A3)"; + codeSave = 1041; + idRes = 36; + } + + // Find pointer to H0, H1, H2 or A3 depending on the value of idRes. + HResPtr = particleDataPtr->particleDataEntryPtr(idRes); + + // Store H0, H1, H2 or A3 mass and width for propagator. + mRes = HResPtr->m0(); + GammaRes = HResPtr->mWidth(); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + +} + + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma1ffbar2H::sigmaKin() { + + // Set up Breit-Wigner. + double width = HResPtr->resWidth(idRes, mH); + sigBW = 4. * M_PI/ ( pow2(sH - m2Res) + pow2(mH * width) ); + + // Width out only includes open channels. + widthOut = width * HResPtr->resOpenFrac(idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2H::sigmaHat() { + + // Calculate mass-dependent incoming width, including colour factor. + int idAbs = abs(id1); + double widthIn = HResPtr->resWidthChan( mH, idAbs, -idAbs); + if (idAbs < 9) widthIn /= 9.; + + // Done. + return widthIn * sigBW * widthOut; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2H::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idRes); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma1ffbar2H::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma1gg2H class. +// Cross section for g g -> H0, H1, H2 or A3 (H0 SM Higgs, H1, H2, A3 BSM). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1gg2H::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "g g -> H (SM)"; + codeSave = 902; + idRes = 25; + } + else if (higgsType == 1) { + nameSave = "g g -> h0(H1)"; + codeSave = 1002; + idRes = 25; + } + else if (higgsType == 2) { + nameSave = "g g -> H0(H2)"; + codeSave = 1022; + idRes = 35; + } + else if (higgsType == 3) { + nameSave = "g g -> A0(A3)"; + codeSave = 1042; + idRes = 36; + } + + // Find pointer to H0, H1, H2 or A3 depending on idRes. + HResPtr = particleDataPtr->particleDataEntryPtr(idRes); + + // Store H0, H1, H2 or A3 mass and width for propagator. + mRes = HResPtr->m0(); + GammaRes = HResPtr->mWidth(); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1gg2H::sigmaKin() { + + // Incoming width for gluons, gives colour factor of 1/8 * 1/8. + double widthIn = HResPtr->resWidthChan( mH, 21, 21) / 64.; + + // Set up Breit-Wigner. + double width = HResPtr->resWidth(idRes, mH); + double sigBW = 8. * M_PI/ ( pow2(sH - m2Res) + pow2(mH * width) ); + + // Width out only includes open channels. + double widthOut = width * HResPtr->resOpenFrac(idRes); + + // Done. + sigma = widthIn * sigBW * widthOut; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1gg2H::setIdColAcol() { + + // Flavours trivial. + setId( 21, 21, idRes); + + // Colour flow topology. + setColAcol( 1, 2, 2, 1, 0, 0); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma1gg2H::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma1gmgm2H class. +// Cross section for gamma gamma -> H0, H1, H2 or H3. +// (H0 SM Higgs, H1, H2 and A3 BSM Higgses). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1gmgm2H::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "gamma gamma -> H (SM)"; + codeSave = 903; + idRes = 25; + } + else if (higgsType == 1) { + nameSave = "gamma gamma -> h0(H1)"; + codeSave = 1003; + idRes = 25; + } + else if (higgsType == 2) { + nameSave = "gamma gamma -> H0(H2)"; + codeSave = 1023; + idRes = 35; + } + else if (higgsType == 3) { + nameSave = "gamma gamma -> A0(A3)"; + codeSave = 1043; + idRes = 36; + } + + // Find pointer to H0, H1, H2 or A3. + HResPtr = particleDataPtr->particleDataEntryPtr(idRes); + + // Store H0, H1, H2 or A3 mass and width for propagator. + mRes = HResPtr->m0(); + GammaRes = HResPtr->mWidth(); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1gmgm2H::sigmaKin() { + + // Incoming width for photons. + double widthIn = HResPtr->resWidthChan( mH, 22, 22); + + // Set up Breit-Wigner. + double width = HResPtr->resWidth(idRes, mH); + double sigBW = 8. * M_PI/ ( pow2(sH - m2Res) + pow2(mH * width) ); + + // Width out only includes open channels. + double widthOut = width * HResPtr->resOpenFrac(idRes); + + // Done. + sigma = widthIn * sigBW * widthOut; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1gmgm2H::setIdColAcol() { + + // Flavours trivial. + setId( 22, 22, idRes); + + // Colour flow trivial. + setColAcol( 0, 0, 0, 0, 0, 0); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma1gmgm2H::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2ffbar2HZ class. +// Cross section for f fbar -> H0 Z0, H1 Z0, H2 Z0 or A3 Z0. +// (H0 SM Higgs, H1, H2 and A3 BSM Higgses). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2HZ::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "f fbar -> H0 Z0 (SM)"; + codeSave = 904; + idRes = 25; + coup2Z = 1.; + } + else if (higgsType == 1) { + nameSave = "f fbar -> h0(H1) Z0"; + codeSave = 1004; + idRes = 25; + coup2Z = settingsPtr->parm("HiggsH1:coup2Z"); + } + else if (higgsType == 2) { + nameSave = "f fbar -> H0(H2) Z0"; + codeSave = 1024; + idRes = 35; + coup2Z = settingsPtr->parm("HiggsH2:coup2Z"); + } + else if (higgsType == 3) { + nameSave = "f fbar -> A0(A3) ZO"; + codeSave = 1044; + idRes = 36; + coup2Z = settingsPtr->parm("HiggsA3:coup2Z"); + } + + // Store Z0 mass and width for propagator. Common coupling factor. + mZ = particleDataPtr->m0(23); + widZ = particleDataPtr->mWidth(23); + mZS = mZ*mZ; + mwZS = pow2(mZ * widZ); + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() + * coupSMPtr->cos2thetaW()); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(idRes, 23); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2HZ::sigmaKin() { + + // Evaluate differential cross section. + sigma0 = (M_PI / sH2) * 8. * pow2(alpEM * thetaWRat * coup2Z) + * (tH * uH - s3 * s4 + 2. * sH * s4) / (pow2(sH - mZS) + mwZS); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2HZ::sigmaHat() { + + // Coupling a_f^2 + v_f^2 to s-channel Z0 and colour factor. + int idAbs = abs(id1); + double sigma = sigma0 * coupSMPtr->vf2af2(idAbs); + if (idAbs < 9) sigma /= 3.; + + // Secondary width for H0 and Z0 or H1 and Z0 or H2 and Z0 or A3 and Z0. + sigma *= openFracPair; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2HZ::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idRes, 23); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2ffbar2HZ::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // If not decay of Z0 created along with Higgs then done. + if (iResBeg != 5 || iResEnd != 6) return 1.; + + // Order so that fbar(1) f(2) -> H() f'(3) fbar'(4). + int i1 = (process[3].id() < 0) ? 3 : 4; + int i2 = 7 - i1; + int i3 = process[6].daughter1(); + int i4 = process[6].daughter2(); + if (process[i3].id() < 0) swap( i3, i4); + + // Find left- and righthanded couplings of fermion pairs. + int idAbs = process[i1].idAbs(); + double liS = pow2( coupSMPtr->lf(idAbs) ); + double riS = pow2( coupSMPtr->rf(idAbs) ); + idAbs = process[i3].idAbs(); + double lfS = pow2( coupSMPtr->lf(idAbs) ); + double rfS = pow2( coupSMPtr->rf(idAbs) ); + + // Evaluate relevant four-products. + double pp13 = process[i1].p() * process[i3].p(); + double pp14 = process[i1].p() * process[i4].p(); + double pp23 = process[i2].p() * process[i3].p(); + double pp24 = process[i2].p() * process[i4].p(); + + // Weight and maximum. + double wt = (liS * lfS + riS * rfS) * pp13 * pp24 + + (liS * rfS + riS * lfS) * pp14 * pp23; + double wtMax = (liS + riS) * (lfS + rfS) * (pp13 + pp14) * (pp23 + pp24); + + // Done. + return wt / wtMax; + +} + +//========================================================================== + +// Sigma2ffbar2HW class. +// Cross section for f fbar -> H0 W+-, H1 W+-, H2 W+- or A3 W+-. +// (H0 SM Higgs, H1, H2 and A3 BSM Higgses). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2HW::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "f fbar -> H0 W+- (SM)"; + codeSave = 905; + idRes = 25; + coup2W = 1.; + } + else if (higgsType == 1) { + nameSave = "f fbar -> h0(H1) W+-"; + codeSave = 1005; + idRes = 25; + coup2W = settingsPtr->parm("HiggsH1:coup2W"); + } + else if (higgsType == 2) { + nameSave = "f fbar -> H0(H2) W+-"; + codeSave = 1025; + idRes = 35; + coup2W = settingsPtr->parm("HiggsH2:coup2W"); + } + else if (higgsType == 3) { + nameSave = "f fbar -> A0(A3) W+-"; + codeSave = 1045; + idRes = 36; + coup2W = settingsPtr->parm("HiggsA3:coup2W"); + } + + // Store W+- mass and width for propagator. Common coupling factor. + mW = particleDataPtr->m0(24); + widW = particleDataPtr->mWidth(24); + mWS = mW*mW; + mwWS = pow2(mW * widW); + thetaWRat = 1. / (4. * coupSMPtr->sin2thetaW()); + + // Secondary open width fractions. + openFracPairPos = particleDataPtr->resOpenFrac(idRes, 24); + openFracPairNeg = particleDataPtr->resOpenFrac(idRes, -24); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2ffbar2HW::sigmaKin() { + + // Evaluate differential cross section. + sigma0 = (M_PI / sH2) * 2. * pow2(alpEM * thetaWRat * coup2W) + * (tH * uH - s3 * s4 + 2. * sH * s4) / (pow2(sH - mWS) + mwWS); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2ffbar2HW::sigmaHat() { + + // CKM and colour factors. + double sigma = sigma0; + if (abs(id1) < 9) sigma *= coupSMPtr->V2CKMid(abs(id1), abs(id2)) / 3.; + + // Secondary width for H0 and W+-. + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + sigma *= (idUp > 0) ? openFracPairPos : openFracPairNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2HW::setIdColAcol() { + + // Sign of outgoing W. + int sign = 1 - 2 * (abs(id1)%2); + if (id1 < 0) sign = -sign; + setId( id1, id2, idRes, 24 * sign); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2ffbar2HW::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // If not decay of W+- created along with Higgs then done. + if (iResBeg != 5 || iResEnd != 6) return 1.; + + // Order so that fbar(1) f(2) -> H() f'(3) fbar'(4). + int i1 = (process[3].id() < 0) ? 3 : 4; + int i2 = 7 - i1; + int i3 = process[6].daughter1(); + int i4 = process[6].daughter2(); + if (process[i3].id() < 0) swap( i3, i4); + + // Evaluate relevant four-products. + double pp13 = process[i1].p() * process[i3].p(); + double pp14 = process[i1].p() * process[i4].p(); + double pp23 = process[i2].p() * process[i3].p(); + double pp24 = process[i2].p() * process[i4].p(); + + // Weight and maximum. + double wt = pp13 * pp24; + double wtMax = (pp13 + pp14) * (pp23 + pp24); + + // Done. + return wt / wtMax; + +} + +//========================================================================== + +// Sigma3ff2HfftZZ class. +// Cross section for f f' -> H f f' (Z0 Z0 fusion of SM or BSM Higgs). +// (H can be H0 SM or H1, H2, A3 from BSM). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3ff2HfftZZ::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "f f' -> H0 f f'(Z0 Z0 fusion) (SM)"; + codeSave = 906; + idRes = 25; + coup2Z = 1.; + } + else if (higgsType == 1) { + nameSave = "f f' -> h0(H1) f f' (Z0 Z0 fusion)"; + codeSave = 1006; + idRes = 25; + coup2Z = settingsPtr->parm("HiggsH1:coup2Z"); + } + else if (higgsType == 2) { + nameSave = "f f' -> H0(H2) f f' (Z0 Z0 fusion)"; + codeSave = 1026; + idRes = 35; + coup2Z = settingsPtr->parm("HiggsH2:coup2Z"); + } + else if (higgsType == 3) { + nameSave = "f f' -> A0(A3) f f' (Z0 Z0 fusion)"; + codeSave = 1046; + idRes = 36; + coup2Z = settingsPtr->parm("HiggsA3:coup2Z"); + } + + // Common fixed mass and coupling factor. + mZS = pow2( particleDataPtr->m0(23) ); + prefac = 0.25 * mZS * pow3( 4. * M_PI / (coupSMPtr->sin2thetaW() + * coupSMPtr->cos2thetaW()) ); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma3ff2HfftZZ::sigmaKin() { + + // Required four-vector products. + double pp12 = 0.5 * sH; + double pp14 = 0.5 * mH * p4cm.pNeg(); + double pp15 = 0.5 * mH * p5cm.pNeg(); + double pp24 = 0.5 * mH * p4cm.pPos(); + double pp25 = 0.5 * mH * p5cm.pPos(); + double pp45 = p4cm * p5cm; + + // Propagator factors and two possible numerators. + double prop = pow2( (2. * pp14 + mZS) * (2. * pp25 + mZS) ); + sigma1 = prefac * pp12 * pp45 / prop; + sigma2 = prefac * pp15 * pp24 / prop; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma3ff2HfftZZ::sigmaHat() { + + // Flavour-dependent coupling factors for two incoming flavours. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + double lf1S = pow2( coupSMPtr->lf(id1Abs) ); + double rf1S = pow2( coupSMPtr->rf(id1Abs) ); + double lf2S = pow2( coupSMPtr->lf(id2Abs) ); + double rf2S = pow2( coupSMPtr->rf(id2Abs) ); + double c1 = lf1S * lf2S + rf1S * rf2S; + double c2 = lf1S * rf2S + rf1S * lf2S; + + // Combine couplings and kinematics factors. + double sigma = pow3(alpEM) * (c1 * sigma1 + c2 * sigma2) * pow2(coup2Z); + + // Secondary width for H0, H1, H2 or A3. + sigma *= openFrac; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3ff2HfftZZ::setIdColAcol() { + + // Trivial flavours: out = in. + setId( id1, id2, idRes, id1, id2); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && abs(id2) < 9 && id1*id2 > 0) + setColAcol( 1, 0, 2, 0, 0, 0, 1, 0, 2, 0); + else if (abs(id1) < 9 && abs(id2) < 9) + setColAcol( 1, 0, 0, 2, 0, 0, 1, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 0, 0, 0, 1, 0, 0, 0); + else if (abs(id2) < 9) setColAcol( 0, 0, 1, 0, 0, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); + if ( (abs(id1) < 9 && id1 < 0) || (abs(id1) > 10 && id2 < 0) ) + swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma3ff2HfftZZ::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma3ff2HfftWW class. +// Cross section for f_1 f_2 -> H0 f_3 f_4 (W+ W- fusion of SM or BSM Higgs). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3ff2HfftWW::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "f_1 f_2 -> H0 f_3 f_4 (W+ W- fusion) (SM)"; + codeSave = 907; + idRes = 25; + coup2W = 1.; + } + else if (higgsType == 1) { + nameSave = "f_1 f_2 -> h0(H1) f_3 f_4 (W+ W- fusion)"; + codeSave = 1007; + idRes = 25; + coup2W = settingsPtr->parm("HiggsH1:coup2W"); + } + else if (higgsType == 2) { + nameSave = "f_1 f_2 -> H0(H2) f_3 f_4 (W+ W- fusion)"; + codeSave = 1027; + idRes = 35; + coup2W = settingsPtr->parm("HiggsH2:coup2W"); + } + else if (higgsType == 3) { + nameSave = "f_1 f_2 -> A0(A3) f_3 f_4 (W+ W- fusion)"; + codeSave = 1047; + idRes = 36; + coup2W = settingsPtr->parm("HiggsA3:coup2W"); + } + + // Common fixed mass and coupling factor. + mWS = pow2( particleDataPtr->m0(24) ); + prefac = mWS * pow3( 4. * M_PI / coupSMPtr->sin2thetaW() ); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma3ff2HfftWW::sigmaKin() { + + // Required four-vector products. + double pp12 = 0.5 * sH; + double pp14 = 0.5 * mH * p4cm.pNeg(); + double pp25 = 0.5 * mH * p5cm.pPos(); + double pp45 = p4cm * p5cm; + + // Cross section: kinematics part. Combine with couplings. + double prop = pow2( (2. * pp14 + mWS) * (2. * pp25 + mWS) ); + sigma0 = prefac * pp12 * pp45 * pow2(coup2W) / prop; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma3ff2HfftWW::sigmaHat() { + + // Some flavour combinations not possible. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + if ( (id1Abs%2 == id2Abs%2 && id1 * id2 > 0) + || (id1Abs%2 != id2Abs%2 && id1 * id2 < 0) ) return 0.; + + // Basic cross section. CKM factors for final states. + double sigma = sigma0 * pow3(alpEM) * coupSMPtr->V2CKMsum(id1Abs) + * coupSMPtr->V2CKMsum(id2Abs); + + // Secondary width for H0, H1, H2 or A3. + sigma *= openFrac; + + // Spin-state extra factor 2 per incoming neutrino. + if (id1Abs == 12 || id1Abs == 14 || id1Abs == 16) sigma *= 2.; + if (id2Abs == 12 || id2Abs == 14 || id2Abs == 16) sigma *= 2.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3ff2HfftWW::setIdColAcol() { + + // Pick out-flavours by relative CKM weights. + id4 = coupSMPtr->V2CKMpick(id1); + id5 = coupSMPtr->V2CKMpick(id2); + setId( id1, id2, idRes, id4, id5); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9 && abs(id2) < 9 && id1*id2 > 0) + setColAcol( 1, 0, 2, 0, 0, 0, 1, 0, 2, 0); + else if (abs(id1) < 9 && abs(id2) < 9) + setColAcol( 1, 0, 0, 2, 0, 0, 1, 0, 0, 2); + else if (abs(id1) < 9) setColAcol( 1, 0, 0, 0, 0, 0, 1, 0, 0, 0); + else if (abs(id2) < 9) setColAcol( 0, 0, 1, 0, 0, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); + if ( (abs(id1) < 9 && id1 < 0) || (abs(id1) > 10 && id2 < 0) ) + swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma3ff2HfftWW::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma3gg2HQQbar class. +// Cross section for g g -> H0 Q Qbar (Q Qbar fusion of SM or BSM Higgs). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3gg2HQQbar::initProc() { + + // Properties specific to Higgs state for the "g g -> H ttbar" process. + // (H can be H0 SM or H1, H2, A3 from BSM). + if (higgsType == 0 && idNew == 6) { + nameSave = "g g -> H t tbar (SM)"; + codeSave = 908; + idRes = 25; + coup2Q = 1.; + } + else if (higgsType == 1 && idNew == 6) { + nameSave = "g g -> h0(H1) t tbar"; + codeSave = 1008; + idRes = 25; + coup2Q = settingsPtr->parm("HiggsH1:coup2u"); + } + else if (higgsType == 2 && idNew == 6) { + nameSave = "g g -> H0(H2) t tbar"; + codeSave = 1028; + idRes = 35; + coup2Q = settingsPtr->parm("HiggsH2:coup2u"); + } + else if (higgsType == 3 && idNew == 6) { + nameSave = "g g -> A0(A3) t tbar"; + codeSave = 1048; + idRes = 36; + coup2Q = settingsPtr->parm("HiggsA3:coup2u"); + } + + // Properties specific to Higgs state for the "g g -> H b bbar" process. + // (H can be H0 SM or H1, H2, A3 from BSM). + if (higgsType == 0 && idNew == 5) { + nameSave = "g g -> H b bbar (SM)"; + codeSave = 912; + idRes = 25; + coup2Q = 1.; + } + else if (higgsType == 1 && idNew == 5) { + nameSave = "g g -> h0(H1) b bbar"; + codeSave = 1012; + idRes = 25; + coup2Q = settingsPtr->parm("HiggsH1:coup2d"); + } + else if (higgsType == 2 && idNew == 5) { + nameSave = "g g -> H0(H2) b bbar"; + codeSave = 1032; + idRes = 35; + coup2Q = settingsPtr->parm("HiggsH2:coup2d"); + } + else if (higgsType == 3 && idNew == 5) { + nameSave = "g g -> A0(A3) b bbar"; + codeSave = 1052; + idRes = 36; + coup2Q = settingsPtr->parm("HiggsA3:coup2d"); + } + + // Common mass and coupling factors. + double mWS = pow2(particleDataPtr->m0(24)); + prefac = (4. * M_PI / coupSMPtr->sin2thetaW()) * pow2(4. * M_PI) + * 0.25 / mWS; + + // Secondary open width fraction. + openFracTriplet = particleDataPtr->resOpenFrac(idRes, idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma3gg2HQQbar::sigmaKin() { + + // Running mass of heavy quark. + double mQ2run = pow2( particleDataPtr->mRun(idNew, mH) ); + + // Linear combination of p_Q and p_Qbar to ensure common mass. + double mQ2 = m4 * m5; + double epsi = 0.; + if (m4 != m5) { + double s45 = (p4cm + p5cm).m2Calc(); + mQ2 = 0.5 * (s4 + s5) - 0.25 * pow2(s4 - s5) / s45; + epsi = 0.5 * (s5 - s4) / s45; + } + + // Set up kinematics: g(4) g(5) -> H(3) Q(1) Qbar(2) in outgoing sense. + Vec4 pTemp[6]; + pTemp[4] = Vec4( 0., 0., -0.5* mH, -0.5* mH); + pTemp[5] = Vec4( 0., 0., 0.5* mH, -0.5* mH); + pTemp[1] = p4cm + epsi * (p4cm + p5cm); + pTemp[2] = p5cm - epsi * (p4cm + p5cm); + pTemp[3] = p3cm; + + // Four-product combinations. + double z1 = pTemp[1] * pTemp[2]; + double z2 = pTemp[1] * pTemp[3]; + double z3 = pTemp[1] * pTemp[4]; + double z4 = pTemp[1] * pTemp[5]; + double z5 = pTemp[2] * pTemp[3]; + double z6 = pTemp[2] * pTemp[4]; + double z7 = pTemp[2] * pTemp[5]; + double z8 = pTemp[3] * pTemp[4]; + double z9 = pTemp[3] * pTemp[5]; + double z10 = pTemp[4] * pTemp[5]; + + // Powers required as shorthand in matriz elements. + double mQ4 = mQ2 * mQ2; + double mQ6 = mQ2 * mQ4; + double z1S = z1 * z1; + double z2S = z2 * z2; + double z3S = z3 * z3; + double z4S = z4 * z4; + double z5S = z5 * z5; + double z6S = z6 * z6; + double z7S = z7 * z7; + double z8S = z8 * z8; + double z9S = z9 * z9; + double z10S = z10 * z10; + + // Evaluate matriz elements for g + g -> Q + Qbar + H. + // (H can be H0 SM or H1, H2, A3 from BSM). + double fm[9][9]; + fm[1][1] = 64*mQ6+16*mQ4*s3+32*mQ4*(z1+2*z2+z4+z9+2* + z7+z5)+8*mQ2*s3*(-z1-z4+2*z7)+16*mQ2*(z2*z9+4*z2* + z7+z2*z5-2*z4*z7-2*z9*z7)+8*s3*z4*z7-16*z2*z9*z7; + fm[1][2] = 16*mQ6+8*mQ4*(-2*z1+z2-2*z3-2*z4-4*z10+z9-z8+2 + *z7-4*z6+z5)+8*mQ2*(-2*z1*z2-2*z2*z4-2*z2*z10+z2*z7-2* + z2*z6-2*z3*z7+2*z4*z7+4*z10*z7-z9*z7-z8*z7)+16*z2*z7*(z4+ + z10); + fm[1][3] = 16*mQ6-4*mQ4*s3+8*mQ4*(-2*z1+2*z2-2*z3-4* + z4-8*z10+z9+z8-2*z7-4*z6+2*z5)-(4*mQ2*s3)*(z1+z4+z10 + +z6)+8*mQ2*(-2*z1*z2-2*z1*z10+z1*z9+z1*z8-2*z1*z5+z2S + -4*z2*z4-5*z2*z10+z2*z8-z2*z7-3*z2*z6+z2*z5+z3*z9+2*z3*z7 + -z3*z5+z4*z8+2*z4*z6-3*z4*z5-5*z10*z5+z9*z8+z9*z6+z9*z5+ + z8*z7-4*z6*z5+z5S)-(16*z2*z5)*(z1+z4+z10+z6); + fm[1][4] = 16*mQ6+4*mQ4*s3+16*mQ4*(-z1+z2-z3-z4+z10- + z9-z8+2*z7+2*z6-z5)+4*mQ2*s3*(z1+z3+z4+z10+2*z7+2*z6 + )+8*mQ2*(4*z1*z10+4*z1*z7+4*z1*z6+2*z2*z10-z2*z9-z2*z8+ + 4*z2*z7+4*z2*z6-z2*z5+4*z10*z5+4*z7*z5+4*z6*z5)-(8*s3* + z1)*(z10+z7+z6)+16*z2*z5*(z10+z7+z6); + fm[1][5] = 8*mQ4*(-2*z1-2*z4+z10-z9)+4*mQ2*(4*z1S-2*z1* + z2+8*z1*z3+6*z1*z10-2*z1*z9+4*z1*z8+4*z1*z7+4*z1*z6+2*z1* + z5+z2*z10+4*z3*z4-z3*z9+2*z3*z7+3*z4*z8-2*z4*z6+2*z4*z5-4 + *z10*z7+3*z10*z5-3*z9*z6+3*z8*z7-4*z7S+4*z7*z5)+8*(z1S + *z9-z1S*z8-z1*z2*z7+z1*z2*z6+z1*z3*z9+z1*z3*z5-z1*z4* + z8-z1*z4*z5+z1*z10*z9+z1*z9*z7+z1*z9*z6-z1*z8*z7-z2*z3*z7 + +z2*z4*z6-z2*z10*z7-z2*z7S+z3*z7*z5-z4*z10*z5-z4*z7*z5- + z4*z6*z5); + fm[1][6] = 16*mQ4*(-4*z1-z4+z9-z7)+4*mQ2*s3*(-2*z1-z4- + z7)+16*mQ2*(-2*z1S-3*z1*z2-2*z1*z4-3*z1*z9-2*z1*z7-3* + z1*z5-2*z2*z4-2*z7*z5)-8*s3*z4*z7+8*(-z1*z2*z9-2*z1*z2 + *z5-z1*z9S-z1*z9*z5+z2S*z7-z2*z4*z5+z2*z9*z7-z2*z7*z5 + +z4*z9*z5+z4*z5S); + fm[1][7] = 8*mQ4*(2*z3+z4+3*z10+z9+2*z8+3*z7+6*z6)+2*mQ2* + s3*(-2*z3-z4+3*z10+3*z7+6*z6)+4*mQ2*(4*z1*z10+4*z1* + z7+8*z1*z6+6*z2*z10+z2*z9+2*z2*z8+6*z2*z7+12*z2*z6-8*z3* + z7+4*z4*z7+4*z4*z6+4*z10*z5+4*z9*z7+4*z9*z6-8*z8*z7+4*z7* + z5+8*z6*z5)+4*s3*(-z1*z10-z1*z7-2*z1*z6+2*z3*z7-z4*z7- + z4*z6)+8*z2*(z10*z5+z9*z7+z9*z6-2*z8*z7+z7*z5+2*z6*z5); + fm[1][8] = 8*mQ4*(2*z3+z4+3*z10+2*z9+z8+3*z7+6*z6)+2*mQ2* + s3*(-2*z3-z4+2*z10+z7+2*z6)+4*mQ2*(4*z1*z10-2*z1*z9+ + 2*z1*z8+4*z1*z7+8*z1*z6+5*z2*z10+2*z2*z9+z2*z8+4*z2*z7+8* + z2*z6-z3*z9-8*z3*z7+2*z3*z5+2*z4*z9-z4*z8+4*z4*z7+4*z4*z6 + +4*z4*z5+5*z10*z5+z9S-z9*z8+2*z9*z7+5*z9*z6+z9*z5-7*z8* + z7+2*z8*z5+2*z7*z5+10*z6*z5)+2*s3*(-z1*z10+z3*z7-2*z4* + z7+z4*z6)+4*(-z1*z9S+z1*z9*z8-2*z1*z9*z5-z1*z8*z5+2*z2* + z10*z5+z2*z9*z7+z2*z9*z6-2*z2*z8*z7+3*z2*z6*z5+z3*z9*z5+ + z3*z5S+z4*z9*z5-2*z4*z8*z5+2*z4*z5S); + fm[2][2] = 16*mQ6+16*mQ4*(-z1+z3-z4-z10+z7-z6)+16*mQ2*( + z3*z10+z3*z7+z3*z6+z4*z7+z10*z7)-16*z3*z10*z7; + fm[2][3] = 16*mQ6+8*mQ4*(-2*z1+z2+2*z3-4*z4-4*z10-z9+z8-2 + *z7-2*z6+z5)+8*mQ2*(-2*z1*z5+4*z3*z10-z3*z9-z3*z8-2*z3* + z7+2*z3*z6+z3*z5-2*z4*z5-2*z10*z5-2*z6*z5)+16*z3*z5*(z10+ + z6); + fm[2][4] = 8*mQ4*(-2*z1-2*z3+z10-z8)+4*mQ2*(4*z1S-2*z1* + z2+8*z1*z4+6*z1*z10+4*z1*z9-2*z1*z8+4*z1*z7+4*z1*z6+2*z1* + z5+z2*z10+4*z3*z4+3*z3*z9-2*z3*z7+2*z3*z5-z4*z8+2*z4*z6-4 + *z10*z6+3*z10*z5+3*z9*z6-3*z8*z7-4*z6S+4*z6*z5)+8*(-z1S + *z9+z1S*z8+z1*z2*z7-z1*z2*z6-z1*z3*z9-z1*z3*z5+z1*z4 + *z8+z1*z4*z5+z1*z10*z8-z1*z9*z6+z1*z8*z7+z1*z8*z6+z2*z3* + z7-z2*z4*z6-z2*z10*z6-z2*z6S-z3*z10*z5-z3*z7*z5-z3*z6* + z5+z4*z6*z5); + fm[2][5] = 16*mQ4*z10+8*mQ2*(2*z1S+2*z1*z3+2*z1*z4+2*z1 + *z10+2*z1*z7+2*z1*z6+z3*z7+z4*z6)+8*(-2*pow3(z1)-2*z1S*z3- + 2*z1S*z4-2*z1S*z10-2*z1S*z7-2*z1S*z6-2*z1*z3*z4- + z1*z3*z10-2*z1*z3*z6-z1*z4*z10-2*z1*z4*z7-z1*z10S-z1* + z10*z7-z1*z10*z6-2*z1*z7*z6+z3S*z7-z3*z4*z7-z3*z4*z6+z3 + *z10*z7+z3*z7S-z3*z7*z6+z4S*z6+z4*z10*z6-z4*z7*z6+z4* + z6S); + fm[2][6] = 8*mQ4*(-2*z1+z10-z9-2*z7)+4*mQ2*(4*z1S+2*z1* + z2+4*z1*z3+4*z1*z4+6*z1*z10-2*z1*z9+4*z1*z8+8*z1*z6-2*z1* + z5+4*z2*z4+3*z2*z10+2*z2*z7-3*z3*z9-2*z3*z7-4*z4S-4*z4* + z10+3*z4*z8+2*z4*z6+z10*z5-z9*z6+3*z8*z7+4*z7*z6)+8*(z1S + *z9-z1S*z8-z1*z2*z7+z1*z2*z6+z1*z3*z9+z1*z3*z5+z1*z4* + z9-z1*z4*z8-z1*z4*z5+z1*z10*z9+z1*z9*z6-z1*z8*z7-z2*z3*z7 + -z2*z4*z7+z2*z4*z6-z2*z10*z7+z3*z7*z5-z4S*z5-z4*z10*z5- + z4*z6*z5); + fm[2][7] = 8*mQ4*(z3+2*z4+3*z10+z7+2*z6)+4*mQ2*(-4*z1*z3- + 2*z1*z4-2*z1*z10+z1*z9-z1*z8-4*z1*z7-2*z1*z6+z2*z3+2*z2* + z4+3*z2*z10+z2*z7+2*z2*z6-6*z3*z4-6*z3*z10-2*z3*z9-2*z3* + z7-4*z3*z6-z3*z5-6*z4S-6*z4*z10-3*z4*z9-z4*z8-4*z4*z7-2 + *z4*z6-2*z4*z5-3*z10*z9-3*z10*z8-6*z10*z7-6*z10*z6+z10*z5 + +z9*z7-2*z8*z7-2*z8*z6-6*z7*z6+z7*z5-6*z6S+2*z6*z5)+4*( + -z1S*z9+z1S*z8-2*z1*z2*z10-3*z1*z2*z7-3*z1*z2*z6+z1* + z3*z9-z1*z3*z5+z1*z4*z9+z1*z4*z8+z1*z4*z5+z1*z10*z9+z1* + z10*z8-z1*z9*z6+z1*z8*z6+z2*z3*z7-3*z2*z4*z7-z2*z4*z6-3* + z2*z10*z7-3*z2*z10*z6-3*z2*z7*z6-3*z2*z6S-2*z3*z4*z5-z3 + *z10*z5-z3*z6*z5-z4S*z5-z4*z10*z5+z4*z6*z5); + fm[2][8] = 8*mQ4*(z3+2*z4+3*z10+z7+2*z6)+4*mQ2*(-4*z1*z3- + 2*z1*z4-2*z1*z10-z1*z9+z1*z8-4*z1*z7-2*z1*z6+z2*z3+2*z2* + z4+z2*z10-z2*z7-2*z2*z6-6*z3*z4-6*z3*z10-2*z3*z9+z3*z8-2* + z3*z7-4*z3*z6+z3*z5-6*z4S-6*z4*z10-2*z4*z9-4*z4*z7-2*z4 + *z6+2*z4*z5-3*z10*z9-3*z10*z8-6*z10*z7-6*z10*z6+3*z10*z5- + z9*z6-2*z8*z7-3*z8*z6-6*z7*z6+z7*z5-6*z6S+2*z6*z5)+4*( + z1S*z9-z1S*z8-z1*z2*z7+z1*z2*z6-3*z1*z3*z5+z1*z4*z9- + z1*z4*z8-3*z1*z4*z5+z1*z10*z9+z1*z10*z8-2*z1*z10*z5+z1*z9 + *z6+z1*z8*z7+z1*z8*z6-z2*z4*z7+z2*z4*z6-z2*z10*z7-z2*z10* + z6-2*z2*z7*z6-z2*z6S-3*z3*z4*z5-3*z3*z10*z5+z3*z7*z5-3* + z3*z6*z5-3*z4S*z5-3*z4*z10*z5-z4*z6*z5); + fm[3][3] = 64*mQ6+16*mQ4*s3+32*mQ4*(z1+z2+2*z3+z8+z6 + +2*z5)+8*mQ2*s3*(-z1+2*z3-z6)+16*mQ2*(z2*z5-2*z3* + z8-2*z3*z6+4*z3*z5+z8*z5)+8*s3*z3*z6-16*z3*z8*z5; + fm[3][4] = 16*mQ4*(-4*z1-z3+z8-z6)+4*mQ2*s3*(-2*z1-z3- + z6)+16*mQ2*(-2*z1S-3*z1*z2-2*z1*z3-3*z1*z8-2*z1*z6-3* + z1*z5-2*z2*z3-2*z6*z5)-8*s3*z3*z6+8*(-z1*z2*z8-2*z1*z2 + *z5-z1*z8S-z1*z8*z5+z2S*z6-z2*z3*z5+z2*z8*z6-z2*z6*z5 + +z3*z8*z5+z3*z5S); + fm[3][5] = 8*mQ4*(-2*z1+z10-z8-2*z6)+4*mQ2*(4*z1S+2*z1* + z2+4*z1*z3+4*z1*z4+6*z1*z10+4*z1*z9-2*z1*z8+8*z1*z7-2*z1* + z5+4*z2*z3+3*z2*z10+2*z2*z6-4*z3S-4*z3*z10+3*z3*z9+2*z3 + *z7-3*z4*z8-2*z4*z6+z10*z5+3*z9*z6-z8*z7+4*z7*z6)+8*(-z1S + *z9+z1S*z8+z1*z2*z7-z1*z2*z6-z1*z3*z9+z1*z3*z8-z1*z3 + *z5+z1*z4*z8+z1*z4*z5+z1*z10*z8-z1*z9*z6+z1*z8*z7+z2*z3* + z7-z2*z3*z6-z2*z4*z6-z2*z10*z6-z3S*z5-z3*z10*z5-z3*z7* + z5+z4*z6*z5); + fm[3][6] = 16*mQ6+4*mQ4*s3+16*mQ4*(-z1-z2+2*z3+2*z4+ + z10-z9-z8-z7-z6+z5)+4*mQ2*s3*(z1+2*z3+2*z4+z10+z7+z6 + )+8*mQ2*(4*z1*z3+4*z1*z4+4*z1*z10+4*z2*z3+4*z2*z4+4*z2* + z10-z2*z5+4*z3*z5+4*z4*z5+2*z10*z5-z9*z5-z8*z5)-(8*s3* + z1)*(z3+z4+z10)+16*z2*z5*(z3+z4+z10); + fm[3][7] = 8*mQ4*(3*z3+6*z4+3*z10+z9+2*z8+2*z7+z6)+2*mQ2* + s3*(z3+2*z4+2*z10-2*z7-z6)+4*mQ2*(4*z1*z3+8*z1*z4+4* + z1*z10+2*z1*z9-2*z1*z8+2*z2*z3+10*z2*z4+5*z2*z10+2*z2*z9+ + z2*z8+2*z2*z7+4*z2*z6-7*z3*z9+2*z3*z8-8*z3*z7+4*z3*z6+4* + z3*z5+5*z4*z8+4*z4*z6+8*z4*z5+5*z10*z5-z9*z8-z9*z6+z9*z5+ + z8S-z8*z7+2*z8*z6+2*z8*z5)+2*s3*(-z1*z10+z3*z7-2*z3* + z6+z4*z6)+4*(-z1*z2*z9-2*z1*z2*z8+z1*z9*z8-z1*z8S+z2S + *z7+2*z2S*z6+3*z2*z4*z5+2*z2*z10*z5-2*z2*z9*z6+z2*z8*z7 + +z2*z8*z6-2*z3*z9*z5+z3*z8*z5+z4*z8*z5); + fm[3][8] = 8*mQ4*(3*z3+6*z4+3*z10+2*z9+z8+2*z7+z6)+2*mQ2* + s3*(3*z3+6*z4+3*z10-2*z7-z6)+4*mQ2*(4*z1*z3+8*z1*z4+ + 4*z1*z10+4*z2*z3+8*z2*z4+4*z2*z10-8*z3*z9+4*z3*z8-8*z3*z7 + +4*z3*z6+6*z3*z5+4*z4*z8+4*z4*z6+12*z4*z5+6*z10*z5+2*z9* + z5+z8*z5)+4*s3*(-z1*z3-2*z1*z4-z1*z10+2*z3*z7-z3*z6-z4 + *z6)+8*z5*(z2*z3+2*z2*z4+z2*z10-2*z3*z9+z3*z8+z4*z8); + fm[4][4] = 64*mQ6+16*mQ4*s3+32*mQ4*(z1+2*z2+z3+z8+2* + z6+z5)+8*mQ2*s3*(-z1-z3+2*z6)+16*mQ2*(z2*z8+4*z2* + z6+z2*z5-2*z3*z6-2*z8*z6)+8*s3*z3*z6-16*z2*z8*z6; + fm[4][5] = 16*mQ6+8*mQ4*(-2*z1+z2-2*z3-2*z4-4*z10-z9+z8-4 + *z7+2*z6+z5)+8*mQ2*(-2*z1*z2-2*z2*z3-2*z2*z10-2*z2*z7+ + z2*z6+2*z3*z6-2*z4*z6+4*z10*z6-z9*z6-z8*z6)+16*z2*z6*(z3+ + z10); + fm[4][6] = 16*mQ6-4*mQ4*s3+8*mQ4*(-2*z1+2*z2-4*z3-2* + z4-8*z10+z9+z8-4*z7-2*z6+2*z5)-(4*mQ2*s3)*(z1+z3+z10 + +z7)+8*mQ2*(-2*z1*z2-2*z1*z10+z1*z9+z1*z8-2*z1*z5+z2S + -4*z2*z3-5*z2*z10+z2*z9-3*z2*z7-z2*z6+z2*z5+z3*z9+2*z3*z7 + -3*z3*z5+z4*z8+2*z4*z6-z4*z5-5*z10*z5+z9*z8+z9*z6+z8*z7+ + z8*z5-4*z7*z5+z5S)-(16*z2*z5)*(z1+z3+z10+z7); + fm[4][7] = 8*mQ4*(-z3-2*z4-3*z10-2*z9-z8-6*z7-3*z6)+2*mQ2 + *s3*(z3+2*z4-3*z10-6*z7-3*z6)+4*mQ2*(-4*z1*z10-8*z1* + z7-4*z1*z6-6*z2*z10-2*z2*z9-z2*z8-12*z2*z7-6*z2*z6-4*z3* + z7-4*z3*z6+8*z4*z6-4*z10*z5+8*z9*z6-4*z8*z7-4*z8*z6-8*z7* + z5-4*z6*z5)+4*s3*(z1*z10+2*z1*z7+z1*z6+z3*z7+z3*z6-2* + z4*z6)+8*z2*(-z10*z5+2*z9*z6-z8*z7-z8*z6-2*z7*z5-z6*z5); + fm[4][8] = 8*mQ4*(-z3-2*z4-3*z10-z9-2*z8-6*z7-3*z6)+2*mQ2 + *s3*(z3+2*z4-2*z10-2*z7-z6)+4*mQ2*(-4*z1*z10-2*z1*z9 + +2*z1*z8-8*z1*z7-4*z1*z6-5*z2*z10-z2*z9-2*z2*z8-8*z2*z7-4 + *z2*z6+z3*z9-2*z3*z8-4*z3*z7-4*z3*z6-4*z3*z5+z4*z8+8*z4* + z6-2*z4*z5-5*z10*z5+z9*z8+7*z9*z6-2*z9*z5-z8S-5*z8*z7-2 + *z8*z6-z8*z5-10*z7*z5-2*z6*z5)+2*s3*(z1*z10-z3*z7+2*z3 + *z6-z4*z6)+4*(-z1*z9*z8+z1*z9*z5+z1*z8S+2*z1*z8*z5-2*z2 + *z10*z5+2*z2*z9*z6-z2*z8*z7-z2*z8*z6-3*z2*z7*z5+2*z3*z9* + z5-z3*z8*z5-2*z3*z5S-z4*z8*z5-z4*z5S); + fm[5][5] = 16*mQ6+16*mQ4*(-z1-z3+z4-z10-z7+z6)+16*mQ2*( + z3*z6+z4*z10+z4*z7+z4*z6+z10*z6)-16*z4*z10*z6; + fm[5][6] = 16*mQ6+8*mQ4*(-2*z1+z2-4*z3+2*z4-4*z10+z9-z8-2 + *z7-2*z6+z5)+8*mQ2*(-2*z1*z5-2*z3*z5+4*z4*z10-z4*z9-z4* + z8+2*z4*z7-2*z4*z6+z4*z5-2*z10*z5-2*z7*z5)+16*z4*z5*(z10+ + z7); + fm[5][7] = 8*mQ4*(-2*z3-z4-3*z10-2*z7-z6)+4*mQ2*(2*z1*z3+ + 4*z1*z4+2*z1*z10+z1*z9-z1*z8+2*z1*z7+4*z1*z6-2*z2*z3-z2* + z4-3*z2*z10-2*z2*z7-z2*z6+6*z3S+6*z3*z4+6*z3*z10+z3*z9+ + 3*z3*z8+2*z3*z7+4*z3*z6+2*z3*z5+6*z4*z10+2*z4*z8+4*z4*z7+ + 2*z4*z6+z4*z5+3*z10*z9+3*z10*z8+6*z10*z7+6*z10*z6-z10*z5+ + 2*z9*z7+2*z9*z6-z8*z6+6*z7S+6*z7*z6-2*z7*z5-z6*z5)+4*(- + z1S*z9+z1S*z8+2*z1*z2*z10+3*z1*z2*z7+3*z1*z2*z6-z1*z3 + *z9-z1*z3*z8-z1*z3*z5-z1*z4*z8+z1*z4*z5-z1*z10*z9-z1*z10* + z8-z1*z9*z7+z1*z8*z7+z2*z3*z7+3*z2*z3*z6-z2*z4*z6+3*z2* + z10*z7+3*z2*z10*z6+3*z2*z7S+3*z2*z7*z6+z3S*z5+2*z3*z4 + *z5+z3*z10*z5-z3*z7*z5+z4*z10*z5+z4*z7*z5); + fm[5][8] = 8*mQ4*(-2*z3-z4-3*z10-2*z7-z6)+4*mQ2*(2*z1*z3+ + 4*z1*z4+2*z1*z10-z1*z9+z1*z8+2*z1*z7+4*z1*z6-2*z2*z3-z2* + z4-z2*z10+2*z2*z7+z2*z6+6*z3S+6*z3*z4+6*z3*z10+2*z3*z8+ + 2*z3*z7+4*z3*z6-2*z3*z5+6*z4*z10-z4*z9+2*z4*z8+4*z4*z7+2* + z4*z6-z4*z5+3*z10*z9+3*z10*z8+6*z10*z7+6*z10*z6-3*z10*z5+ + 3*z9*z7+2*z9*z6+z8*z7+6*z7S+6*z7*z6-2*z7*z5-z6*z5)+4*( + z1S*z9-z1S*z8-z1*z2*z7+z1*z2*z6+z1*z3*z9-z1*z3*z8+3* + z1*z3*z5+3*z1*z4*z5-z1*z10*z9-z1*z10*z8+2*z1*z10*z5-z1*z9 + *z7-z1*z9*z6-z1*z8*z7-z2*z3*z7+z2*z3*z6+z2*z10*z7+z2*z10* + z6+z2*z7S+2*z2*z7*z6+3*z3S*z5+3*z3*z4*z5+3*z3*z10*z5+ + z3*z7*z5+3*z4*z10*z5+3*z4*z7*z5-z4*z6*z5); + fm[6][6] = 64*mQ6+16*mQ4*s3+32*mQ4*(z1+z2+2*z4+z9+z7 + +2*z5)+8*mQ2*s3*(-z1+2*z4-z7)+16*mQ2*(z2*z5-2*z4* + z9-2*z4*z7+4*z4*z5+z9*z5)+8*s3*z4*z7-16*z4*z9*z5; + fm[6][7] = 8*mQ4*(-6*z3-3*z4-3*z10-2*z9-z8-z7-2*z6)+2*mQ2 + *s3*(-2*z3-z4-2*z10+z7+2*z6)+4*mQ2*(-8*z1*z3-4*z1*z4 + -4*z1*z10+2*z1*z9-2*z1*z8-10*z2*z3-2*z2*z4-5*z2*z10-z2*z9 + -2*z2*z8-4*z2*z7-2*z2*z6-5*z3*z9-4*z3*z7-8*z3*z5-2*z4*z9+ + 7*z4*z8-4*z4*z7+8*z4*z6-4*z4*z5-5*z10*z5-z9S+z9*z8-2*z9 + *z7+z9*z6-2*z9*z5+z8*z7-z8*z5)+2*s3*(z1*z10-z3*z7+2*z4 + *z7-z4*z6)+4*(2*z1*z2*z9+z1*z2*z8+z1*z9S-z1*z9*z8-2* + z2S*z7-z2S*z6-3*z2*z3*z5-2*z2*z10*z5-z2*z9*z7-z2*z9*z6+ + 2*z2*z8*z7-z3*z9*z5-z4*z9*z5+2*z4*z8*z5); + fm[6][8] = 8*mQ4*(-6*z3-3*z4-3*z10-z9-2*z8-z7-2*z6)+2*mQ2 + *s3*(-6*z3-3*z4-3*z10+z7+2*z6)+4*mQ2*(-8*z1*z3-4*z1* + z4-4*z1*z10-8*z2*z3-4*z2*z4-4*z2*z10-4*z3*z9-4*z3*z7-12* + z3*z5-4*z4*z9+8*z4*z8-4*z4*z7+8*z4*z6-6*z4*z5-6*z10*z5-z9 + *z5-2*z8*z5)+4*s3*(2*z1*z3+z1*z4+z1*z10+z3*z7+z4*z7-2* + z4*z6)+8*z5*(-2*z2*z3-z2*z4-z2*z10-z3*z9-z4*z9+2*z4*z8); + fm[7][7] = 72*mQ4*z10+18*mQ2*s3*z10+8*mQ2*(z1*z10+9* + z2*z10+7*z3*z7+2*z3*z6+2*z4*z7+7*z4*z6+z10*z5+2*z9*z7+7* + z9*z6+7*z8*z7+2*z8*z6)+2*s3*(-z1*z10-7*z3*z7-2*z3*z6-2 + *z4*z7-7*z4*z6)+4*z2*(z10*z5+2*z9*z7+7*z9*z6+7*z8*z7+2*z8 + *z6); + fm[7][8] = 72*mQ4*z10+2*mQ2*s3*z10+4*mQ2*(2*z1*z10+ + 10*z2*z10+7*z3*z9+2*z3*z8+14*z3*z7+4*z3*z6+2*z4*z9+7*z4* + z8+4*z4*z7+14*z4*z6+10*z10*z5+z9S+7*z9*z8+2*z9*z7+7*z9* + z6+z8S+7*z8*z7+2*z8*z6)+2*s3*(7*z1*z10-7*z3*z7-2*z3* + z6-2*z4*z7-7*z4*z6)+2*(-2*z1*z9S-14*z1*z9*z8-2*z1*z8S + +2*z2*z10*z5+2*z2*z9*z7+7*z2*z9*z6+7*z2*z8*z7+2*z2*z8*z6+ + 7*z3*z9*z5+2*z3*z8*z5+2*z4*z9*z5+7*z4*z8*z5); + fm[8][8] = 72*mQ4*z10+18*mQ2*s3*z10+8*mQ2*(z1*z10+z2 + *z10+7*z3*z9+2*z3*z8+7*z3*z7+2*z3*z6+2*z4*z9+7*z4*z8+2*z4 + *z7+7*z4*z6+9*z10*z5)+2*s3*(-z1*z10-7*z3*z7-2*z3*z6-2* + z4*z7-7*z4*z6)+4*z5*(z2*z10+7*z3*z9+2*z3*z8+2*z4*z9+7*z4* + z8); + double fm99 = -4*mQ4*z10-mQ2*s3*z10+4*mQ2*(-z1*z10-z2*z10+ + z3*z7+z4*z6-z10*z5+z9*z6+z8*z7)+s3*(z1*z10-z3*z7-z4*z6 + )+2*z2*(-z10*z5+z9*z6+z8*z7); + double fm910 = -4*mQ4*z10-mQ2*s3*z10+2*mQ2*(-2*z1*z10-2*z2* + z10+2*z3*z9+2*z3*z7+2*z4*z6-2*z10*z5+z9*z8+2*z8*z7)+s3 + *(z1*z10-z3*z7-z4*z6)+2*(-z1*z9*z8-z2*z10*z5+z2*z8*z7+z3* + z9*z5); + double fmxx = -4*mQ4*z10-mQ2*s3*z10+2*mQ2*(-2*z1*z10-2*z2* + z10+2*z4*z8+2*z4*z6+2*z3*z7-2*z10*z5+z9*z8+2*z9*z6)+s3 + *(z1*z10-z3*z7-z4*z6)+2*(-z1*z9*z8-z2*z10*z5+z2*z9*z6+z4* + z8*z5); + fm910 = 0.5*(fmxx+fm910); + double fm1010 = -4*mQ4*z10-mQ2*s3*z10+4*mQ2*(-z1*z10-z2*z10+ + z3*z7+z4*z6-z10*z5+z9*z3+z8*z4)+s3*(z1*z10-z3*z7-z4*z6 + )+2*z5*(-z10*z2+z9*z3+z8*z4); + fm[7][7] -= 2. * fm99; + fm[7][8] -= 2. * fm910; + fm[8][8] -= 2. * fm1010; + + // Propagators. + double ss1 = (pTemp[1] + pTemp[3]).m2Calc() - mQ2; + double ss2 = (pTemp[1] + pTemp[4]).m2Calc() - mQ2; + double ss3 = (pTemp[1] + pTemp[5]).m2Calc() - mQ2; + double ss4 = (pTemp[2] + pTemp[3]).m2Calc() - mQ2; + double ss5 = (pTemp[2] + pTemp[4]).m2Calc() - mQ2; + double ss6 = (pTemp[2] + pTemp[5]).m2Calc() - mQ2; + double ss7 = sH; + + // Propagator combinations. + double dz[9]; + dz[1] = ss1 * ss6; + dz[2] = ss2 * ss6; + dz[3] = ss2 * ss4; + dz[4] = ss1 * ss5; + dz[5] = ss3 * ss5; + dz[6] = ss3 * ss4; + dz[7] = ss7 * ss1; + dz[8] = ss7 * ss4; + + // Colour factors. + double clr[9][9]; + for (int i = 1; i < 4; ++i) + for (int j = 1; j < 4; ++j) { + clr[i][j] = 16. / 3.; + clr[i][j+3] = -2. / 3.; + clr[i+3][j] = -2. / 3.; + clr[i+3][j+3] = 16. / 3.; + } + for (int i = 1; i < 4; ++i) + for (int j = 1; j < 3; ++j) { + clr[i][j+6] = -6.; + clr[i+3][j+6] = 6.; + clr[j+6][i] = -6.; + clr[j+6][i+3] = 6.; + } + for (int i = 1; i < 3; ++i) + for (int j = 1; j < 3; ++j) + clr[i+6][j+6] = 12.; + + // Produce final result: matrix elements * colours * propagators. + double wtSum = 0.; + for (int i = 1; i < 9; ++i) + for (int j = i; j < 9; ++j) { + double fac = (j == i) ? 4. : 8.; + wtSum += fm[i][j] * fac * clr[i][j] / (dz[i] * dz[j]); + } + wtSum *= -1./256.; + + // Combine factors. + sigma = prefac * alpEM * pow2(alpS) * mQ2run * wtSum *pow2(coup2Q); + + // Secondary width for H, Q and Qbar (latter for top only). + // (H can be H0 SM or H1, H2, A3 from BSM). + sigma *= openFracTriplet; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3gg2HQQbar::setIdColAcol() { + + // Pick out-flavours by relative CKM weights. + setId( id1, id2, idRes, idNew, -idNew); + + // Colour flow topologies. + if (rndmPtr->flat() < 0.5) setColAcol( 1, 2, 2, 3, 0, 0, 1, 0, 0, 3); + else setColAcol( 1, 2, 3, 1, 0, 0, 3, 0, 0, 2); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma3gg2HQQbar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma3qqbar2HQQbar class. +// Cross section for q qbar -> H0 Q Qbar (Q Qbar fusion of SM Higgs). +// REDUCE output and part of the rest courtesy Z. Kunszt, +// see Z. Kunszt, Nucl. Phys. B247 (1984) 339. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3qqbar2HQQbar::initProc() { + + // Properties specific to Higgs state for the "q qbar -> H ttbar" process. + // (H can be H0 SM or H1, H2, A3 from BSM). + + if (higgsType == 0 && idNew == 6) { + nameSave = "q qbar -> H t tbar (SM)"; + codeSave = 909; + idRes = 25; + coup2Q = 1.; + } + else if (higgsType == 1 && idNew == 6) { + nameSave = "q qbar -> h0(H1) t tbar"; + codeSave = 1009; + idRes = 25; + coup2Q = settingsPtr->parm("HiggsH1:coup2u"); + } + else if (higgsType == 2 && idNew == 6) { + nameSave = "q qbar -> H0(H2) t tbar"; + codeSave = 1029; + idRes = 35; + coup2Q = settingsPtr->parm("HiggsH2:coup2u"); + } + else if (higgsType == 3 && idNew == 6) { + nameSave = "q qbar -> A0(A3) t tbar"; + codeSave = 1049; + idRes = 36; + coup2Q = settingsPtr->parm("HiggsA3:coup2u"); + } + + // Properties specific to Higgs state for the "q qbar -> H b bbar" process. + // (H can be H0 SM or H1, H2, A3 from BSM). + if (higgsType == 0 && idNew == 5) { + nameSave = "q qbar -> H b bbar (SM)"; + codeSave = 913; + idRes = 25; + coup2Q = 1.; + } + else if (higgsType == 1 && idNew == 5) { + nameSave = "q qbar -> h0(H1) b bbar"; + codeSave = 1013; + idRes = 25; + coup2Q = settingsPtr->parm("HiggsH1:coup2d"); + } + else if (higgsType == 2 && idNew == 5) { + nameSave = "q qbar -> H0(H2) b bbar"; + codeSave = 1033; + idRes = 35; + coup2Q = settingsPtr->parm("HiggsH2:coup2d"); + } + else if (higgsType == 3 && idNew == 5) { + nameSave = "q qbar -> A0(A3) b bbar"; + codeSave = 1053; + idRes = 36; + coup2Q = settingsPtr->parm("HiggsA3:coup2d"); + } + + // Common mass and coupling factors. + double mWS = pow2(particleDataPtr->m0(24)); + prefac = (4. * M_PI / coupSMPtr->sin2thetaW()) * pow2(4. * M_PI) + * 0.25 / mWS; + + // Secondary open width fraction. + openFracTriplet = particleDataPtr->resOpenFrac(idRes, idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigma(sHat), part independent of incoming flavour. + +void Sigma3qqbar2HQQbar::sigmaKin() { + + // Running mass of heavy quark. + double mQ2run = pow2( particleDataPtr->mRun(idNew, mH) ); + + // Linear combination of p_Q and p_Qbar to ensure common mass. + double mQ2 = m4 * m5; + double epsi = 0.; + if (m4 != m5) { + double s45 = (p4cm + p5cm).m2Calc(); + mQ2 = 0.5 * (s4 + s5) - 0.25 * pow2(s4 - s5) / s45; + epsi = 0.5 * (s5 - s4) / s45; + } + + // Set up kinematics: q(4) qbar(5) -> H(3) Q(1) Qbar(2) in outgoing sense. + Vec4 pTemp[6]; + pTemp[4] = Vec4( 0., 0., -0.5* mH, -0.5* mH); + pTemp[5] = Vec4( 0., 0., 0.5* mH, -0.5* mH); + pTemp[1] = p4cm + epsi * (p4cm + p5cm); + pTemp[2] = p5cm - epsi * (p4cm + p5cm); + pTemp[3] = p3cm; + + // Four-product combinations. + double z1 = pTemp[1] * pTemp[2]; + double z2 = pTemp[1] * pTemp[3]; + double z3 = pTemp[1] * pTemp[4]; + double z4 = pTemp[1] * pTemp[5]; + double z5 = pTemp[2] * pTemp[3]; + double z6 = pTemp[2] * pTemp[4]; + double z7 = pTemp[2] * pTemp[5]; + double z8 = pTemp[3] * pTemp[4]; + double z9 = pTemp[3] * pTemp[5]; + double z10 = pTemp[4] * pTemp[5]; + + // Powers required as shorthand in matriz elements. + double mQ4 = mQ2 * mQ2; + + // Evaluate matrix elements for q + qbar -> Q + Qbar + H. + // (H can be H0 SM or H1, H2, A3 from BSM). + double a11 = -8.*mQ4*z10-2.*mQ2*s3*z10-(8.*mQ2)*(z2*z10+z3 + *z7+z4*z6+z9*z6+z8*z7)+2.*s3*(z3*z7+z4*z6)-(4.*z2)*(z9 + *z6+z8*z7); + double a12 = -8.*mQ4*z10+4.*mQ2*(-z2*z10-z3*z9-2.*z3*z7-z4*z8- + 2.*z4*z6-z10*z5-z9*z8-z9*z6-z8*z7)+2.*s3*(-z1*z10+z3*z7 + +z4*z6)+2.*(2.*z1*z9*z8-z2*z9*z6-z2*z8*z7-z3*z9*z5-z4*z8* + z5); + double a22 = -8.*mQ4*z10-2.*mQ2*s3*z10-(8.*mQ2)*(z3*z9+z3* + z7+z4*z8+z4*z6+z10*z5)+2.*s3*(z3*z7+z4*z6)-(4.*z5)*(z3 + *z9+z4*z8); + + // Propagators and propagator combinations. + double ss1 = (pTemp[1] + pTemp[3]).m2Calc() - mQ2; + double ss4 = (pTemp[2] + pTemp[3]).m2Calc() - mQ2; + double ss7 = sH; + double dz7 = ss7 * ss1; + double dz8 = ss7 * ss4; + + // Produce final result: matrix elements * propagators. + a11 /= (dz7 * dz7); + a12 /= (dz7 * dz8); + a22 /= (dz8 * dz8); + double wtSum = -(a11 + a22 + 2.*a12) * (8./9.); + + // Combine factors. + sigma = prefac * alpEM * pow2(alpS) * mQ2run * wtSum * pow2(coup2Q); + + // Secondary width for H, Q and Qbar (latter for top only). + // (H can be H0 SM or H1, H2, A3 from BSM). + sigma *= openFracTriplet; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qqbar2HQQbar::setIdColAcol() { + + // Pick out-flavours by relative CKM weights. + setId( id1, id2, idRes, idNew, -idNew); + + // Colour flow topologies. + if (id1 > 0) setColAcol( 1, 0, 0, 2, 0, 0, 1, 0, 0, 2); + else setColAcol( 0, 1, 2, 0, 0, 0, 2, 0, 0, 1); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma3qqbar2HQQbar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2qg2Hq class. +// Cross section for q g -> H q. +// (H can be H0 SM or H1, H2, A3 from BSM). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2Hq::initProc() { + + // Properties specific to Higgs state for the "c g -> H c" process. + // (H can be H0 SM or H1, H2, A3 from BSM). + if (higgsType == 0 && idNew == 4) { + nameSave = "c g -> H c (SM)"; + codeSave = 911; + idRes = 25; + } + else if (higgsType == 1 && idNew == 4) { + nameSave = "c g -> h0(H1) c"; + codeSave = 1011; + idRes = 25; + } + else if (higgsType == 2 && idNew == 4) { + nameSave = "c g -> H0(H2) c"; + codeSave = 1031; + idRes = 35; + } + else if (higgsType == 3 && idNew == 4) { + nameSave = "c g -> A0(A3) c"; + codeSave = 1051; + idRes = 36; + } + + // Properties specific to Higgs state for the "b g -> H b" process. + // (H can be H0 SM or H1, H2, A3 from BSM). + if (higgsType == 0 && idNew == 5) { + nameSave = "b g -> H b (SM)"; + codeSave = 911; + idRes = 25; + } + else if (higgsType == 1 && idNew == 5) { + nameSave = "b g -> h0(H1) b"; + codeSave = 1011; + idRes = 25; + } + else if (higgsType == 2 && idNew == 5) { + nameSave = "b g -> H0(H2) b"; + codeSave = 1031; + idRes = 35; + } + else if (higgsType == 3 && idNew == 5) { + nameSave = "b g -> A0(A3) b"; + codeSave = 1051; + idRes = 36; + } + + // Standard parameters. + m2W = pow2( particleDataPtr->m0(24) ); + thetaWRat = 1. / (24. * coupSMPtr->sin2thetaW()); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idRes); + + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qg2Hq::sigmaKin() { + + // Running mass provides coupling. + double m2Run = pow2( particleDataPtr->mRun(idNew, mH) ); + + // Cross section, including couplings and kinematics. + sigma = (M_PI / sH2) * alpS * alpEM * thetaWRat * (m2Run/m2W) + * (sH / (s4 - uH) + 2. * s4 * (s3 - uH) / pow2(s4 - uH) + + (s4 - uH) / sH - 2. * s4 / (s4 - uH) + + 2. * (s3 - uH) * (s3 - s4 - sH) / ((s4 - uH) * sH) ); + + // Include secondary width for H0, H1, H2 or A3. Done. + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma2qg2Hq::sigmaHat() { + + // Check that specified flavour present. + if (abs(id1) != idNew && abs(id2) != idNew) return 0.; + + // Answer. + return sigma; + +} + + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2Hq::setIdColAcol() { + + // Flavour set up for q g -> H0 q. + int idq = (id2 == 21) ? id1 : id2; + setId( id1, id2, idRes, idq); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2qg2Hq::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2gg2Hglt class. +// Cross section for g g -> H g (H SM Higgs or BSM Higgs) via top loop. +// (H can be H0 SM or H1, H2, A3 from BSM). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2Hglt::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "g g -> H g (SM; top loop)"; + codeSave = 914; + idRes = 25; + } + else if (higgsType == 1) { + nameSave = "g g -> h0(H1) g (BSM; top loop)"; + codeSave = 1014; + idRes = 25; + } + else if (higgsType == 2) { + nameSave = "g g -> H0(H2) g (BSM; top loop)"; + codeSave = 1034; + idRes = 35; + } + else if (higgsType == 3) { + nameSave = "g g -> A0(A3) g (BSM; top loop)"; + codeSave = 1054; + idRes = 36; + } + + // Normalization factor by g g -> H partial width. + // (H can be H0 SM or H1, H2, A3 from BSM). + double mHiggs = particleDataPtr->m0(idRes); + widHgg = particleDataPtr->resWidthChan(idRes, mHiggs, 21, 21); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2gg2Hglt::sigmaKin() { + + // Evaluate cross section. Secondary width for H0, H1, H2 or A3. + sigma = (M_PI / sH2) * (3. / 16.) * alpS * (widHgg / m3) + * (sH2 * sH2 + tH2 * tH2 + uH2 * uH2 + pow4(s3)) + / (sH * tH * uH * s3); + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2Hglt::setIdColAcol() { + + // Flavour set up for g g -> H g trivial. + // (H can be H0 SM or H1, H2, A3 from BSM). + setId( 21, 21, idRes, 21); + + // Colour flow topologies: random choice between two mirrors. + if (rndmPtr->flat() < 0.5) setColAcol( 1, 2, 2, 3, 0, 0, 1, 3); + else setColAcol( 1, 2, 3, 1, 0, 0, 3, 2); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2gg2Hglt::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2qg2Hqlt class. +// Cross section for q g -> H q (H SM or BSM Higgs) via top loop. +// (H can be H0 SM or H1, H2, A3 from BSM). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2Hqlt::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "q g -> H q (SM; top loop)"; + codeSave = 915; + idRes = 25; + } + else if (higgsType == 1) { + nameSave = "q g -> h0(H1) q (BSM; top loop)"; + codeSave = 1015; + idRes = 25; + } + else if (higgsType == 2) { + nameSave = "q g -> H0(H2) q (BSM; top loop)"; + codeSave = 1035; + idRes = 35; + } + else if (higgsType == 3) { + nameSave = "q g -> A0(A3) q (BSM; top loop)"; + codeSave = 1055; + idRes = 36; + } + + // Normalization factor by g g -> H partial width. + // (H can be H0 SM or H1, H2, A3 from BSM). + double mHiggs = particleDataPtr->m0(idRes); + widHgg = particleDataPtr->resWidthChan(idRes, mHiggs, 21, 21); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idRes); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat, part independent of incoming flavour). + +void Sigma2qg2Hqlt::sigmaKin() { + + // Evaluate cross section. Secondary width for H0, H1, H2 or A3. + sigma = (M_PI / sH2) * (1. / 12.) * alpS * (widHgg / m3) + * (sH2 + uH2) / (-tH * s3); + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2Hqlt::setIdColAcol() { + + // Flavour set up for q g -> H q. + // (H can be H0 SM or H1, H2, A3 from BSM). + int idq = (id2 == 21) ? id1 : id2; + setId( id1, id2, idRes, idq); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2qg2Hqlt::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2qqbar2Hglt class. +// Cross section for q qbar -> H g (H SM or BSM Higgs) via top loop. +// (H can be H0 SM or H1, H2, A3 from BSM). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2Hglt::initProc() { + + // Properties specific to Higgs state. + if (higgsType == 0) { + nameSave = "q qbar -> H g (SM; top loop)"; + codeSave = 916; + idRes = 25; + } + else if (higgsType == 1) { + nameSave = "q qbar -> h0(H1) g (BSM; top loop)"; + codeSave = 1016; + idRes = 25; + } + else if (higgsType == 2) { + nameSave = "q qbar -> H0(H2) g (BSM; top loop)"; + codeSave = 1036; + idRes = 35; + } + else if (higgsType == 3) { + nameSave = "q qbar -> A0(A3) g (BSM; top loop)"; + codeSave = 1056; + idRes = 36; + } + + // Normalization factor by g g -> H partial width. + // (H can be H0 SM or H1, H2, A3 from BSM). + double mHiggs = particleDataPtr->m0(idRes); + widHgg = particleDataPtr->resWidthChan(idRes, mHiggs, 21, 21); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(idRes); + + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qqbar2Hglt::sigmaKin() { + + // Evaluate cross section. Secondary width for H0, H1, H2 or A3. + sigma = (M_PI / sH2) * (2. / 9.) * alpS * (widHgg / m3) + * (tH2 + uH2) / (sH * s3); + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2Hglt::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idRes, 21); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 0, 0, 1, 2); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2qqbar2Hglt::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + + +//========================================================================== + +// Sigma1ffbar2Hchg class. +// Cross section for f fbar -> H+- (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2Hchg::initProc() { + + // Find pointer to H+-. + HResPtr = particleDataPtr->particleDataEntryPtr(37); + + // Store H+- mass and width for propagator. + mRes = HResPtr->m0(); + GammaRes = HResPtr->mWidth(); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Couplings. + m2W = pow2(particleDataPtr->m0(24)); + thetaWRat = 1. / (8. * coupSMPtr->sin2thetaW()); + tan2Beta = pow2(settingsPtr->parm("HiggsHchg:tanBeta")); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma1ffbar2Hchg::sigmaKin() { + + // Set up Breit-Wigner. Width out only includes open channels. + sigBW = 4. * M_PI / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + widthOutPos = HResPtr->resWidthOpen( 37, mH); + widthOutNeg = HResPtr->resWidthOpen(-37, mH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2Hchg::sigmaHat() { + + // Only allow generation-diagonal states. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + int idUp = max(id1Abs, id2Abs); + int idDn = min(id1Abs, id2Abs); + if (idUp%2 != 0 || idUp - idDn != 1) return 0.; + + // Calculate mass-dependent incoming width. Total cross section. + double m2RunUp = pow2(particleDataPtr->mRun(idUp, mH)); + double m2RunDn = pow2(particleDataPtr->mRun(idDn, mH)); + double widthIn = alpEM * thetaWRat * (mH/m2W) + * (m2RunDn * tan2Beta + m2RunUp / tan2Beta); + int idUpChg = (id1Abs%2 == 0) ? id1 : id2; + double sigma = (idUpChg > 0) ? widthIn * sigBW * widthOutPos + : widthIn * sigBW * widthOutNeg; + + // Colour factor. Answer. + if (idUp < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2Hchg::setIdColAcol() { + + // Charge of Higgs. Fill flavours. + int idUpChg = (abs(id1)%2 == 0) ? id1 : id2; + int idHchg = (idUpChg > 0) ? 37 : -37; + setId( id1, id2, idHchg); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma1ffbar2Hchg::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2qg2Hq class. +// Cross section for q g -> H+- q'. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2Hchgq::initProc() { + + // Standard parameters. + m2W = pow2( particleDataPtr->m0(24) ); + thetaWRat = 1. / (24. * coupSMPtr->sin2thetaW()); + tan2Beta = pow2(settingsPtr->parm("HiggsHchg:tanBeta")); + + // Incoming flavour within same doublet. Uptype and downtype flavours. + idOld = (idNew%2 == 0) ? idNew - 1 : idNew + 1; + idUp = max(idOld, idNew); + idDn = min(idOld, idNew); + + // Secondary open width fraction. + openFracPos = (idOld%2 == 0) ? particleDataPtr->resOpenFrac( 37, idNew) + : particleDataPtr->resOpenFrac(-37, idNew); + openFracNeg = (idOld%2 == 0) ? particleDataPtr->resOpenFrac(-37, -idNew) + : particleDataPtr->resOpenFrac( 37, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qg2Hchgq::sigmaKin() { + + // Running masses provides coupling. + double m2RunUp = pow2(particleDataPtr->mRun(idUp, mH)); + double m2RunDn = pow2(particleDataPtr->mRun(idDn, mH)); + + // Cross section, including couplings and kinematics. + sigma = (M_PI / sH2) * alpS * alpEM * thetaWRat + * (m2RunDn * tan2Beta + m2RunUp / tan2Beta) / m2W + * (sH / (s4 - uH) + 2. * s4 * (s3 - uH) / pow2(s4 - uH) + + (s4 - uH) / sH - 2. * s4 / (s4 - uH) + + 2. * (s3 - uH) * (s3 - s4 - sH) / ((s4 - uH) * sH) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma2qg2Hchgq::sigmaHat() { + + // Check that specified flavour present. + if (abs(id1) != idOld && abs(id2) != idOld) return 0.; + + // Answer. + return (id1 == idOld || id2 == idOld) ? sigma * openFracPos + : sigma * openFracNeg; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2Hchgq::setIdColAcol() { + + // Flavour set up for q g -> H+- q'. + int idq = (id2 == 21) ? id1 : id2; + id3 = ( (idq > 0 && idOld%2 == 0) || (idq < 0 && idOld%2 != 0) ) + ? 37 : -37; + id4 = (idq > 0) ? idNew : -idNew; + setId( id1, id2, id3, id4); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2qg2Hchgq::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2ffbar2A3H12 class. +// Cross section for f fbar -> A0(H_3) h0(H_1) or A0(H_3) H0(H_2). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2A3H12::initProc() { + + // Set up whether h0(H_1) or H0(H_2). + higgs12 = (higgsType == 1) ? 25 : 35; + codeSave = (higgsType == 1) ? 1081 : 1082; + nameSave = (higgsType == 1) ? "f fbar -> A0(H3) h0(H1)" + : "f fbar -> A0(H3) H0(H2)"; + coupZA3H12 = (higgsType == 1) ? settingsPtr->parm("HiggsA3:coup2H1Z") + : settingsPtr->parm("HiggsA3:coup2H2Z"); + + // Standard parameters. + double mZ = particleDataPtr->m0(23); + double GammaZ = particleDataPtr->mWidth(23); + m2Z = mZ * mZ; + mGammaZ = mZ * GammaZ; + thetaWRat = 1. / (4. * coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(36, higgs12); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2ffbar2A3H12::sigmaKin() { + + // Common kinematics factora. + sigma0 = (M_PI / sH2) * pow2(alpEM * thetaWRat * coupZA3H12) + * (uH * tH - s3 * s4) / ( pow2(sH - m2Z) + pow2(mGammaZ) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma2ffbar2A3H12::sigmaHat() { + + // Couplings for incoming flavour. + int idAbs = abs(id1); + double lIn = coupSMPtr->lf(idAbs); + double rIn = coupSMPtr->rf(idAbs); + + // Combine to total cross section. Colour factor. + double sigma = (pow2(lIn) + pow2(rIn)) * sigma0 * openFrac; + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2A3H12::setIdColAcol() { + + // Flavours trivial + setId( id1, id2, 36, higgs12); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2ffbar2A3H12::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2ffbar2HchgH12 class. +// Cross section for f fbar -> H+- h0(H_1) or H+- H0(H_2). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2HchgH12::initProc() { + + // Set up whether h0(H_1) or H0(H_2). + higgs12 = (higgsType == 1) ? 25 : 35; + codeSave = (higgsType == 1) ? 1083 : 1084; + nameSave = (higgsType == 1) ? "f fbar' -> H+- h0(H1)" + : "f fbar' -> H+- H0(H2)"; + coupWHchgH12 = (higgsType == 1) ? settingsPtr->parm("HiggsHchg:coup2H1W") + : settingsPtr->parm("HiggsHchg:coup2H2W"); + + // Standard parameters. + double mW = particleDataPtr->m0(24); + double GammaW = particleDataPtr->mWidth(24); + m2W = mW * mW; + mGammaW = mW * GammaW; + thetaWRat = 1. / (2. * coupSMPtr->sin2thetaW()); + + // Secondary open width fraction. + openFracPos = particleDataPtr->resOpenFrac( 37, higgs12); + openFracNeg = particleDataPtr->resOpenFrac(-37, higgs12); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2ffbar2HchgH12::sigmaKin() { + + // Common kinematics factora. + sigma0 = 0.5 * (M_PI / sH2) * pow2(alpEM * thetaWRat * coupWHchgH12) + * (uH * tH - s3 * s4) / ( pow2(sH - m2W) + pow2(mGammaW) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma2ffbar2HchgH12::sigmaHat() { + + // Combine to total cross section. CKM and colour factor. + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + double sigma = (idUp > 0) ? sigma0 * openFracPos : sigma0 * openFracNeg; + if (abs(id1) < 9) sigma *= coupSMPtr->V2CKMid(abs(id1), abs(id2)) / 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2HchgH12::setIdColAcol() { + + // Charge of Higgs. Fill flavours. + int idUpChg = (abs(id1)%2 == 0) ? id1 : id2; + int idHchg = (idUpChg > 0) ? 37 : -37; + setId( id1, id2, idHchg, higgs12); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2ffbar2HchgH12::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2ffbar2HposHneg class. +// Cross section for q g -> H+- q'. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2HposHneg::initProc() { + + // Standard parameters. + double mZ = particleDataPtr->m0(23); + double GammaZ = particleDataPtr->mWidth(23); + m2Z = mZ * mZ; + mGammaZ = mZ * GammaZ; + thetaWRat = 1. / (4. * coupSMPtr->sin2thetaW() * coupSMPtr->cos2thetaW()); + + // Charged Higgs coupling to gamma and Z0. + eH = -1.; + lH = -1. + 2. * coupSMPtr->sin2thetaW(); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(37, -37); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2ffbar2HposHneg::sigmaKin() { + + // Common kinematics factora. + double preFac = M_PI * pow2(alpEM) * ((uH * tH - s3 * s4) / sH2); + double propZ = 1. / ( pow2(sH - m2Z) + pow2(mGammaZ) ); + + // Separate parts for gamma*, interference and Z0. + gamSig = preFac * 2. * pow2(eH) / sH2; + intSig = preFac * 2. * eH * lH * thetaWRat * propZ * (sH - m2Z) / sH; + resSig = preFac * pow2(lH * thetaWRat) * propZ; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma2ffbar2HposHneg::sigmaHat() { + + // Couplings for incoming flavour. + int idAbs = int(id1); + double eIn = coupSMPtr->ef(idAbs); + double lIn = coupSMPtr->lf(idAbs); + double rIn = coupSMPtr->rf(idAbs); + + // Combine to total cross section. Colour factor. + double sigma = (pow2(eIn) * gamSig + eIn * (lIn + rIn) * intSig + + (pow2(lIn) + pow2(rIn)) * resSig) * openFrac; + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2HposHneg::setIdColAcol() { + + // Flavours trivial + setId( id1, id2, 37, -37); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma2ffbar2HposHneg::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For Higgs decay hand over to standard routine. + if (idMother == 25 || idMother == 35 || idMother == 36) + return weightHiggsDecay( process, iResBeg, iResEnd); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaLeftRightSym.cxx b/PYTHIA8/pythia8140/src/SigmaLeftRightSym.cxx new file mode 100644 index 00000000000..be52f96c30e --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaLeftRightSym.cxx @@ -0,0 +1,808 @@ +// SigmaLeftRightSym.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// left-right-symmetry simulation classes. + +#include "SigmaLeftRightSym.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma1ffbar2ZRight class. +// Cross section for f fbar -> Z_R^0 (righthanded gauge boson). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2ZRight::initProc() { + + // Store Z_R mass and width for propagator. + idZR = 9900023; + mRes = particleDataPtr->m0(idZR); + GammaRes = particleDataPtr->mWidth(idZR); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + sin2tW = coupSMPtr->sin2thetaW(); + + // Set pointer to particle properties and decay table. + ZRPtr = particleDataPtr->particleDataEntryPtr(idZR); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2ZRight::sigmaKin() { + + // Set up Breit-Wigner. Width out only includes open channels. + double sigBW = 12. * M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double widthOut = ZRPtr->resWidthOpen(idZR, mH); + + // Prefactor for incoming widths. Combine. Done. + double preFac = alpEM * mH / ( 48. * sin2tW * (1. - sin2tW) + * (1. - 2. * sin2tW) ); + sigma0 = preFac * sigBW * widthOut; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2ZRight::sigmaHat() { + + // Vector and axial couplings of incoming fermion pair. + int idAbs = abs(id1); + double af = 0.; + double vf = 0.; + if (idAbs < 9 && idAbs%2 == 1) { + af = -1. + 2. * sin2tW; + vf = -1. + 4. * sin2tW / 3.; + } else if (idAbs < 9) { + af = 1. - 2. * sin2tW; + vf = 1. - 8. * sin2tW / 3.; + } else if (idAbs < 19 && idAbs%2 == 1) { + af = -1. + 2. * sin2tW; + vf = -1. + 4. * sin2tW; + } + + // Colour factor. Answer. + double sigma = (vf*vf + af*af) * sigma0; + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2ZRight::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, idZR); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for Z_R decay angle. + +double Sigma1ffbar2ZRight::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Z_R should sit in entry 5. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Couplings for in- and out-flavours. + double ai, vi, af, vf; + int idInAbs = process[3].idAbs(); + if (idInAbs < 9 && idInAbs%2 == 1) { + ai = -1. + 2. * sin2tW; + vi = -1. + 4. * sin2tW / 3.; + } else if (idInAbs < 9) { + ai = 1. - 2. * sin2tW; + vi = 1. - 8. * sin2tW / 3.; + } else { + ai = -1. + 2. * sin2tW; + vi = -1. + 4. * sin2tW; + } + int idOutAbs = process[6].idAbs(); + if (idOutAbs < 9 && idOutAbs%2 == 1) { + af = -1. + 2. * sin2tW; + vf = -1. + 4. * sin2tW / 3.; + } else if (idOutAbs < 9) { + af = 1. - 2. * sin2tW; + vf = 1. - 8. * sin2tW / 3.; + } else { + af = -1. + 2. * sin2tW; + vf = -1. + 4. * sin2tW; + } + + // Phase space factors. Reconstruct decay angle. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + + // Angular weight and its maximum. + double wt1 = (vi*vi + ai*ai) * (vf*vf + af*af * betaf*betaf); + double wt2 = (1. - betaf*betaf) * (vi*vi + ai*ai) * vf*vf; + double wt3 = betaf * 4. * vi * ai * vf * af; + if (process[3].id() * process[6].id() < 0) wt3 = -wt3; + double wt = wt1 * (1. + cosThe*cosThe) + wt2 * (1. - cosThe*cosThe) + + 2. * wt3 * cosThe; + double wtMax = 2. * (wt1 + abs(wt3)); + + // Done. + return wt / wtMax; + +} + +//========================================================================== + +// Sigma1ffbar2WRight class. +// Cross section for f fbar' -> W_R^+- (righthanded gauge boson). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2WRight::initProc() { + + // Store W_R^+- mass and width for propagator. + idWR = 9900024; + mRes = particleDataPtr->m0(idWR); + GammaRes = particleDataPtr->mWidth(idWR); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(idWR); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2WRight::sigmaKin() { + + // Common coupling factors. + double colQ = 3. * (1. + alpS / M_PI); + + // Reset quantities to sum. Declare variables inside loop. + double widOutPos = 0.; + double widOutNeg = 0.; + int id1Now, id2Now, id1Abs, id2Abs, id1Neg, id2Neg, onMode; + double widNow, widSecPos, widSecNeg, mf1, mf2, mr1, mr2, kinFac; + + // Loop over all W_R^+- decay channels. + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + widNow = 0.; + id1Now = particlePtr->channel(i).product(0); + id2Now = particlePtr->channel(i).product(1); + id1Abs = abs(id1Now); + id2Abs = abs(id2Now); + + // Check that above threshold. Phase space. + mf1 = particleDataPtr->m0(id1Abs); + mf2 = particleDataPtr->m0(id2Abs); + if (mH > mf1 + mf2 + MASSMARGIN) { + mr1 = pow2(mf1 / mH); + mr2 = pow2(mf2 / mH); + kinFac = (1. - 0.5 * (mr1 + mr2) - 0.5 * pow2(mr1 - mr2)) + * sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2 ); + + // Combine kinematics with colour factor and CKM couplings. + widNow = kinFac; + if (id1Abs < 9) widNow *= colQ * coupSMPtr->V2CKMid(id1Abs, id2Abs); + + // Secondary width from top and righthanded neutrino decay. + id1Neg = (id1Abs < 19) ? -id1Now : id1Abs; + id2Neg = (id2Abs < 19) ? -id2Now : id2Abs; + widSecPos = particleDataPtr->resOpenFrac(id1Now, id2Now); + widSecNeg = particleDataPtr->resOpenFrac(id1Neg, id2Neg); + + // Add weight for channels on for all, W_R^+ and W_R^-, respectively. + onMode = particlePtr->channel(i).onMode(); + if (onMode == 1 || onMode == 2) widOutPos += widNow * widSecPos; + if (onMode == 1 || onMode == 3) widOutNeg += widNow * widSecNeg; + + // End loop over fermions. + } + } + + // Set up Breit-Wigner. Cross section for W_R^+ and W_R^- separately. + double sigBW = 12. * M_PI * pow2(alpEM * thetaWRat) * sH + / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + sigma0Pos = sigBW * widOutPos; + sigma0Neg = sigBW * widOutNeg; + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2WRight::sigmaHat() { + + // Secondary width for W_R^+ or W_R^-. CKM and colour factors. + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + double sigma = (idUp > 0) ? sigma0Pos : sigma0Neg; + if (abs(id1) < 9) sigma *= coupSMPtr->V2CKMid(abs(id1), abs(id2)) / 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2WRight::setIdColAcol() { + + // Sign of outgoing W_R. + int sign = (abs(id1)%2 == 0) ? 1 : -1; + if (id1 < 0) sign = -sign; + setId( id1, id2, idWR * sign); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for W_R decay angle. + +double Sigma1ffbar2WRight::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // W_R should sit in entry 5. + if (iResBeg != 5 || iResEnd != 5) return 1.; + + // Phase space factors. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double betaf = sqrtpos( pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + + // Sign of asymmetry. + double eps = (process[3].id() * process[6].id() > 0) ? 1. : -1.; + + // Reconstruct decay angle and weight for it. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * betaf); + double wtMax = 4.; + double wt = pow2(1. + betaf * eps * cosThe) - pow2(mr1 - mr2); + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma1ll2Hchgchg class. +// Cross section for l l -> H_L^++-- or H_R^++-- (doubly charged Higgs). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ll2Hchgchg::initProc() { + + // Set process properties: H_L^++-- or H_R^++--. + if (leftRight == 1) { + idHLR = 9900041; + codeSave = 3121; + nameSave = "l l -> H_L^++--"; + } else { + idHLR = 9900042; + codeSave = 3141; + nameSave = "l l -> H_R^++--"; + } + + // Read in Yukawa matrix for couplings to a lepton pair. + yukawa[1][1] = settingsPtr->parm("LeftRightSymmmetry:coupHee"); + yukawa[2][1] = settingsPtr->parm("LeftRightSymmmetry:coupHmue"); + yukawa[2][2] = settingsPtr->parm("LeftRightSymmmetry:coupHmumu"); + yukawa[3][1] = settingsPtr->parm("LeftRightSymmmetry:coupHtaue"); + yukawa[3][2] = settingsPtr->parm("LeftRightSymmmetry:coupHtaumu"); + yukawa[3][3] = settingsPtr->parm("LeftRightSymmmetry:coupHtautau"); + + // Store H_L/R mass and width for propagator. + mRes = particleDataPtr->m0(idHLR); + GammaRes = particleDataPtr->mWidth(idHLR); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(idHLR); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ll2Hchgchg::sigmaHat() { + + // Initial state must consist of two identical-sign leptons. + if (id1 * id2 < 0) return 0.; + int id1Abs = abs(id1); + int id2Abs = abs(id2); + if (id1Abs != 11 && id1Abs != 13 && id1Abs != 15) return 0.; + if (id2Abs != 11 && id2Abs != 13 && id2Abs != 15) return 0.; + + // Set up Breit-Wigner, inwidth and outwidth. + double sigBW = 8. * M_PI / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double widIn = pow2(yukawa[(id1Abs-9)/2][(id2Abs-9)/2]) + * mH / (8. * M_PI); + int idSgn = (id1 < 0) ? idHLR : -idHLR; + double widOut = particlePtr->resWidthOpen( idSgn, mH); + + // Answer. + return widIn * sigBW * widOut; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ll2Hchgchg::setIdColAcol() { + + // Sign of outgoing H_L/R. + int idSgn = (id1 < 0) ? idHLR : -idHLR; + setId( id1, id2, idSgn); + + // No colours whatsoever. + setColAcol( 0, 0, 0, 0, 0, 0); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for H_L/R sequential decay angles. + +double Sigma1ll2Hchgchg::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else isotropic decay. + return 1.; + +} + +//========================================================================== + +// Sigma2lgm2Hchgchgl class. +// Cross section for l l -> H_L^++-- or H_R^++-- (doubly charged Higgs). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2lgm2Hchgchgl::initProc() { + + // Set process properties: H_L^++-- or H_R^++-- and e/mu/tau. + idHLR = (leftRight == 1) ? 9900041 : 9900042; + codeSave = (leftRight == 1) ? 3122 : 3142; + if (idLep == 13) codeSave += 2; + if (idLep == 15) codeSave += 4; + if (codeSave == 3122) nameSave = "l^+- gamma -> H_L^++-- e^-+"; + else if (codeSave == 3123) nameSave = "l^+- gamma -> H_L^++-- mu^-+"; + else if (codeSave == 3124) nameSave = "l^+- gamma -> H_L^++-- tau^-+"; + else if (codeSave == 3142) nameSave = "l^+- gamma -> H_R^++-- e^-+"; + else if (codeSave == 3143) nameSave = "l^+- gamma -> H_R^++-- mu^-+"; + else nameSave = "l^+- gamma -> H_R^++-- tau^-+"; + + // Read in relevantYukawa matrix for couplings to a lepton pair. + if (idLep == 11) { + yukawa[1] = settingsPtr->parm("LeftRightSymmmetry:coupHee"); + yukawa[2] = settingsPtr->parm("LeftRightSymmmetry:coupHmue"); + yukawa[3] = settingsPtr->parm("LeftRightSymmmetry:coupHtaue"); + } else if (idLep == 13) { + yukawa[1] = settingsPtr->parm("LeftRightSymmmetry:coupHmue"); + yukawa[2] = settingsPtr->parm("LeftRightSymmmetry:coupHmumu"); + yukawa[3] = settingsPtr->parm("LeftRightSymmmetry:coupHtaumu"); + } else { + yukawa[1] = settingsPtr->parm("LeftRightSymmmetry:coupHtaue"); + yukawa[2] = settingsPtr->parm("LeftRightSymmmetry:coupHtaumu"); + yukawa[3] = settingsPtr->parm("LeftRightSymmmetry:coupHtautau"); + } + + // Secondary open width fractions. + openFracPos = particleDataPtr->resOpenFrac( idHLR); + openFracNeg = particleDataPtr->resOpenFrac(-idHLR); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma2lgm2Hchgchgl::sigmaHat() { + + // Initial state must consist of a lepton and a photon. + int idIn = (id2 == 22) ? id1 : id2; + int idInAbs = abs(idIn); + if (idInAbs != 11 && idInAbs != 13 && idInAbs != 15) return 0.; + + // Incoming squared lepton mass. + double s1 = pow2( particleDataPtr->m0(idInAbs) ); + + // Kinematical expressions. + double smm1 = 8. * (sH + tH - s3) * (sH + tH - 2. * s3 - s1 - s4) + / pow2(uH - s3); + double smm2 = 2. * ( (2. * s3 - 3. * s1) * s4 + (s1 - 2. * s4) * tH + - (tH - s4) * sH ) / pow2(tH - s4); + double smm3 = 2. * ( (2. * s3 - 3. * s4 + tH) * s1 + - (2. * s1 - s4 + tH) * sH ) / pow2(sH - s1); + double smm12 = 4. * ( (2. * s1 - s4 - 2. * s3 + tH) * sH + + (tH - 3. * s3 - 3. * s4) * tH + (2. * s3 - 2. * s1 + + 3. * s4) * s3 ) / ( (uH - s3) * (tH - s4) ); + double smm13 = -4. * ( (tH + s1 - 2. * s4) * tH - (s3 + 3. * s1 - 2. * s4) + * s3 + (s3 + 3. * s1 + tH) * sH - pow2(tH - s3 + sH) ) + / ( (uH - s3) * (sH - s1) ); + double smm23 = -4. * ( (s1 - s4 + s3) * tH - s3*s3 + s3 * (s1 + s4) + - 3. * s1 * s4 - (s1 - s4 - s3 + tH) * sH) + / ( (sH - s1) * (tH - s4) ); + double sigma = alpEM * pow2(sH / (sH - s1) ) * (smm1 + smm2 + smm3 + + smm12 + smm13 + smm23) / (4. * sH2); + + // Lepton Yukawa and secondary widths. + sigma *= pow2(yukawa[(idInAbs-9)/2]); + sigma *= (idIn < 0) ? openFracPos : openFracNeg; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2lgm2Hchgchgl::setIdColAcol() { + + // Sign of outgoing H_L/R. + int idIn = (id2 == 22) ? id1 : id2; + int idSgn = (idIn < 0) ? idHLR : -idHLR; + int idOut = (idIn < 0) ? idLep : -idLep; + setId( id1, id2, idSgn, idOut); + + // tHat is defined between incoming lepton and outgoing Higgs. + if (id1 == 22) swapTU = true; + + // No colours whatsoever. + setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for H_L/R sequential decay angles. + +double Sigma2lgm2Hchgchgl::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else isotropic decay. + return 1.; + +} + +//========================================================================== + +// Sigma3ff2HchgchgfftWW class. +// Cross section for f_1 f_2 -> H_(L/R)^++-- f_3 f_4 (W+- W+- fusion). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3ff2HchgchgfftWW::initProc() { + + // Set process properties: H_L^++-- or H_R^++--. + if (leftRight == 1) { + idHLR = 9900041; + codeSave = 3125; + nameSave = "f_1 f_2 -> H_L^++-- f_3 f_4 (W+- W+- fusion)"; + } else { + idHLR = 9900042; + codeSave = 3145; + nameSave = "f_1 f_2 -> H_R^++-- f_3 f_4 (W+- W+- fusion)"; + } + + // Common fixed mass and coupling factor. + double mW = particleDataPtr->m0(24); + double mWR = particleDataPtr->m0(9900024); + mWS = (leftRight == 1) ? pow2(mW) : pow2(mWR); + double gL = settingsPtr->parm("LeftRightSymmmetry:gL"); + double gR = settingsPtr->parm("LeftRightSymmmetry:gR"); + double vL = settingsPtr->parm("LeftRightSymmmetry:vL"); + prefac = (leftRight == 1) ? pow2(pow4(gL) * vL) + : 2. * pow2(pow3(gR) * mWR); + // Secondary open width fractions. + openFracPos = particleDataPtr->resOpenFrac( idHLR); + openFracNeg = particleDataPtr->resOpenFrac(-idHLR); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma3ff2HchgchgfftWW::sigmaKin() { + + // Required four-vector products. + double pp12 = 0.5 * sH; + double pp14 = 0.5 * mH * p4cm.pNeg(); + double pp15 = 0.5 * mH * p5cm.pNeg(); + double pp24 = 0.5 * mH * p4cm.pPos(); + double pp25 = 0.5 * mH * p5cm.pPos(); + double pp45 = p4cm * p5cm; + + // Cross section: kinematics part. Combine with couplings. + double propT = 1. / ( (2. * pp14 + mWS) * (2. * pp25 + mWS) ); + double propU = 1. / ( (2. * pp24 + mWS) * (2. * pp15 + mWS) ); + sigma0TU = prefac * pp12 * pp45 * pow2(propT + propU); + sigma0T = prefac * pp12 * pp45 * 2. * pow2(propT); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma3ff2HchgchgfftWW::sigmaHat() { + + // Do not allow creation of righthanded neutrinos for H_R. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + if ( leftRight == 2 && (id1Abs > 10 || id2Abs > 10) ) return 0.; + + // Many flavour combinations not possible because of charge. + int chg1 = (( id1Abs%2 == 0 && id1 > 0) + || (id1Abs%2 == 1 && id1 < 0) ) ? 1 : -1; + int chg2 = (( id2Abs%2 == 0 && id2 > 0) + || (id2Abs%2 == 1 && id2 < 0) ) ? 1 : -1; + if (abs(chg1 + chg2) != 2) return 0.; + + // Basic cross section. CKM factors for final states. + double sigma = (id2 == id1 && id1Abs > 10) ? sigma0TU : sigma0T; + sigma *= coupSMPtr->V2CKMsum(id1Abs) * coupSMPtr->V2CKMsum(id2Abs); + + // Secondary width for H0. + sigma *= (chg1 + chg2 == 2) ? openFracPos : openFracNeg; + + // Spin-state extra factor 2 per incoming neutrino. + if (id1Abs == 12 || id1Abs == 14 || id1Abs == 16) sigma *= 2.; + if (id2Abs == 12 || id2Abs == 14 || id2Abs == 16) sigma *= 2.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3ff2HchgchgfftWW::setIdColAcol() { + + // Pick out-flavours by relative CKM weights. + int id1Abs = abs(id1); + int id2Abs = abs(id2); + id4 = coupSMPtr->V2CKMpick(id1); + id5 = coupSMPtr->V2CKMpick(id2); + + // Find charge of Higgs . + id3 = (( id1Abs%2 == 0 && id1 > 0) || (id1Abs%2 == 1 && id1 < 0) ) + ? idHLR : -idHLR; + setId( id1, id2, id3, id4, id5); + + // Colour flow topologies. Swap when antiquarks. + if (id1Abs < 9 && id2Abs < 9 && id1*id2 > 0) + setColAcol( 1, 0, 2, 0, 0, 0, 1, 0, 2, 0); + else if (id1Abs < 9 && id2Abs < 9) + setColAcol( 1, 0, 0, 2, 0, 0, 1, 0, 0, 2); + else if (id1Abs < 9) setColAcol( 1, 0, 0, 0, 0, 0, 1, 0, 0, 0); + else if (id2Abs < 9) setColAcol( 0, 0, 1, 0, 0, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0); + if ( (id1Abs < 9 && id1 < 0) || (id1Abs > 10 && id2 < 0) ) + swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles. + +double Sigma3ff2HchgchgfftWW::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else done. + return 1.; + +} + +//========================================================================== + +// Sigma2ffbar2HchgchgHchgchg class. +// Cross section for f fbar -> H_(L/R)^++ H_(L/R)^-- (doubly charged Higgs). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2ffbar2HchgchgHchgchg::initProc() { + + // Set process properties: H_L^++ H_L^-- or H_R^++ H_R^--. + if (leftRight == 1) { + idHLR = 9900041; + codeSave = 3126; + nameSave = "f fbar -> H_L^++ H_L^--"; + } else { + idHLR = 9900042; + codeSave = 3146; + nameSave = "f fbar -> H_R^++ H_R^--"; + } + + // Read in Yukawa matrix for couplings to a lepton pair. + yukawa[1][1] = settingsPtr->parm("LeftRightSymmmetry:coupHee"); + yukawa[2][1] = settingsPtr->parm("LeftRightSymmmetry:coupHmue"); + yukawa[2][2] = settingsPtr->parm("LeftRightSymmmetry:coupHmumu"); + yukawa[3][1] = settingsPtr->parm("LeftRightSymmmetry:coupHtaue"); + yukawa[3][2] = settingsPtr->parm("LeftRightSymmmetry:coupHtaumu"); + yukawa[3][3] = settingsPtr->parm("LeftRightSymmmetry:coupHtautau"); + + // Electroweak parameters. + mRes = particleDataPtr->m0(23); + GammaRes = particleDataPtr->mWidth(23); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + sin2tW = coupSMPtr->sin2thetaW(); + preFac = (1. - 2. * sin2tW) / ( 8. * sin2tW * (1. - sin2tW) ); + + // Open fraction from secondary widths. + openFrac = particleDataPtr->resOpenFrac( idHLR, -idHLR); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma2ffbar2HchgchgHchgchg::sigmaHat() { + + // Electroweak couplings to gamma^*/Z^0. + int idAbs = abs(id1); + double ei = coupSMPtr->ef(idAbs); + double vi = coupSMPtr->vf(idAbs); + double ai = coupSMPtr->af(idAbs); + + // Part via gamma^*/Z^0 propagator.No Z^0 coupling to H_R. + double resProp = 1. / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double sigma = 8. * pow2(alpEM) * ei*ei / sH2; + if (leftRight == 1) sigma += 8. * pow2(alpEM) + * (2. * ei * vi * preFac * (sH - m2Res) * resProp / sH + + (vi * vi + ai * ai) * pow2(preFac) * resProp); + + // Part via t-channel lepton + interference; sum over possibilities. + if (idAbs == 11 || idAbs == 13 || idAbs == 15) { + double yuk2Sum; + if (idAbs == 11) yuk2Sum + = pow2(yukawa[1][1]) + pow2(yukawa[2][1]) + pow2(yukawa[3][1]); + else if (idAbs == 13) yuk2Sum + = pow2(yukawa[2][1]) + pow2(yukawa[2][2]) + pow2(yukawa[3][2]); + else yuk2Sum + = pow2(yukawa[3][1]) + pow2(yukawa[3][2]) + pow2(yukawa[3][3]); + yuk2Sum /= 4. * M_PI; + sigma += 8. * alpEM * ei * yuk2Sum / (sH * tH) + + 4. * pow2(yuk2Sum) / tH2; + if (leftRight == 1) sigma += 8. * alpEM * (vi + ai) * yuk2Sum + * preFac * (sH - m2Res) * resProp / tH; + } + + // Common kinematical factor. Colour factor. + sigma *= M_PI * (tH * uH - s3 * s4) / sH2; + if (idAbs < 9) sigma /= 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2ffbar2HchgchgHchgchg::setIdColAcol() { + + // Outgoing flavours trivial. + setId( id1, id2, idHLR, -idHLR); + + // tHat is defined between incoming fermion and outgoing H--. + if (id1 > 0) swapTU = true; + + // No colours at all or one flow topology. Swap if first is antiquark. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for H_L/R sequential decay angles. + +double Sigma2ffbar2HchgchgHchgchg::weightDecay( Event& process, + int iResBeg, int iResEnd) { + + // Identity of mother of decaying reseonance(s). + int idMother = process[process[iResBeg].mother1()].idAbs(); + + // For top decay hand over to standard routine. + if (idMother == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Else isotropic decay. + return 1.; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaLeptoquark.cxx b/PYTHIA8/pythia8140/src/SigmaLeptoquark.cxx new file mode 100644 index 00000000000..3b7df361c74 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaLeptoquark.cxx @@ -0,0 +1,310 @@ +// SigmaLeptoquark.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// leptoquark simulation classes. + +#include "SigmaLeptoquark.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma1ql2LeptoQuark class. +// Cross section for q l -> LQ (leptoquark state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ql2LeptoQuark::initProc() { + + // Store LQ mass and width for propagator. + mRes = particleDataPtr->m0(42); + GammaRes = particleDataPtr->mWidth(42); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Yukawa coupling strength. + kCoup = settingsPtr->parm("LeptoQuark:kCoup"); + + // Set pointer to particle properties and decay table. + LQPtr = particleDataPtr->particleDataEntryPtr(42); + + // Read out quark and lepton the LQ couples to. + idQuark = LQPtr->channel(0).product(0); + idLepton = LQPtr->channel(0).product(1); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ql2LeptoQuark::sigmaKin() { + + // Incoming width for correct quark-lepton pair. + widthIn = 0.25 * alpEM * kCoup * mH; + + // Set up Breit-Wigner. + sigBW = 4. * M_PI/ ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat) for specific incoming flavours. + +double Sigma1ql2LeptoQuark::sigmaHat() { + + // Identify whether correct incoming flavours. + int idLQ = 0; + if (id1 == idQuark && id2 == idLepton) idLQ = 42; + else if (id2 == idQuark && id1 == idLepton) idLQ = 42; + else if (id1 == -idQuark && id2 == -idLepton) idLQ = -42; + else if (id2 == -idQuark && id1 == -idLepton) idLQ = -42; + if (idLQ == 0) return 0.; + + // Outgoing width and total sigma. Done. + return widthIn * sigBW * LQPtr->resWidthOpen(idLQ, mH); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ql2LeptoQuark::setIdColAcol() { + + // Flavours. + int idq = (abs(id1) < 9) ? id1 : id2; + int idLQ = (idq > 0) ? 42 : -42; + setId( id1, id2, idLQ); + + // Colour flow topology. + if (id1 == idq) setColAcol( 1, 0, 0, 0, 1, 0); + else setColAcol( 0, 0, 1, 0, 1, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qg2LeptoQuarkl class. +// Cross section for q g -> LQ l (leptoquark state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2LeptoQuarkl::initProc() { + + // Store LQ mass and width for propagator. + mRes = particleDataPtr->m0(42); + GammaRes = particleDataPtr->mWidth(42); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Yukawa coupling strength. + kCoup = settingsPtr->parm("LeptoQuark:kCoup"); + + // Read out quark and lepton the LQ couples to. + ParticleDataEntry* LQPtr = particleDataPtr->particleDataEntryPtr(42); + idQuark = LQPtr->channel(0).product(0); + idLepton = LQPtr->channel(0).product(1); + + // Secondary open width fraction. + openFracPos = LQPtr->resOpenFrac( 42); + openFracNeg = LQPtr->resOpenFrac(-42); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qg2LeptoQuarkl::sigmaKin() { + + // Evaluate cross section. + sigma0 = (M_PI / sH2) * kCoup * (alpS * alpEM / 6.) * (-tH / sH) + * (uH2 + s3 * s3) / pow2(uH - s3); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat) for specific incoming flavours. + +double Sigma2qg2LeptoQuarkl::sigmaHat() { + + // Check that correct incoming flavour. + if (abs(id1) != idQuark && abs(id2) != idQuark) return 0.; + + // Answer, with secondary width correction. + double sigma = sigma0; + sigma *= (id1 == idQuark || id2 == idQuark) ? openFracPos : openFracNeg; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2LeptoQuarkl::setIdColAcol() { + + // Flavour set up for q g -> H q. + int idq = (id2 == 21) ? id1 : id2; + int idLQ = (idq > 0) ? 42 : -42; + int idlp = (idq > 0) ? idLepton : -idLepton; + setId( id1, id2, idLQ, idlp); + + // tH defined between f and f': must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 2, 0, 0, 0); + else setColAcol( 2, 1, 1, 0, 2, 0, 0, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2LQLQbar class. +// Cross section for g g -> LQ LQbar (leptoquark state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2LQLQbar::initProc() { + + // Store LQ mass and width for propagator. + mRes = particleDataPtr->m0(42); + GammaRes = particleDataPtr->mWidth(42); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(42, -42); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2gg2LQLQbar::sigmaKin() { + + // Average outgoing masses and adjust kinematics accordingly. + double delta = 0.25 * pow2(s3 - s4) / sH; + double m2avg = 0.5 * (s3 + s4) - delta; + double tHavg = tH - delta; + double uHavg = uH - delta; + + // Evaluate cross section. Secondary width for G*. + sigma = (M_PI / sH2) * 0.5 * pow2(alpS) + * ( 7. / 48. + 3. * pow2(uHavg - tHavg) / (16. * sH2) ) + * ( 1. + 2. * m2avg * tHavg / pow2(tHavg - m2avg) + + 2. * m2avg * uHavg / pow2(uHavg - m2avg) + + 4. * m2avg * m2avg / ((tHavg - m2avg) * (uHavg - m2avg)) ); + sigma *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2LQLQbar::setIdColAcol() { + + // Flavours trivial. + setId( 21, 21, 42, -42); + + // Colour flow topologies: random choice between two mirrors. + if (rndmPtr->flat() < 0.5) setColAcol( 1, 2, 2, 3, 1, 0, 0, 3); + else setColAcol( 1, 2, 3, 1, 3, 0, 0, 2); + +} + +//========================================================================== + +// Sigma2qqbar2LQLQbar class. +// Cross section for q qbar -> LQ LQbar (leptoquark state). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2LQLQbar::initProc() { + + // Store LQ mass and width for propagator. + mRes = particleDataPtr->m0(42); + GammaRes = particleDataPtr->mWidth(42); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + + // Yukawa coupling strength. + kCoup = settingsPtr->parm("LeptoQuark:kCoup"); + + // Read out quark and lepton the LQ couples to. + ParticleDataEntry* LQPtr = particleDataPtr->particleDataEntryPtr(42); + idQuark = LQPtr->channel(0).product(0); + + // Secondary open width fraction. + openFrac = particleDataPtr->resOpenFrac(42, -42); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma2qqbar2LQLQbar::sigmaKin() { + + // Average outgoing masses and adjust kinematics accordingly. + double delta = 0.25 * pow2(s3 - s4) / sH; + double m2avg = 0.5 * (s3 + s4) - delta; + double tHavg = tH - delta; + double uHavg = uH - delta; + + // Evaluate cross section for quark of different flavour than LQ. + sigmaDiff = (M_PI / sH2) * (pow2(alpS) / 9.) + * ( sH * (sH - 4. * m2avg) - pow2(uHavg - tHavg) ) / sH2; + + // Evaluate cross section for quark of same flavour as LQ. + sigmaSame = sigmaDiff + (M_PI / sH2) * (pow2(kCoup * alpEM) / 8.) + * (-sH * tHavg - pow2(m2avg-tHavg)) / pow2(tHavg) + + (M_PI / sH2) * (kCoup * alpEM * alpS / 18.) * ( (m2avg - tHavg) + * (uHavg - tHavg) + sH * (m2avg + tHavg) ) / (sH * tHavg); + + // Open fraction. + sigmaDiff *= openFrac; + sigmaSame *= openFrac; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2LQLQbar::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, 42, -42); + + // tH defined between f and LQ: must swap tHat <-> uHat if qbar q in. + swapTU = (id1 < 0); + + // Colour flow topologies. + if (id1 > 0) setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + else setColAcol( 0, 2, 1, 0, 1, 0, 0, 2); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaNewGaugeBosons.cxx b/PYTHIA8/pythia8140/src/SigmaNewGaugeBosons.cxx new file mode 100644 index 00000000000..b365cef6ea9 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaNewGaugeBosons.cxx @@ -0,0 +1,757 @@ +// SigmaNewGaugeBosons.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// leptoquark simulation classes. + +#include "SigmaNewGaugeBosons.h" + +namespace Pythia8 { + + +//========================================================================== + +// Sigma1ffbarZprimeWprime class. +// Collects common methods for f fbar -> Z'/W' -> WW/WZ -> 4 fermions. +// Copied from SigmaEW for gauge-boson-pair production. + +//-------------------------------------------------------------------------- + +// Calculate and store internal products. + +void Sigma1ffbarZprimeWprime::setupProd( Event& process, int i1, int i2, + int i3, int i4, int i5, int i6) { + + // Store incoming and outgoing momenta, + pRot[1] = process[i1].p(); + pRot[2] = process[i2].p(); + pRot[3] = process[i3].p(); + pRot[4] = process[i4].p(); + pRot[5] = process[i5].p(); + pRot[6] = process[i6].p(); + + // Do random rotation to avoid accidental zeroes in HA expressions. + bool smallPT = false; + do { + smallPT = false; + double thetaNow = acos(2. * rndmPtr->flat() - 1.); + double phiNow = 2. * M_PI * rndmPtr->flat(); + for (int i = 1; i <= 6; ++i) { + pRot[i].rot( thetaNow, phiNow); + if (pRot[i].pT2() < 1e-4 * pRot[i].pAbs2()) smallPT = true; + } + } while (smallPT); + + // Calculate internal products. + for (int i = 1; i < 6; ++i) { + for (int j = i + 1; j <= 6; ++j) { + hA[i][j] = + sqrt( (pRot[i].e() - pRot[i].pz()) * (pRot[j].e() + pRot[j].pz()) + / pRot[i].pT2() ) * complex( pRot[i].px(), pRot[i].py() ) + - sqrt( (pRot[i].e() + pRot[i].pz()) * (pRot[j].e() - pRot[j].pz()) + / pRot[j].pT2() ) * complex( pRot[j].px(), pRot[j].py() ); + hC[i][j] = conj( hA[i][j] ); + if (i <= 2) { + hA[i][j] *= complex( 0., 1.); + hC[i][j] *= complex( 0., 1.); + } + hA[j][i] = - hA[i][j]; + hC[j][i] = - hC[i][j]; + } + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate the F function of Gunion and Kunszt. + +complex Sigma1ffbarZprimeWprime::fGK(int j1, int j2, int j3, int j4, + int j5, int j6) { + + return 4. * hA[j1][j3] * hC[j2][j6] + * ( hA[j1][j5] * hC[j1][j4] + hA[j3][j5] * hC[j3][j4] ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate the Xi function of Gunion and Kunszt. + +double Sigma1ffbarZprimeWprime::xiGK( double tHnow, double uHnow, + double s3now, double s4now) { + + return - 4. * s3now * s4now + tHnow * (3. * tHnow + 4. * uHnow) + + tHnow * tHnow * ( tHnow * uHnow / (s3now * s4now) + - 2. * (1. / s3now + 1./s4now) * (tHnow + uHnow) + + 2. * (s3now / s4now + s4now / s3now) ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate the Xj function of Gunion and Kunszt. + +double Sigma1ffbarZprimeWprime::xjGK( double tHnow, double uHnow, + double s3now, double s4now) { + + return 8. * pow2(s3now + s4now) - 8. * (s3now + s4now) * (tHnow + uHnow) + - 6. * tHnow * uHnow - 2. * tHnow * uHnow * ( tHnow * uHnow + / (s3now * s4now) - 2. * (1. / s3now + 1. / s4now) * (tHnow + uHnow) + + 2. * (s3now / s4now + s4now / s3now) ); + +} + +//========================================================================== + +// Sigma1ffbar2gmZZprime class. +// Cross section for f fbar -> gamma*/Z0/Z'0 (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2gmZZprime::initProc() { + + // Allow to pick only parts of full gamma*/Z0/Z'0 expression. + gmZmode = settingsPtr->mode("Zprime:gmZmode"); + + // Store Z'0 mass and width for propagator. + mRes = particleDataPtr->m0(32); + GammaRes = particleDataPtr->mWidth(32); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + sin2tW = coupSMPtr->sin2thetaW(); + cos2tW = 1. - sin2tW; + thetaWRat = 1. / (16. * sin2tW * cos2tW); + + // Properties of Z0 resonance also needed. + mZ = particleDataPtr->m0(23); + GammaZ = particleDataPtr->mWidth(23); + m2Z = mZ*mZ; + GamMRatZ = GammaZ / mZ; + + // Ensure that arrays initially are empty. + for (int i = 0; i < 20; ++i) afZp[i] = 0.; + for (int i = 0; i < 20; ++i) vfZp[i] = 0.; + + // Store first-generation axial and vector couplings. + afZp[1] = settingsPtr->parm("Zprime:ad"); + afZp[2] = settingsPtr->parm("Zprime:au"); + afZp[11] = settingsPtr->parm("Zprime:ae"); + afZp[12] = settingsPtr->parm("Zprime:anue"); + vfZp[1] = settingsPtr->parm("Zprime:vd"); + vfZp[2] = settingsPtr->parm("Zprime:vu"); + vfZp[11] = settingsPtr->parm("Zprime:ve"); + vfZp[12] = settingsPtr->parm("Zprime:vnue"); + + // Second and third generation could be carbon copy of this... + if (settingsPtr->flag("Zprime:universality")) { + for (int i = 3; i <= 6; ++i) { + afZp[i] = afZp[i-2]; + vfZp[i] = vfZp[i-2]; + afZp[i+10] = afZp[i+8]; + vfZp[i+10] = vfZp[i+8]; + } + + // ... or could have different couplings. + } else { + afZp[3] = settingsPtr->parm("Zprime:as"); + afZp[4] = settingsPtr->parm("Zprime:ac"); + afZp[5] = settingsPtr->parm("Zprime:ab"); + afZp[6] = settingsPtr->parm("Zprime:at"); + afZp[13] = settingsPtr->parm("Zprime:amu"); + afZp[14] = settingsPtr->parm("Zprime:anumu"); + afZp[15] = settingsPtr->parm("Zprime:atau"); + afZp[16] = settingsPtr->parm("Zprime:anutau"); + vfZp[3] = settingsPtr->parm("Zprime:vs"); + vfZp[4] = settingsPtr->parm("Zprime:vc"); + vfZp[5] = settingsPtr->parm("Zprime:vb"); + vfZp[6] = settingsPtr->parm("Zprime:vt"); + vfZp[13] = settingsPtr->parm("Zprime:vmu"); + vfZp[14] = settingsPtr->parm("Zprime:vnumu"); + vfZp[15] = settingsPtr->parm("Zprime:vtau"); + vfZp[16] = settingsPtr->parm("Zprime:vnutau"); + } + + // Coupling for Z' -> W+ W- and decay angular admixture. + coupZpWW = settingsPtr->parm("Zprime:coup2WW"); + anglesZpWW = settingsPtr->parm("Zprime:anglesWW"); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(32); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2gmZZprime::sigmaKin() { + + // Common coupling factors. + double colQ = 3. * (1. + alpS / M_PI); + + // Reset quantities to sum. Declare variables in loop. + gamSum = 0.; + gamZSum = 0.; + ZSum = 0.; + gamZpSum = 0.; + ZZpSum = 0.; + ZpSum = 0.; + int idAbs, onMode; + double mf, mr, ps, kinFacA, kinFacV, ef, af, vf, apf, vpf, + ef2, efvf, vaf2, efvpf, vafvapf, vapf2, colf; + + // Loop over all open Z'0 decay channels. + for (int i = 0; i < particlePtr->sizeChannels(); ++i) { + onMode = particlePtr->channel(i).onMode(); + if (onMode != 1 && onMode != 2) continue; + idAbs = abs( particlePtr->channel(i).product(0) ); + + // Contributions from three fermion generations. + if ( (idAbs > 0 && idAbs < 7) || ( idAbs > 10 && idAbs < 17) ) { + mf = particleDataPtr->m0(idAbs); + + // Check that above threshold. + if (mH > 2. * mf + MASSMARGIN) { + mr = pow2(mf / mH); + ps = sqrtpos(1. - 4. * mr); + + // Couplings of gamma^*/Z^0/Z'^0 to final flavour + ef = coupSMPtr->ef(idAbs); + af = coupSMPtr->af(idAbs); + vf = coupSMPtr->vf(idAbs); + apf = afZp[idAbs]; + vpf = vfZp[idAbs]; + + // Combine couplings with kinematical factors. + kinFacA = pow3(ps); + kinFacV = ps * (1. + 2. * mr); + ef2 = ef * ef * kinFacV; + efvf = ef * vf * kinFacV; + vaf2 = vf * vf * kinFacV + af * af * kinFacA; + efvpf = ef * vpf * kinFacV; + vafvapf = vf * vpf * kinFacV + af * apf * kinFacA; + vapf2 = vpf * vpf * kinFacV + apf * apf * kinFacA; + + // Colour factor. Additionally secondary width for top. + colf = (idAbs < 9) ? colQ : 1.; + if (idAbs == 6) colf *= particleDataPtr->resOpenFrac(6, -6); + + // Store sum of combinations. + gamSum += colf * ef2; + gamZSum += colf * efvf; + ZSum += colf * vaf2; + gamZpSum += colf * efvpf; + ZZpSum += colf * vafvapf; + ZpSum += colf * vapf2; + } + + // Optional contribution from W+ W-. + } else if (idAbs == 24) { + mf = particleDataPtr->m0(idAbs); + if (mH > 2. * mf + MASSMARGIN) { + mr = pow2(mf / mH); + ps = sqrtpos(1. - 4. * mr); + ZpSum += pow2(coupZpWW * cos2tW) * pow3(ps) + * (1. + 20. * mr + 12. * mr*mr) + * particleDataPtr->resOpenFrac(24, -24); + } + } + } + + // Calculate prefactors for gamma/Z0/Z'0 cross section terms. + double propZ = sH / ( pow2(sH - m2Z) + pow2(sH * GamMRatZ) ); + double propZp = sH / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + gamNorm = 4. * M_PI * pow2(alpEM) / (3. * sH); + gamZNorm = gamNorm * 2. * thetaWRat * (sH - m2Z) * propZ; + ZNorm = gamNorm * pow2(thetaWRat) * sH * propZ; + gamZpNorm = gamNorm * 2. * thetaWRat * (sH - m2Res) * propZp; + ZZpNorm = gamNorm * 2. * pow2(thetaWRat) * ((sH - m2Z) * (sH - m2Res) + + sH * GamMRatZ * sH * GamMRat) * propZ * propZp; + ZpNorm = gamNorm * pow2(thetaWRat) * sH * propZp; + + // Optionally only keep some of gamma*, Z0 and Z' terms. + if (gmZmode == 1) {gamZNorm = 0; ZNorm = 0.; gamZpNorm = 0.; + ZZpNorm = 0.; ZpNorm = 0.;} + if (gmZmode == 2) {gamNorm = 0.; gamZNorm = 0.; gamZpNorm = 0.; + ZZpNorm = 0.; ZpNorm = 0.;} + if (gmZmode == 3) {gamNorm = 0.; gamZNorm = 0.; ZNorm = 0.; + gamZpNorm = 0.; ZZpNorm = 0.;} + if (gmZmode == 4) {gamZpNorm = 0.; ZZpNorm = 0.; ZpNorm = 0.;} + if (gmZmode == 5) {gamZNorm = 0.; ZNorm = 0.; ZZpNorm = 0.;} + if (gmZmode == 6) {gamNorm = 0.; gamZNorm = 0.; gamZpNorm = 0.;} + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2gmZZprime::sigmaHat() { + + // Couplings to an incoming flavour. + int idAbs = abs(id1); + double ei = coupSMPtr->ef(idAbs); + double ai = coupSMPtr->af(idAbs); + double vi = coupSMPtr->vf(idAbs); + double api = afZp[idAbs]; + double vpi = vfZp[idAbs]; + double ei2 = ei * ei; + double eivi = ei * vi; + double vai2 = vi * vi + ai * ai; + double eivpi = ei * vpi; + double vaivapi = vi * vpi + ai * api;; + double vapi2 = vpi * vpi + api * api; + + // Combine gamma, interference and Z0 parts. + double sigma = ei2 * gamNorm * gamSum + eivi * gamZNorm * gamZSum + + vai2 * ZNorm * ZSum + eivpi * gamZpNorm * gamZpSum + + vaivapi * ZZpNorm * ZZpSum + vapi2 * ZpNorm * ZpSum; + + // Colour factor. Answer. + if (idAbs < 9) sigma /= 3.; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2gmZZprime::setIdColAcol() { + + // Flavours trivial. + setId( id1, id2, 32); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for gamma*/Z0/Z'0 decay angle. + +double Sigma1ffbar2gmZZprime::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Default values, in- and out-flavours in process. + double wt = 1.; + double wtMax = 1.; + int idInAbs = process[3].idAbs(); + int idOutAbs = process[6].idAbs(); + + // Angular weight for outgoing fermion pair. + if (iResBeg == 5 && iResEnd == 5 && + (idOutAbs < 7 || ( idOutAbs > 10 && idOutAbs < 17)) ) { + + // Couplings for in- and out-flavours. + double ei = coupSMPtr->ef(idInAbs); + double vi = coupSMPtr->vf(idInAbs); + double ai = coupSMPtr->af(idInAbs); + double vpi = vfZp[idInAbs]; + double api = afZp[idInAbs]; + double ef = coupSMPtr->ef(idOutAbs); + double vf = coupSMPtr->vf(idOutAbs); + double af = coupSMPtr->af(idOutAbs); + double vpf = vfZp[idOutAbs]; + double apf = afZp[idOutAbs]; + + // Phase space factors. (One power of beta left out in formulae.) + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double ps = sqrtpos(pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + double mrAvg = 0.5 * (mr1 + mr2) - 0.25 * pow2(mr1 - mr2); + + // Coefficients of angular expression. + double coefTran = ei*ei * gamNorm * ef*ef + ei * vi * gamZNorm * ef * vf + + (vi*vi + ai*ai) * ZNorm * (vf*vf + ps*ps * af*af) + + ei * vpi * gamZpNorm * ef * vpf + + (vi * vpi + ai * api) * ZZpNorm * (vf * vpf + ps*ps * af * apf) + + (vpi*vpi + api*api) * ZpNorm * (vpf*vpf + ps*ps * apf*apf); + double coefLong = 4. * mrAvg * ( ei*ei * gamNorm * ef*ef + + ei * vi * gamZNorm * ef * vf + (vi*vi + ai*ai) * ZNorm * vf*vf + + ei * vpi * gamZpNorm * ef * vpf + + (vi * vpi + ai * api) * ZZpNorm * vf * vpf + + (vpi*vpi + api*api) * ZpNorm * vpf*vpf ); + double coefAsym = ps * ( ei * ai * gamZNorm * ef * af + + 4. * vi * ai * ZNorm * vf * af + ei * api * gamZpNorm * ef * apf + + (vi * api + vpi * ai) * ZZpNorm * (vf * apf + vpf * af) + + 4. * vpi * api * ZpNorm * vpf * apf ); + + // Flip asymmetry for in-fermion + out-antifermion. + if (process[3].id() * process[6].id() < 0) coefAsym = -coefAsym; + + // Reconstruct decay angle and weight for it. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * ps); + wt = coefTran * (1. + pow2(cosThe)) + + coefLong * (1. - pow2(cosThe)) + 2. * coefAsym * cosThe; + wtMax = 2. * (coefTran + abs(coefAsym)); + } + + // Angular weight for Z' -> W+ W-. + else if (iResBeg == 5 && iResEnd == 5 && idOutAbs == 24) { + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double ps = sqrtpos(pow2(1. - mr1 -mr2) - 4. * mr1 * mr2); + double cCos2 = - (1./16.) * ps*ps * (1. - 2. * mr1 - 2. * mr2 + + mr1*mr1 + mr2*mr2 + 10. * mr1 * mr2); + double cFlat = -cCos2 + 0.5 * (mr1 + mr2) + * (1. - 2. * mr1 - 2. * mr2 + pow2(mr1 - mr2)); + + // Reconstruct decay angle and weight for it. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * ps); + wt = cFlat + cCos2 * cosThe*cosThe; + wtMax = cFlat + max(0., cCos2); + } + + // Angular weight for f + fbar -> Z' -> W+ + W- -> 4 fermions. + else if (iResBeg == 6 && iResEnd == 7 && idOutAbs == 24) { + + // Order so that fbar(1) f(2) -> f'(3) fbar'(4) f"(5) fbar"(6). + // with f' fbar' from W- and f" fbar" from W+. + int i1 = (process[3].id() < 0) ? 3 : 4; + int i2 = 7 - i1; + int i3 = (process[8].id() > 0) ? 8 : 9; + int i4 = 17 - i3; + int i5 = (process[10].id() > 0) ? 10 : 11; + int i6 = 21 - i5; + if (process[6].id() > 0) {swap(i3, i5); swap(i4, i6);} + + // Decay distribution like in f fbar -> Z^* -> W+ W-. + if (rndmPtr->flat() > anglesZpWW) { + + // Set up four-products and internal products. + setupProd( process, i1, i2, i3, i4, i5, i6); + + // tHat and uHat of fbar f -> W- W+, and their squared masses. + int iNeg = (process[6].id() < 0) ? 6 : 7; + int iPos = 13 - iNeg; + double tHres = (process[i1].p() - process[iNeg].p()).m2Calc(); + double uHres = (process[i1].p() - process[iPos].p()).m2Calc(); + double s3now = process[iNeg].m2(); + double s4now = process[iPos].m2(); + + // Kinematics combinations (norm(x) = |x|^2). + double fGK135 = norm(fGK( 1, 2, 3, 4, 5, 6) - fGK( 1, 2, 5, 6, 3, 4) ); + double fGK253 = norm(fGK( 2, 1, 5, 6, 3, 4) - fGK( 2, 1, 3, 4, 5, 6) ); + double xiT = xiGK( tHres, uHres, s3now, s4now); + double xiU = xiGK( uHres, tHres, s3now, s4now); + double xjTU = xjGK( tHres, uHres, s3now, s4now); + + // Couplings of incoming (anti)fermion. Combine with kinematics. + int idAbs = process[i1].idAbs(); + double li = 0.5 * (vfZp[idAbs] + afZp[idAbs]); + double ri = 0.5 * (vfZp[idAbs] - afZp[idAbs]); + wt = li*li * fGK135 + ri*ri * fGK253; + wtMax = 4. * s3now * s4now * (li*li + ri*ri) + * (xiT + xiU - xjTU); + + // Decay distribution like in f fbar -> h^0 -> W+ W-. + } else { + double p35 = 2. * process[i3].p() * process[i5].p(); + double p46 = 2. * process[i4].p() * process[i6].p(); + wt = 16. * p35 * p46; + wtMax = sH2; + } + } + + // Angular weight in top decay by standard routine. + else if (process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + + // Done. + return (wt / wtMax); + +} + +//========================================================================== + +// Sigma1ffbar2Wprime class. +// Cross section for f fbar' -> W'+- (f is quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2Wprime::initProc() { + + // Store W+- mass and width for propagator. + mRes = particleDataPtr->m0(34); + GammaRes = particleDataPtr->mWidth(34); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + + // Axial and vector couplings of fermions. + aqWp = settingsPtr->parm("Wprime:aq"); + vqWp = settingsPtr->parm("Wprime:vq"); + alWp = settingsPtr->parm("Wprime:al"); + vlWp = settingsPtr->parm("Wprime:vl"); + + // Coupling for W' -> W Z and decay angular admixture. + coupWpWZ = settingsPtr->parm("Wprime:coup2WZ"); + anglesWpWZ = settingsPtr->parm("Wprime:anglesWZ"); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(34); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2Wprime::sigmaKin() { + + // Set up Breit-Wigner. Cross section for W+ and W- separately. + double sigBW = 12. * M_PI / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double preFac = alpEM * thetaWRat * mH; + sigma0Pos = preFac * sigBW * particlePtr->resWidthOpen(34, mH); + sigma0Neg = preFac * sigBW * particlePtr->resWidthOpen(-34, mH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2Wprime::sigmaHat() { + + // Secondary width for W+ or W-. CKM and colour factors. + int idUp = (abs(id1)%2 == 0) ? id1 : id2; + double sigma = (idUp > 0) ? sigma0Pos : sigma0Neg; + if (abs(id1) < 7) sigma *= coupSMPtr->V2CKMid(abs(id1), abs(id2)) / 3.; + + // Couplings. + if (abs(id1) < 7) sigma *= 0.5 * (aqWp * aqWp + vqWp * vqWp); + else sigma *= 0.5 * (alWp * alWp + vlWp * vlWp); + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2Wprime::setIdColAcol() { + + // Sign of outgoing W. + int sign = 1 - 2 * (abs(id1)%2); + if (id1 < 0) sign = -sign; + setId( id1, id2, 34 * sign); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for W decay angle. + +double Sigma1ffbar2Wprime::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // Default values, in- and out-flavours in process. + double wt = 1.; + double wtMax = 1.; + int idInAbs = process[3].idAbs(); + int idOutAbs = process[6].idAbs(); + + // Angular weight for outgoing fermion pair. + if (iResBeg == 5 && iResEnd == 5 && + (idOutAbs < 7 || ( idOutAbs > 10 && idOutAbs < 17)) ) { + + // Couplings for in- and out-flavours. + double ai = (idInAbs < 9) ? aqWp : alWp; + double vi = (idInAbs < 9) ? vqWp : vlWp; + double af = (idOutAbs < 9) ? aqWp : alWp; + double vf = (idOutAbs < 9) ? vqWp : vlWp; + + // Asymmetry expression. + double coefAsym = 8. * vi * ai * vf * af + / ((vi*vi + ai*ai) * (vf*vf + af*af)); + + // Flip asymmetry for in-fermion + out-antifermion. + if (process[3].id() * process[6].id() < 0) coefAsym = -coefAsym; + + // Phase space factors. + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double ps = sqrtpos(pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + + // Reconstruct decay angle and weight for it. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * ps); + wt = 1. + coefAsym * cosThe + cosThe * cosThe; + wtMax = 2. + abs(coefAsym); + } + + // Angular weight for W' -> W Z. + else if (iResBeg == 5 && iResEnd == 5 && idOutAbs == 24) { + double mr1 = pow2(process[6].m()) / sH; + double mr2 = pow2(process[7].m()) / sH; + double ps = sqrtpos(pow2(1. - mr1 - mr2) - 4. * mr1 * mr2); + double cCos2 = - (1./16.) * ps*ps * (1. - 2. * mr1 - 2. * mr2 + + mr1*mr1 + mr2*mr2 + 10. * mr1 * mr2); + double cFlat = -cCos2 + 0.5 * (mr1 + mr2) + * (1. - 2. * mr1 - 2. * mr2 + pow2(mr1 - mr2)); + + // Reconstruct decay angle and weight for it. + double cosThe = (process[3].p() - process[4].p()) + * (process[7].p() - process[6].p()) / (sH * ps); + wt = cFlat + cCos2 * cosThe*cosThe; + wtMax = cFlat + max(0., cCos2); + } + + // Angular weight for f + fbar -> W' -> W + Z -> 4 fermions. + else if (iResBeg == 6 && iResEnd == 7 + && (idOutAbs == 24 || idOutAbs == 23)) { + + // Order so that fbar(1) f(2) -> f'(3) fbar'(4) f"(5) fbar"(6). + // with f' fbar' from W and f" fbar" from Z. + int i1 = (process[3].id() < 0) ? 3 : 4; + int i2 = 7 - i1; + int i3 = (process[8].id() > 0) ? 8 : 9; + int i4 = 17 - i3; + int i5 = (process[10].id() > 0) ? 10 : 11; + int i6 = 21 - i5; + if (process[6].id() == 23) {swap(i3, i5); swap(i4, i6);} + + // Decay distribution like in f fbar -> Z^* -> W+ W-. + if (rndmPtr->flat() > anglesWpWZ) { + + // Set up four-products and internal products. + setupProd( process, i1, i2, i3, i4, i5, i6); + + // tHat and uHat of fbar f -> W Z, and their squared masses. + int iW = (process[6].id() == 23) ? 7 : 6; + int iZ = 13 - iW; + double tHres = (process[i1].p() - process[iW].p()).m2Calc(); + double uHres = (process[i1].p() - process[iZ].p()).m2Calc(); + double s3now = process[iW].m2(); + double s4now = process[iZ].m2(); + + // Kinematics combinations (norm(x) = |x|^2). + double fGK135 = norm(fGK( 1, 2, 3, 4, 5, 6) - fGK( 1, 2, 5, 6, 3, 4) ); + double fGK136 = norm(fGK( 1, 2, 3, 4, 6, 5) - fGK( 1, 2, 6, 5, 3, 4) ); + double xiT = xiGK( tHres, uHres, s3now, s4now); + double xiU = xiGK( uHres, tHres, s3now, s4now); + double xjTU = xjGK( tHres, uHres, s3now, s4now); + + // Couplings of outgoing fermion from Z. Combine with kinematics. + int idAbs = process[i5].idAbs(); + double lfZ = coupSMPtr->lf(idAbs); + double rfZ = coupSMPtr->rf(idAbs); + wt = lfZ*lfZ * fGK135 + rfZ*rfZ * fGK136; + wtMax = 4. * s3now * s4now * (lfZ*lfZ + rfZ*rfZ) + * (xiT + xiU - xjTU); + + // Decay distribution like in f fbar -> H^+- -> W+- Z0. + } else { + double p35 = 2. * process[i3].p() * process[i5].p(); + double p46 = 2. * process[i4].p() * process[i6].p(); + wt = 16. * p35 * p46; + wtMax = sH2; + } + } + + // Angular weight in top decay by standard routine. + else if (process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + + // Done. + return (wt / wtMax); + +} + + +//========================================================================== + +// Sigma1ffbar2Rhorizontal class. +// Cross section for f fbar' -> R^0 (f is a quark or lepton). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma1ffbar2Rhorizontal::initProc() { + + // Store R^0 mass and width for propagator. + mRes = particleDataPtr->m0(41); + GammaRes = particleDataPtr->mWidth(41); + m2Res = mRes*mRes; + GamMRat = GammaRes / mRes; + thetaWRat = 1. / (12. * coupSMPtr->sin2thetaW()); + + // Set pointer to particle properties and decay table. + particlePtr = particleDataPtr->particleDataEntryPtr(41); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), part independent of incoming flavour. + +void Sigma1ffbar2Rhorizontal::sigmaKin() { + + // Set up Breit-Wigner. Cross section for W+ and W- separately. + double sigBW = 12. * M_PI / ( pow2(sH - m2Res) + pow2(sH * GamMRat) ); + double preFac = alpEM * thetaWRat * mH; + sigma0Pos = preFac * sigBW * particlePtr->resWidthOpen(41, mH); + sigma0Neg = preFac * sigBW * particlePtr->resWidthOpen(-41, mH); + +} + +//-------------------------------------------------------------------------- + +// Evaluate sigmaHat(sHat), including incoming flavour dependence. + +double Sigma1ffbar2Rhorizontal::sigmaHat() { + + // Check for allowed flavour combinations, one generation apart. + if (id1 * id2 > 0 || abs(id1 + id2) != 2) return 0.; + + // Find whether R0 or R0bar. Colour factors. + double sigma = (id1 + id2 > 0) ? sigma0Pos : sigma0Neg; + if (abs(id1) < 7) sigma /= 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma1ffbar2Rhorizontal::setIdColAcol() { + + // Outgoing R0 or R0bar. + id3 = (id1 +id2 > 0) ? 41 : -41; + setId( id1, id2, id3); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaOnia.cxx b/PYTHIA8/pythia8140/src/SigmaOnia.cxx new file mode 100644 index 00000000000..42ef70922e5 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaOnia.cxx @@ -0,0 +1,626 @@ +// SigmaOnia.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// charmonia/bottomonia simulation classes. + +#include "SigmaOnia.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma2gg2QQbar3S11g class. +// Cross section g g -> QQbar[3S1(1)] g (Q = c or b). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2QQbar3S11g::initProc() { + + // Produced state. Process name. Onium matrix element. + idHad = (idNew == 4) ? 443 : 553; + nameSave = (idNew == 4) ? "g g -> ccbar[3S1(1)] g" + : "g g -> bbbar[3S1(1)] g"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi3S11") + : settingsPtr->parm("Bottomonium:OUpsilon3S11"); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat); no explicit flavour dependence. + +void Sigma2gg2QQbar3S11g::sigmaKin() { + + // Calculate kinematics dependence. + double stH = sH + tH; + double tuH = tH + uH; + double usH = uH + sH; + double sig = (10. * M_PI / 81.) * m3 * ( pow2(sH * tuH) + + pow2(tH * usH) + pow2(uH * stH) ) / pow2( stH * tuH * usH ); + + // Answer. + sigma = (M_PI/sH2) * pow3(alpS) * oniumME * sig; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2QQbar3S11g::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idHad, 21); + + // Two orientations of colour flow.. + setColAcol( 1, 2, 2, 3, 0, 0, 1, 3); + if (rndmPtr->flat() > 0.5) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2QQbar3PJ1g class. +// Cross section g g -> QQbar[3PJ(1)] g (Q = c or b, J = 0, 1 or 2). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2QQbar3PJ1g::initProc() { + + // Produced state. Process name. Onium matrix element. + idHad = 0; + nameSave = "illegal process"; + if (jSave == 0) { + idHad = (idNew == 4) ? 10441 : 10551; + nameSave = (idNew == 4) ? "g g -> ccbar[3P0(1)] g" + : "g g -> bbbar[3P0(1)] g"; + } else if (jSave == 1) { + idHad = (idNew == 4) ? 20443 : 20553; + nameSave = (idNew == 4) ? "g g -> ccbar[3P1(1)] g" + : "g g -> bbbar[3P1(1)] g"; + } else if (jSave == 2) { + idHad = (idNew == 4) ? 445 : 555; + nameSave = (idNew == 4) ? "g g -> ccbar[3P2(1)] g" + : "g g -> bbbar[3P2(1)] g"; + } + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:Ochic03P01") + : settingsPtr->parm("Bottomonium:Ochib03P01"); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat); no explicit flavour dependence. + +void Sigma2gg2QQbar3PJ1g::sigmaKin() { + + // Useful derived kinematics quantities. + double pRat = (sH * uH + uH * tH + tH * sH)/ sH2; + double qRat = tH * uH / sH2; + double rRat = s3 / sH; + double pRat2 = pRat * pRat; + double pRat3 = pRat2 * pRat; + double pRat4 = pRat3 * pRat; + double qRat2 = qRat * qRat; + double qRat3 = qRat2 * qRat; + double qRat4 = qRat3 * qRat; + double rRat2 = rRat * rRat; + double rRat3 = rRat2 * rRat; + double rRat4 = rRat3 * rRat; + + // Calculate kinematics dependence. + double sig = 0.; + if (jSave == 0) { + sig = (8. * M_PI / (9. * m3 * sH)) + * ( 9. * rRat2 * pRat4 * (rRat4 - 2. * rRat2 * pRat + pRat2) + - 6. * rRat * pRat3 * qRat * (2. * rRat4 - 5. * rRat2 * pRat + + pRat2) - pRat2 * qRat2 * (rRat4 + 2. * rRat2 * pRat - pRat2) + + 2. * rRat * pRat * qRat3 * (rRat2 - pRat) + 6. * rRat2 * qRat4) + / (qRat * pow4(qRat - rRat * pRat)); + } else if (jSave == 1) { + sig = (8. * M_PI / (3.* m3 * sH)) * pRat2 + * (rRat * pRat2 * (rRat2 - 4. * pRat) + + 2. * qRat * (-rRat4 + 5. * rRat2 * pRat + pRat2) + - 15. * rRat * qRat2) / pow4(qRat - rRat * pRat); + } else if (jSave == 2) { + sig = (8. * M_PI / (9. * m3 * sH)) + * (12. * rRat2 * pRat4 * (rRat4 - 2. * rRat2 * pRat + pRat2) + - 3. * rRat * pRat3 * qRat * (8. * rRat4 - rRat2 * pRat + 4. * pRat2) + + 2. * pRat2 * qRat2 * (-7. * rRat4 + 43. * rRat2 * pRat + pRat2) + + rRat * pRat * qRat3 * (16. * rRat2 - 61. * pRat) + + 12. * rRat2 * qRat4) / (qRat * pow4(qRat-rRat * pRat)); + } + + // Answer. + sigma = (M_PI/sH2) * pow3(alpS) * oniumME * sig; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2QQbar3PJ1g::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idHad, 21); + + // Two orientations of colour flow. + setColAcol( 1, 2, 2, 3, 0, 0, 1, 3); + if (rndmPtr->flat() > 0.5) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qg2QQbar3PJ1q class. +// Cross section q g -> QQbar[3PJ(1)] q (Q = c or b, J = 0, 1 or 2). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2QQbar3PJ1q::initProc() { + + // Produced state. Process name. Onium matrix element. + idHad = 0; + nameSave = "illegal process"; + if (jSave == 0) { + idHad = (idNew == 4) ? 10441 : 10551; + nameSave = (idNew == 4) ? "q g -> ccbar[3P0(1)] q" + : "q g -> bbbar[3P0(1)] q"; + } else if (jSave == 1) { + idHad = (idNew == 4) ? 20443 : 20553; + nameSave = (idNew == 4) ? "q g -> ccbar[3P1(1)] q" + : "q g -> bbbar[3P1(1)] q"; + } else if (jSave == 2) { + idHad = (idNew == 4) ? 445 : 555; + nameSave = (idNew == 4) ? "q g -> ccbar[3P2(1)] q" + : "q g -> bbbar[3P2(1)] q"; + } + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:Ochic03P01") + : settingsPtr->parm("Bottomonium:Ochib03P01"); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat); no explicit flavour dependence. + +void Sigma2qg2QQbar3PJ1q::sigmaKin() { + + // Calculate kinematics dependence. + double usH = uH + sH; + double sig = 0.; + if (jSave == 0) { + sig = - (16. * M_PI / 81.) * pow2(tH - 3. * s3) * (sH2 + uH2) + / (m3 * tH * pow4(usH)); + } else if (jSave == 1) { + sig = - (32. * M_PI / 27.) * (4. * s3 * sH * uH + tH * (sH2 + uH2)) + / (m3 * pow4(usH)); + } else if (jSave == 2) { + sig = - (32. *M_PI / 81.) * ( (6. * s3*s3 + tH2) * pow2(usH) + - 2. * sH * uH * (tH2 + 6. * s3 * usH)) / (m3 * tH * pow4(usH)); + } + + // Answer. + sigma = (M_PI/sH2) * pow3(alpS) * oniumME * sig; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2QQbar3PJ1q::setIdColAcol() { + + // Flavours are trivial. + int idq = (id2 == 21) ? id1 : id2; + setId( id1, id2, idHad, idq); + + // tH defined between q_in and q_out: must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Colour flow topologies. Swap when antiquarks. + if (id2 == 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 2, 1, 1, 0, 0, 0, 2, 0); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2QQbar3PJ1g class. +// Cross section q qbar -> QQbar[3PJ(1)] g (Q = c or b, J = 0, 1 or 2). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2QQbar3PJ1g::initProc() { + + // Produced state. Process name. Onium matrix element. + idHad = 0; + nameSave = "illegal process"; + if (jSave == 0) { + idHad = (idNew == 4) ? 10441 : 10551; + nameSave = (idNew == 4) ? "q qbar -> ccbar[3P0(1)] g" + : "q qbar -> bbbar[3P0(1)] g"; + } else if (jSave == 1) { + idHad = (idNew == 4) ? 20443 : 20553; + nameSave = (idNew == 4) ? "q qbar -> ccbar[3P1(1)] g" + : "q qbar -> bbbar[3P1(1)] g"; + } else if (jSave == 2) { + idHad = (idNew == 4) ? 445 : 555; + nameSave = (idNew == 4) ? "q qbar -> ccbar[3P2(1)] g" + : "q qbar -> bbbar[3P2(1)] g"; + } + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:Ochic03P01") + : settingsPtr->parm("Bottomonium:Ochib03P01"); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat); no explicit flavour dependence. + +void Sigma2qqbar2QQbar3PJ1g::sigmaKin() { + + // Calculate kinematics dependence. + double tuH = tH + uH; + double sig = 0.; + if (jSave == 0) { + sig =(128. * M_PI / 243.) * pow2(sH - 3. * s3) * (tH2 + uH2) + / (m3 * sH * pow4(tuH)); + } else if (jSave == 1) { + sig = (256. * M_PI / 81.) * (4. * s3 * tH * uH + sH * (tH2 + uH2)) + / (m3 * pow4(tuH)); + } else if (jSave == 2) { + sig = (256. * M_PI / 243.) * ( (6. * s3*s3 + sH2) * pow2(tuH) + - 2. * tH * uH * (sH2 + 6. * s3 * tuH) )/ (m3 * sH * pow4(tuH)); + } + + // Answer. + sigma = (M_PI/sH2) * pow3(alpS) * oniumME * sig; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2QQbar3PJ1g::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idHad, 21); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 0, 0, 1, 2); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2QQbarX8g class. +// Cross section g g -> QQbar[X(8)] g (Q = c or b, X = 3S1, 1S0 or 3PJ). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2QQbarX8g::initProc() { + + // Produced state. Process name. Onium matrix element. + idHad = 0; + nameSave = "illegal process"; + if (stateSave == 0) { + idHad = (idNew == 4) ? 9900443 : 9900553; + nameSave = (idNew == 4) ? "g g -> ccbar[3S1(8)] g" + : "g g -> bbbar[3S1(8)] g"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi3S18") + : settingsPtr->parm("Bottomonium:OUpsilon3S18"); + } else if (stateSave == 1) { + idHad = (idNew == 4) ? 9900441 : 9900551; + nameSave = (idNew == 4) ? "g g -> ccbar[1S0(8)] g" + : "g g -> bbbar[1S0(8)] g"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi1S08") + : settingsPtr->parm("Bottomonium:OUpsilon1S08"); + } else if (stateSave == 2) { + idHad = (idNew == 4) ? 9910441 : 9910551; + nameSave = (idNew == 4) ? "g g -> ccbar[3PJ(8)] g" + : "g g -> bbbar[3PJ(8)] g"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi3P08") + : settingsPtr->parm("Bottomonium:OUpsilon3P08"); + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat); no explicit flavour dependence. + +void Sigma2gg2QQbarX8g::sigmaKin() { + + // Calculate kinematics dependence. + double stH = sH + tH; + double tuH = tH + uH; + double usH = uH + sH; + double sig = 0.; + if (stateSave == 0) { + sig = (M_PI / 72.) * m3 * ( 27. * (pow2(stH) + pow2(tuH) + + pow2(usH)) / (s3*s3) - 16. ) * ( pow2(sH * tuH) + + pow2(tH * usH) + pow2(uH * stH) ) / pow2( stH * tuH * usH ); + } else if (stateSave == 1) { + sig = (5. * M_PI / 16.) * m3 * ( pow2(uH / (tuH * usH)) + + pow2(sH / (stH * usH)) + pow2(tH / (stH * tuH)) ) * ( 12. + + (pow4(stH) + pow4(tuH) + pow4(usH)) / (s3 * sH * tH * uH) ); + } else if (stateSave == 2) { + double sH3 = sH2 * sH; + double sH4 = sH3 * sH; + double sH5 = sH4 * sH; + double sH6 = sH5 * sH; + double sH7 = sH6 * sH; + double sH8 = sH7 * sH; + double tH3 = tH2 * tH; + double tH4 = tH3 * tH; + double tH5 = tH4 * tH; + double tH6 = tH5 * tH; + double tH7 = tH6 * tH; + double tH8 = tH7 * tH; + double ssttH = sH * sH + sH * tH + tH * tH; + sig = 5. * M_PI * (3. * sH * tH * stH * pow4(ssttH) + - s3 * pow2(ssttH) * (7. * sH6 + 36. * sH5 * tH + 45. * sH4 * tH2 + + 28. * sH3 * tH3 + 45. * sH2 * tH4 + 36. * sH * tH5 + 7. * tH6) + + pow2(s3) * stH * (35. *sH8 + 169. * sH7 * tH + 299. * sH6 * tH2 + + 401. * sH5 * tH3 + 418. * sH4 * tH4 + 401. * sH3 * tH5 + + 299. * sH2 * tH6 + 169. * sH * tH7 + 35. * tH8) + - pow3(s3) * (84. *sH8+432. *sH7*tH+905. *sH6*tH2 + + 1287. * sH5 * tH3 + 1436. * sH4 * tH4 +1287. * sH3 * tH5 + + 905. * sH2 * tH6 + 432. * sH * tH7 + 84. * tH8) + + pow4(s3) * stH * (126. * sH6 + 451. * sH5 * tH +677. * sH4 * tH2 + + 836. * sH3 * tH3 + 677. * sH2 * tH4 + 451. * sH * tH5 + + 126. * tH6) + - pow5(s3) * 3. * (42. * sH6 + 171. * sH5 * tH + 304. * sH4 * tH2 + + 362. * sH3 * tH3 + 304. * sH2 * tH4 + 171. * sH * tH5 + + 42. * tH6) + + pow3(s3 * s3) * 2. * stH * (42. * sH4 + 106. * sH3 * tH + + 119. * sH2 * tH2 + 106. * sH * tH3 + 42. * tH4) + - pow4(s3) * pow3(s3) * (35. * sH4 + 99. * sH3 * tH + + 120. * sH2 * tH2 + 99. * sH * tH3 + 35. * tH4) + + pow4(s3 * s3) * 7. * stH * ssttH) + / (sH * tH * uH * s3 * m3 * pow3(stH * tuH * usH)); + } + + // Answer. + sigma = (M_PI/sH2) * pow3(alpS) * oniumME * sig; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2QQbarX8g::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idHad, 21); + + // Split total contribution into different colour flows just like in + // g g -> g g (with kinematics recalculated for massless partons). + double sHr = - (tH + uH); + double sH2r = sHr * sHr; + double sigTS = tH2/sH2r + 2.*tH/sHr + 3. + 2.*sHr/tH + sH2r/tH2; + double sigUS = uH2/sH2r + 2.*uH/sHr + 3. + 2.*sHr/uH + sH2r/uH2; + double sigTU = tH2/uH2 + 2.*tH/uH + 3. + 2.*uH/tH + uH2/tH2; + double sigSum = sigTS + sigUS + sigTU; + + // Three colour flow topologies, each with two orientations. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 2, 2, 3, 1, 4, 4, 3); + else if (sigRand < sigTS + sigUS) + setColAcol( 1, 2, 3, 1, 3, 4, 4, 2); + else setColAcol( 1, 2, 3, 4, 1, 4, 3, 2); + if (rndmPtr->flat() > 0.5) swapColAcol(); + + +} + +//========================================================================== + +// Sigma2qg2QQbarX8q class. +// Cross section q g -> QQbar[X(8)] q (Q = c or b, X = 3S1, 1S0 or 3PJ). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2QQbarX8q::initProc() { + + // Produced state. Process name. Onium matrix element. + idHad = 0; + nameSave = "illegal process"; + if (stateSave == 0) { + idHad = (idNew == 4) ? 9900443 : 9900553; + nameSave = (idNew == 4) ? "q g -> ccbar[3S1(8)] q" + : "q g -> bbbar[3S1(8)] q"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi3S18") + : settingsPtr->parm("Bottomonium:OUpsilon3S18"); + } else if (stateSave == 1) { + idHad = (idNew == 4) ? 9900441 : 9900551; + nameSave = (idNew == 4) ? "q g -> ccbar[1S0(8)] q" + : "q g -> bbbar[1S0(8)] q"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi1S08") + : settingsPtr->parm("Bottomonium:OUpsilon1S08"); + } else if (stateSave == 2) { + idHad = (idNew == 4) ? 9910441 : 9910551; + nameSave = (idNew == 4) ? "q g -> ccbar[3PJ(8)] q" + : "q g -> bbbar[3PJ(8)] q"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi3P08") + : settingsPtr->parm("Bottomonium:OUpsilon3P08"); + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat); no explicit flavour dependence. + +void Sigma2qg2QQbarX8q::sigmaKin() { + + // Calculate kinematics dependence. + double stH = sH + tH; + double tuH = tH + uH; + double usH = uH + sH; + double stH2 = stH * stH; + double tuH2 = tuH * tuH; + double usH2 = usH * usH; + double sig = 0.; + if (stateSave == 0) { + sig = - (M_PI / 27.)* (4. * (sH2 + uH2) - sH * uH) * (stH2 +tuH2) + / (s3 * m3 * sH * uH * usH2); + } else if (stateSave == 1) { + sig = - (5. * M_PI / 18.) * (sH2 + uH2) / (m3 * tH * usH2); + } else if (stateSave == 2) { + sig = - (10. * M_PI / 9.) * ( (7. * usH + 8. * tH) * (sH2 + uH2) + + 4. * tH * (2. * pow2(s3) - stH2 - tuH2) ) + / (s3 * m3 * tH * usH2 * usH); + } + + // Answer. + sigma = (M_PI/sH2) * pow3(alpS) * oniumME * sig; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2QQbarX8q::setIdColAcol() { + + // Flavours are trivial. + int idq = (id2 == 21) ? id1 : id2; + setId( id1, id2, idHad, idq); + + // tH defined between q_in and q_out: must swap tHat <-> uHat if q g in. + swapTU = (id2 == 21); + + // Split total contribution into different colour flows just like in + // q g -> q g (with kinematics recalculated for massless partons). + double sHr = - (tH + uH); + double sH2r = sHr * sHr; + double sigTS = uH2/tH2 - (4./9.) * uH/sHr; + double sigTU = sH2r/tH2 - (4./9.) * sHr/uH; + double sigSum = sigTS + sigTU; + + // Two colour flow topologies. Swap if first is gluon, or when antiquark. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 0, 2, 1, 2, 3, 3, 0); + else setColAcol( 1, 0, 2, 3, 1, 3, 2, 0); + if (id1 == 21) swapCol12(); + if (idq < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2QQbarX8g class. +// Cross section q qbar -> QQbar[X(8)] g (Q = c or b, X = 3S1, 1S0 or 3PJ). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2QQbarX8g::initProc() { + + // Produced state. Process name. Onium matrix element. + idHad = 0; + nameSave = "illegal process"; + if (stateSave == 0) { + idHad = (idNew == 4) ? 9900443 : 9900553; + nameSave = (idNew == 4) ? "q qbar -> ccbar[3S1(8)] g" + : "q qbar -> bbbar[3S1(8)] g"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi3S18") + : settingsPtr->parm("Bottomonium:OUpsilon3S18"); + } else if (stateSave == 1) { + idHad = (idNew == 4) ? 9900441 : 9900551; + nameSave = (idNew == 4) ? "q qbar -> ccbar[1S0(8)] g" + : "q qbar -> bbbar[1S0(8)] g"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi1S08") + : settingsPtr->parm("Bottomonium:OUpsilon1S08"); + } else if (stateSave == 2) { + idHad = (idNew == 4) ? 9910441 : 9910551; + nameSave = (idNew == 4) ? "q qbar -> ccbar[3PJ(8)] g" + : "q qbar -> bbbar[3PJ(8)] g"; + oniumME = (idNew == 4) ? settingsPtr->parm("Charmonium:OJpsi3P08") + : settingsPtr->parm("Bottomonium:OUpsilon3P08"); + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat); no explicit flavour dependence. + +void Sigma2qqbar2QQbarX8g::sigmaKin() { + + // Calculate kinematics dependence. + double stH = sH + tH; + double tuH = tH + uH; + double usH = uH + sH; + double stH2 = stH * stH; + double tuH2 = tuH * tuH; + double usH2 = usH * usH; + double sig = 0.; + if (stateSave == 0) { + sig = (8. * M_PI / 81.) * (4. * (tH2 + uH2) - tH * uH) + * (stH2 + usH2) / (s3 * m3 * tH * uH * tuH2); + } else if (stateSave == 1) { + sig = (20. * M_PI / 27.) * (tH2 + uH2) / (m3 * sH * tuH2); + } else if (stateSave == 2) { + sig = (80. * M_PI / 27.) * ( (7. * tuH + 8. * sH) * (tH2 + uH2) + + 4. * sH * (2. * pow2(s3) - stH2 -usH2) ) + / (s3 * m3 * sH * tuH2 * tuH); + } + + // Answer. + sigma = (M_PI/sH2) * pow3(alpS) * oniumME * sig; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2QQbarX8g::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idHad, 21); + + // Split total contribution into different colour flows just like in + // q qbar -> g g (with kinematics recalculated for massless partons). + double sHr = - (tH + uH); + double sH2r = sHr * sHr; + double sigTS = (4. / 9.) * uH / tH - uH2 / sH2r; + double sigUS = (4. / 9.) * tH / uH - tH2 / sH2r; + double sigSum = sigTS + sigUS; + + // Two colour flow topologies. Swap if first is antiquark. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 0, 0, 2, 1, 3, 3, 2); + else setColAcol( 1, 0, 0, 2, 3, 2, 1, 3); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/SigmaProcess.cxx b/PYTHIA8/pythia8140/src/SigmaProcess.cxx new file mode 100644 index 00000000000..d4510593266 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaProcess.cxx @@ -0,0 +1,1111 @@ +// SigmaProcess.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// SigmaProcess class, and classes derived from it. + +#include "SigmaProcess.h" + +namespace Pythia8 { + +//========================================================================== + +// The SigmaProcess class. +// Base class for cross sections. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Conversion of GeV^{-2} to mb for cross section. +const double SigmaProcess::CONVERT2MB = 0.389380; + +// The sum of outgoing masses must not be too close to the cm energy. +const double SigmaProcess::MASSMARGIN = 0.1; + +//-------------------------------------------------------------------------- + +// Perform simple initialization and store pointers. + +void SigmaProcess::init(Info* infoPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, BeamParticle* beamAPtrIn, + BeamParticle* beamBPtrIn, CoupSM* coupSMPtrIn, SigmaTotal* sigmaTotPtrIn, + CoupSUSY* coupSUSYPtrIn, SusyLesHouches* slhaPtrIn) { + + // Store pointers. + infoPtr = infoPtrIn; + settingsPtr = settingsPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + coupSMPtr = coupSMPtrIn; + sigmaTotPtr = sigmaTotPtrIn; + coupSUSYPtr = coupSUSYPtrIn; + slhaPtr = slhaPtrIn; + + // Read out some properties of beams to allow shorthand. + idA = (beamAPtr > 0) ? beamAPtr->id() : 0; + idB = (beamBPtr > 0) ? beamBPtr->id() : 0; + mA = (beamAPtr > 0) ? beamAPtr->m() : 0.; + mB = (beamBPtr > 0) ? beamBPtr->m() : 0.; + isLeptonA = (beamAPtr > 0) ? beamAPtr->isLepton() : false; + isLeptonB = (beamBPtr > 0) ? beamBPtr->isLepton() : false; + hasLeptonBeams = isLeptonA || isLeptonB; + + // K factor, multiplying resolved processes. (But not here for MI.) + Kfactor = settingsPtr->parm("SigmaProcess:Kfactor"); + + // Maximum incoming quark flavour. + nQuarkIn = settingsPtr->mode("PDFinProcess:nQuarkIn"); + + // Renormalization scale choice. + renormScale1 = settingsPtr->mode("SigmaProcess:renormScale1"); + renormScale2 = settingsPtr->mode("SigmaProcess:renormScale2"); + renormScale3 = settingsPtr->mode("SigmaProcess:renormScale3"); + renormScale3VV = settingsPtr->mode("SigmaProcess:renormScale3VV"); + renormMultFac = settingsPtr->parm("SigmaProcess:renormMultFac"); + renormFixScale = settingsPtr->parm("SigmaProcess:renormFixScale"); + + // Factorization scale choice. + factorScale1 = settingsPtr->mode("SigmaProcess:factorScale1"); + factorScale2 = settingsPtr->mode("SigmaProcess:factorScale2"); + factorScale3 = settingsPtr->mode("SigmaProcess:factorScale3"); + factorScale3VV = settingsPtr->mode("SigmaProcess:factorScale3VV"); + factorMultFac = settingsPtr->parm("SigmaProcess:factorMultFac"); + factorFixScale = settingsPtr->parm("SigmaProcess:factorFixScale"); + + // CP violation parameters for the BSM Higgs sector. + higgsH1parity = settingsPtr->mode("HiggsH1:parity"); + higgsH1eta = settingsPtr->parm("HiggsH1:etaParity"); + higgsH2parity = settingsPtr->mode("HiggsH2:parity"); + higgsH2eta = settingsPtr->parm("HiggsH2:etaParity"); + higgsA3parity = settingsPtr->mode("HiggsA3:parity"); + higgsA3eta = settingsPtr->parm("HiggsA3:etaParity"); + + // If BSM not switched on then H1 should have SM properties. + if (!settingsPtr->flag("Higgs:useBSM")){ + higgsH1parity = 1; + higgsH1eta = 0.; + } + +} + +//-------------------------------------------------------------------------- + +// Set up allowed flux of incoming partons. +// addBeam: set up PDF's that need to be evaluated for the two beams. +// addPair: set up pairs of incoming partons from the two beams. + +bool SigmaProcess::initFlux() { + + // Reset arrays (in case of several init's in same run). + inBeamA.clear(); + inBeamB.clear(); + inPair.clear(); + + // Read in process-specific channel information. + string fluxType = inFlux(); + + // Case with g g incoming state. + if (fluxType == "gg") { + addBeamA(21); + addBeamB(21); + addPair(21, 21); + } + + // Case with q g incoming state. + else if (fluxType == "qg") { + for (int i = -nQuarkIn; i <= nQuarkIn; ++i) { + int idNow = (i == 0) ? 21 : i; + addBeamA(idNow); + addBeamB(idNow); + } + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addPair(idNow, 21); + addPair(21, idNow); + } + } + + // Case with q q', q qbar' or qbar qbar' incoming state. + else if (fluxType == "qq") { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addBeamB(idNow); + } + for (int id1Now = -nQuarkIn; id1Now <= nQuarkIn; ++id1Now) + if (id1Now != 0) + for (int id2Now = -nQuarkIn; id2Now <= nQuarkIn; ++id2Now) + if (id2Now != 0) + addPair(id1Now, id2Now); + } + + // Case with q qbar incoming state. + else if (fluxType == "qqbarSame") { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addBeamB(idNow); + } + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) + addPair(idNow, -idNow); + } + + // Case with f f', f fbar', fbar fbar' incoming state. + else if (fluxType == "ff") { + // If beams are leptons then they are also the colliding partons. + if ( isLeptonA && isLeptonB ) { + addBeamA(idA); + addBeamB(idB); + addPair(idA, idB); + // First beam is lepton and second is hadron. + } else if ( isLeptonA ) { + addBeamA(idA); + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamB(idNow); + addPair(idA, idNow); + } + // First beam is hadron and second is lepton. + } else if ( isLeptonB ) { + addBeamB(idB); + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addPair(idNow, idB); + } + // Hadron beams gives quarks. + } else { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addBeamB(idNow); + } + for (int id1Now = -nQuarkIn; id1Now <= nQuarkIn; ++id1Now) + if (id1Now != 0) + for (int id2Now = -nQuarkIn; id2Now <= nQuarkIn; ++id2Now) + if (id2Now != 0) + addPair(id1Now, id2Now); + } + } + + // Case with f fbar incoming state. + else if (fluxType == "ffbarSame") { + // If beams are antiparticle pair and leptons then also colliding partons. + if ( idA + idB == 0 && isLeptonA ) { + addBeamA(idA); + addBeamB(idB); + addPair(idA, idB); + // Else assume both to be hadrons, for better or worse. + } else { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addBeamB(idNow); + } + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) + addPair(idNow, -idNow); + } + } + + // Case with f fbar' charged(+-1) incoming state. + else if (fluxType == "ffbarChg") { + // If beams are leptons then also colliding partons. + if ( isLeptonA && isLeptonB && abs( particleDataPtr->chargeType(idA) + + particleDataPtr->chargeType(idB) ) == 3 ) { + addBeamA(idA); + addBeamB(idB); + addPair(idA, idB); + // Hadron beams gives quarks. + } else { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addBeamB(idNow); + } + for (int id1Now = -nQuarkIn; id1Now <= nQuarkIn; ++id1Now) + if (id1Now != 0) + for (int id2Now = -nQuarkIn; id2Now <= nQuarkIn; ++id2Now) + if (id2Now != 0 && id1Now * id2Now < 0 + && (abs(id1Now) + abs(id2Now))%2 == 1) addPair(id1Now, id2Now); + } + } + + // Case with f fbar' generic incoming state. + else if (fluxType == "ffbar") { + // If beams are leptons then also colliding partons. + if (isLeptonA && isLeptonB && idA * idB < 0) { + addBeamA(idA); + addBeamB(idB); + addPair(idA, idB); + // Hadron beams gives quarks. + } else { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addBeamB(idNow); + } + for (int id1Now = -nQuarkIn; id1Now <= nQuarkIn; ++id1Now) + if (id1Now != 0) + for (int id2Now = -nQuarkIn; id2Now <= nQuarkIn; ++id2Now) + if (id2Now != 0 && id1Now * id2Now < 0) + addPair(id1Now, id2Now); + } + } + + // Case with f gamma incoming state. + else if (fluxType == "fgm") { + // Fermion from incoming side A. + if ( isLeptonA ) { + addBeamA(idA); + addPair(idA, 22); + } else { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamA(idNow); + addPair(idNow, 22); + } + } + // Fermion from incoming side B. + if ( isLeptonB ) { + addBeamB( idB); + addPair(22, idB); + } else { + for (int idNow = -nQuarkIn; idNow <= nQuarkIn; ++idNow) + if (idNow != 0) { + addBeamB(idNow); + addPair(22, idNow); + } + } + // Photons in the beams. + addBeamA(22); + addBeamB(22); + } + + // Case with gamma gamma incoming state. + else if (fluxType == "ggm") { + addBeamA(21); + addBeamA(22); + addBeamB(21); + addBeamB(22); + addPair(21, 22); + addPair(22, 21); + } + + // Case with gamma gamma incoming state. + else if (fluxType == "gmgm") { + addBeamA(22); + addBeamB(22); + addPair(22, 22); + } + + // Unrecognized fluxType is bad sign. Else done. + else { + infoPtr->errorMsg("Error in SigmaProcess::initFlux: " + "unrecognized inFlux type", fluxType); + return false; + } + return true; + +} + +//-------------------------------------------------------------------------- + +// Convolute matrix-element expression(s) with parton flux and K factor. + +double SigmaProcess::sigmaPDF() { + + // Evaluate and store the required parton densities. + for (int j = 0; j < sizeBeamA(); ++j) + inBeamA[j].pdf = beamAPtr->xfHard( inBeamA[j].id, x1Save, Q2FacSave); + for (int j = 0; j < sizeBeamB(); ++j) + inBeamB[j].pdf = beamBPtr->xfHard( inBeamB[j].id, x2Save, Q2FacSave); + + // Loop over allowed incoming channels. + sigmaSumSave = 0.; + for (int i = 0; i < sizePair(); ++i) { + + // Evaluate hard-scattering cross section. Include K factor. + inPair[i].pdfSigma = Kfactor + * sigmaHatWrap(inPair[i].idA, inPair[i].idB); + + // Multiply by respective parton densities. + for (int j = 0; j < sizeBeamA(); ++j) + if (inPair[i].idA == inBeamA[j].id) { + inPair[i].pdfA = inBeamA[j].pdf; + inPair[i].pdfSigma *= inBeamA[j].pdf; + break; + } + for (int j = 0; j < sizeBeamB(); ++j) + if (inPair[i].idB == inBeamB[j].id) { + inPair[i].pdfB = inBeamB[j].pdf; + inPair[i].pdfSigma *= inBeamB[j].pdf; + break; + } + + // Sum for all channels. + sigmaSumSave += inPair[i].pdfSigma; + } + + // Done. + return sigmaSumSave; + +} + +//-------------------------------------------------------------------------- + +// Select incoming parton channel and extract parton densities (resolved). + +void SigmaProcess::pickInState(int id1in, int id2in) { + + // Multiple interactions: partons already selected. + if (id1in != 0 && id2in != 0) { + id1 = id1in; + id2 = id2in; + } + + // Pick channel. Extract channel flavours and pdf's. + double sigmaRand = sigmaSumSave * rndmPtr->flat(); + for (int i = 0; i < sizePair(); ++i) { + sigmaRand -= inPair[i].pdfSigma; + if (sigmaRand <= 0.) { + id1 = inPair[i].idA; + id2 = inPair[i].idB; + pdf1Save = inPair[i].pdfA; + pdf2Save = inPair[i].pdfB; + break; + } + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for W decay distribution in t -> W b -> f fbar b. + +double SigmaProcess::weightTopDecay( Event& process, int iResBeg, + int iResEnd) { + + // If not pair W d/s/b and mother t then return unit weight. + if (iResEnd - iResBeg != 1) return 1.; + int iW1 = iResBeg; + int iB2 = iResBeg + 1; + int idW1 = process[iW1].idAbs(); + int idB2 = process[iB2].idAbs(); + if (idW1 != 24) { + swap(iW1, iB2); + swap(idW1, idB2); + } + if (idW1 != 24 || (idB2 != 1 && idB2 != 3 && idB2 != 5)) return 1.; + int iT = process[iW1].mother1(); + if (iT <= 0 || process[iT].idAbs() != 6) return 1.; + + // Find sign-matched order of W decay products. + int iF = process[iW1].daughter1(); + int iFbar = process[iW1].daughter2(); + if (iFbar - iF != 1) return 1.; + if (process[iT].id() * process[iF].id() < 0) swap(iF, iFbar); + + // Weight and maximum weight. + double wt = (process[iT].p() * process[iFbar].p()) + * (process[iF].p() * process[iB2].p()); + double wtMax = ( pow4(process[iT].m()) - pow4(process[iW1].m()) ) / 8.; + + // Done. + return wt / wtMax; + +} + + +//-------------------------------------------------------------------------- + +// Evaluate weight for Z0/W+- decay distributions in H -> Z0/W+ Z0/W- -> 4f. + +double SigmaProcess::weightHiggsDecay( Event& process, int iResBeg, + int iResEnd) { + + // If not pair Z0 Z0 or W+ W- then return unit weight. + if (iResEnd - iResBeg != 1) return 1.; + int iZW1 = iResBeg; + int iZW2 = iResBeg + 1; + int idZW1 = process[iZW1].id(); + int idZW2 = process[iZW2].id(); + if (idZW1 < 0) { + swap(iZW1, iZW2); + swap(idZW1, idZW2); + } + if ( (idZW1 != 23 || idZW2 != 23) && (idZW1 != 24 || idZW2 != -24) ) + return 1.; + + // If mother is not Higgs then return unit weight. + int iH = process[iZW1].mother1(); + if (iH <= 0) return 1.; + int idH = process[iH].id(); + if (idH != 25 && idH != 35 && idH !=36) return 1.; + + // Parameters depend on Higgs type: H0(H_1), H^0(H_2) or A^0(H_3). + int higgsParity = higgsH1parity; + double higgsEta = higgsH1eta; + if (idH == 35) { + higgsParity = higgsH2parity; + higgsEta = higgsH2eta; + } else if (idH == 36) { + higgsParity = higgsA3parity; + higgsEta = higgsA3eta; + } + + // Option with isotropic decays. + if (higgsParity == 0) return 1.; + + // Maximum and initial weight. + double wtMax = pow4(process[iH].m()); + double wt = wtMax; + + // Find sign-matched order of Z0/W+- decay products. + int i3 = process[iZW1].daughter1(); + int i4 = process[iZW1].daughter2(); + if (process[i3].id() < 0) swap( i3, i4); + int i5 = process[iZW2].daughter1(); + int i6 = process[iZW2].daughter2(); + if (process[i5].id() < 0) swap( i5, i6); + + // Evaluate four-vector products and find masses.. + double p35 = 2. * process[i3].p() * process[i5].p(); + double p36 = 2. * process[i3].p() * process[i6].p(); + double p45 = 2. * process[i4].p() * process[i5].p(); + double p46 = 2. * process[i4].p() * process[i6].p(); + double p34 = 2. * process[i3].p() * process[i4].p(); + double p56 = 2. * process[i5].p() * process[i6].p(); + double mZW1 = process[iZW1].m(); + double mZW2 = process[iZW2].m(); + + // For mixed CP states need epsilon product and gauge boson masses. + double epsilonProd = 0.; + if (higgsParity == 3) { + double p[4][4]; + for (int i = 0; i < 4; ++i) { + int ii = i3; + if (i == 1) ii = i4; + if (i == 2) ii = i5; + if (i == 3) ii = i6; + p[i][0] = process[ii].e(); + p[i][1] = process[ii].px(); + p[i][2] = process[ii].py(); + p[i][3] = process[ii].pz(); + } + epsilonProd + = p[0][0]*p[1][1]*p[2][2]*p[3][3] - p[0][0]*p[1][1]*p[2][3]*p[3][2] + - p[0][0]*p[1][2]*p[2][1]*p[3][3] + p[0][0]*p[1][2]*p[2][3]*p[3][1] + + p[0][0]*p[1][3]*p[2][1]*p[3][2] - p[0][0]*p[1][3]*p[2][2]*p[3][1] + - p[0][1]*p[1][0]*p[2][2]*p[3][3] + p[0][1]*p[1][0]*p[2][3]*p[3][2] + + p[0][1]*p[1][2]*p[2][0]*p[3][3] - p[0][1]*p[1][2]*p[2][3]*p[3][0] + - p[0][1]*p[1][3]*p[2][0]*p[3][2] + p[0][1]*p[1][3]*p[2][2]*p[3][0] + + p[0][2]*p[1][0]*p[2][1]*p[3][3] - p[0][2]*p[1][0]*p[2][3]*p[3][1] + - p[0][2]*p[1][1]*p[2][0]*p[3][3] + p[0][2]*p[1][1]*p[2][3]*p[3][0] + + p[0][2]*p[1][3]*p[2][0]*p[3][1] - p[0][2]*p[1][3]*p[2][1]*p[3][0] + - p[0][3]*p[1][0]*p[2][1]*p[3][2] + p[0][3]*p[1][0]*p[2][2]*p[3][1] + + p[0][3]*p[1][1]*p[2][0]*p[3][2] - p[0][3]*p[1][1]*p[2][2]*p[3][0] + - p[0][3]*p[1][2]*p[2][0]*p[3][1] + p[0][3]*p[1][2]*p[2][1]*p[3][0]; + } + + // Z0 Z0 decay: vector and axial couplings of two fermion pairs. + if (idZW1 == 23) { + double vf1 = coupSMPtr->vf(process[i3].idAbs()); + double af1 = coupSMPtr->af(process[i3].idAbs()); + double vf2 = coupSMPtr->vf(process[i5].idAbs()); + double af2 = coupSMPtr->af(process[i5].idAbs()); + double va12asym = 4. * vf1 * af1 * vf2 * af2 + / ( (vf1*vf1 + af1*af1) * (vf2*vf2 + af2*af2) ); + double etaMod = higgsEta / pow2( particleDataPtr->m0(23) ); + + // Normal CP-even decay. + if (higgsParity == 1) wt = 8. * (1. + va12asym) * p35 * p46 + + 8. * (1. - va12asym) * p36 * p45; + + // CP-odd decay (normal for A0(H_3)). + else if (higgsParity == 2) wt = ( pow2(p35 + p46) + + pow2(p36 + p45) - 2. * p34 * p56 + - 2. * pow2(p35 * p46 - p36 * p45) / (p34 * p56) + + va12asym * (p35 + p36 - p45 - p46) * (p35 + p45 - p36 - p46) ) + / (1. + va12asym); + + // Mixed CP states. + else wt = 32. * ( 0.25 * ( (1. + va12asym) * p35 * p46 + + (1. - va12asym) * p36 * p45 ) - 0.5 * etaMod * epsilonProd + * ( (1. + va12asym) * (p35 + p46) - (1. - va12asym) * (p36 + p45) ) + + 0.0625 * etaMod * etaMod * (-2. * pow2(p34 * p56) + - 2. * pow2(p35 * p46 - p36 * p45) + + p34 * p56 * (pow2(p35 + p46) + pow2(p36 + p45)) + + va12asym * p34 * p56 * (p35 + p36 - p45 - p46) + * (p35 + p45 - p36 - p46) ) ) / ( 1. + 2. * etaMod * mZW1 * mZW2 + + 2. * pow2(etaMod * mZW1 * mZW2) * (1. + va12asym) ); + + // W+ W- decay. + } else if (idZW1 == 24) { + double etaMod = higgsEta / pow2( particleDataPtr->m0(24) ); + + // Normal CP-even decay. + if (higgsParity == 1) wt = 16. * p35 * p46; + + // CP-odd decay (normal for A0(H_3)). + else if (higgsParity == 2) wt = 0.5 * ( pow2(p35 + p46) + + pow2(p36 + p45) - 2. * p34 * p56 + - 2. * pow2(p35 * p46 - p36 * p45) / (p34 * p56) + + (p35 + p36 - p45 - p46) * (p35 + p45 - p36 - p46) ); + + // Mixed CP states. + else wt = 32. * ( 0.25 * 2. * p35 * p46 + - 0.5 * etaMod * epsilonProd * 2. * (p35 + p46) + + 0.0625 * etaMod * etaMod * (-2. * pow2(p34 * p56) + - 2. * pow2(p35 * p46 - p36 * p45) + + p34 * p56 * (pow2(p35 + p46) + pow2(p36 + p45)) + + p34 * p56 * (p35 + p36 - p45 - p46) * (p35 + p45 - p36 - p46) ) ) + / ( 1. * 2. * etaMod * mZW1 * mZW2 + 2. * pow2(etaMod * mZW1 * mZW2) ); + } + + // Done. + return wt / wtMax; + +} + +//========================================================================== + +// The Sigma1Process class. +// Base class for resolved 2 -> 1 cross sections; derived from SigmaProcess. + +//-------------------------------------------------------------------------- + +// Input and complement kinematics for resolved 2 -> 1 process. + +void Sigma1Process::store1Kin( double x1in, double x2in, double sHin) { + + // Default value only sensible for these processes. + swapTU = false; + + // Incoming parton momentum fractions and sHat. + x1Save = x1in; + x2Save = x2in; + sH = sHin; + mH = sqrt(sH); + sH2 = sH * sH; + + // Special kinematics setup for |M|^2 evaluations e.g. with MadGraph. + mME[0] = 0.; + pME[0] = 0.5 * mH * Vec4( 0., 0., 1., 1.); + mME[1] = 0.; + pME[1] = 0.5 * mH * Vec4( 0., 0., -1., 1.); + mME[2] = mH; + pME[2] = Vec4( 0., 0., 0., mH); + + // Different options for renormalization scale, but normally sHat. + Q2RenSave = renormMultFac * sH; + if (renormScale1 == 2) Q2RenSave = renormFixScale; + + // Different options for factorization scale, but normally sHat. + Q2FacSave = factorMultFac * sH; + if (factorScale1 == 2) Q2FacSave = factorFixScale; + + // Evaluate alpha_strong and alpha_EM. + alpS = coupSMPtr->alphaS(Q2RenSave); + alpEM = coupSMPtr->alphaEM(Q2RenSave); + +} + +//========================================================================== + +// The Sigma2Process class. +// Base class for resolved 2 -> 2 cross sections; derived from SigmaProcess. + +//-------------------------------------------------------------------------- + +// Input and complement kinematics for resolved 2 -> 2 process. + +void Sigma2Process::store2Kin( double x1in, double x2in, double sHin, + double tHin, double m3in, double m4in, double runBW3in, double runBW4in) { + + // Default ordering of particles 3 and 4. + swapTU = false; + + // Incoming parton momentum fractions. + x1Save = x1in; + x2Save = x2in; + + // Incoming masses and their squares. + bool masslessKin = (id3Mass() == 0) && (id4Mass() == 0); + if (masslessKin) { + m3 = 0.; + m4 = 0.; + } else { + m3 = m3in; + m4 = m4in; + } + mSave[3] = m3; + mSave[4] = m4; + s3 = m3 * m3; + s4 = m4 * m4; + + // Standard Mandelstam variables and their squares. + sH = sHin; + tH = tHin; + uH = (masslessKin) ? -(sH + tH) : s3 + s4 - (sH + tH); + mH = sqrt(sH); + sH2 = sH * sH; + tH2 = tH * tH; + uH2 = uH * uH; + + // The nominal Breit-Wigner factors with running width. + runBW3 = runBW3in; + runBW4 = runBW4in; + + // Calculate squared transverse momentum. + pT2 = (masslessKin) ? tH * uH / sH : (tH * uH - s3 * s4) / sH; + + // Special kinematics setup for |M|^2 evaluations e.g. with MadGraph. + mME[0] = 0.; + pME[0] = 0.5 * mH * Vec4( 0., 0., 1., 1.); + mME[1] = 0.; + pME[1] = 0.5 * mH * Vec4( 0., 0., -1., 1.); + double sH34 = sqrtpos( pow2(sH - s3 - s4) - 4. * s3 * s4); + double cThe = (tH - uH) / sH34; + double sThe = sqrtpos(1. - cThe * cThe); + double pAbs = 0.5 * sH34 / mH; + // Normally allowed with unequal (or vanishing) masses. + if (id3Mass() == 0 || abs(id3Mass()) != abs(id4Mass())) { + mME[2] = m3; + pME[2] = Vec4( pAbs * sThe, 0., pAbs * cThe, 0.5 * (sH + s3 - s4) / mH); + mME[3] = m4; + pME[3] = Vec4( -pAbs * sThe, 0., -pAbs * cThe, 0.5 * (sH + s4 - s3) / mH); + // For equal (anti)particles (e.g. W+ W-) use averaged mass. + } else { + mME[2] = sqrtpos(0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH); + pME[2] = Vec4( pAbs * sThe, 0., pAbs * cThe, 0.5 * mH); + mME[3] = mME[2]; + pME[3] = Vec4( -pAbs * sThe, 0., -pAbs * cThe, 0.5 * mH); + } + + // Special case: pick scale as if 2 -> 1 process in disguise. + if (isSChannel()) { + + // Different options for renormalization scale, but normally sHat. + Q2RenSave = renormMultFac * sH; + if (renormScale1 == 2) Q2RenSave = renormFixScale; + + // Different options for factorization scale, but normally sHat. + Q2FacSave = factorMultFac * sH; + if (factorScale1 == 2) Q2FacSave = factorFixScale; + + // Normal case with "true" 2 -> 2. + } else { + + // Different options for renormalization scale. + if (masslessKin) Q2RenSave = (renormScale2 < 4) ? pT2 : sH; + else if (renormScale2 == 1) Q2RenSave = pT2 + min(s3, s4); + else if (renormScale2 == 2) Q2RenSave = sqrt((pT2 + s3) * (pT2 + s4)); + else if (renormScale2 == 3) Q2RenSave = pT2 + 0.5 * (s3 + s4); + else Q2RenSave = sH; + Q2RenSave *= renormMultFac; + if (renormScale2 == 5) Q2RenSave = renormFixScale; + + // Different options for factorization scale. + if (masslessKin) Q2FacSave = (factorScale2 < 4) ? pT2 : sH; + else if (factorScale2 == 1) Q2FacSave = pT2 + min(s3, s4); + else if (factorScale2 == 2) Q2FacSave = sqrt((pT2 + s3) * (pT2 + s4)); + else if (factorScale2 == 3) Q2FacSave = pT2 + 0.5 * (s3 + s4); + else Q2FacSave = sH; + Q2FacSave *= factorMultFac; + if (factorScale2 == 5) Q2FacSave = factorFixScale; + } + + // Evaluate alpha_strong and alpha_EM. + alpS = coupSMPtr->alphaS(Q2RenSave); + alpEM = coupSMPtr->alphaEM(Q2RenSave); + +} + +//-------------------------------------------------------------------------- + +// As above, special kinematics for multiple interactions. + +void Sigma2Process::store2KinMI( double x1in, double x2in, + double sHin, double tHin, double uHin, double alpSin, double alpEMin, + bool needMasses, double m3in, double m4in) { + + // Default ordering of particles 3 and 4. + swapTU = false; + + // Incoming x values. + x1Save = x1in; + x2Save = x2in; + + // Standard Mandelstam variables and their squares. + sH = sHin; + tH = tHin; + uH = uHin; + mH = sqrt(sH); + sH2 = sH * sH; + tH2 = tH * tH; + uH2 = uH * uH; + + // Strong and electroweak couplings. + alpS = alpSin; + alpEM = alpEMin; + + // Assume vanishing masses. (Will be modified in final kinematics.) + m3 = 0.; + s3 = 0.; + m4 = 0.; + s4 = 0.; + sHBeta = sH; + + // Scattering angle. + cosTheta = (tH - uH) / sH; + sinTheta = 2. * sqrtpos( tH * uH ) / sH; + + // In some cases must use masses and redefine meaning of tHat and uHat. + if (needMasses) { + m3 = m3in; + s3 = m3 * m3; + m4 = m4in; + s4 = m4 * m4; + sHMass = sH - s3 - s4; + sHBeta = sqrtpos(sHMass*sHMass - 4. * s3 * s4); + tH = -0.5 * (sHMass - sHBeta * cosTheta); + uH = -0.5 * (sHMass + sHBeta * cosTheta); + tH2 = tH * tH; + uH2 = uH * uH; + } + + // pT2 with masses (at this stage) included. + pT2Mass = 0.25 * sHBeta * pow2(sinTheta); + +} + +//-------------------------------------------------------------------------- + +// Perform kinematics for a Multiple Interaction, including a rescattering. + +bool Sigma2Process::final2KinMI( int i1Res, int i2Res, Vec4 p1Res, Vec4 p2Res, + double m1Res, double m2Res) { + + // Have to set flavours and colours. + setIdColAcol(); + + // Check that masses of outgoing particles not too big. + m3 = particleDataPtr->m0(idSave[3]); + m4 = particleDataPtr->m0(idSave[4]); + mH = sqrt(sH); + if (m3 + m4 + MASSMARGIN > mH) return false; + s3 = m3 * m3; + s4 = m4 * m4; + + // Do kinematics of the production; without or with masses. + double e1In = 0.5 * mH; + double e2In = e1In; + double pzIn = e1In; + if (i1Res > 0 || i2Res > 0) { + double s1 = m1Res * m1Res; + double s2 = m2Res * m2Res; + e1In = 0.5 * (sH + s1 - s2) / mH; + e2In = 0.5 * (sH + s2 - s1) / mH; + pzIn = sqrtpos( e1In*e1In - s1 ); + } + + // Do kinematics of the decay. + double e3 = 0.5 * (sH + s3 - s4) / mH; + double e4 = 0.5 * (sH + s4 - s3) / mH; + double pAbs = sqrtpos( e3*e3 - s3 ); + phi = 2. * M_PI * rndmPtr->flat(); + double pZ = pAbs * cosTheta; + pTFin = pAbs * sinTheta; + double pX = pTFin * sin(phi); + double pY = pTFin * cos(phi); + double scale = 0.5 * mH * sinTheta; + + // Fill particle info. + int status1 = (i1Res == 0) ? -31 : -34; + int status2 = (i2Res == 0) ? -31 : -34; + parton[1] = Particle( idSave[1], status1, 0, 0, 3, 4, + colSave[1], acolSave[1], 0., 0., pzIn, e1In, m1Res, scale); + parton[2] = Particle( idSave[2], status2, 0, 0, 3, 4, + colSave[2], acolSave[2], 0., 0., -pzIn, e2In, m2Res, scale); + parton[3] = Particle( idSave[3], 33, 1, 2, 0, 0, + colSave[3], acolSave[3], pX, pY, pZ, e3, m3, scale); + parton[4] = Particle( idSave[4], 33, 1, 2, 0, 0, + colSave[4], acolSave[4], -pX, -pY, -pZ, e4, m4, scale); + + // Boost particles from subprocess rest frame to event rest frame. + // Normal multiple interaction: only longitudinal boost. + if (i1Res == 0 && i2Res == 0) { + double betaZ = (x1Save - x2Save) / (x1Save + x2Save); + for (int i = 1; i <= 4; ++i) parton[i].bst(0., 0., betaZ); + // Rescattering: generic rotation and boost required. + } else { + RotBstMatrix M; + M.fromCMframe( p1Res, p2Res); + for (int i = 1; i <= 4; ++i) parton[i].rotbst(M); + } + + // Done. + return true; + +} + +//========================================================================== + +// The Sigma3Process class. +// Base class for resolved 2 -> 3 cross sections; derived from SigmaProcess. + +//-------------------------------------------------------------------------- + +// Input and complement kinematics for resolved 2 -> 3 process. + +void Sigma3Process::store3Kin( double x1in, double x2in, double sHin, + Vec4 p3cmIn, Vec4 p4cmIn, Vec4 p5cmIn, double m3in, double m4in, + double m5in, double runBW3in, double runBW4in, double runBW5in) { + + // Default ordering of particles 3 and 4 - not relevant here. + swapTU = false; + + // Incoming parton momentum fractions. + x1Save = x1in; + x2Save = x2in; + + // Incoming masses and their squares. + if (id3Mass() == 0 && id4Mass() == 0 && id5Mass() == 0) { + m3 = 0.; + m4 = 0.; + m5 = 0.; + } else { + m3 = m3in; + m4 = m4in; + m5 = m5in; + } + mSave[3] = m3; + mSave[4] = m4; + mSave[5] = m5; + s3 = m3 * m3; + s4 = m4 * m4; + s5 = m5 * m5; + + // Standard Mandelstam variables and four-momenta in rest frame. + sH = sHin; + mH = sqrt(sH); + p3cm = p3cmIn; + p4cm = p4cmIn; + p5cm = p5cmIn; + + // Special kinematics setup for |M|^2 evaluations e.g. with MadGraph. + mME[0] = 0.; + pME[0] = 0.5 * mH * Vec4( 0., 0., 1., 1.); + mME[1] = 0.; + pME[1] = 0.5 * mH * Vec4( 0., 0., -1., 1.); + mME[2] = m3; + pME[2] = p3cm; + mME[3] = m4; + pME[3] = p4cm; + mME[4] = m5; + pME[4] = p5cm; + + // The nominal Breit-Wigner factors with running width. + runBW3 = runBW3in; + runBW4 = runBW4in; + runBW5 = runBW5in; + + // Special case: pick scale as if 2 -> 1 process in disguise. + if (isSChannel()) { + + // Different options for renormalization scale, but normally sHat. + Q2RenSave = renormMultFac * sH; + if (renormScale1 == 2) Q2RenSave = renormFixScale; + + // Different options for factorization scale, but normally sHat. + Q2FacSave = factorMultFac * sH; + if (factorScale1 == 2) Q2RenSave = factorFixScale; + + // "Normal" 2 -> 3 processes, i.e. not vector boson fusion. + } else if ( idTchan1() != 23 && idTchan1() != 24 && idTchan2() != 23 + && idTchan2() != 24 ) { + double mT3S = s3 + p3cm.pT2(); + double mT4S = s4 + p4cm.pT2(); + double mT5S = s5 + p5cm.pT2(); + + // Different options for renormalization scale. + if (renormScale3 == 1) Q2RenSave = min( mT3S, min(mT4S, mT5S) ); + else if (renormScale3 == 2) Q2RenSave = sqrt( mT3S * mT4S * mT5S + / max( mT3S, max(mT4S, mT5S) ) ); + else if (renormScale3 == 3) Q2RenSave = pow( mT3S * mT4S * mT5S, + 1./3. ); + else if (renormScale3 == 4) Q2RenSave = (mT3S + mT4S + mT5S) / 3.; + else Q2RenSave = sH; + Q2RenSave *= renormMultFac; + if (renormScale3 == 6) Q2RenSave = renormFixScale; + + // Different options for factorization scale. + if (factorScale3 == 1) Q2FacSave = min( mT3S, min(mT4S, mT5S) ); + else if (factorScale3 == 2) Q2FacSave = sqrt( mT3S * mT4S * mT5S + / max( mT3S, max(mT4S, mT5S) ) ); + else if (factorScale3 == 3) Q2FacSave = pow( mT3S * mT4S * mT5S, + 1./3. ); + else if (factorScale3 == 4) Q2FacSave = (mT3S + mT4S + mT5S) / 3.; + else Q2FacSave = sH; + Q2FacSave *= factorMultFac; + if (factorScale3 == 6) Q2FacSave = factorFixScale; + + // Vector boson fusion 2 -> 3 processes; recoils in positions 4 and 5. + } else { + double sV4 = pow2( particleDataPtr->m0(idTchan1()) ); + double sV5 = pow2( particleDataPtr->m0(idTchan2()) ); + double mT3S = s3 + p3cm.pT2(); + double mTV4S = sV4 + p4cm.pT2(); + double mTV5S = sV5 + p5cm.pT2(); + + // Different options for renormalization scale. + if (renormScale3VV == 1) Q2RenSave = max( sV4, sV5); + else if (renormScale3VV == 2) Q2RenSave = sqrt( mTV4S * mTV5S ); + else if (renormScale3VV == 3) Q2RenSave = pow( mT3S * mTV4S * mTV5S, + 1./3. ); + else if (renormScale3VV == 4) Q2RenSave = (mT3S * mTV4S * mTV5S) / 3.; + else Q2RenSave = sH; + Q2RenSave *= renormMultFac; + if (renormScale3VV == 6) Q2RenSave = renormFixScale; + + // Different options for factorization scale. + if (factorScale3VV == 1) Q2FacSave = max( sV4, sV5); + else if (factorScale3VV == 2) Q2FacSave = sqrt( mTV4S * mTV5S ); + else if (factorScale3VV == 3) Q2FacSave = pow( mT3S * mTV4S * mTV5S, + 1./3. ); + else if (factorScale3VV == 4) Q2FacSave = (mT3S * mTV4S * mTV5S) / 3.; + else Q2FacSave = sH; + Q2FacSave *= factorMultFac; + if (factorScale3VV == 6) Q2FacSave = factorFixScale; + } + + // Evaluate alpha_strong and alpha_EM. + alpS = coupSMPtr->alphaS(Q2RenSave); + alpEM = coupSMPtr->alphaEM(Q2RenSave); + +} + +//========================================================================== + +// The SigmaLHAProcess class. +// Wrapper for Les Houches Accord external input; derived from SigmaProcess. +// Note: arbitrary subdivision into PhaseSpaceLHA and SigmaLHAProcess tasks. + +//-------------------------------------------------------------------------- + +// Set scale, alpha_strong and alpha_EM when not set. + +void SigmaLHAProcess::setScale() { + + // If scale has not been set, then to set. + double scaleLHA = lhaUpPtr->scale(); + if (scaleLHA < 0.) { + + // Final-state partons and their invariant mass. + vector iFin; + Vec4 pFinSum; + for (int i = 3; i < lhaUpPtr->sizePart(); ++i) + if (lhaUpPtr->mother1(i) == 1) { + iFin.push_back(i); + pFinSum += Vec4( lhaUpPtr->px(i), lhaUpPtr->py(i), + lhaUpPtr->pz(i), lhaUpPtr->e(i) ); + } + int nFin = iFin.size(); + double sH = pFinSum * pFinSum; + + // If 1 final-state particle then use Sigma1Process logic. + if (nFin == 1) { + Q2RenSave = renormMultFac * sH; + if (renormScale1 == 2) Q2RenSave = renormFixScale; + Q2FacSave = factorMultFac * sH; + if (factorScale1 == 2) Q2FacSave = factorFixScale; + + // If 2 final-state particles then use Sigma2Process logic. + } else if (nFin == 2) { + double s3 = pow2(lhaUpPtr->m(iFin[0])); + double s4 = pow2(lhaUpPtr->m(iFin[1])); + double pT2 = pow2(lhaUpPtr->px(iFin[0])) + pow2(lhaUpPtr->py(iFin[0])); + if (renormScale2 == 1) Q2RenSave = pT2 + min(s3, s4); + else if (renormScale2 == 2) Q2RenSave = sqrt((pT2 + s3) * (pT2 + s4)); + else if (renormScale2 == 3) Q2RenSave = pT2 + 0.5 * (s3 + s4); + else Q2RenSave = sH; + Q2RenSave *= renormMultFac; + if (renormScale2 == 5) Q2RenSave = renormFixScale; + if (factorScale2 == 1) Q2FacSave = pT2 + min(s3, s4); + else if (factorScale2 == 2) Q2FacSave = sqrt((pT2 + s3) * (pT2 + s4)); + else if (factorScale2 == 3) Q2FacSave = pT2 + 0.5 * (s3 + s4); + else Q2FacSave = sH; + Q2FacSave *= factorMultFac; + if (factorScale2 == 5) Q2FacSave = factorFixScale; + + // If 3 or more final-state particles then use Sigma3Process logic. + } else { + double mTSlow = sH; + double mTSmed = sH; + double mTSprod = 1.; + double mTSsum = 0.; + for (int i = 0; i < nFin; ++i) { + double mTSnow = pow2(lhaUpPtr->m(iFin[i])) + + pow2(lhaUpPtr->px(iFin[i])) + pow2(lhaUpPtr->py(iFin[i])); + if (mTSnow < mTSlow) {mTSmed = mTSlow; mTSlow = mTSnow;} + else if (mTSnow < mTSmed) mTSmed = mTSnow; + mTSprod *= mTSnow; + mTSsum += mTSnow; + } + if (renormScale3 == 1) Q2RenSave = mTSlow; + else if (renormScale3 == 2) Q2RenSave = sqrt(mTSlow * mTSmed); + else if (renormScale3 == 3) Q2RenSave = pow(mTSprod, 1. / nFin); + else if (renormScale3 == 4) Q2RenSave = mTSsum / nFin; + else Q2RenSave = sH; + Q2RenSave *= renormMultFac; + if (renormScale3 == 6) Q2RenSave = renormFixScale; + if (factorScale3 == 1) Q2FacSave = mTSlow; + else if (factorScale3 == 2) Q2FacSave = sqrt(mTSlow * mTSmed); + else if (factorScale3 == 3) Q2FacSave = pow(mTSprod, 1. / nFin); + else if (factorScale3 == 4) Q2FacSave = mTSsum / nFin; + else Q2FacSave = sH; + Q2FacSave *= factorMultFac; + if (factorScale3 == 6) Q2FacSave = factorFixScale; + } + } + + // If alpha_strong and alpha_EM have not been set, then set them. + if (lhaUpPtr->alphaQCD() < 0.001) { + double Q2RenNow = (scaleLHA < 0.) ? Q2RenSave : pow2(scaleLHA); + alpS = coupSMPtr->alphaS(Q2RenNow); + } + if (lhaUpPtr->alphaQED() < 0.001) { + double Q2RenNow = (scaleLHA < 0.) ? Q2RenSave : pow2(scaleLHA); + alpEM = coupSMPtr->alphaEM(Q2RenNow); + } + +} + +//-------------------------------------------------------------------------- + +// Obtain number of final-state partons from LHA object. + +int SigmaLHAProcess::nFinal() const { + + // At initialization size unknown, so return 0. + if (lhaUpPtr->sizePart() <= 0) return 0; + + // Sum up all particles that has first mother = 1. + int nFin = 0; + for (int i = 3; i < lhaUpPtr->sizePart(); ++i) + if (lhaUpPtr->mother1(i) == 1) ++nFin; + return nFin; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaQCD.cxx b/PYTHIA8/pythia8140/src/SigmaQCD.cxx new file mode 100644 index 00000000000..980f02768c5 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaQCD.cxx @@ -0,0 +1,1533 @@ +// SigmaQCD.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// QCD simulation classes. + +#include "SigmaQCD.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma0AB2AB class. +// Cross section for elastic scattering A B -> A B. + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma0AB2AB::setIdColAcol() { + + // Flavours and colours are trivial. + setId( idA, idB, idA, idB); + setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); +} + +//========================================================================== + +// Sigma0AB2XB class. +// Cross section for single diffractive scattering A B -> X B. + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma0AB2XB::setIdColAcol() { + + // Flavours and colours are trivial. + int idX = 10* (abs(idA) / 10) + 9900000; + if (idA < 0) idX = -idX; + setId( idA, idB, idX, idB); + setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + +} + +//========================================================================== + +// Sigma0AB2AX class. +// Cross section for single diffractive scattering A B -> A X. + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma0AB2AX::setIdColAcol() { + + // Flavours and colours are trivial. + int idX = 10* (abs(idB) / 10) + 9900000; + if (idB < 0) idX = -idX; + setId( idA, idB, idA, idX); + setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + +} + +//========================================================================== + +// Sigma0AB2XX class. +// Cross section for double diffractive scattering A B -> X X. + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma0AB2XX::setIdColAcol() { + + // Flavours and colours are trivial. + int idX1 = 10* (abs(idA) / 10) + 9900000; + if (idA < 0) idX1 = -idX1; + int idX2 = 10* (abs(idB) / 10) + 9900000; + if (idB < 0) idX2 = -idX2; + setId( idA, idB, idX1, idX2); + setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + +} + +//========================================================================== + +// Sigma2gg2gg class. +// Cross section for g g -> g g. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2gg2gg::sigmaKin() { + + // Calculate kinematics dependence. + sigTS = (9./4.) * (tH2 / sH2 + 2. * tH / sH + 3. + 2. * sH / tH + + sH2 / tH2); + sigUS = (9./4.) * (uH2 / sH2 + 2. * uH / sH + 3. + 2. * sH / uH + + sH2 / uH2); + sigTU = (9./4.) * (tH2 / uH2 + 2. * tH / uH + 3. + 2. * uH / tH + + uH2 / tH2); + sigSum = sigTS + sigUS + sigTU; + + // Answer contains factor 1/2 from identical gluons. + sigma = (M_PI / sH2) * pow2(alpS) * 0.5 * sigSum; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2gg::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, 21, 21); + + // Three colour flow topologies, each with two orientations. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 2, 2, 3, 1, 4, 4, 3); + else if (sigRand < sigTS + sigUS) + setColAcol( 1, 2, 3, 1, 3, 4, 4, 2); + else setColAcol( 1, 2, 3, 4, 1, 4, 3, 2); + if (rndmPtr->flat() > 0.5) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2qqbar class. +// Cross section for g g -> q qbar (q = u, d, s, i.e. almost massless). + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2qqbar::initProc() { + + // Read number of quarks to be considered in massless approximation. + nQuarkNew = settingsPtr->mode("HardQCD:nQuarkNew"); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2gg2qqbar::sigmaKin() { + + // Pick new flavour. + idNew = 1 + int( nQuarkNew * rndmPtr->flat() ); + mNew = particleDataPtr->m0(idNew); + m2New = mNew*mNew; + + // Calculate kinematics dependence. + sigTS = 0.; + sigUS = 0.; + if (sH > 4. * m2New) { + sigTS = (1./6.) * uH / tH - (3./8.) * uH2 / sH2; + sigUS = (1./6.) * tH / uH - (3./8.) * tH2 / sH2; + } + sigSum = sigTS + sigUS; + + // Answer is proportional to number of outgoing flavours. + sigma = (M_PI / sH2) * pow2(alpS) * nQuarkNew * sigSum; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2qqbar::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idNew, -idNew); + + // Two colour flow topologies. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 2, 2, 3, 1, 0, 0, 3); + else setColAcol( 1, 2, 3, 1, 3, 0, 0, 2); + +} + +//========================================================================== + +// Sigma2qg2qg class. +// Cross section for q g -> q g. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2qg2qg::sigmaKin() { + + // Calculate kinematics dependence. + sigTS = uH2 / tH2 - (4./9.) * uH / sH; + sigTU = sH2 / tH2 - (4./9.) * sH / uH; + sigSum = sigTS + sigTU; + + // Answer. + sigma = (M_PI / sH2) * pow2(alpS) * sigSum; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2qg::setIdColAcol() { + + // Outgoing = incoming flavours. + setId( id1, id2, id1, id2); + + // Two colour flow topologies. Swap if first is gluon, or when antiquark. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 0, 2, 1, 3, 0, 2, 3); + else setColAcol( 1, 0, 2, 3, 2, 0, 1, 3); + if (id1 == 21) swapCol1234(); + if (id1 < 0 || id2 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qq2qq class. +// Cross section for q qbar' -> q qbar' or q q' -> q q' +// (qbar qbar' -> qbar qbar'), q' may be same as q. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qq2qq::sigmaKin() { + + // Calculate kinematics dependence for different terms. + sigT = (4./9.) * (sH2 + uH2) / tH2; + sigU = (4./9.) * (sH2 + tH2) / uH2; + sigTU = - (8./27.) * sH2 / (tH * uH); + sigST = - (8./27.) * uH2 / (sH * tH); + +} + +//-------------------------------------------------------------------------- + + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qq2qq::sigmaHat() { + + // Combine cross section terms; factor 1/2 when identical quarks. + if (id2 == id1) sigSum = 0.5 * (sigT + sigU + sigTU); + else if (id2 == -id1) sigSum = sigT + sigST; + else sigSum = sigT; + + // Answer. + return (M_PI/sH2) * pow2(alpS) * sigSum; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qq2qq::setIdColAcol() { + + // Outgoing = incoming flavours. + setId( id1, id2, id1, id2); + + // Colour flow topologies. Swap when antiquarks. + if (id1 * id2 > 0) setColAcol( 1, 0, 2, 0, 2, 0, 1, 0); + else setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + if (id2 == id1 && (sigT + sigU) * rndmPtr->flat() > sigT) + setColAcol( 1, 0, 2, 0, 1, 0, 2, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2gg class. +// Cross section for q qbar -> g g. + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2qqbar2gg::sigmaKin() { + + // Calculate kinematics dependence. + sigTS = (32./27.) * uH / tH - (8./3.) * uH2 / sH2; + sigUS = (32./27.) * tH / uH - (8./3.) * tH2 / sH2; + sigSum = sigTS + sigUS; + + // Answer contains factor 1/2 from identical gluons. + sigma = (M_PI / sH2) * pow2(alpS) * 0.5 * sigSum; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2gg::setIdColAcol() { + + // Outgoing flavours trivial. + setId( id1, id2, 21, 21); + + // Two colour flow topologies. Swap if first is antiquark. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 0, 0, 2, 1, 3, 3, 2); + else setColAcol( 1, 0, 0, 2, 3, 2, 1, 3); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2qqbarNew class. +// Cross section q qbar -> q' qbar'. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2qqbarNew::initProc() { + + // Read number of quarks to be considered in massless approximation. + nQuarkNew = settingsPtr->mode("HardQCD:nQuarkNew"); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2qqbar2qqbarNew::sigmaKin() { + + // Pick new flavour. + idNew = 1 + int( nQuarkNew * rndmPtr->flat() ); + mNew = particleDataPtr->m0(idNew); + m2New = mNew*mNew; + + // Calculate kinematics dependence. + sigS = 0.; + if (sH > 4. * m2New) sigS = (4./9.) * (tH2 + uH2) / sH2; + + // Answer is proportional to number of outgoing flavours. + sigma = (M_PI / sH2) * pow2(alpS) * nQuarkNew * sigS; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2qqbarNew::setIdColAcol() { + + // Set outgoing flavours ones. + id3 = (id1 > 0) ? idNew : -idNew; + setId( id1, id2, id3, -id3); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2QQbar class. +// Cross section g g -> Q Qbar (Q = c, b or t). +// Only provided for fixed m3 = m4 so do some gymnastics: +// i) s34Avg picked so that beta34 same when s3, s4 -> s34Avg. +// ii) tHQ = tH - mQ^2 = -0.5 sH (1 - beta34 cos(thetaH)) for m3 = m4 = mQ, +// but tH - uH = sH beta34 cos(thetaH) also for m3 != m4, so use +// tH, uH selected for m3 != m4 to derive tHQ, uHQ valid for m3 = m4. + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2QQbar::initProc() { + + // Process name. + nameSave = "g g -> Q Qbar"; + if (idNew == 4) nameSave = "g g -> c cbar"; + if (idNew == 5) nameSave = "g g -> b bbar"; + if (idNew == 6) nameSave = "g g -> t tbar"; + if (idNew == 7) nameSave = "g g -> b' b'bar"; + if (idNew == 8) nameSave = "g g -> t' t'bar"; + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2gg2QQbar::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + double s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + double tHQ = -0.5 * (sH - tH + uH); + double uHQ = -0.5 * (sH + tH - uH); + double tHQ2 = tHQ * tHQ; + double uHQ2 = uHQ * uHQ; + + // Calculate kinematics dependence. + double tumHQ = tHQ * uHQ - s34Avg * sH; + sigTS = ( uHQ / tHQ - 2.25 * uHQ2 / sH2 + 4.5 * s34Avg * tumHQ + / ( sH * tHQ2) + 0.5 * s34Avg * (tHQ + s34Avg) / tHQ2 + - s34Avg*s34Avg / (sH * tHQ) ) / 6.; + sigUS = ( tHQ / uHQ - 2.25 * tHQ2 / sH2 + 4.5 * s34Avg * tumHQ + / ( sH * uHQ2) + 0.5 * s34Avg * (uHQ + s34Avg) / uHQ2 + - s34Avg*s34Avg / (sH * uHQ) ) / 6.; + sigSum = sigTS + sigUS; + + // Answer. + sigma = (M_PI / sH2) * pow2(alpS) * sigSum * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2QQbar::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, idNew, -idNew); + + // Two colour flow topologies. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 2, 2, 3, 1, 0, 0, 3); + else setColAcol( 1, 2, 3, 1, 3, 0, 0, 2); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles of W in top decay. + +double Sigma2gg2QQbar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // For top decay hand over to standard routine, else done. + if (idNew == 6 && process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + else return 1.; + +} + +//========================================================================== + +// Sigma2qqbar2QQbar class. +// Cross section q qbar -> Q Qbar (Q = c, b or t). +// Only provided for fixed m3 = m4 so do some gymnastics: +// i) s34Avg picked so that beta34 same when s3, s4 -> s34Avg. +// ii) tHQ = tH - mQ^2 = -0.5 sH (1 - beta34 cos(thetaH)) for m3 = m4 = mQ, +// but tH - uH = sH beta34 cos(thetaH) also for m3 != m4, so use +// tH, uH selected for m3 != m4 to derive tHQ, uHQ valid for m3 = m4. + +//-------------------------------------------------------------------------- + +// Initialize process, especially parton-flux object. + +void Sigma2qqbar2QQbar::initProc() { + + // Process name. + nameSave = "q qbar -> Q Qbar"; + if (idNew == 4) nameSave = "q qbar -> c cbar"; + if (idNew == 5) nameSave = "q qbar -> b bbar"; + if (idNew == 6) nameSave = "q qbar -> t tbar"; + if (idNew == 7) nameSave = "q qbar -> b' b'bar"; + if (idNew == 8) nameSave = "q qbar -> t' t'bar"; + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(idNew, -idNew); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2qqbar2QQbar::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + double s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + double tHQ = -0.5 * (sH - tH + uH); + double uHQ = -0.5 * (sH + tH - uH); + double tHQ2 = tHQ * tHQ; + double uHQ2 = uHQ * uHQ; + + // Calculate kinematics dependence. + double sigS = (4./9.) * ((tHQ2 + uHQ2) / sH2 + 2. * s34Avg / sH); + + // Answer. + sigma = (M_PI / sH2) * pow2(alpS) * sigS * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2QQbar::setIdColAcol() { + + // Set outgoing flavours. + id3 = (id1 > 0) ? idNew : -idNew; + setId( id1, id2, id3, -id3); + + // Colour flow topologies. Swap when antiquarks. + setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Evaluate weight for decay angles of W in top decay. + +double Sigma2qqbar2QQbar::weightDecay( Event& process, int iResBeg, + int iResEnd) { + + // For top decay hand over to standard routine, else done. + if (idNew == 6 && process[process[iResBeg].mother1()].idAbs() == 6) + return weightTopDecay( process, iResBeg, iResEnd); + else return 1.; + +} + + +//========================================================================== + +// Sigma3gg2ggg class. +// Cross section for g g -> g g g. + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence. + +void Sigma3gg2ggg::sigmaKin() { + + // Calculate all four-vector products. + Vec4 p1cm( 0., 0., 0.5 * mH, 0.5 * mH); + Vec4 p2cm( 0., 0., -0.5 * mH, 0.5 * mH); + pp[1][2] = p1cm * p2cm; + pp[1][3] = p1cm * p3cm; + pp[1][4] = p1cm * p4cm; + pp[1][5] = p1cm * p5cm; + pp[2][3] = p2cm * p3cm; + pp[2][4] = p2cm * p4cm; + pp[2][5] = p2cm * p5cm; + pp[3][4] = p3cm * p4cm; + pp[3][5] = p3cm * p5cm; + pp[4][5] = p4cm * p5cm; + for (int i = 1; i < 5; ++i) + for (int j = i + 1; j < 6; ++j) pp[j][i] = pp[i][j]; + + // Cross section, in three main sections. + double num1 = cycle(1,2,3,4,5) + cycle(1,2,3,5,4) + cycle(1,2,4,3,5) + + cycle(1,2,4,5,3) + cycle(1,2,5,3,4) + cycle(1,2,5,4,3) + + cycle(1,3,2,4,5) + cycle(1,3,2,5,4) + cycle(1,3,4,2,5) + + cycle(1,3,5,2,4) + cycle(1,4,2,3,5) + cycle(1,4,3,2,5); + double num2 = pow4(pp[1][2]) + pow4(pp[1][3]) + pow4(pp[1][4]) + + pow4(pp[1][5]) + pow4(pp[2][3]) + pow4(pp[2][4]) + + pow4(pp[2][5]) + pow4(pp[3][4]) + pow4(pp[3][5]) + + pow4(pp[4][5]); + double den = pp[1][2] * pp[1][3] * pp[1][4] * pp[1][5] * pp[2][3] + * pp[2][4] * pp[2][5] * pp[3][4] * pp[3][5] * pp[4][5]; + + // Answer has a factor 6 due to identical gluons + // This is cancelled by phase space factor (1 / 6) + sigma = pow3(4. * M_PI * alpS) * (27./16.) * num1 * num2 / den; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3gg2ggg::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, 21, 21, 21); + + // Three colour flow topologies, each with two orientations. + /* + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 2, 2, 3, 1, 4, 4, 3); + else if (sigRand < sigTS + sigUS) + setColAcol( 1, 2, 3, 1, 3, 4, 4, 2); + else setColAcol( 1, 2, 3, 4, 1, 4, 3, 2); + if (rndmPtr->flat() > 0.5) swapColAcol(); + */ + + // Temporary solution. + setColAcol( 1, 2, 2, 3, 1, 4, 4, 5, 5, 3); +} + + +//========================================================================== + +// Sigma3qqbar2ggg class. +// Cross section for q qbar -> g g g. + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence. +void Sigma3qqbar2ggg::sigmaKin() { + + // Setup four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + pCM[2] = p3cm; + pCM[3] = p4cm; + pCM[4] = p5cm; + + // Calculate |M|^2 + // Answer has a factor 6 due to identical gluons, + // which is cancelled by phase space factor (1 / 6) + sigma = m2Calc(); + +} + +//-------------------------------------------------------------------------- + +// |M|^2 + +inline double Sigma3qqbar2ggg::m2Calc() { + + // Calculate four-products + double sHnow = (pCM[0] + pCM[1]).m2Calc(); + double sHhalf = sH / 2.; + + // qbar (p+) + q(p-) -> g(k1) g(k2) g(k3) + // a_i = (p+ . ki), i = 1, 2, 3 + // b_i = (p- . ki), i = 1, 2, 3 + a[0] = pCM[0] * pCM[2]; + a[1] = pCM[0] * pCM[3]; + a[2] = pCM[0] * pCM[4]; + b[0] = pCM[1] * pCM[2]; + b[1] = pCM[1] * pCM[3]; + b[2] = pCM[1] * pCM[4]; + + pp[0][1] = pCM[2] * pCM[3]; + pp[1][2] = pCM[3] * pCM[4]; + pp[2][0] = pCM[4] * pCM[2]; + + // ab[i][j] = a_i * b_j + a_j * b_i + ab[0][1] = a[0] * b[1] + a[1] * b[0]; + ab[1][2] = a[1] * b[2] + a[2] * b[1]; + ab[2][0] = a[2] * b[0] + a[0] * b[2]; + + // Cross section + double num1 = a[0] * b[0] * (a[0] * a[0] + b[0] * b[0]) + + a[1] * b[1] * (a[1] * a[1] + b[1] * b[1]) + + a[2] * b[2] * (a[2] * a[2] + b[2] * b[2]); + double den1 = a[0] * a[1] * a[2] * b[0] * b[1] * b[2]; + double num2 = - ( ab[0][1] / pp[0][1] ) + - ( ab[1][2] / pp[1][2] ) + - ( ab[2][0] / pp[2][0] ); + double num3 = a[2] * b[2] * ab[0][1] / (pp[1][2] * pp[2][0] ) + + a[0] * b[0] * ab[1][2] / (pp[2][0] * pp[0][1] ) + + a[1] * b[1] * ab[2][0] / (pp[0][1] * pp[1][2] ); + + // Final answer + return pow3(4. * M_PI * alpS) * (8. / 324.) * (num1 / den1) * + ( sHhalf + 9. * (sHhalf + num2) + (2. * 81. / sHnow) * num3 ); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qqbar2ggg::setIdColAcol(){ + + // Flavours are trivial. + setId( id1, id2, 21, 21, 21); + + // Temporary solution. + setColAcol( 1, 0, 0, 2, 1, 3, 3, 4, 4, 2); + if (id1 < 0) swapColAcol(); +} + +//-------------------------------------------------------------------------- + +// Map a final state configuration + +inline void Sigma3qqbar2ggg::mapFinal() { + switch (config) { + case 0: pCM[2] = p3cm; pCM[3] = p4cm; pCM[4] = p5cm; break; + case 1: pCM[2] = p3cm; pCM[3] = p5cm; pCM[4] = p4cm; break; + case 2: pCM[2] = p4cm; pCM[3] = p3cm; pCM[4] = p5cm; break; + case 3: pCM[2] = p4cm; pCM[3] = p5cm; pCM[4] = p3cm; break; + case 4: pCM[2] = p5cm; pCM[3] = p3cm; pCM[4] = p4cm; break; + case 5: pCM[2] = p5cm; pCM[3] = p4cm; pCM[4] = p3cm; break; + } +} + +//========================================================================== + +// Sigma3qg2qgg class. +// Cross section for q g -> q g g. +// Crossed relation from q qbar -> g g g: +// qbar(p+) q(p-) -> g(k1) g(k2) g(k3) + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence +// Note: two different contributions from gq and qg incoming + +void Sigma3qg2qgg::sigmaKin() { + + // Pick a final state configuration + pickFinal(); + + // gq and qg incoming + for (int i = 0; i < 2; i++) { + + // Map incoming four-vectors to p+, p-, k1, k2, k3 + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + mapFinal(); + + // Crossing + swap(pCM[i], pCM[2]); + + // |M|^2 + // XXX - Extra factor of (3) from selecting a final state + // configuration (already a factor of 2 in the original + // answer due to two identical final state gluons)??? + // Extra factor of (3 / 8) as average over incoming gluon + sigma[i] = 3. * (3. / 8.) * m2Calc(); + + } // for (int i = 0; i < 2; i++) + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - incoming flavour dependence +// Pick from two configurations calculated previously + +double Sigma3qg2qgg::sigmaHat() { + // gq or qg incoming + return (id1 == 21) ? sigma[0] : sigma[1]; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qg2qgg::setIdColAcol(){ + // Outgoing flavours; only need to know where the quark is + int qIdx = config / 2; + int idTmp[3] = { 21, 21, 21 }; + idTmp[qIdx] = (id1 == 21) ? id2 : id1; + setId( id1, id2, idTmp[0], idTmp[1], idTmp[2]); + + // Temporary solution + if (qIdx == 0) setColAcol(1, 0, 2, 1, 4, 0, 3, 4, 2, 3); + else if (qIdx == 1) setColAcol(1, 0, 2, 1, 3, 4, 4, 0, 2, 3); + else setColAcol(1, 0, 2, 1, 3, 4, 2, 3, 4, 0); + // gq or qg incoming + if (id1 == 21) { + swap( colSave[1], colSave[2]); + swap(acolSave[1], acolSave[2]); + } + // qbar rather than q incoming + if (id1 < 0 || id2 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma3gg2qqbarg class. +// Cross section for g g -> q qbar g +// Crossed relation from q qbar -> g g g + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3gg2qqbarg::initProc() { + + // Read number of quarks to be considered in massless approximation. + nQuarkNew = double(settingsPtr->mode("HardQCD:nQuarkNew")); + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence. + +void Sigma3gg2qqbarg::sigmaKin() { + + // Incoming four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + + // Pick and map a final state configuration + pickFinal(); + mapFinal(); + + // Crossing + swap(pCM[0], pCM[2]); + swap(pCM[1], pCM[3]); + + // |M|^2 + // Extra factor of (6.) from picking a final state configuration + // Extra factor of nQuarkNew + // Extra factor of (3. / 8.) ^ 2 as averaging over two incoming gluons + sigma = 6. * double(nQuarkNew) * (3. / 8.) * (3. / 8.) * m2Calc(); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3gg2qqbarg::setIdColAcol(){ + + // Pick new flavour + int idNew = 1 + int( nQuarkNew * rndmPtr->flat() ); + + // Outgoing flavours; easiest just to map by hand + switch (config) { + case 0: id3 = idNew; id4 = -idNew; id5 = 21; break; + case 1: id3 = idNew; id4 = 21; id5 = -idNew; break; + case 2: id3 = -idNew; id4 = idNew; id5 = 21; break; + case 3: id3 = 21; id4 = idNew; id5 = -idNew; break; + case 4: id3 = -idNew; id4 = 21; id5 = idNew; break; + case 5: id3 = 21; id4 = -idNew; id5 = idNew; break; + } + setId(id1, id2, id3, id4, id5); + + // Temporary solution + switch (config) { + case 0: setColAcol( 1, 2, 2, 3, 4, 0, 0, 3, 1, 4 ); break; + case 1: setColAcol( 1, 2, 2, 3, 4, 0, 1, 4, 0, 3 ); break; + case 2: setColAcol( 1, 2, 2, 3, 0, 3, 4, 0, 1, 4 ); break; + case 3: setColAcol( 1, 2, 2, 3, 1, 4, 4, 0, 0, 3 ); break; + case 4: setColAcol( 1, 2, 2, 3, 0, 3, 1, 4, 4, 0 ); break; + case 5: setColAcol( 1, 2, 2, 3, 1, 4, 0, 3, 4, 0 ); break; + } + +} + +//========================================================================== + +// Sigma3qq2qqgDiff class. +// Cross section for q q' -> q q' g, q != q' + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence + +void Sigma3qq2qqgDiff::sigmaKin() { + + // q1(p+) q2(p-) -> q1(q+) q2(q-) g(k) + + // Incoming four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + // Pick and map a final state configuration + pickFinal(); + mapFinal(); + + // |M|^2 + // Extra factor of (6.) from picking a final state configuration + sigma = 6. * m2Calc(); +} + +//-------------------------------------------------------------------------- + +// |M|^2 + +inline double Sigma3qq2qqgDiff::m2Calc() { + + // Four-products + s = (pCM[0] + pCM[1]).m2Calc(); + t = (pCM[0] - pCM[2]).m2Calc(); + u = (pCM[0] - pCM[3]).m2Calc(); + up = (pCM[1] - pCM[2]).m2Calc(); + sp = (pCM[2] + pCM[3]).m2Calc(); + tp = (pCM[1] - pCM[3]).m2Calc(); + + // |M|^2 + double num1 = (s * s + sp * sp + u * u + up * up) / (t * tp); + double den1 = (pCM[0] * pCM[4]) * (pCM[1] * pCM[4]) * + (pCM[2] * pCM[4]) * (pCM[3] * pCM[4]); + double num2 = (u + up) * (s * sp + t * tp - u * up) + + u * (s * t + sp * tp) + up * (s * tp + sp * t); + double num3 = (s + sp) * (s * sp - t * tp - u * up) + + 2. * t * tp * (u + up) + 2. * u * up * (t + tp); + + // (N^2 - 1)^2 / 4N^3 = 16. / 27. + // (N^2 - 1) / 4N^3 = 2. / 27. + return (1. / 8.) * pow3(4. * M_PI * alpS) * num1 / den1 * + ( (16. / 27.) * num2 - (2. / 27.) * num3 ); + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - incoming flavour dependence + +double Sigma3qq2qqgDiff::sigmaHat() { + // Different incoming flavours only + if (abs(id1) == abs(id2)) return 0.; + return sigma; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qq2qqgDiff::setIdColAcol(){ + + // Outgoing flavours; easiest just to map by hand + switch (config) { + case 0: id3 = id1; id4 = id2; id5 = 21; break; + case 1: id3 = id1; id4 = 21; id5 = id2; break; + case 2: id3 = id2; id4 = id1; id5 = 21; break; + case 3: id3 = 21; id4 = id1; id5 = id2; break; + case 4: id3 = id2; id4 = 21; id5 = id1; break; + case 5: id3 = 21; id4 = id2; id5 = id1; break; + } + setId(id1, id2, id3, id4, id5); + + // Temporary solution; id1 and id2 can be q/qbar independently + int cols[5][2]; + if (id1 > 0) { + cols[0][0] = 1; cols[0][1] = 0; + cols[2][0] = 1; cols[2][1] = 0; + } else { + cols[0][0] = 0; cols[0][1] = 1; + cols[2][0] = 0; cols[2][1] = 1; + } + if (id2 > 0) { + cols[1][0] = 2; cols[1][1] = 0; + cols[3][0] = 3; cols[3][1] = 0; + cols[4][0] = 2; cols[4][1] = 3; + } else { + cols[1][0] = 0; cols[1][1] = 2; + cols[3][0] = 0; cols[3][1] = 3; + cols[4][0] = 3; cols[4][1] = 2; + } + // Map correct final state configuration + int i3 = 0, i4 = 0, i5 = 0; + switch (config) { + case 0: i3 = 2; i4 = 3; i5 = 4; break; + case 1: i3 = 2; i4 = 4; i5 = 3; break; + case 2: i3 = 3; i4 = 2; i5 = 4; break; + case 3: i3 = 4; i4 = 2; i5 = 3; break; + case 4: i3 = 3; i4 = 4; i5 = 2; break; + case 5: i3 = 4; i4 = 3; i5 = 2; break; + } + // Put colours in place + setColAcol(cols[0][0], cols[0][1], cols[1][0], cols[1][1], + cols[i3][0], cols[i3][1], cols[i4][0], cols[i4][1], + cols[i5][0], cols[i5][1]); + +} + +//-------------------------------------------------------------------------- + +// Map a final state configuration + +inline void Sigma3qq2qqgDiff::mapFinal() { + switch (config) { + case 0: pCM[2] = p3cm; pCM[3] = p4cm; pCM[4] = p5cm; break; + case 1: pCM[2] = p3cm; pCM[3] = p5cm; pCM[4] = p4cm; break; + case 2: pCM[2] = p4cm; pCM[3] = p3cm; pCM[4] = p5cm; break; + case 3: pCM[2] = p4cm; pCM[3] = p5cm; pCM[4] = p3cm; break; + case 4: pCM[2] = p5cm; pCM[3] = p3cm; pCM[4] = p4cm; break; + case 5: pCM[2] = p5cm; pCM[3] = p4cm; pCM[4] = p3cm; break; + } +} + + +//========================================================================== + +// Sigma3qqbar2qqbargDiff +// Cross section for q qbar -> q' qbar' g +// Crossed relation from q q' -> q q' g, q != q' + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3qqbar2qqbargDiff::initProc() { + + // Read number of quarks to be considered in massless approximation. + nQuarkNew = double(settingsPtr->mode("HardQCD:nQuarkNew")); + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence. + +void Sigma3qqbar2qqbargDiff::sigmaKin() { + // Overall 6 possibilities for final state ordering + // To keep symmetry between final states, always map to: + // 1) q1(p+) qbar1(p-) -> qbar2(q+) q2(q-) g(k) + // 2) qbar1(p+) q1(p-) -> q2(q+) qbar2(q-) g(k) + // Crossing p- and q+ gives: + // 1) q1(p+) q2(-q+) -> q1(-p-) q2(q-) g(k) + // 2) qbar1(p+) qbar2(-q+) -> qbar1(-p-) qbar2(q-) g(k) + + // Incoming four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + // Pick and map a final state configuration + pickFinal(); + mapFinal(); + + // Crossing + swap(pCM[1], pCM[2]); + pCM[1] = -pCM[1]; + pCM[2] = -pCM[2]; + + // |M|^2 + // Extra factor of (6.) from picking a final state configuration + // Extra factor of (nQuarkNew - 1) from new q/qbar pairs + // XXX - Extra factor of (2.) from second possible crossing??? + sigma = 6. * (nQuarkNew - 1) * 2. * m2Calc(); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qqbar2qqbargDiff::setIdColAcol(){ + + // Pick new q qbar flavour with incoming flavour disallowed + int idNew = 1 + int( (nQuarkNew - 1) * rndmPtr->flat() ); + if (idNew >= abs(id1)) ++idNew; + // For qbar q incoming, q+ is always mapped to q2 + // For q qbar incoming, q+ is always mapped to qbar2 + if (id1 > 0) idNew = -idNew; + + // Outgoing flavours; easiest just to map by hand + switch (config) { + case 0: id3 = idNew; id4 = -idNew; id5 = 21; break; + case 1: id3 = idNew; id4 = 21; id5 = -idNew; break; + case 2: id3 = -idNew; id4 = idNew; id5 = 21; break; + case 3: id3 = 21; id4 = idNew; id5 = -idNew; break; + case 4: id3 = -idNew; id4 = 21; id5 = idNew; break; + case 5: id3 = 21; id4 = -idNew; id5 = idNew; break; + } + setId(id1, id2, id3, id4, id5); + + // Temporary solution; start with q qbar -> qbar q g + int cols[5][2]; + cols[0][0] = 1; cols[0][1] = 0; + cols[1][0] = 0; cols[1][1] = 2; + cols[2][0] = 0; cols[2][1] = 3; + cols[3][0] = 1; cols[3][1] = 0; + cols[4][0] = 3; cols[4][1] = 2; + // Map into correct place + int i3 = 0, i4 = 0, i5 = 0; + switch (config) { + case 0: i3 = 2; i4 = 3; i5 = 4; break; + case 1: i3 = 2; i4 = 4; i5 = 3; break; + case 2: i3 = 3; i4 = 2; i5 = 4; break; + case 3: i3 = 4; i4 = 2; i5 = 3; break; + case 4: i3 = 3; i4 = 4; i5 = 2; break; + case 5: i3 = 4; i4 = 3; i5 = 2; break; + } + setColAcol(cols[0][0], cols[0][1], cols[1][0], cols[1][1], + cols[i3][0], cols[i3][1], cols[i4][0], cols[i4][1], + cols[i5][0], cols[i5][1]); + // Swap for qbar q incoming + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma3qg2qqqbarDiff class. +// Cross section for q g -> q q' qbar' +// Crossed relation from q q' -> q q' g, q != q' +// q1(p+) q2(p-) -> q1(q+) q2(q-) g(k) + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma3qg2qqqbarDiff::initProc() { + + // Read number of quarks to be considered in massless approximation. + nQuarkNew = settingsPtr->mode("HardQCD:nQuarkNew"); + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence + +void Sigma3qg2qqqbarDiff::sigmaKin() { + + // Pick a final state configuration + pickFinal(); + + // gq or qg incoming + for (int i = 0; i < 2; i++) { + + // Map incoming four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + mapFinal(); + + // Crossing (note extra -ve sign in total sigma) + swap(pCM[i], pCM[4]); + pCM[i] = -pCM[i]; + pCM[4] = -pCM[4]; + + // |M|^2 + // Extra factor of (6) from picking a final state configuration + // Extra factor of (3 / 8) as averaging over incoming gluon + // Extra factor of (nQuarkNew - 1) due to new q/qbar pair + sigma[i] = -6. * (3. / 8.) * (nQuarkNew - 1) * m2Calc(); + + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - incoming flavour dependence + +double Sigma3qg2qqqbarDiff::sigmaHat() { + // gq or qg incoming + return (id1 == 21) ? sigma[0] : sigma[1]; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qg2qqqbarDiff::setIdColAcol(){ + // Pick new q qbar flavour with incoming flavour disallowed + int sigmaIdx = (id1 == 21) ? 0 : 1; + int idIn = (id1 == 21) ? id2 : id1; + int idNew = 1 + int( (nQuarkNew - 1) * rndmPtr->flat() ); + if (idNew >= abs(idIn)) ++idNew; + + // qbar instead of q incoming means swap outgoing q/qbar pair + int id3Tmp = idIn, id4Tmp = idNew, id5Tmp = -idNew; + if (idIn < 0) swap(id4Tmp, id5Tmp); + // If g q incoming rather than q g, idIn and idNew + // should be exchanged (see sigmaKin) + if (sigmaIdx == 0) swap(id3Tmp, id4Tmp); + // Outgoing flavours; now just map as if q g incoming + switch (config) { + case 0: id3 = id3Tmp; id4 = id4Tmp; id5 = id5Tmp; break; + case 1: id3 = id3Tmp; id4 = id5Tmp; id5 = id4Tmp; break; + case 2: id3 = id4Tmp; id4 = id3Tmp; id5 = id5Tmp; break; + case 3: id3 = id5Tmp; id4 = id3Tmp; id5 = id4Tmp; break; + case 4: id3 = id4Tmp; id4 = id5Tmp; id5 = id3Tmp; break; + case 5: id3 = id5Tmp; id4 = id4Tmp; id5 = id3Tmp; break; + } + setId(id1, id2, id3, id4, id5); + + // Temporary solution; start with either + // g q1 -> q1 q2 qbar2 + // g qbar1 -> qbar1 qbar2 q2 + int cols[5][2]; + cols[0][0] = 1; cols[0][1] = 2; + if (idIn > 0) { + cols[1][0] = 3; cols[1][1] = 0; + cols[2][0] = 1; cols[2][1] = 0; + cols[3][0] = 3; cols[3][1] = 0; + cols[4][0] = 0; cols[4][1] = 2; + } else { + cols[1][0] = 0; cols[1][1] = 3; + cols[2][0] = 0; cols[2][1] = 2; + cols[3][0] = 0; cols[3][1] = 3; + cols[4][0] = 1; cols[4][1] = 0; + } + // Swap incoming if q/qbar g instead + if (id2 == 21) { + swap(cols[0][0], cols[1][0]); + swap(cols[0][1], cols[1][1]); + } + // Map final state + int i3 = 0, i4 = 0, i5 = 0; + if (sigmaIdx == 0) { + switch (config) { + case 0: i3 = 3; i4 = 2; i5 = 4; break; + case 1: i3 = 3; i4 = 4; i5 = 2; break; + case 2: i3 = 2; i4 = 3; i5 = 4; break; + case 3: i3 = 4; i4 = 3; i5 = 2; break; + case 4: i3 = 2; i4 = 4; i5 = 3; break; + case 5: i3 = 4; i4 = 2; i5 = 3; break; + } + } else { + switch (config) { + case 0: i3 = 2; i4 = 3; i5 = 4; break; + case 1: i3 = 2; i4 = 4; i5 = 3; break; + case 2: i3 = 3; i4 = 2; i5 = 4; break; + case 3: i3 = 4; i4 = 2; i5 = 3; break; + case 4: i3 = 3; i4 = 4; i5 = 2; break; + case 5: i3 = 4; i4 = 3; i5 = 2; break; + } + } + setColAcol(cols[0][0], cols[0][1], cols[1][0], cols[1][1], + cols[i3][0], cols[i3][1], cols[i4][0], cols[i4][1], + cols[i5][0], cols[i5][1]); +} + +//========================================================================== + +// Sigma3qq2qqgSame class. +// Cross section for q q' -> q q' g, q == q'. + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence + +void Sigma3qq2qqgSame::sigmaKin() { + // q1(p+) q2(p-) -> q1(q+) q2(q-) g(k) + + // Incoming four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + // Pick/map a final state configuration + pickFinal(); + mapFinal(); + + // |M|^2 + // Extra factor (3) from picking final state configuration + // (original answer already has a factor 2 from identical + // quarks in the final state) + sigma = 3. * m2Calc(); + +} + +//-------------------------------------------------------------------------- + +// |M|^2 + +inline double Sigma3qq2qqgSame::m2Calc() { + + // Four-products + s = (pCM[0] + pCM[1]).m2Calc(); + t = (pCM[0] - pCM[2]).m2Calc(); + u = (pCM[0] - pCM[3]).m2Calc(); + sp = (pCM[2] + pCM[3]).m2Calc(); + tp = (pCM[1] - pCM[3]).m2Calc(); + up = (pCM[1] - pCM[2]).m2Calc(); + + // |M|^2 + ssp = s * sp; + ttp = t * tp; + uup = u * up; + s_sp = s + sp; + t_tp = t + tp; + u_up = u + up; + + double den1 = (pCM[0] * pCM[4]) * (pCM[1] * pCM[4]) * + (pCM[2] * pCM[4]) * (pCM[3] * pCM[4]); + + double fac1 = s * (t * u + tp * up) + sp * (t * up + tp * u); + double fac2 = ssp - ttp - uup; + double fac3 = 2. * (ttp * u_up + uup * t_tp); + + double num1 = u_up * (ssp + ttp - uup) + fac1; + double num2 = s_sp * fac2 + fac3; + double num3 = (s * s + sp * sp + u * u + up * up) / (t * tp); + + double num4 = t_tp * (ssp - ttp + uup) + fac1; + double num5 = (s * s + sp * sp + t * t + tp * tp) / (u * up); + + double num6 = s_sp * fac2 - fac3 - 2. * fac1; + double num7 = (s * s + sp * sp) * fac2; + double den7 = (ttp * uup); + + // C1 = (N^2 - 1)^2 / 4N^3 = 16. / 27. + // C2 = (N^2 - 1) / 4N^3 = 2. / 27. + // C3 = (N^4 - 1) / 8N^4 = 10. / 81. + // C4 = (N^2 - 1)^2 / 8N^4 = 8. / 81. + return (1. / 8.) * pow3(4. * M_PI * alpS) * + ( ( (16. / 27.) * num1 - (2. / 27.) * num2 ) * num3 + + ( (16. / 27.) * num4 - (2. / 27.) * num2 ) * num5 + + ( (10. / 81.) * num2 + (8. / 81.) * num6 ) * + ( num7 / den7 ) ) / den1; + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - incoming flavour dependence + +double Sigma3qq2qqgSame::sigmaHat() { + // q q / qbar qbar incoming states only + if (id1 != id2) return 0.; + return sigma; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qq2qqgSame::setIdColAcol(){ + + // Need to know where the gluon was mapped (pCM[4]) + int gIdx = 0; + switch (config) { + case 3: case 5: gIdx = 0; break; + case 1: case 4: gIdx = 1; break; + case 0: case 2: gIdx = 2; break; + } + + // Outgoing flavours + int idTmp[3] = { id1, id1, id1 }; + idTmp[gIdx] = 21; + setId(id1, id2, idTmp[0], idTmp[1], idTmp[2]); + + // Temporary solution; start with q q -> q q g + setColAcol(1, 0, 2, 0, 1, 0, 3, 0, 2, 3); + // Map gluon + swap( colSave[5], colSave[gIdx + 3]); + swap(acolSave[5], acolSave[gIdx + 3]); + // Swap if qbar qbar incoming + if (id1 < 0) swapColAcol(); + +} + +//-------------------------------------------------------------------------- + +// Map a final state configuration +inline void Sigma3qq2qqgSame::mapFinal() { + switch (config) { + case 0: pCM[2] = p3cm; pCM[3] = p4cm; pCM[4] = p5cm; break; + case 1: pCM[2] = p3cm; pCM[3] = p5cm; pCM[4] = p4cm; break; + case 2: pCM[2] = p4cm; pCM[3] = p3cm; pCM[4] = p5cm; break; + case 3: pCM[2] = p4cm; pCM[3] = p5cm; pCM[4] = p3cm; break; + case 4: pCM[2] = p5cm; pCM[3] = p3cm; pCM[4] = p4cm; break; + case 5: pCM[2] = p5cm; pCM[3] = p4cm; pCM[4] = p3cm; break; + } +} + +//========================================================================== + +// Sigma3qqbar2qqbargSame class. +// Cross section for q qbar -> q qbar g +// Crossed relation from q(bar) q(bar) -> q(bar) q(bar) g: +// q1(p+) q2(p-) -> q1(q+) q2(q-) g(k) +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence + +void Sigma3qqbar2qqbargSame::sigmaKin() { + + // Incoming four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + + // Pick and map a final state configuration + pickFinal(); + mapFinal(); + + // Crossing + swap(pCM[1], pCM[3]); + pCM[1] = -pCM[1]; + pCM[3] = -pCM[3]; + + // |M|^2 + // Extra factor of (6) from picking a final state configuration + sigma = 6. * m2Calc(); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qqbar2qqbargSame::setIdColAcol(){ + // Outgoing flavours; easiest to map by hand + switch (config) { + case 0: id3 = id1; id4 = id2; id5 = 21; break; + case 1: id3 = id1; id4 = 21; id5 = id2; break; + case 2: id3 = id2; id4 = id1; id5 = 21; break; + case 3: id3 = 21; id4 = id1; id5 = id2; break; + case 4: id3 = id2; id4 = 21; id5 = id1; break; + case 5: id3 = 21; id4 = id2; id5 = id1; break; + } + setId(id1, id2, id3, id4, id5); + + // Temporary solution; start with q qbar -> q qbar g + int cols[5][2]; + cols[0][0] = 1; cols[0][1] = 0; + cols[1][0] = 0; cols[1][1] = 2; + cols[2][0] = 1; cols[2][1] = 0; + cols[3][0] = 0; cols[3][1] = 3; + cols[4][0] = 3; cols[4][1] = 2; + // Map final state + int i3 = 0, i4 = 0, i5 = 0; + switch (config) { + case 0: i3 = 2; i4 = 3; i5 = 4; break; + case 1: i3 = 2; i4 = 4; i5 = 3; break; + case 2: i3 = 3; i4 = 2; i5 = 4; break; + case 3: i3 = 4; i4 = 2; i5 = 3; break; + case 4: i3 = 3; i4 = 4; i5 = 2; break; + case 5: i3 = 4; i4 = 3; i5 = 2; break; + } + setColAcol(cols[0][0], cols[0][1], cols[1][0], cols[1][1], + cols[i3][0], cols[i3][1], cols[i4][0], cols[i4][1], + cols[i5][0], cols[i5][1]); + // Swap for qbar q incoming + if (id1 < 0) swapColAcol(); +} + +//========================================================================== + +// Sigma3qg2qqqbarSame class. +// Cross section for q g -> q q qbar. +// Crossed relation from q(bar) q(bar) -> q(bar) q(bar) g: +// q1(p+) q1(p-) -> q1(q+) q1(q-) g(k) + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - no incoming flavour dependence + +void Sigma3qg2qqqbarSame::sigmaKin() { + + // Pick a final state configuration + pickFinal(); + + // gq and qg incoming + for (int i = 0; i < 2; i++) { + + // Map incoming four-vectors + pCM[0] = Vec4( 0., 0., 0.5 * mH, 0.5 * mH); + pCM[1] = Vec4( 0., 0., -0.5 * mH, 0.5 * mH); + mapFinal(); + + // Crossing (note extra -ve sign in total sigma) + swap(pCM[i], pCM[4]); + pCM[i] = -pCM[i]; + pCM[4] = -pCM[4]; + + // |M|^2 + // XXX - Extra factor of (3) from picking a final state configuration??? + // Extra factor of (3 / 8) as averaging over incoming gluon + sigma[i] = -3. * (3. / 8.) * m2Calc(); + + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate |M|^2 - incoming flavour dependence + +double Sigma3qg2qqqbarSame::sigmaHat() { + // gq or qg incoming + return (id1 == 21) ? sigma[0] : sigma[1]; +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma3qg2qqqbarSame::setIdColAcol(){ + + // Pick outgoing flavour configuration + int idIn = (id1 == 21) ? id2 : id1; + + // Outgoing flavours; easiest just to map by hand + switch (config) { + case 0: id3 = idIn; id4 = idIn; id5 = -idIn; break; + case 1: id3 = idIn; id4 = -idIn; id5 = idIn; break; + case 2: id3 = idIn; id4 = idIn; id5 = -idIn; break; + case 3: id3 = -idIn; id4 = idIn; id5 = idIn; break; + case 4: id3 = idIn; id4 = -idIn; id5 = idIn; break; + case 5: id3 = -idIn; id4 = idIn; id5 = idIn; break; + } + setId(id1, id2, id3, id4, id5); + + // Temporary solution; start with either + // g q1 -> q1 q2 qbar2 + // g qbar1 -> qbar1 qbar2 q2 + int cols[5][2]; + cols[0][0] = 1; cols[0][1] = 2; + if (idIn > 0) { + cols[1][0] = 3; cols[1][1] = 0; + cols[2][0] = 1; cols[2][1] = 0; + cols[3][0] = 3; cols[3][1] = 0; + cols[4][0] = 0; cols[4][1] = 2; + } else { + cols[1][0] = 0; cols[1][1] = 3; + cols[2][0] = 0; cols[2][1] = 2; + cols[3][0] = 0; cols[3][1] = 3; + cols[4][0] = 1; cols[4][1] = 0; + } + // Swap incoming if q/qbar g instead + if (id2 == 21) { + swap(cols[0][0], cols[1][0]); + swap(cols[0][1], cols[1][1]); + } + // Map final state + int i3 = 0, i4 = 0, i5 = 0; + switch (config) { + case 0: i3 = 2; i4 = 3; i5 = 4; break; + case 1: i3 = 2; i4 = 4; i5 = 3; break; + case 2: i3 = 3; i4 = 2; i5 = 4; break; + case 3: i3 = 4; i4 = 2; i5 = 3; break; + case 4: i3 = 3; i4 = 4; i5 = 2; break; + case 5: i3 = 4; i4 = 3; i5 = 2; break; + } + setColAcol(cols[0][0], cols[0][1], cols[1][0], cols[1][1], + cols[i3][0], cols[i3][1], cols[i4][0], cols[i4][1], + cols[i5][0], cols[i5][1]); +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SigmaSUSY.cxx b/PYTHIA8/pythia8140/src/SigmaSUSY.cxx new file mode 100644 index 00000000000..35771155561 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaSUSY.cxx @@ -0,0 +1,1939 @@ +// SigmaSUSY.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Peter Skands, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// supersymmetry simulation classes. + +#include "SigmaSUSY.h" + +namespace Pythia8 { + +//========================================================================== + +// Sigma2qqbar2chi0chi0 +// Cross section for gaugino pair production: neutralino pair + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2chi0chi0::initProc() { + + // Construct name of process. + nameSave = "q qbar' -> " + particleDataPtr->name(id3) + " " + + particleDataPtr->name(id4); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(id3, id4); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2chi0chi0::sigmaKin() { + + // Common flavour-independent factor. + sigma0 = 4 * (M_PI / sH2 / pow2(coupSUSYPtr->sin2W)) * pow2(alpEM) + * openFracPair; + + // Factor 1/2 for identical final particles. + if (id3 == id4) sigma0 *= 0.5; + + // Auxiliary factors for use below + ui = uH - s3; + uj = uH - s4; + ti = tH - s3; + tj = tH - s4; + double sV= sH - pow2(coupSUSYPtr->mZpole); + double d = pow2(sV) + pow2(coupSUSYPtr->mZpole * coupSUSYPtr->wZpole); + propZ = complex( sV / d, coupSUSYPtr->mZpole * coupSUSYPtr->wZpole / d); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2chi0chi0::sigmaHat() { + + // Only allow quark-antiquark incoming states + if (id1*id2 >= 0) { + return 0.0; + } + + // Only allow incoming states with sum(charge) = 0 + if ((id1+id2) % 2 != 0) { + return 0.0; + } + + // Shorthands + int idAbs1 = abs(id1); + int idAbs2 = abs(id2); + + // Flavour-dependent kinematics-dependent couplings. + complex QuLL(0.0),QtLL(0.0),QuRR(0.0),QtRR(0.0); + complex QuLR(0.0),QtLR(0.0),QuRL(0.0),QtRL(0.0); + if (idAbs1 == idAbs2) { + QuLL = coupSUSYPtr->LqqZ[idAbs1] * coupSUSYPtr->OLpp[id3chi][id4chi]; + QtLL = coupSUSYPtr->LqqZ[idAbs1] * coupSUSYPtr->ORpp[id3chi][id4chi]; + QuRR = coupSUSYPtr->RqqZ[idAbs1] * coupSUSYPtr->ORpp[id3chi][id4chi]; + QtRR = coupSUSYPtr->RqqZ[idAbs1] * coupSUSYPtr->OLpp[id3chi][id4chi]; + QuLL *= propZ / 4.0 / (1.0-coupSUSYPtr->sin2W); + QtLL *= propZ / 4.0 / (1.0-coupSUSYPtr->sin2W); + QuRR *= propZ / 4.0 / (1.0-coupSUSYPtr->sin2W); + QtRR *= propZ / 4.0 / (1.0-coupSUSYPtr->sin2W); + } + + // Add t-channel squark flavour sums to QmXY couplings + for (int ksq=1; ksq<=6; ksq++) { + + // Flavour indices + int ifl1 = (idAbs1+1) / 2; + int ifl2 = (idAbs2+1) / 2; + + // squark id and squark-subtracted u and t + int idsq=((ksq+2)/3)*1000000 + 2*((ksq-1) % 3) + (idAbs1+1) % 2 + 1; + double msq2=pow(particleDataPtr->m0(idsq),2); + double usq = uH - msq2; + double tsq = tH - msq2; + + // Couplings + complex Lsqq1X3 = coupSUSYPtr->LsuuX[ksq][ifl1][id3chi]; + complex Lsqq1X4 = coupSUSYPtr->LsuuX[ksq][ifl1][id4chi]; + complex Lsqq2X3 = coupSUSYPtr->LsuuX[ksq][ifl2][id3chi]; + complex Lsqq2X4 = coupSUSYPtr->LsuuX[ksq][ifl2][id4chi]; + complex Rsqq1X3 = coupSUSYPtr->RsuuX[ksq][ifl1][id3chi]; + complex Rsqq1X4 = coupSUSYPtr->RsuuX[ksq][ifl1][id4chi]; + complex Rsqq2X3 = coupSUSYPtr->RsuuX[ksq][ifl2][id3chi]; + complex Rsqq2X4 = coupSUSYPtr->RsuuX[ksq][ifl2][id4chi]; + if (idAbs1 % 2 != 0) { + Lsqq1X3 = coupSUSYPtr->LsddX[ksq][ifl1][id3chi]; + Lsqq1X4 = coupSUSYPtr->LsddX[ksq][ifl1][id4chi]; + Lsqq2X3 = coupSUSYPtr->LsddX[ksq][ifl2][id3chi]; + Lsqq2X4 = coupSUSYPtr->LsddX[ksq][ifl2][id4chi]; + Rsqq1X3 = coupSUSYPtr->RsddX[ksq][ifl1][id3chi]; + Rsqq1X4 = coupSUSYPtr->RsddX[ksq][ifl1][id4chi]; + Rsqq2X3 = coupSUSYPtr->RsddX[ksq][ifl2][id3chi]; + Rsqq2X4 = coupSUSYPtr->RsddX[ksq][ifl2][id4chi]; + } + + // QuXY + QuLL += conj(Lsqq1X4)*Lsqq2X3/usq; + QuLR += conj(Lsqq1X4)*Rsqq2X3/usq; + QuRL += conj(Rsqq1X4)*Lsqq2X3/usq; + QuRR += conj(Rsqq1X4)*Rsqq2X3/usq; + + // QtXY + QtLL -= conj(Lsqq1X3)*Lsqq2X4/tsq; + QtLR -= conj(Lsqq1X3)*Rsqq2X4/tsq; + QtRL -= conj(Rsqq1X3)*Lsqq2X4/tsq; + QtRR -= conj(Rsqq1X3)*Rsqq2X4/tsq; + + } + + // Compute matrix element weight + double weight = 0; + // Average over separate helicity contributions + // LL (ha = -1, hb = +1) (divided by 4 for average) + weight += norm(QuLL) * ui * uj + norm(QtLL) * ti * tj + + 2 * real(conj(QuLL) * QtLL) * m3 * m4 * sH; + // RR (ha = 1, hb = -1) (divided by 4 for average) + weight += norm(QtRR) * ti * tj + norm(QuRR) * ui * uj + + 2 * real(conj(QuRR) * QtRR) * m3 * m4 * sH; + // RL (ha = 1, hb = 1) (divided by 4 for average) + weight += norm(QuRL) * ui * uj + norm(QtRL) * ti * tj + - real(conj(QuRL) * QtRL) * (uH * tH - s3 * s4); + // LR (ha = -1, hb = -1) (divided by 4 for average) + weight += norm(QuLR) * ui * uj + norm(QtLR) * ti * tj + - real(conj(QuLR) * QtLR) * (uH * tH - s3 * s4); + + // Cross section, including colour factor. + double sigma = sigma0 * weight; + if (idAbs1 < 9) sigma /= 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2chi0chi0::setIdColAcol() { + + // Set flavours. + setId( id1, id2, id3, id4); + + // Colour flow topologies. Swap when antiquarks. + if (abs(id1) < 9) setColAcol( 1, 0, 0, 1, 0, 0, 0, 0); + else setColAcol( 0, 0, 0, 0, 0, 0, 0, 0); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2charchi0 +// Cross section for gaugino pair production: neutralino-chargino + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2charchi0::sigmaKin() { + + // Common flavour-independent factor. + sigma0 = 4 * (M_PI / sH2 / pow2(coupSUSYPtr->sin2W) ) * pow2(alpEM) ; + + // Auxiliary factors for use below + ui = uH - s3; + uj = uH - s4; + ti = tH - s3; + tj = tH - s4; + double sW = sH - pow2(coupSUSYPtr->mWpole); + double d = pow2(sW) + pow2(coupSUSYPtr->mWpole * coupSUSYPtr->wWpole); + propW = complex( sW / d, coupSUSYPtr->mWpole * coupSUSYPtr->wWpole / d); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2charchi0::sigmaHat() { + + // Only allow particle-antiparticle incoming states + if (id1*id2 >= 0) { + return 0.0; + } + + // Only allow incoming states with sum(charge) = final state + if (abs(id1) % 2 == abs(id2) % 2) return 0.0; + int isPos = (id3chi > 0 ? 1 : 0); + if (id1 < 0 && id1 > -10 && abs(id1) % 2 == 1-isPos ) return 0.0; + else if (id1 > 0 && id1 < 10 && abs(id1) % 2 == isPos ) return 0.0; + + // Flavour-dependent kinematics-dependent couplings. + int idAbs1 = abs(id1); + complex QuLL(0.0),QtLL(0.0),QuRR(0.0),QtRR(0.0); + complex QuLR(0.0),QtLR(0.0),QuRL(0.0),QtRL(0.0); + + // Calculate everything from udbar -> ~chi+ ~chi0 template process + int id1tmp = id1; + int id2tmp = id2; + double uHtmp = uH; + double tHtmp = tH; + double uitmp = ui; + double ujtmp = uj; + double titmp = ti; + double tjtmp = tj; + + // u dbar , ubar d : do nothing + if (idAbs1 % 2 == 0) { + } + + // dbar u , d ubar : swap 1<->2 and t<->u + else if (idAbs1 % 2 == 1) { + id1tmp = id2; + id2tmp = id1; + uHtmp = tH; + tHtmp = uH; + uitmp = ti; + ujtmp = tj; + titmp = ui; + tjtmp = uj; + } + + // Generation indices + int iGu = abs(id1tmp)/2; + int iGd = (abs(id2tmp)+1)/2; + + // s-channel W contribution + QuLL = conj(coupSUSYPtr->LudW[iGu][iGd]) + * conj(coupSUSYPtr->OL[id4chi][abs(id3chi)]) + * propW / 4.0 / coupSUSYPtr->cosW; + QtLL = conj(coupSUSYPtr->LudW[iGu][iGd]) + * conj(coupSUSYPtr->OR[id4chi][abs(id3chi)]) + * propW / 4.0 / coupSUSYPtr->cosW; + + // Add t-channel squark flavour sums to QmXY couplings + for (int jsq=1; jsq<=6; jsq++) { + + int idsu=((jsq+2)/3)*1000000 + 2*((jsq-1) % 3) + 2; + int idsd=((jsq+2)/3)*1000000 + 2*((jsq-1) % 3) + 1; + double msd2 = pow(particleDataPtr->m0(idsd),2); + double msu2 = pow(particleDataPtr->m0(idsu),2); + double tsq = tHtmp - msd2; + double usq = uHtmp - msu2; + + QuLL += conj(coupSUSYPtr->LsuuX[jsq][iGu][id4chi]) + *coupSUSYPtr->LsudX[jsq][iGd][abs(id3chi)]/usq; + QuRR += conj(coupSUSYPtr->RsuuX[jsq][iGu][id4chi]) + *coupSUSYPtr->RsudX[jsq][iGd][abs(id3chi)]/usq; + QuLR += conj(coupSUSYPtr->LsuuX[jsq][iGu][id4chi]) + *coupSUSYPtr->RsudX[jsq][iGd][abs(id3chi)]/usq; + QuRL += conj(coupSUSYPtr->RsuuX[jsq][iGu][id4chi]) + *coupSUSYPtr->LsudX[jsq][iGd][abs(id3chi)]/usq; + QtLL -= conj(coupSUSYPtr->LsduX[jsq][iGu][abs(id3chi)]) + *coupSUSYPtr->LsddX[jsq][iGd][id4chi]/tsq; + QtRR -= conj(coupSUSYPtr->RsduX[jsq][iGu][abs(id3chi)]) + *coupSUSYPtr->RsddX[jsq][iGd][id4chi]/tsq; + QtLR -= conj(coupSUSYPtr->LsduX[jsq][iGu][abs(id3chi)]) + *coupSUSYPtr->RsddX[jsq][iGd][id4chi]/tsq; + QtRL -= conj(coupSUSYPtr->RsduX[jsq][iGu][abs(id3chi)]) + *coupSUSYPtr->LsddX[jsq][iGd][id4chi]/tsq; + + } + + // Compute matrix element weight + double weight = 0; + + // Average over separate helicity contributions + // (if swapped, swap ha, hb if computing polarized cross sections) + // LL (ha = -1, hb = +1) (divided by 4 for average) + weight += norm(QuLL) * uitmp * ujtmp + norm(QtLL) * titmp * tjtmp + + 2 * real(conj(QuLL) * QtLL) * m3 * m4 * sH; + // RR (ha = 1, hb = -1) (divided by 4 for average) + weight += norm(QtRR) * titmp * tjtmp + norm(QuRR) * uitmp * ujtmp + + 2 * real(conj(QuRR) * QtRR) * m3 * m4 * sH; + // RL (ha = 1, hb = 1) (divided by 4 for average) + weight += norm(QuRL) * uitmp * ujtmp + norm(QtRL) * titmp * tjtmp + - real(conj(QuRL) * QtRL) * (uHtmp * tHtmp - s3 * s4); + // LR (ha = -1, hb = -1) (divided by 4 for average) + weight += norm(QuLR) * uitmp * ujtmp + norm(QtLR) * titmp * tjtmp + - real(conj(QuLR) * QtLR) * (uHtmp * tHtmp - s3 * s4); + + // Cross section, including colour factor. + double sigma = sigma0 * weight; + if (idAbs1 < 9) sigma /= 3.; + + // Answer. + return sigma; + +} + +//========================================================================== + +// Sigma2qqbar2charchar +// Cross section for gaugino pair production: chargino-chargino + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2charchar::sigmaKin() { + + // Common flavour-independent factor. + sigma0 = M_PI / sH2 / pow2(coupSUSYPtr->sin2W) * pow2(alpEM) ; + + // Auxiliary factors for use below + ui = uH - s3; + uj = uH - s4; + ti = tH - s3; + tj = tH - s4; + double sV= sH - pow2(coupSUSYPtr->mZpole); + double d = pow2(sV) + pow2(coupSUSYPtr->mZpole * coupSUSYPtr->wZpole); + propZ = complex( sV / d, coupSUSYPtr->mZpole * coupSUSYPtr->wZpole / d); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2charchar::sigmaHat() { + + // Only allow quark-antiquark incoming states + if (id1*id2 >= 0) { + return 0.0; + } + + // Only allow incoming states with sum(charge) = 0 + if ((id1+id2) % 2 != 0) { + return 0.0; + } + + //if (id1 > 0 || id1==-1 || id1==-3 || id1==-5) return 0.0; + //if (id1 < 0 || id1==1 || id1==3 || id1==5) return 0.0; + + // Flavour-dependent kinematics-dependent couplings. + int idAbs1 = abs(id1); + int idAbs2 = abs(id2); + int i3 = abs(id3chi); + int i4 = abs(id4chi); + + // Flavour-dependent kinematics-dependent couplings. + complex QuLL(0.0),QtLL(0.0),QuRR(0.0),QtRR(0.0); + complex QuLR(0.0),QtLR(0.0),QuRL(0.0),QtRL(0.0); + + // Add Z/gamma* for same-flavour in-quarks + if (idAbs1 == idAbs2) { + + // s-channel Z ( L<->R for qbar q incoming ) + QuLL = coupSUSYPtr->LqqZ[idAbs1] * (id1 > 0 ? coupSUSYPtr->OLp[i3][i4] + : coupSUSYPtr->ORp[i3][i4]); + QtLL = coupSUSYPtr->LqqZ[idAbs1] * (id1 > 0 ? coupSUSYPtr->ORp[i3][i4] + : coupSUSYPtr->OLp[i3][i4]); + QuRR = coupSUSYPtr->RqqZ[idAbs1] * (id1 > 0 ? coupSUSYPtr->ORp[i3][i4] + : coupSUSYPtr->OLp[i3][i4]); + QtRR = coupSUSYPtr->RqqZ[idAbs1] * (id1 > 0 ? coupSUSYPtr->OLp[i3][i4] + : coupSUSYPtr->ORp[i3][i4]); + QuLL *= propZ / 2.0 / (1.0-coupSUSYPtr->sin2W); + QtLL *= propZ / 2.0 / (1.0-coupSUSYPtr->sin2W); + QuRR *= propZ / 2.0 / (1.0-coupSUSYPtr->sin2W); + QtRR *= propZ / 2.0 / (1.0-coupSUSYPtr->sin2W); + + // s-channel gamma* (only for same-type charginos) + if (i3 == i4) { + + // Charge of in-particles + double q = 2.0/3.0; + if (idAbs1 % 2 == 1) q = -1.0/3.0; + QuLL -= q * coupSUSYPtr->sin2W / sH; + QuRR -= q * coupSUSYPtr->sin2W / sH; + QtLL -= q * coupSUSYPtr->sin2W / sH; + QtRR -= q * coupSUSYPtr->sin2W / sH; + + } + } + + // Add t- or u-channel squark flavour sums to QmXY couplings + for (int ksq=1; ksq<=6; ksq++) { + + // Positive-sign on side 1: t-channel diagrams only + if (particleDataPtr->chargeType(id1) > 0) { + + // u ubar -> chi+ chi- : add t-channel ~d + if (id1 % 2 == 0) { + int iG1 = (abs(id1)+1)/2; + int iG2 = (abs(id2)+1)/2; + int idsd = ((ksq+2)/3)*1000000 + 2*((ksq-1) % 3) + 1; + double msq = particleDataPtr->m0(idsd); + double tsq = tH - pow2(msq); + QtLL -= conj(coupSUSYPtr->LsduX[ksq][iG1][i3]) + *coupSUSYPtr->LsduX[ksq][iG2][i4]*2.0/tsq; + QtLR -= conj(coupSUSYPtr->LsduX[ksq][iG1][i3]) + *coupSUSYPtr->RsduX[ksq][iG2][i4]*2.0/tsq; + QtRL -= conj(coupSUSYPtr->RsduX[ksq][iG1][i3]) + *coupSUSYPtr->LsduX[ksq][iG2][i4]*2.0/tsq; + QtRR -= conj(coupSUSYPtr->RsduX[ksq][iG1][i3]) + *coupSUSYPtr->RsduX[ksq][iG2][i4]*2.0/tsq; + } + + // dbar d -> chi+ chi- : add t-channel ~u + // But with QtXY <-> -conj(QtYX) since qbar incoming + else { + int iG1 = (abs(id1)+1)/2; + int iG2 = (abs(id2)+1)/2; + int idsu = ((ksq+2)/3)*1000000 + 2*((ksq-1) % 3) + 2; + double msq = particleDataPtr->m0(idsu); + double tsq = tH - pow2(msq); + QtLL += conj(coupSUSYPtr->LsudX[ksq][iG2][i4]) + *coupSUSYPtr->LsudX[ksq][iG1][i3]*2.0/tsq; + QtLR += conj(coupSUSYPtr->LsudX[ksq][iG2][i4]) + *coupSUSYPtr->RsudX[ksq][iG1][i3]*2.0/tsq; + QtRL += conj(coupSUSYPtr->RsudX[ksq][iG2][i4]) + *coupSUSYPtr->LsudX[ksq][iG1][i3]*2.0/tsq; + QtRR += conj(coupSUSYPtr->RsudX[ksq][iG2][i4]) + *coupSUSYPtr->RsudX[ksq][iG1][i3]*2.0/tsq; + } + + } + + // Negative-sign on side 1: u-channel diagrams only + else { + + // ubar u -> chi+ chi- : add u-channel ~d + // But with QuXY <-> -conj(QuYX) since qbar incoming + if (id1 % 2 == 0) { + int iG1 = abs(id1)/2; + int iG2 = abs(id2)/2; + int idsd = ((ksq+2)/3)*1000000 + 2*((ksq-1) % 3) + 1; + double msq = particleDataPtr->m0(idsd); + double usq = uH - pow2(msq); + QuLL -= conj(coupSUSYPtr->LsduX[ksq][iG2][i3]) + *coupSUSYPtr->LsduX[ksq][iG1][i4]*2.0/usq; + QuLR -= conj(coupSUSYPtr->LsduX[ksq][iG2][i3]) + *coupSUSYPtr->RsduX[ksq][iG1][i4]*2.0/usq; + QuRL -= conj(coupSUSYPtr->RsduX[ksq][iG2][i3]) + *coupSUSYPtr->LsduX[ksq][iG1][i4]*2.0/usq; + QuRR -= conj(coupSUSYPtr->RsduX[ksq][iG2][i3]) + *coupSUSYPtr->RsduX[ksq][iG1][i4]*2.0/usq; + } + + // d dbar -> chi+ chi- : add u-channel ~u + else { + int iG1 = (abs(id1)+1)/2; + int iG2 = (abs(id2)+1)/2; + int idsu = ((ksq+2)/3)*1000000 + 2*((ksq-1) % 3) + 2; + double msq = particleDataPtr->m0(idsu); + double usq = uH - pow2(msq); + QuLL += conj(coupSUSYPtr->LsudX[ksq][iG1][i4]) + *coupSUSYPtr->LsudX[ksq][iG2][i3]*2.0/usq; + QuLR += conj(coupSUSYPtr->LsudX[ksq][iG1][i4]) + *coupSUSYPtr->RsudX[ksq][iG2][i3]*2.0/usq; + QuRL += conj(coupSUSYPtr->RsudX[ksq][iG1][i4]) + *coupSUSYPtr->LsudX[ksq][iG2][i3]*2.0/usq; + QuRR += conj(coupSUSYPtr->RsudX[ksq][iG1][i4]) + *coupSUSYPtr->RsudX[ksq][iG2][i3]*2.0/usq; + } + + } + } + + // Compute matrix element weight + double weight = 0; + + // Average over separate helicity contributions + // LL (ha = -1, hb = +1) (divided by 4 for average) + weight += norm(QuLL) * ui * uj + norm(QtLL) * ti * tj + + 2 * real(conj(QuLL) * QtLL) * m3 * m4 * sH; + // RR (ha = 1, hb = -1) (divided by 4 for average) + weight += norm(QtRR) * ti * tj + norm(QuRR) * ui * uj + + 2 * real(conj(QuRR) * QtRR) * m3 * m4 * sH; + // RL (ha = 1, hb = 1) (divided by 4 for average) + weight += norm(QuRL) * ui * uj + norm(QtRL) * ti * tj + - real(conj(QuRL) * QtRL) * (uH * tH - s3 * s4); + // LR (ha = -1, hb = -1) (divided by 4 for average) + weight += norm(QuLR) * ui * uj + norm(QtLR) * ti * tj + - real(conj(QuLR) * QtLR) * (uH * tH - s3 * s4); + + // Cross section, including colour factor. + double sigma = sigma0 * weight; + if (idAbs1 < 9) sigma /= 3.; + + // Answer. + return sigma; + +} + +//========================================================================== + +// Sigma2qgchi0squark +// Cross section for gaugino-squark production: neutralino-squark + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2chi0squark::initProc() { + + // Construct name of process. + if (id4 % 2 == 0) { + nameSave = "q g -> " + particleDataPtr->name(id3) + " " + + particleDataPtr->name(id4) + " + c.c. (q=u,c)"; + } + else { + nameSave = "q g -> " + particleDataPtr->name(id3) + " " + + particleDataPtr->name(id4) + " + c.c. (q=d,s,b)"; + } + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(id3, id4); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qg2chi0squark::sigmaKin() { + + // Common flavour-independent factor. + // tmp: alphaS = 0.1 for counter-checks + sigma0 = M_PI / sH2 / coupSUSYPtr->sin2W * alpEM * alpS + * openFracPair; + + // Auxiliary factors for use below + ui = uH - s3; + uj = uH - s4; + ti = tH - s3; + tj = tH - s4; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qg2chi0squark::sigmaHat() { + + // Antiquark -> antisquark + int idq = id1; + if (id1 == 21 || id1 == 22) idq = id2; + if (idq < 0) { + id4 = -abs(id4); + } else { + id4 = abs(id4); + } + + // tmp: only allow incoming quarks on side 1 + // if (id1 < 0 || id1 == 21) return 0.0; + + // Generation index + int iGq = (abs(idq)+1)/2; + + // Only accept u(bar) -> ~u(bar) and d(bar) -> ~d(bar) + if (particleDataPtr->chargeType(idq) != particleDataPtr->chargeType(id4)) + return 0.0; + + // Couplings + complex LsqqX, RsqqX; + if (idq % 2 == 0) { + LsqqX = coupSUSYPtr->LsuuX[id4sq][iGq][id3chi]; + RsqqX = coupSUSYPtr->RsuuX[id4sq][iGq][id3chi]; + } + else { + LsqqX = coupSUSYPtr->LsddX[id4sq][iGq][id3chi]; + RsqqX = coupSUSYPtr->RsddX[id4sq][iGq][id3chi]; + } + + // Prefactors : swap u and t if gq instead of qg + double fac1, fac2; + if (idq == id1) { + fac1 = -ui/sH + 2.0 * ( uH*tH - s4*s3 )/sH/tj; + fac2 = ti/tj * ( (tH + s4)/tj + (ti - uj)/sH ); + } else { + fac1 = -ti/sH + 2.0 * ( uH*tH - s4*s3 )/sH/uj; + fac2 = ui/uj * ( (uH + s4)/uj + (ui - tj)/sH ); + } + + // Compute matrix element weight + double weight = 0.0; + + // Average over separate helicity contributions + // (for qbar g : ha -> -ha ) + // LL (ha = -1, hb = +1) (divided by 4 for average) + weight += fac2 * norm(LsqqX) / 2.0; + // RR (ha = 1, hb = -1) (divided by 4 for average) + weight += fac2 * norm(RsqqX) / 2.0; + // RL (ha = 1, hb = 1) (divided by 4 for average) + weight += fac2 * norm(RsqqX) / 2.0 + fac1 * norm(RsqqX); + // LR (ha = -1, hb = -1) (divided by 4 for average) + weight += fac2 * norm(LsqqX) / 2.0 + fac1 * norm(LsqqX); + + double sigma = sigma0 * weight; + if (abs(idq) < 9) sigma /= 3.; + + // Answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2chi0squark::setIdColAcol() { + + // Set flavours. + setId( id1, id2, id3, (id1*id2 > 0 ? abs(id4) : -abs(id4))); + + // Colour flow topology. Swap if first is gluon, or when antiquark. + if (id1 != 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 1, 2, 2, 0, 0, 0, 1, 0); + if (id1*id2 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qg2charsquark +// Cross section for gaugino-squark production: chargino-squark + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2charsquark::initProc() { + + // Construct name of process. + if (id4 % 2 == 0) { + nameSave = "q g -> " + particleDataPtr->name(id3) + " " + + particleDataPtr->name(id4) + " + c.c. (q=d,s,b)"; + } + else { + nameSave = "q g -> " + particleDataPtr->name(id3) + " " + + particleDataPtr->name(id4) + " + c.c. (q=u,c)"; + } + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(id3Sav, id4Sav); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qg2charsquark::sigmaHat() { + + // Antiquark -> antisquark + int idq = (id1 == 21) ? id2 : id1; + if (idq > 0) { + id3 = id3Sav; + id4 = id4Sav; + } else { + id3 = -id3Sav; + id4 = -id4Sav; + } + + // Only accept u(bar) -> ~d(bar) and d(bar) -> ~u(bar) + if (particleDataPtr->chargeType(idq) == particleDataPtr->chargeType(id4)) + return 0.0; + + // Generation index + int iGq = (abs(idq)+1)/2; + + // Couplings + complex LsqqX, RsqqX; + if (idq % 2 == 0) { + LsqqX = coupSUSYPtr->LsduX[id4sq][iGq][id3chi]; + RsqqX = coupSUSYPtr->RsduX[id4sq][iGq][id3chi]; + } + else { + LsqqX = coupSUSYPtr->LsduX[id4sq][iGq][id3chi]; + RsqqX = coupSUSYPtr->RsduX[id4sq][iGq][id3chi]; + } + + // Prefactors : swap u and t if gq instead of qg + double fac1, fac2; + if (idq == id1) { + fac1 = -ui/sH + 2.0 * ( uH*tH - s4*s3 )/sH/tj; + fac2 = ti/tj * ( (tH + s4)/tj + (ti - uj)/sH ); + } else { + fac1 = -ti/sH + 2.0 * ( uH*tH - s4*s3 )/sH/uj; + fac2 = ui/uj * ( (uH + s4)/uj + (ui - tj)/sH ); + } + + // Compute matrix element weight + double weight = 0.0; + + // Average over separate helicity contributions + // (a, b refers to qg configuration) + // LL (ha = -1, hb = +1) (divided by 4 for average) + weight += fac2 * norm(LsqqX) / 2.0; + // RR (ha = 1, hb = -1) (divided by 4 for average) + weight += fac2 * norm(RsqqX) / 2.0; + // RL (ha = 1, hb = 1) (divided by 4 for average) + weight += fac2 * norm(RsqqX) / 2.0 + fac1 * norm(RsqqX); + // LR (ha = -1, hb = -1) (divided by 4 for average) + weight += fac2 * norm(LsqqX) / 2.0 + fac1 * norm(LsqqX); + + double sigma = sigma0 * weight; + if (abs(idq) < 9) sigma /= 3.; + + // Answer. + return sigma * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2charsquark::setIdColAcol() { + + // Set flavours. + if (id1 > 0 && id2 > 0) { + setId( id1, id2, id3Sav, id4Sav); + } else { + setId( id1, id2,-id3Sav,-id4Sav); + } + + // Colour flow topology. Swap if first is gluon, or when antiquark. + if (id1 != 21) setColAcol( 1, 0, 2, 1, 0, 0, 2, 0); + else setColAcol( 1, 2, 2, 0, 0, 0, 1, 0); + if (id1 < 0 || id2 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qq2squarksquark +// Cross section for squark-squark production + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qq2squarksquark::initProc() { + + // Extract mass-ordering indices + iGen3 = 3*(abs(id3Sav)/2000000) + (abs(id3Sav)%10+1)/2; + iGen4 = 3*(abs(id4Sav)/2000000) + (abs(id4Sav)%10+1)/2; + + // Is this a ~u_i ~d_j fial state or ~d_i ~d_j, ~u_i ~u_j + if (abs(id3Sav) % 2 == abs(id4Sav) % 2) isUD = false; + else isUD = true; + + // Derive name + nameSave = "q q' -> "+particleDataPtr->name(abs(id3Sav))+" " + +particleDataPtr->name(abs(id4Sav))+" + c.c."; + + // Count 5 neutralinos in NMSSM + nNeut = (coupSUSYPtr->isNMSSM ? 5 : 4); + + // Store mass squares of all possible internal propagator lines + m2Glu = pow2(particleDataPtr->m0(1000021)); + m2Neut.resize(nNeut+1); + for (int iNeut=1;iNeut<=nNeut;iNeut++) { + m2Neut[iNeut] = pow2(particleDataPtr->m0(coupSUSYPtr->idNeut(iNeut))); + } + m2Char.resize(3); + m2Char[1] = pow2(particleDataPtr->m0(coupSUSYPtr->idChar(1))); + m2Char[2] = pow2(particleDataPtr->m0(coupSUSYPtr->idChar(2))); + + // Set sizes of some arrays to be used below + tNeut.resize(nNeut+1); + uNeut.resize(nNeut+1); + tChar.resize(3); + uChar.resize(3); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(id3Sav, id4Sav); +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qq2squarksquark::sigmaKin() { + + // Weak mixing + double xW = coupSUSYPtr->sin2W; + + // pi/sH2 + double comFac = M_PI/sH2 * openFracPair; + + // Channel-dependent but flavor-independent pre-factors + sigmaNeut = comFac * pow2(alpEM) / pow2(xW) / pow2(1-xW); + sigmaGlu = comFac * 2.0 * pow2(alpS) / 9.0; + if (isUD) { + sigmaChar = comFac * pow2(alpEM) / 4.0 / pow2(xW); + sigmaCharNeut = comFac * pow2(alpEM) / 3.0 / pow2(xW) / (1-xW); + sigmaCharGlu = comFac * 4.0 * alpEM * alpS / 9.0 / xW; + sigmaNeutGlu = 0.0; + } else { + sigmaChar = 0.0; + sigmaCharNeut = 0.0; + sigmaCharGlu = 0.0; + sigmaNeutGlu = comFac * 8.0 * alpEM * alpS / 9.0 / xW/(1-xW); + } + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qq2squarksquark::sigmaHat() { + + // In-pair must be same-sign + if (id1 * id2 < 0) return 0.0; + + // Check correct charge sum + if (isUD && abs(id1) %2 == abs(id2) % 2) return 0.0; + if (!isUD && abs(id1) % 2 != abs(id2) % 2) return 0.0; + if (!isUD && abs(id1) % 2 != abs(id3Sav) % 2) return 0.0; + + // Coded sigma is for ud -> ~q~q'. Swap t and u for du -> ~q~q'. + swapTU = (isUD and abs(id1) % 2 == 0); + int idIn1A = (swapTU) ? abs(id2) : abs(id1); + int idIn2A = (swapTU) ? abs(id1) : abs(id2); + + // Auxiliary factors for use below + tGlu = tH - m2Glu; + uGlu = uH - m2Glu; + for (int i=1; i<= nNeut; i++) { + tNeut[i] = tH - m2Neut[i]; + uNeut[i] = uH - m2Neut[i]; + if (isUD && i <= 2) { + tChar[i] = tH - m2Char[i]; + uChar[i] = uH - m2Char[i]; + } + } + + // Generation indices of incoming particles + int iGen1 = (abs(idIn1A)+1)/2; + int iGen2 = (abs(idIn2A)+1)/2; + + // Initial values for pieces used for color-flow selection below + sumCt = 0.0; + sumCu = 0.0; + sumNt = 0.0; + sumNu = 0.0; + sumGt = 0.0; + sumGu = 0.0; + sumInterference = 0.0; + + // Common factor for LR and RL contributions + double facTU = uH*tH-s3*s4; + + // Case A) Opposite-isospin: qq' -> ~d~u + if ( isUD ) { + + // t-channel Charginos + for (int k=1;k<=2;k++) { + + // Skip if only including gluinos + if (settingsPtr->flag("SUSY:qq2squarksquark:gluinoOnly")) continue; + + for (int l=1;l<=2;l++) { + + // kl-dependent factor for LL and RR contributions + double facMS = sH*sqrt(m2Char[k]*m2Char[l]); + + // Note: Ckl defined as in [Boz07] with sigmaChar factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + complex Ckl[3][3]; + Ckl[1][1] = facMS + * coupSUSYPtr->LsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->LsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->LsudX[iGen4][iGen2][l]) + * coupSUSYPtr->LsduX[iGen3][iGen1][l]; + Ckl[1][2] = facTU + * coupSUSYPtr->RsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->LsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->RsudX[iGen4][iGen2][l]) + * coupSUSYPtr->LsduX[iGen3][iGen1][l]; + Ckl[2][1] = facTU + * coupSUSYPtr->LsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->RsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->LsudX[iGen4][iGen2][l]) + * coupSUSYPtr->RsduX[iGen3][iGen1][l]; + Ckl[2][2] = facMS + * coupSUSYPtr->RsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->RsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->RsudX[iGen4][iGen2][l]) + * coupSUSYPtr->RsduX[iGen3][iGen1][l]; + + // Add to sum of t-channel charginos + sumCt += sigmaChar * real(Ckl[1][1] + Ckl[1][2] + Ckl[2][1] + Ckl[2][2]) + / tChar[k] / tChar[l]; + + } + } + + // u-channel Neutralinos + for (int k=1;k<=nNeut;k++) { + + // Skip if only including gluinos + if (settingsPtr->flag("SUSY:qq2squarksquark:gluinoOnly")) continue; + + for (int l=1;l<=nNeut;l++) { + + // kl-dependent factor for LL, RR contributions + double facMS = sH*sqrt(m2Neut[k]*m2Neut[l]); + + // Note: Nkl defined as in [Boz07] with sigmaNeut factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + complex Nkl[3][3]; + Nkl[1][1] = facMS + * conj(coupSUSYPtr->LsuuX[iGen4][iGen1][k]) + * conj(coupSUSYPtr->LsddX[iGen3][iGen2][k]) + * coupSUSYPtr->LsuuX[iGen4][iGen1][l] + * coupSUSYPtr->LsddX[iGen3][iGen2][l]; + Nkl[1][2] = facTU + * conj(coupSUSYPtr->LsuuX[iGen4][iGen1][k]) + * conj(coupSUSYPtr->RsddX[iGen3][iGen2][k]) + * coupSUSYPtr->LsuuX[iGen4][iGen1][l] + * coupSUSYPtr->RsddX[iGen3][iGen2][l]; + Nkl[2][1] = facTU + * conj(coupSUSYPtr->RsuuX[iGen4][iGen1][k]) + * conj(coupSUSYPtr->LsddX[iGen3][iGen2][k]) + * coupSUSYPtr->RsuuX[iGen4][iGen1][l] + * coupSUSYPtr->LsddX[iGen3][iGen2][l]; + Nkl[2][2] = facMS + * conj(coupSUSYPtr->RsuuX[iGen4][iGen1][k]) + * conj(coupSUSYPtr->RsddX[iGen3][iGen2][k]) + * coupSUSYPtr->RsuuX[iGen4][iGen1][l] + * coupSUSYPtr->RsddX[iGen3][iGen2][l]; + + // Add to sum of u-channel neutralinos + sumNu += sigmaNeut / uNeut[k] / uNeut[l] + * real(Nkl[1][1] + Nkl[1][2] + Nkl[2][1] + Nkl[2][2]); + + } + } + + // u-channel gluino + // Note: Gij defined as in [Boz07] with sigmaGlu factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + double Gij[3][3]; + Gij[1][1] = norm(coupSUSYPtr->LsuuG[iGen4][iGen1] + * coupSUSYPtr->LsddG[iGen3][iGen2]); + Gij[1][2] = norm(coupSUSYPtr->LsuuG[iGen4][iGen1] + * coupSUSYPtr->RsddG[iGen3][iGen2]); + Gij[2][1] = norm(coupSUSYPtr->RsuuG[iGen4][iGen1] + * coupSUSYPtr->LsddG[iGen3][iGen2]); + Gij[2][2] = norm(coupSUSYPtr->RsuuG[iGen4][iGen1] + * coupSUSYPtr->RsddG[iGen3][iGen2]); + Gij[1][1] *= sH*m2Glu; + Gij[1][2] *= facTU-s3*s4; + Gij[2][1] *= facTU-s3*s4; + Gij[2][2] *= sH*m2Glu; + // Sum over polarizations + sumGu += sigmaGlu * (Gij[1][1] + Gij[1][2] + Gij[2][1] + Gij[2][2]) + / pow2(uGlu); + + // chargino-neutralino interference + for (int k=1;k<=2;k++) { + for (int l=1;l<=nNeut;l++) { + + // Skip if only including gluinos + if (settingsPtr->flag("SUSY:qq2squarksquark:gluinoOnly")) continue; + + // Note: CNkl defined as in [Boz07] with pi/sH2 factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + double CNkl[3][3]; + CNkl[1][1] = real(coupSUSYPtr->LsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->LsduX[iGen3][iGen1][k]) + * coupSUSYPtr->LsuuX[iGen4][iGen1][l] + * coupSUSYPtr->LsddX[iGen3][iGen2][l]); + CNkl[1][2] = real(coupSUSYPtr->RsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->LsduX[iGen3][iGen1][k]) + * coupSUSYPtr->LsuuX[iGen4][iGen1][l] + * coupSUSYPtr->RsddX[iGen3][iGen2][l]); + CNkl[2][1] = real(coupSUSYPtr->LsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->RsduX[iGen3][iGen1][k]) + * coupSUSYPtr->RsuuX[iGen4][iGen1][l] + * coupSUSYPtr->LsddX[iGen3][iGen2][l]); + CNkl[2][2] = real(coupSUSYPtr->RsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->RsduX[iGen3][iGen1][k]) + * coupSUSYPtr->RsuuX[iGen4][iGen1][l] + * coupSUSYPtr->RsddX[iGen3][iGen2][l]); + CNkl[1][1] *= sH*sqrt(m2Char[k]*m2Neut[l]); + CNkl[1][2] *= uH*tH-s3*s4; + CNkl[2][1] *= uH*tH-s3*s4; + CNkl[2][2] *= sH*sqrt(m2Char[k]*m2Neut[l]); + // Sum over polarizations + sumInterference += sigmaCharNeut * (CNkl[1][1] + CNkl[1][2] + CNkl[2][1] + + CNkl[2][2]) / tChar[k] / uNeut[l]; + } + } + + // chargino-gluino interference + for (int k=1;k<=2;k++) { + + // Skip if only including gluinos + if (settingsPtr->flag("SUSY:qq2squarksquark:gluinoOnly")) continue; + + // Note: CGk defined as in [Boz07] with sigmaCharGlu factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + double CGk[3][3]; + CGk[1][1] = real(coupSUSYPtr->LsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->LsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->LsuuG[iGen4][iGen1]) + * conj(coupSUSYPtr->LsddG[iGen3][iGen2])); + CGk[1][2] = real(coupSUSYPtr->RsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->LsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->LsuuG[iGen4][iGen1]) + * conj(coupSUSYPtr->RsddG[iGen3][iGen2])); + CGk[2][1] = real(coupSUSYPtr->LsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->RsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->RsuuG[iGen4][iGen1]) + * conj(coupSUSYPtr->LsddG[iGen3][iGen2])); + CGk[2][2] = real(coupSUSYPtr->RsudX[iGen4][iGen2][k] + * conj(coupSUSYPtr->RsduX[iGen3][iGen1][k]) + * conj(coupSUSYPtr->RsuuG[iGen4][iGen1]) + * conj(coupSUSYPtr->RsddG[iGen3][iGen2])); + CGk[1][1] *= sH*sqrt(m2Glu*m2Char[k]); + CGk[1][2] *= uH*tH-s3*s4; + CGk[2][1] *= uH*tH-s3*s4; + CGk[2][2] *= sH*sqrt(m2Glu*m2Char[k]); + // Sum over polarizations + sumInterference += sigmaGlu * (CGk[1][1] + CGk[1][2] + CGk[2][1] + + CGk[2][2]) / uGlu / tChar[k]; + } + } + + // Case B) Same-isospin: qq' -> ~d~d , ~u~u + else { + + // t-channel + u-channel Neutralinos + t/u interference + for (int k=1;k<=nNeut;k++) { + + // Skip if only including gluinos + if (settingsPtr->flag("SUSY:qq2squarksquark:gluinoOnly")) continue; + + for (int l=1;l<=nNeut;l++) { + + // kl-dependent factor for LL and RR contributions + double facMS = sH * particleDataPtr->m0(coupSUSYPtr->idNeut(k)) + * particleDataPtr->m0(coupSUSYPtr->idNeut(l)); + + // Note: Nxkl defined as in [Boz07] with sigmaNeut factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + complex NTkl[3][3], NUkl[3][3], NTUkl[3][3]; + NTkl[1][1] = facMS + * conj(coupSUSYPtr->getLsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getLsqqX(iGen4,idIn2A,l) + * coupSUSYPtr->getLsqqX(iGen3,idIn1A,l); + NTkl[1][2] = facTU + * conj(coupSUSYPtr->getRsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getRsqqX(iGen4,idIn2A,l) + * coupSUSYPtr->getLsqqX(iGen3,idIn1A,l); + NTkl[2][1] = facTU + * conj(coupSUSYPtr->getLsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getLsqqX(iGen4,idIn2A,l) + * coupSUSYPtr->getRsqqX(iGen3,idIn1A,l); + NTkl[2][2] = facMS + * conj(coupSUSYPtr->getRsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getRsqqX(iGen4,idIn2A,l) + * coupSUSYPtr->getRsqqX(iGen3,idIn1A,l); + NUkl[1][1] = facMS + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen4,idIn1A,k)) + * coupSUSYPtr->getLsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getLsqqX(iGen4,idIn1A,l); + NUkl[1][2] = facTU + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen4,idIn1A,k)) + * coupSUSYPtr->getRsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getLsqqX(iGen4,idIn1A,l); + NUkl[2][1] = facTU + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen4,idIn1A,k)) + * coupSUSYPtr->getLsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getRsqqX(iGen4,idIn1A,l); + NUkl[2][2] = facMS + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen4,idIn1A,k)) + * coupSUSYPtr->getRsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getRsqqX(iGen4,idIn1A,l); + NTUkl[1][1] = facMS + * real( conj(coupSUSYPtr->getLsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getLsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getLsqqX(iGen4,idIn1A,l) ); + NTUkl[1][2] = facTU + * real( conj(coupSUSYPtr->getRsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getRsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getLsqqX(iGen4,idIn1A,l) ); + NTUkl[2][1] = facTU + * real( conj(coupSUSYPtr->getLsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getLsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getRsqqX(iGen4,idIn1A,l) ); + NTUkl[2][2] = facMS + * real( conj(coupSUSYPtr->getRsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn1A,k)) + * coupSUSYPtr->getRsqqX(iGen3,idIn2A,l) + * coupSUSYPtr->getRsqqX(iGen4,idIn1A,l) ); + + // Add to sums + sumNt += sigmaNeut / tNeut[k] / tNeut[l] + * real(NTkl[1][1] + NTkl[1][2] + NTkl[2][1] + NTkl[2][2]); + sumNu += sigmaNeut / uNeut[k] / uNeut[l] + * real(NUkl[1][1] + NUkl[1][2] + NUkl[2][1] + NUkl[2][2]); + sumInterference += 2.0 / 3.0 * sigmaNeut + * real(NTUkl[1][1] + NTUkl[1][2] + NTUkl[2][1] + NTUkl[2][2]) + / tNeut[k] / uNeut[l]; + } + + // Neutralino / Gluino interference + + // k-dependent factor for LL and RR contributions + double facMS = sH * particleDataPtr->m0(coupSUSYPtr->idNeut(k)) + * particleDataPtr->m0(1000021); + + // Note: Nxkl defined as in [Boz07] with sigmaNeutGlu factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + complex NGA[3][3], NGB[3][3]; + NGA[1][1] = facMS + * real( conj(coupSUSYPtr->getLsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn1A,k)) + * conj(coupSUSYPtr->getLsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn1A)) ); + NGA[1][2] = facTU + * real( conj(coupSUSYPtr->getRsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen3,idIn1A,k)) + * conj(coupSUSYPtr->getLsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn1A)) ); + NGA[2][1] = facTU + * real( conj(coupSUSYPtr->getLsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn1A,k)) + * conj(coupSUSYPtr->getRsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn1A)) ); + NGA[2][2] = facMS + * real( conj(coupSUSYPtr->getRsqqX(iGen4,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen3,idIn1A,k)) + * conj(coupSUSYPtr->getRsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn1A)) ); + NGB[1][1] = facMS + * real( conj(coupSUSYPtr->getLsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen4,idIn1A,k)) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn2A)) + * conj(coupSUSYPtr->getLsqqG(iGen3,idIn1A)) ); + NGB[1][2] = facMS + * real( conj(coupSUSYPtr->getRsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getLsqqX(iGen4,idIn1A,k)) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn2A)) + * conj(coupSUSYPtr->getLsqqG(iGen3,idIn1A)) ); + NGB[2][1] = facMS + * real( conj(coupSUSYPtr->getLsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen4,idIn1A,k)) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn2A)) + * conj(coupSUSYPtr->getRsqqG(iGen3,idIn1A)) ); + NGB[2][2] = facMS + * real( conj(coupSUSYPtr->getRsqqX(iGen3,idIn2A,k)) + * conj(coupSUSYPtr->getRsqqX(iGen4,idIn1A,k)) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn2A)) + * conj(coupSUSYPtr->getRsqqG(iGen3,idIn1A)) ); + + // Add to sums + sumInterference += sigmaNeutGlu * + ( real(NGA[1][1] + NGA[1][2] + NGA[2][1] + NGA[2][2]) / tNeut[k] / uGlu + + real(NGB[1][1] + NGB[1][2] + NGB[2][1] + NGB[2][2]) / uNeut[k] / tGlu ); + } + + // t-channel + u-channel Gluinos + t/u interference + + // factor for LL and RR contributions + double facMS = sH * m2Glu; + + // Note: GT, GU defined as in [Boz07] with sigmaGlu factored out + // [1][1] = LL, [1][2] = LR, [2][1] = RL, [2][2] = RR + complex GT[3][3], GU[3][3], GTU[3][3]; + GT[1][1] = facMS + * norm(coupSUSYPtr->getLsqqG(iGen4,idIn2A) + * coupSUSYPtr->getLsqqG(iGen3,idIn1A)); + GT[1][2] = facTU + * norm(coupSUSYPtr->getRsqqG(iGen4,idIn2A) + * coupSUSYPtr->getLsqqG(iGen3,idIn1A)); + GT[2][1] = facTU + * norm(coupSUSYPtr->getLsqqG(iGen4,idIn2A) + * coupSUSYPtr->getRsqqG(iGen3,idIn1A)); + GT[2][2] = facMS + * norm(coupSUSYPtr->getRsqqG(iGen4,idIn2A) + * coupSUSYPtr->getRsqqG(iGen3,idIn1A)); + GU[1][1] = facMS + * norm(coupSUSYPtr->getLsqqG(iGen3,idIn2A) + * coupSUSYPtr->getLsqqG(iGen4,idIn1A)); + GU[1][2] = facTU + * norm(coupSUSYPtr->getLsqqG(iGen3,idIn2A) + * coupSUSYPtr->getRsqqG(iGen4,idIn1A)); + GU[2][1] = facTU + * norm(coupSUSYPtr->getRsqqG(iGen3,idIn2A) + * coupSUSYPtr->getLsqqG(iGen4,idIn1A)); + GU[2][2] = facMS + * norm(coupSUSYPtr->getRsqqG(iGen3,idIn2A) + * coupSUSYPtr->getRsqqG(iGen4,idIn1A)); + GTU[1][1] = facMS + * real(coupSUSYPtr->getLsqqG(iGen3,idIn1A) + * coupSUSYPtr->getLsqqG(iGen4,idIn2A) + * conj(coupSUSYPtr->getLsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn1A)) ); + GTU[1][2] = facTU + * real(coupSUSYPtr->getLsqqG(iGen3,idIn1A) + * coupSUSYPtr->getRsqqG(iGen4,idIn2A) + * conj(coupSUSYPtr->getLsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn1A)) ); + GTU[2][1] = facTU + * real(coupSUSYPtr->getRsqqG(iGen3,idIn1A) + * coupSUSYPtr->getLsqqG(iGen4,idIn2A) + * conj(coupSUSYPtr->getRsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn1A)) ); + GTU[2][2] = facMS + * real(coupSUSYPtr->getRsqqG(iGen3,idIn1A) + * coupSUSYPtr->getRsqqG(iGen4,idIn2A) + * conj(coupSUSYPtr->getRsqqG(iGen3,idIn2A)) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn1A)) ); + + // Add to sums + sumGt += sigmaGlu * real(GT[1][1] + GT[1][2] + GT[2][1] + GT[2][2]) + / pow2(tGlu) ; + sumGu += sigmaGlu * real(GU[1][1] + GU[1][2] + GU[2][1] + GU[2][2]) + / pow2(uGlu) ; + sumInterference += - 2.0 / 3.0 * sigmaGlu + * real(GTU[1][1] + GTU[1][2] + GTU[2][1] + GTU[2][2]) + / tGlu / uGlu; + + } + + // Cross section + double sigma = sumNt + sumNu + sumCt + sumCu + sumGt + sumGu + + sumInterference; + + // Identical particles? + if (id3Sav == id4Sav) sigma /= 2.0; + + // Return answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qq2squarksquark::setIdColAcol() { + + // Set flavours. + if (id1 > 0 && id2 > 0) { + setId( id1, id2, id3Sav, id4Sav); + } else { + // 1,2 -> -3,-4 + setId( id1, id2,-id3Sav,-id4Sav); + } + + // Coded sigma is for ud -> ~q~q'. Swap t and u for du -> ~q~q'. + swapTU = (isUD and abs(id1) % 2 == 0); + + // Select colour flow topology + // A: t-channel neutralino, t-channel chargino, or u-channel gluino + double fracA = sumNt + sumCt + sumGu + / (sumNt + sumNu + sumCt + sumCu + sumGt + sumGu); + if (swapTU) fracA = 1.0 - fracA; + setColAcol( 1, 0, 2, 0, 1, 0, 2, 0); + // B: t-channel gluino or u-channel neutralino + if (rndmPtr->flat() > fracA) setColAcol( 1, 0, 2, 0, 2, 0, 1, 0); + + // Switch to anti-colors if antiquarks + if (id1 < 0 || id2 < 0) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2squarkantisquark +// Cross section for qqbar-initiated squark-antisquark production + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2squarkantisquark::initProc() { + + // Extract isospin and mass-ordering indices + iGen3 = 3*(abs(id3Sav)/2000000) + (abs(id3Sav)%10+1)/2; + iGen4 = 3*(abs(id4Sav)/2000000) + (abs(id4Sav)%10+1)/2; + + // Is this a ~u_i ~d*_j, ~d_i ~u*_j final state or ~d_i ~d*_j, ~u_i ~u*_j + if (abs(id3Sav) % 2 == abs(id4Sav) % 2) isUD = false; + else isUD = true; + + // Derive name + nameSave = "q qbar' -> "+particleDataPtr->name(abs(id3Sav))+" "+ + particleDataPtr->name(-abs(id4Sav)); + if (isUD && abs(id3Sav) != abs(id4Sav)) nameSave +=" + c.c."; + + // Count 5 neutralinos in NMSSM + nNeut = (coupSUSYPtr->isNMSSM ? 5 : 4); + + // Store mass squares of all possible internal propagator lines + m2Glu = pow2(particleDataPtr->m0(1000021)); + m2Neut.resize(nNeut+1); + for (int iNeut=1;iNeut<=nNeut;iNeut++) + m2Neut[iNeut] = pow2(particleDataPtr->m0(coupSUSYPtr->idNeut(iNeut))); + + // Set sizes of some arrays to be used below + tNeut.resize(nNeut+1); + uNeut.resize(nNeut+1); + + // Shorthand for Weak mixing + xW = coupSUSYPtr->sin2W; + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(id3Sav, id4Sav); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qqbar2squarkantisquark::sigmaKin() { + + // Z/W propagator + if (! isUD) { + double sV= sH - pow2(coupSUSYPtr->mZpole); + double d = pow2(sV) + pow2(coupSUSYPtr->mZpole * coupSUSYPtr->wZpole); + propZW = complex( sV / d, coupSUSYPtr->mZpole * coupSUSYPtr->wZpole / d); + } else { + double sV= sH - pow2(coupSUSYPtr->mWpole); + double d = pow2(sV) + pow2(coupSUSYPtr->mWpole * coupSUSYPtr->wWpole); + propZW = complex( sV / d, coupSUSYPtr->mWpole * coupSUSYPtr->wWpole / d); + } + + // Flavor-independent pre-factors + double comFac = M_PI/sH2 * openFracPair; + sigmaEW = comFac * pow2(alpEM); + sigmaGlu = comFac * 2.0 * pow2(alpS) / 9.0; + sigmaEWG = comFac * 8.0 * alpEM * alpS / 9.0; + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2squarkantisquark::sigmaHat() { + + // In-pair must be opposite-sign + if (id1 * id2 > 0) return 0.0; + + // Check correct charge sum + if (isUD && abs(id1) %2 == abs(id2) % 2) return 0.0; + if (!isUD && abs(id1) % 2 != abs(id2) % 2) return 0.0; + + // Coded UD sigma is for udbar -> ~u~d'*. Swap t<->u for dbaru -> ~u~d'*. + swapTU = (isUD and abs(id1) % 2 != 0); + + // Coded QQ sigma is for qqbar -> ~q~q*. Swap t<->u for qbarq -> ~q~q*. + if (!isUD && id1 < 0) swapTU = true; + + // Generation indices of incoming particles + int idIn1A = (swapTU) ? abs(id2) : abs(id1); + int idIn2A = (swapTU) ? abs(id1) : abs(id2); + int iGen1 = (idIn1A+1)/2; + int iGen2 = (idIn2A+1)/2; + + // Auxiliary factors for use below + tGlu = tH - m2Glu; + uGlu = uH - m2Glu; + for (int i=1; i<= nNeut; i++) { + tNeut[i] = tH - m2Neut[i]; + uNeut[i] = uH - m2Neut[i]; + } + + // Initial values for pieces used for color-flow selection below + sumColS = 0.0; + sumColT = 0.0; + sumInterference = 0.0; + + // Common factor for LR and RL contributions + double facTU = uH*tH-s3*s4; + + // Case A) Opposite-isospin: udbar -> ~u~d* + if ( isUD ) { + + // s-channel W contribution (only contributes to LL helicities) + sumColS += sigmaEW / 16.0 / pow2(xW) / pow2(1.0-xW) + * norm(conj(coupSUSYPtr->LudW[iGen1][iGen2]) + * coupSUSYPtr->LsusdW[iGen3][iGen4]) * facTU + * norm(propZW); + + // t-channel gluino contributions + double GT[3][3]; + double facLR = m2Glu * sH; + // LL, LR, RL, RR + GT[1][1] = facTU * norm(conj(coupSUSYPtr->LsddG[iGen4][iGen2]) + *coupSUSYPtr->LsuuG[iGen3][iGen1]); + GT[1][2] = facLR * norm(conj(coupSUSYPtr->RsddG[iGen4][iGen2]) + *coupSUSYPtr->LsuuG[iGen3][iGen1]); + GT[2][1] = facLR * norm(conj(coupSUSYPtr->LsddG[iGen4][iGen2]) + *coupSUSYPtr->RsuuG[iGen3][iGen1]); + GT[2][2] = facTU * norm(conj(coupSUSYPtr->RsddG[iGen4][iGen2]) + *coupSUSYPtr->RsuuG[iGen3][iGen1]); + // leading color flow for t-channel gluino is annihilation-like + sumColS += sigmaGlu / pow2(tGlu) + * (GT[1][1] + GT[1][2] + GT[2][1] + GT[2][2]); + + // W-Gluino interference (only contributes to LL helicities) + sumColS += sigmaEWG / 4.0 / xW / (1-xW) + * real(conj(coupSUSYPtr->LsuuG[iGen3][iGen1]) + * coupSUSYPtr->LsddG[iGen4][iGen2] + * conj(coupSUSYPtr->LudW[iGen1][iGen2]) + * coupSUSYPtr->LsusdW[iGen3][iGen4]) * facTU + / tGlu * sqrt(norm(propZW)); + + // t-channel neutralinos + // NOT YET IMPLEMENTED ! + } + + // Case B) Same-isospin: qqbar -> ~d~d* , ~u~u* + else { + + double eQ = (idIn1A % 2 == 0) ? 2./3. : 1./3. ; + double eSq = (abs(id3Sav) % 2 == 0) ? 2./3. : 1./3. ; + + // s-channel gluon (strictly flavor-diagonal) + if (abs(id3Sav) == abs(id4Sav) && abs(id1) == abs(id2)) { + // Factor 2 since contributes to both ha != hb helicities + sumColT += 2. * sigmaGlu * facTU / pow2(sH); + } + + // Skip the rest if only including gluons + if (settingsPtr->flag("SUSY:qqbar2squarkantisquark:gluonOnly")) + return sumColT; + + // t-channel gluino (only for in-isospin = out-isospin). + if (eQ == eSq) { + // Sum over helicities. + double GT[3][3]; + double facLR = sH * m2Glu; + GT[1][1] = facTU * norm(coupSUSYPtr->getLsqqG(iGen3,idIn1A) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn2A))); + GT[1][2] = facLR * norm(coupSUSYPtr->getLsqqG(iGen3,idIn1A) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn2A))); + GT[2][1] = facLR * norm(coupSUSYPtr->getRsqqG(iGen3,idIn1A) + * conj(coupSUSYPtr->getLsqqG(iGen4,idIn2A))); + GT[2][2] = facTU * norm(coupSUSYPtr->getRsqqG(iGen3,idIn1A) + * conj(coupSUSYPtr->getRsqqG(iGen4,idIn2A))); + // Add contribution to color topology: S + sumColS += sigmaGlu / pow2(tGlu) + * ( GT[1][1] + GT[1][2] + GT[2][1] + GT[2][2]); + + // gluon-gluino interference (strictly flavor-diagonal) + if (abs(id3Sav) == abs(id4Sav) && abs(id1) == abs(id2)) { + double GG11, GG22; + GG11 = - facTU * 2./3. * real( conj(coupSUSYPtr->getLsqqG(iGen3,idIn1A)) + * coupSUSYPtr->getLsqqG(iGen4,idIn2A)); + GG22 = - facTU * 2./3. * real( conj(coupSUSYPtr->getLsqqG(iGen3,idIn1A)) + * coupSUSYPtr->getLsqqG(iGen4,idIn2A)); + // Sum over two contributing helicities + sumInterference += sigmaGlu / sH / tGlu + * ( GG11 + GG22 ); + } + + } + + // s-channel photon (strictly flavor-diagonal) and Z/gamma interference + if (abs(id3Sav) == abs(id4Sav) && abs(id1) == abs(id2)) { + + // gamma + // Factor 2 since contributes to both ha != hb helicities + sumColS += 2. * pow2(eQ) * pow2(eSq) * sigmaEW * facTU / pow2(sH); + + // Z/gamma interference + double CsqZ = real(coupSUSYPtr->LsusuZ[iGen3][iGen4] + + coupSUSYPtr->RsusuZ[iGen3][iGen4]); + if (abs(id3Sav)%2 != 0) CsqZ = real(coupSUSYPtr->LsdsdZ[iGen3][iGen4] + + coupSUSYPtr->RsdsdZ[iGen3][iGen4]); + sumColS += eQ * eSq * sigmaEW * facTU / 2.0 / xW / (1.-xW) + * sqrt(norm(propZW)) / sH * CsqZ + * (coupSUSYPtr->LqqZ[idIn1A] + coupSUSYPtr->LqqZ[idIn2A]); + + // Gluino/gamma interference (only for same-isospin) + if (eQ == eSq) { + double CsqG11 = real(conj(coupSUSYPtr->LsuuG[iGen3][iGen1]) + *coupSUSYPtr->LsuuG[iGen4][iGen2]); + double CsqG22 = real(conj(coupSUSYPtr->RsuuG[iGen3][iGen1]) + *coupSUSYPtr->RsuuG[iGen4][iGen2]); + if (id3Sav%2 != 0) { + CsqG11 = real(conj(coupSUSYPtr->LsddG[iGen3][iGen1]) + *coupSUSYPtr->LsddG[iGen4][iGen2]); + CsqG22 = real(conj(coupSUSYPtr->RsddG[iGen3][iGen1]) + *coupSUSYPtr->RsddG[iGen4][iGen2]); + } + sumColS += eQ * eSq * sigmaEWG * facTU + * (CsqG11 + CsqG22) / sH / tGlu; + } + } + + // s-channel Z (only for q flavor = qbar flavor) + if (abs(id1) == abs(id2)) { + double CsqZ = norm(coupSUSYPtr->LsusuZ[iGen3][iGen4] + + coupSUSYPtr->RsusuZ[iGen3][iGen4]); + if (abs(id3Sav)%2 != 0) CsqZ = norm(coupSUSYPtr->LsdsdZ[iGen3][iGen4] + + coupSUSYPtr->RsdsdZ[iGen3][iGen4]); + sumColS += sigmaEW * facTU / 16.0 / pow2(xW) / pow2(1.0-xW) + * norm(propZW) * CsqZ + * ( pow2(coupSUSYPtr->LqqZ[idIn1A]) + pow2(coupSUSYPtr->RqqZ[idIn1A]) ); + + // Z/gluino interference (only for in-isospin = out-isospin) + if (eQ == eSq) { + double GZ11 = real(conj(coupSUSYPtr->getLsqqG(iGen3,idIn1A)) + *coupSUSYPtr->getLsqqG(iGen4,idIn2A) + *(coupSUSYPtr->getLsqsqZ(id3Sav,id4Sav) + +coupSUSYPtr->getRsqsqZ(id3Sav,id4Sav))) + *coupSUSYPtr->LqqZ[idIn1A]; + double GZ22 = real(conj(coupSUSYPtr->getRsqqG(iGen3,idIn1A)) + *coupSUSYPtr->getRsqqG(iGen4,idIn2A) + *(coupSUSYPtr->getLsqsqZ(id3Sav,id4Sav) + +coupSUSYPtr->getRsqsqZ(id3Sav,id4Sav))) + *coupSUSYPtr->RqqZ[idIn1A]; + sumColS += sigmaEWG * facTU / 4.0 / xW / (1.-xW) + * ( GZ11 + GZ22 ) * sqrt(norm(propZW)) / tGlu; + } + } + + // t-channel neutralinos + // NOT YET IMPLEMENTED ! + + } + + // Cross section + double sigma = sumColS + sumColT + sumInterference; + + // Return answer. + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2squarkantisquark::setIdColAcol() { + + // Check if charge conjugate final state? + isCC = false; + if (isUD && ( (id1-1)%2 < 0 || (id2-1)%2 < 0 )) isCC = true; + + //check if charge conjugate + id3 = (isCC) ? -id3Sav : id3Sav; + id4 = (isCC) ? -id4Sav : id4Sav; + + // Set flavours. + setId( id1, id2, id3, id4); + + // Coded UD sigma is for udbar -> ~u~d'*. Swap t<->u for dbaru -> ~u~d'*. + // Coded QQ sigma is for qqbar -> ~q~q*. Swap t<->u for qbarq -> ~q~q*. + if (isUD) { + swapTU = (abs(id1) % 2 != 0); + } else { + swapTU = (id1 < 0); + } + + // Select colour flow topology + double R = rndmPtr->flat(); + double fracS = sumColS / (sumColS + sumColT) ; + // S: color flow as in S-channel singlet + if (R < fracS) { + setColAcol( 1, 0, 0, 1, 2, 0, 0, 2); + if (swapTU) setColAcol( 0, 1, 1, 0, 2, 0, 0, 2); + } + // T: color flow as in T-channel singlet + else { + setColAcol( 1, 0, 0, 2, 1, 0, 0, 2); + if (swapTU) setColAcol( 0, 1, 2, 0, 2, 0, 0, 1); + } + + if (isCC) swapColAcol(); + +} + +//========================================================================== + +// Sigma2gg2squarkantisquark +// Cross section for gg-initiated squark-antisquark production + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2squarkantisquark::initProc() { + + // Process Name + nameSave = "g g -> "+particleDataPtr->name(abs(id3Sav))+" " + +particleDataPtr->name(-abs(id4Sav)); + + // Squark pole mass + m2Sq = pow2(particleDataPtr->m0(id3Sav)); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(id3Sav, id4Sav); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2gg2squarkantisquark::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + // tHSq = tHat - m_squark^2; uHSq = uHat - m_squark^2. + // double s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + double tHSq = -0.5 * (sH - tH + uH); + double uHSq = -0.5 * (sH + tH - uH); + // ! (NEED TO CHECK THAT THESE APPLIED CORRECTLY BELOW) ! + // ! (PRELIMINARY CROSS-CHECKS WITH PYTHIA 6 COME OUT OK) ! + + // Helicity-independent prefactor + double comFac = M_PI/sH2 * pow2(alpS) / 128.0 + * ( 24.0 * (1.0 - 2*tHSq*uHSq/sH2) - 8.0/3.0 ); + + // Helicity-dependent factors + sigma = 0.0; + for (int ha=-1;ha<=1;ha += 2) { + for (int hb=-1;hb<=1;hb += 2) { + // Divide by 4 for helicity average + sigma += comFac / 4.0 + * ( (1.0-ha*hb) + - 2.0 * sH*m2Sq/tHSq/uHSq + * ( 1.0 - ha*hb - sH*m2Sq/tHSq/uHSq)); + } + } + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2squarkantisquark::setIdColAcol() { + + // Set flavours. + setId( id1, id2, id3Sav, id4Sav); + + // Set color flow (random for now) + double R = rndmPtr->flat(); + if (R < 0.5) setColAcol( 1, 2, 2, 3, 1, 0, 0, 3); + else setColAcol( 1, 2, 3, 1, 3, 0, 0, 2); + +} + +//========================================================================== + +// Sigma2qg2squarkgluino +// Cross section for squark-gluino production + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qg2squarkgluino::initProc() { + + // Derive name + nameSave = "q g -> "+particleDataPtr->name(abs(id3Sav))+" gluino + c.c."; + + // Final-state mass squares + m2Glu = pow2(particleDataPtr->m0(1000021)); + m2Sq = pow2(particleDataPtr->m0(id3Sav)); + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(id3Sav, 1000021); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat), part independent of incoming flavour. + +void Sigma2qg2squarkgluino::sigmaKin() { + + // Common pre-factor + comFac = (M_PI / sH2) * pow2(alpS) * 0.5 * openFracPair; + + // Invariants (still with Pythia 6 sign convention) + double tGlu = m2Glu-tH; + double uGlu = m2Glu-uH; + double tSq = m2Sq-tH; + double uSq = m2Sq-uH; + + // Color flow A: quark color annihilates with anticolor of g + sigmaA = 0.5*4./9.* tGlu/sH + (tGlu*sH+2.*m2Glu*tSq)/pow2(tGlu) - + ( (sH-m2Sq+m2Glu)*(-tSq)-sH*m2Glu )/sH/(-tGlu) + + 0.5*1./2.*( tSq*(tH+2.*uH+m2Glu)-tGlu*(sH-2.*tSq) + + (-uGlu)*(tH+m2Glu+2.*m2Sq) )/2./tGlu/uSq; + // Color flow B: quark and gluon colors iterchanged + sigmaB = 4./9.*(-uGlu)*(uH+m2Sq)/pow2(uSq) + + 1./18.* (sH*(uH+m2Glu) + 2.*(m2Sq-m2Glu)*uGlu)/sH/(-uSq) + + 0.5*4./9.*tGlu/sH + + 0.5*1./2.*(tSq*(tH+2.*uH+m2Glu)-tGlu*(sH-2.*tSq) + + (-uGlu)*(tH+m2Glu+2.*m2Sq))/2./tGlu/uSq; + +} + +double Sigma2qg2squarkgluino::sigmaHat() { + + // Check whether right incoming flavor + int idQA = (id1 == 21) ? abs(id2) : abs(id1); + int idSqSM = id3Sav%1000000; + if (idQA != idSqSM) return 0.0; + // NOTE: ONLY WORKS FOR SLHA1 ENUMERATION !!! + // (should replace this by squark mixing matrix squares) + + return comFac * (sigmaA + sigmaB); + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qg2squarkgluino::setIdColAcol() { + + // Check if charge conjugate final state? + int idQ = (id1 == 21) ? id2 : id1; + id3 = (idQ > 0) ? id3Sav : -id3Sav; + id4 = 1000021; + + // Set flavors + setId( id1, id2, id3, id4); + + // Select color flow A or B (see above) + double R = rndmPtr->flat()*(sigmaA+sigmaB); + if (idQ == id1) { + setColAcol(1,0,2,1,3,0,2,3); + if (R > sigmaA) setColAcol(1,0,2,3,2,0,1,3); + } else { + setColAcol(2,1,1,0,3,0,2,3); + if (R > sigmaB) setColAcol(2,3,1,0,2,0,1,3); + } + if (idQ < 0) swapColAcol(); + + // Use reflected kinematics if gq initial state + if (id1 == 21) swapTU = true; + +} + +//========================================================================== + +// Sigma2gg2gluinogluino +// Cross section for gluino pair production from gg initial states +// (validated against Pythia 6) + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2gg2gluinogluino::initProc() { + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(1000021, 1000021); + +} + +//-------------------------------------------------------------------------- + +// Evaluate d(sigmaHat)/d(tHat) - no incoming flavour dependence. + +void Sigma2gg2gluinogluino::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + // tHG = tHat - m_gluino^2; uHG = uHat - m_gluino^2. + double s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + double tHG = -0.5 * (sH - tH + uH); + double uHG = -0.5 * (sH + tH - uH); + double tHG2 = tHG * tHG; + double uHG2 = uHG * uHG; + + // Calculate kinematics dependence. + sigTS = (tHG * uHG - 2. * s34Avg * (tHG + 2. * s34Avg)) / tHG2 + + (tHG * uHG + s34Avg * (uHG - tHG)) / (sH * tHG); + sigUS = (tHG * uHG - 2. * s34Avg * (uHG + 2. * s34Avg)) / uHG2 + + (tHG * uHG + s34Avg * (tHG - uHG)) / (sH * uHG); + sigTU = 2. * tHG * uHG / sH2 + s34Avg * (sH - 4. * s34Avg) + / (tHG * uHG); + sigSum = sigTS + sigUS + sigTU; + + // Answer contains factor 1/2 from identical gluinos. + sigma = (M_PI / sH2) * pow2(alpS) * (9./4.) * 0.5 * sigSum + * openFracPair; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2gg2gluinogluino::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, 1000021, 1000021); + + // Three colour flow topologies, each with two orientations. + double sigRand = sigSum * rndmPtr->flat(); + if (sigRand < sigTS) setColAcol( 1, 2, 2, 3, 1, 4, 4, 3); + else if (sigRand < sigTS + sigUS) + setColAcol( 1, 2, 3, 1, 3, 4, 4, 2); + else setColAcol( 1, 2, 3, 4, 1, 4, 3, 2); + if (rndmPtr->flat() > 0.5) swapColAcol(); + +} + +//========================================================================== + +// Sigma2qqbar2gluinogluino +// Cross section for gluino pair production from qqbar initial states +// (validated against Pythia 6) + +//-------------------------------------------------------------------------- + +// Initialize process. + +void Sigma2qqbar2gluinogluino::initProc() { + + // Secondary open width fraction. + openFracPair = particleDataPtr->resOpenFrac(1000021, 1000021); + +} + +//-------------------------------------------------------------------------- + +// Begin evaluate d(sigmaHat)/d(tHat); flavour-independent part. + +void Sigma2qqbar2gluinogluino::sigmaKin() { + + // Modified Mandelstam variables for massive kinematics with m3 = m4. + // tHG = tHat - m_gluino^2; uHG = uHat - m_gluino^2. + s34Avg = 0.5 * (s3 + s4) - 0.25 * pow2(s3 - s4) / sH; + tHG = -0.5 * (sH - tH + uH); + uHG = -0.5 * (sH + tH - uH); + tHG2 = tHG * tHG; + uHG2 = uHG * uHG; + + // s-channel contribution. + sigS = (tHG2 + uHG2 + 2. * s34Avg * sH) / sH2; + +} + +//-------------------------------------------------------------------------- + + +// Evaluate d(sigmaHat)/d(tHat), including incoming flavour dependence. + +double Sigma2qqbar2gluinogluino::sigmaHat() { + + // Squarks (L/R or 1/2) can contribute in t or u channel. + // Assume identical CKM matrices in quark and squark sector. + double sQL = pow2( particleDataPtr->m0(1000000 + abs(id1)) ); + double tHQL = tHG + s34Avg - sQL; + double uHQL = uHG + s34Avg - sQL; + double sQR = pow2( particleDataPtr->m0(2000000 + abs(id1)) ); + double tHQR = tHG + s34Avg - sQR; + double uHQR = uHG + s34Avg - sQR; + + // Calculate kinematics dependence. + double sigQL = (4./9.) * (tHG2 / pow2(tHQL) + uHG2 / pow2(uHQL)) + + (1./9.) * s34Avg * sH / (tHQL * uHQL) + + (tHG2 + sH * s34Avg) /(sH * tHQL) + + (uHG2 + sH * s34Avg) /(sH * uHQL); + double sigQR = (4./9.) * (tHG2 / pow2(tHQR) + uHG2 / pow2(uHQR)) + + (1./9.) * s34Avg * sH / (tHQR * uHQR) + + (tHG2 + sH * s34Avg) /(sH * tHQR) + + (uHG2 + sH * s34Avg) /(sH * uHQR); + double sigSum = sigS + 0.5 * (sigQL + sigQR); + + // Answer contains factor 1/2 from identical gluinos. + double sigma = (M_PI / sH2) * pow2(alpS) * (8./3.) * 0.5 * sigSum + * openFracPair; + return sigma; + +} + +//-------------------------------------------------------------------------- + +// Select identity, colour and anticolour. + +void Sigma2qqbar2gluinogluino::setIdColAcol() { + + // Flavours are trivial. + setId( id1, id2, 1000021, 1000021); + + // Two colour flow topologies. Swap if first is antiquark. + if (rndmPtr->flat() < 0.5) setColAcol( 1, 0, 0, 2, 1, 3, 3, 2); + else setColAcol( 1, 0, 0, 2, 3, 2, 1, 3); + if (id1 < 0) swapColAcol(); + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/SigmaTotal.cxx b/PYTHIA8/pythia8140/src/SigmaTotal.cxx new file mode 100644 index 00000000000..4d0ae19ea94 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SigmaTotal.cxx @@ -0,0 +1,332 @@ +// SigmaTotal.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the SigmaTotal class. + +#include "SigmaTotal.h" + +namespace Pythia8 { + +//========================================================================== + +// The SigmaTotal class. + +// Formulae are taken from: +// G.A. Schuler and T. Sjostrand, Phys. Rev. D49 (1994) 2257, +// Z. Phys. C73 (1997) 677 +// which borrows some total cross sections from +// A. Donnachie and P.V. Landshoff, Phys. Lett. B296 (1992) 227. + +// Implemented processes with their process number iProc: +// = 0 : p + p; = 1 : pbar + p; +// = 2 : pi+ + p; = 3 : pi- + p; = 4 : pi0/rho0 + p; +// = 5 : phi + p; = 6 : J/psi + p; +// = 7 : rho + rho; = 8 : rho + phi; = 9 : rho + J/psi; +// = 10 : phi + phi; = 11 : phi + J/psi; = 12 : J/psi + J/psi. +// = 13 : Pom + p (preliminary). + +//-------------------------------------------------------------------------- + +// Definitions of static variables. +// Note that a lot of parameters are hardcoded as const here, rather +// than being interfaced for public change, since any changes would +// have to be done in a globally consistent manner. Which basically +// means a rewrite/replacement of the whole class. + +// Minimum threshold below which no cross sections will be defined. +const double SigmaTotal::MMIN = 2.; + +// General constants in total cross section parametrization: +// sigmaTot = X * s^epsilon + Y * s^eta (pomeron + reggeon). +const double SigmaTotal::EPSILON = 0.0808; +const double SigmaTotal::ETA = -0.4525; +const double SigmaTotal::X[] = { 21.70, 21.70, 13.63, 13.63, 13.63, + 10.01, 0.970, 8.56, 6.29, 0.609, 4.62, 0.447, 0.0434}; +const double SigmaTotal::Y[] = { 56.08, 98.39, 27.56, 36.02, 31.79, + 1.51, -0.146, 13.08, -0.62, -0.060, 0.030, -0.0028, 0.00028}; + +// Type of the two incoming hadrons as function of the process number: +// = 0 : p/n ; = 1 : pi/rho/omega; = 2 : phi; = 3 : J/psi. +const int SigmaTotal::IHADATABLE[] = { 0, 0, 1, 1, 1, 2, 3, 1, 1, + 1, 2, 2, 3}; +const int SigmaTotal::IHADBTABLE[] = { 0, 0, 0, 0, 0, 0, 0, 1, 2, + 3, 2, 3, 3}; + +// Hadron-Pomeron coupling beta(t) = beta(0) * exp(b*t). +const double SigmaTotal::BETA0[] = { 4.658, 2.926, 2.149, 0.208}; +const double SigmaTotal::BHAD[] = { 2.3, 1.4, 1.4, 0.23}; + +// Pomeron trajectory alpha(t) = 1 + epsilon + alpha' * t +const double SigmaTotal::ALPHAPRIME = 0.25; + +// Conversion coefficients = 1/(16pi) * (mb <-> GeV^2) * (G_3P)^n, +// with n = 0 elastic, n = 1 single and n = 2 double diffractive. +const double SigmaTotal::CONVERTEL = 0.0510925; +const double SigmaTotal::CONVERTSD = 0.0336; +const double SigmaTotal::CONVERTDD = 0.0084; + +// Diffractive mass spectrum starts at m + MMIN0 and has a low-mass +// enhancement, factor cRes, up to around m + mRes0. +const double SigmaTotal::MMIN0 = 0.28; +const double SigmaTotal::CRES = 2.0; +const double SigmaTotal::MRES0 = 1.062; + +// Parameters and coefficients for single diffractive scattering. +const int SigmaTotal::ISDTABLE[] = { 0, 0, 1, 1, 1, 2, 3, 4, 5, + 6, 7, 8, 9}; +const double SigmaTotal::CSD[10][8] = { + { 0.213, 0.0, -0.47, 150., 0.213, 0.0, -0.47, 150., } , + { 0.213, 0.0, -0.47, 150., 0.267, 0.0, -0.47, 100., } , + { 0.213, 0.0, -0.47, 150., 0.232, 0.0, -0.47, 110., } , + { 0.213, 7.0, -0.55, 800., 0.115, 0.0, -0.47, 110., } , + { 0.267, 0.0, -0.46, 75., 0.267, 0.0, -0.46, 75., } , + { 0.232, 0.0, -0.46, 85., 0.267, 0.0, -0.48, 100., } , + { 0.115, 0.0, -0.50, 90., 0.267, 6.0, -0.56, 420., } , + { 0.232, 0.0, -0.48, 110., 0.232, 0.0, -0.48, 110., } , + { 0.115, 0.0, -0.52, 120., 0.232, 6.0, -0.56, 470., } , + { 0.115, 5.5, -0.58, 570., 0.115, 5.5, -0.58, 570. } }; + +// Parameters and coefficients for double diffractive scattering. +const int SigmaTotal::IDDTABLE[] = { 0, 0, 1, 1, 1, 2, 3, 4, 5, + 6, 7, 8, 9}; +const double SigmaTotal::CDD[10][9] = { + { 3.11, -7.34, 9.71, 0.068, -0.42, 1.31, -1.37, 35.0, 118., } , + { 3.11, -7.10, 10.6, 0.073, -0.41, 1.17, -1.41, 31.6, 95., } , + { 3.12, -7.43, 9.21, 0.067, -0.44, 1.41, -1.35, 36.5, 132., } , + { 3.13, -8.18, -4.20, 0.056, -0.71, 3.12, -1.12, 55.2, 1298., } , + { 3.11, -6.90, 11.4, 0.078, -0.40, 1.05, -1.40, 28.4, 78., } , + { 3.11, -7.13, 10.0, 0.071, -0.41, 1.23, -1.34, 33.1, 105., } , + { 3.12, -7.90, -1.49, 0.054, -0.64, 2.72, -1.13, 53.1, 995., } , + { 3.11, -7.39, 8.22, 0.065, -0.44, 1.45, -1.36, 38.1, 148., } , + { 3.18, -8.95, -3.37, 0.057, -0.76, 3.32, -1.12, 55.6, 1472., } , + { 4.18, -29.2, 56.2, 0.074, -1.36, 6.67, -1.14, 116.2, 6532. } }; +const double SigmaTotal::SPROTON = 0.880; + +//-------------------------------------------------------------------------- + +// Store pointer to Info and initialize data members. + +void SigmaTotal::init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn) { + + // Store pointers. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + + // User-set values for cross sections. + setTotal = settings.flag("SigmaTotal:setOwn"); + sigTotOwn = settings.parm("SigmaTotal:sigmaTot"); + sigElOwn = settings.parm("SigmaTotal:sigmaEl"); + sigXBOwn = settings.parm("SigmaTotal:sigmaXB"); + sigAXOwn = settings.parm("SigmaTotal:sigmaAX"); + sigXXOwn = settings.parm("SigmaTotal:sigmaXX"); + + // User-set values to dampen diffractive cross sections. + doDampen = settings.flag("SigmaDiffractive:dampen"); + maxXBOwn = settings.parm("SigmaDiffractive:maxXB"); + maxAXOwn = settings.parm("SigmaDiffractive:maxAX"); + maxXXOwn = settings.parm("SigmaDiffractive:maxXX"); + + // User-set values for handling of elastic sacattering. + setElastic = settings.flag("SigmaElastic:setOwn"); + bSlope = settings.parm("SigmaElastic:bSlope"); + rho = settings.parm("SigmaElastic:rho"); + lambda = settings.parm("SigmaElastic:lambda"); + tAbsMin = settings.parm("SigmaElastic:tAbsMin"); + alphaEM0 = settings.parm("StandardModel:alphaEM0"); + + // Parameter for diffractive systems. + sigmaPomP = settings.parm("Diffraction:sigmaPomP"); + +} + +//-------------------------------------------------------------------------- + +// Function that calculates the relevant properties. + +bool SigmaTotal::calc( int idA, int idB, double eCM) { + + // Derived quantities. + alP2 = 2. * ALPHAPRIME; + s0 = 1. / ALPHAPRIME; + + // Reset everything to zero to begin with. + isCalc = false; + sigTot = sigEl = sigXB = sigAX = sigXX = sigND = bEl = s = bA = bB = 0.; + + // Order flavour of incoming hadrons: idAbsA < idAbsB (restore later). + int idAbsA = abs(idA); + int idAbsB = abs(idB); + bool swapped = false; + if (idAbsA > idAbsB) { + swap( idAbsA, idAbsB); + swapped = true; + } + double sameSign = (idA * idB > 0); + + // Find process number. + int iProc = -1; + if (idAbsA > 1000) { + iProc = (sameSign) ? 0 : 1; + } else if (idAbsA > 100 && idAbsB > 1000) { + iProc = (sameSign) ? 2 : 3; + if (idAbsA/10 == 11 || idAbsA/10 == 22) iProc = 4; + if (idAbsA > 300) iProc = 5; + if (idAbsA > 400) iProc = 6; + if (idAbsA > 900) iProc = 13; + } else if (idAbsA > 100) { + iProc = 7; + if (idAbsB > 300) iProc = 8; + if (idAbsB > 400) iProc = 9; + if (idAbsA > 300) iProc = 10; + if (idAbsA > 300 && idAbsB > 400) iProc = 11; + if (idAbsA > 400) iProc = 12; + } + if (iProc == -1) return false; + + // Primitive implementation of Pomeron + p. + if (iProc == 13) { + s = eCM*eCM; + sigTot = sigmaPomP; + sigND = sigTot; + isCalc = true; + return true; + } + + // Find hadron masses and check that energy is enough. + // For mesons use the corresponding vector meson masses. + int idModA = (idAbsA > 1000) ? idAbsA : 10 * (idAbsA/10) + 3; + int idModB = (idAbsB > 1000) ? idAbsB : 10 * (idAbsB/10) + 3; + double mA = particleDataPtr->m0(idModA); + double mB = particleDataPtr->m0(idModB); + if (eCM < mA + mB + MMIN) { + infoPtr->errorMsg("Error in SigmaTotal::calc: too low energy"); + return false; + } + + // Evaluate the total cross section. + s = eCM*eCM; + double sEps = pow( s, EPSILON); + double sEta = pow( s, ETA); + sigTot = X[iProc] * sEps + Y[iProc] * sEta; + + // Slope of hadron form factors. + int iHadA = IHADATABLE[iProc]; + int iHadB = IHADBTABLE[iProc]; + bA = BHAD[iHadA]; + bB = BHAD[iHadB]; + + // Elastic slope parameter and cross section. + bEl = 2.*bA + 2.*bB + 4.*sEps - 4.2; + sigEl = CONVERTEL * pow2(sigTot) / bEl; + + // Lookup coefficients for single and double diffraction. + int iSD = ISDTABLE[iProc]; + int iDD = IDDTABLE[iProc]; + double sum1, sum2, sum3, sum4; + + // Single diffractive scattering A + B -> X + B cross section. + mMinXBsave = mA + MMIN0; + double sMinXB = pow2(mMinXBsave); + mResXBsave = mA + MRES0; + double sResXB = pow2(mResXBsave); + double sRMavgXB = mResXBsave * mMinXBsave; + double sRMlogXB = log(1. + sResXB/sMinXB); + double sMaxXB = CSD[iSD][0] * s + CSD[iSD][1]; + double BcorrXB = CSD[iSD][2] + CSD[iSD][3] / s; + sum1 = log( (2.*bB + alP2 * log(s/sMinXB)) + / (2.*bB + alP2 * log(s/sMaxXB)) ) / alP2; + sum2 = CRES * sRMlogXB / (2.*bB + alP2 * log(s/sRMavgXB) + BcorrXB) ; + sigXB = CONVERTSD * X[iProc] * BETA0[iHadB] * max( 0., sum1 + sum2); + + // Single diffractive scattering A + B -> A + X cross section. + mMinAXsave = mB + MMIN0; + double sMinAX = pow2(mMinAXsave); + mResAXsave = mB + MRES0; + double sResAX = pow2(mResAXsave); + double sRMavgAX = mResAXsave * mMinAXsave; + double sRMlogAX = log(1. + sResAX/sMinAX); + double sMaxAX = CSD[iSD][4] * s + CSD[iSD][5]; + double BcorrAX = CSD[iSD][6] + CSD[iSD][7] / s; + sum1 = log( (2.*bA + alP2 * log(s/sMinAX)) + / (2.*bA + alP2 * log(s/sMaxAX)) ) / alP2; + sum2 = CRES * sRMlogAX / (2.*bA + alP2 * log(s/sRMavgAX) + BcorrAX) ; + sigAX = CONVERTSD * X[iProc] * BETA0[iHadA] * max( 0., sum1 + sum2); + + // Order single diffractive correctly. + if (swapped) { + swap( bB, bA); + swap( sigXB, sigAX); + swap( mMinXBsave, mMinAXsave); + swap( mResXBsave, mResAXsave); + } + + // Double diffractive scattering A + B -> X1 + X2 cross section. + double y0min = log( s * SPROTON / (sMinXB * sMinAX) ) ; + double sLog = log(s); + double Delta0 = CDD[iDD][0] + CDD[iDD][1] / sLog + + CDD[iDD][2] / pow2(sLog); + sum1 = (y0min * (log( max( 1e-10, y0min/Delta0) ) - 1.) + Delta0)/ alP2; + if (y0min < 0.) sum1 = 0.; + double sMaxXX = s * ( CDD[iDD][3] + CDD[iDD][4] / sLog + + CDD[iDD][5] / pow2(sLog) ); + double sLogUp = log( max( 1.1, s * s0 / (sMinXB * sRMavgAX) )); + double sLogDn = log( max( 1.1, s * s0 / (sMaxXX * sRMavgAX) )); + sum2 = CRES * log( sLogUp / sLogDn ) * sRMlogAX / alP2; + sLogUp = log( max( 1.1, s * s0 / (sMinAX * sRMavgXB) )); + sLogDn = log( max( 1.1, s * s0 / (sMaxXX * sRMavgXB) )); + sum3 = CRES * log(sLogUp / sLogDn) * sRMlogXB / alP2; + double BcorrXX = CDD[iDD][6] + CDD[iDD][7] / eCM + CDD[iDD][8] / s; + sum4 = pow2(CRES) * sRMlogAX * sRMlogXB + / max( 0.1, alP2 * log( s * s0 / (sRMavgAX * sRMavgXB) ) + BcorrXX); + sigXX = CONVERTDD * X[iProc] * max( 0., sum1 + sum2 + sum3 + sum4); + + // Option with user-requested damping of diffractive cross sections. + if (doDampen) { + sigXB = sigXB * maxXBOwn / (sigXB + maxXBOwn); + sigAX = sigAX * maxAXOwn / (sigAX + maxAXOwn); + sigXX = sigXX * maxXXOwn / (sigXX + maxXXOwn); + } + + // Option with user-set values for total and partial cross sections. + // (Is not done earlier since want diffractive slopes anyway.) + double sigNDOwn = sigTotOwn - sigElOwn - sigXBOwn - sigAXOwn - sigXXOwn; + double sigElMax = sigEl; + if (setTotal && sigNDOwn > 0.) { + sigTot = sigTotOwn; + sigEl = sigElOwn; + sigXB = sigXBOwn; + sigAX = sigAXOwn; + sigXX = sigXXOwn; + sigElMax = sigEl; + + // Sub-option to set elastic parameters, including Coulomb contribution. + if (setElastic) { + bEl = bSlope; + sigEl = CONVERTEL * pow2(sigTot) * (1. + rho*rho) / bSlope; + sigElMax = 2. * (sigEl * exp(-bSlope * tAbsMin) + + alphaEM0 * alphaEM0 / (4. * CONVERTEL * tAbsMin) ); + } + } + + // Inelastic nondiffractive by unitarity. + sigND = sigTot - sigEl - sigXB - sigAX - sigXX; + if (sigND < 0.) infoPtr->errorMsg("Error in SigmaTotal::init: " + "sigND < 0"); + else if (sigND < 0.4 * sigTot) infoPtr->errorMsg("Warning in " + "SigmaTotal::init: sigND suspiciously low"); + + // Upper estimate of elastic, including Coulomb term, where appropriate. + sigEl = sigElMax; + + // Done. + isCalc = true; + return true; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SpaceShower.cxx b/PYTHIA8/pythia8140/src/SpaceShower.cxx new file mode 100644 index 00000000000..cab97f5dc5a --- /dev/null +++ b/PYTHIA8/pythia8140/src/SpaceShower.cxx @@ -0,0 +1,1787 @@ +// SpaceShower.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// SpaceShower class. + +#include "SpaceShower.h" + +namespace Pythia8 { + +//========================================================================== + +// The SpaceShower class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Turn to true to allow debug printout. +const bool SpaceShower::DEBUG = false; + +// Leftover companion can give PDF > 0 at small Q2 where other PDF's = 0, +// and then one can end in infinite loop of impossible kinematics. +const int SpaceShower::MAXLOOPTINYPDF = 10; + +// Switch to alternative (but equivalent) backwards evolution for +// g -> Q Qbar (Q = c or b) when below QTHRESHOLD * mQ2. +const double SpaceShower::CTHRESHOLD = 2.0; +const double SpaceShower::BTHRESHOLD = 2.0; + +// Renew evaluation of PDF's when the pT2 step is bigger than this +// (in addition to initial scale and c and b thresholds.) +const double SpaceShower::EVALPDFSTEP = 0.1; + +// Lower limit on PDF value in order to avoid division by zero. +const double SpaceShower::TINYPDF = 1e-10; + +// Lower limit on estimated evolution rate, below which stop. +const double SpaceShower::TINYKERNELPDF = 1e-6; + +// Lower limit on pT2, below which branching is rejected. +const double SpaceShower::TINYPT2 = 0.25e-6; + +// No attempt to do backwards evolution of a heavy (c or b) quark +// if evolution starts at a scale pT2 < HEAVYPT2EVOL * mQ2. +const double SpaceShower::HEAVYPT2EVOL = 1.1; + +// No attempt to do backwards evolution of a heavy (c or b) quark +// if evolution starts at a x > HEAVYXEVOL * x_max, where +// x_max is the largest possible x value for a g -> Q Qbar branching. +const double SpaceShower::HEAVYXEVOL = 0.9; + +// When backwards evolution Q -> g + Q creates a heavy quark Q, +// an earlier branching g -> Q + Qbar will restrict kinematics +// to M_{Q Qbar}^2 > EXTRASPACEQ * 4 m_Q^2. (Smarter to be found??) +const double SpaceShower::EXTRASPACEQ = 2.0; + +// Never pick pT so low that alphaS is evaluated too close to Lambda_3. +const double SpaceShower::LAMBDA3MARGIN = 1.1; + +// Cutoff for f_e^e at x < 1 - 10^{-10} to be used in z selection. +// Note: the x_min quantity come from 1 - x_max. +const double SpaceShower::LEPTONXMIN = 1e-10; +const double SpaceShower::LEPTONXMAX = 1. - 1e-10; + +// Stop l -> l gamma evolution slightly above m2l. +const double SpaceShower::LEPTONPT2MIN = 1.2; + +// Enhancement of l -> l gamma trial rate to compensate imperfect modelling. +const double SpaceShower::LEPTONFUDGE = 10.; + +//-------------------------------------------------------------------------- + +// Initialize alphaStrong, alphaEM and related pTmin parameters. + +void SpaceShower::init( BeamParticle* beamAPtrIn, + BeamParticle* beamBPtrIn) { + + // Store input pointers for future use. + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + + // Main flags to switch on and off branchings. + doQCDshower = settingsPtr->flag("SpaceShower:QCDshower"); + doQEDshowerByQ = settingsPtr->flag("SpaceShower:QEDshowerByQ"); + doQEDshowerByL = settingsPtr->flag("SpaceShower:QEDshowerByL"); + + // Matching in pT of hard interaction to shower evolution. + pTmaxMatch = settingsPtr->mode("SpaceShower:pTmaxMatch"); + pTdampMatch = settingsPtr->mode("SpaceShower:pTdampMatch"); + pTmaxFudge = settingsPtr->parm("SpaceShower:pTmaxFudge"); + pTmaxFudgeMI = settingsPtr->parm("SpaceShower:pTmaxFudgeMI"); + pTdampFudge = settingsPtr->parm("SpaceShower:pTdampFudge"); + + // Optionally force emissions to be ordered in rapidity/angle. + doRapidityOrder = settingsPtr->flag("SpaceShower:rapidityOrder"); + + // Charm, bottom and lepton mass thresholds. + mc = particleDataPtr->m0(4); + mb = particleDataPtr->m0(5); + m2c = pow2(mc); + m2b = pow2(mb); + + // Parameters of alphaStrong generation. + alphaSvalue = settingsPtr->parm("SpaceShower:alphaSvalue"); + alphaSorder = settingsPtr->mode("SpaceShower:alphaSorder"); + alphaS2pi = 0.5 * alphaSvalue / M_PI; + + // Initialize alpha_strong generation. + alphaS.init( alphaSvalue, alphaSorder); + + // Lambda for 5, 4 and 3 flavours. + Lambda5flav = alphaS.Lambda5(); + Lambda4flav = alphaS.Lambda4(); + Lambda3flav = alphaS.Lambda3(); + Lambda5flav2 = pow2(Lambda5flav); + Lambda4flav2 = pow2(Lambda4flav); + Lambda3flav2 = pow2(Lambda3flav); + + // Regularization of QCD evolution for pT -> 0. Can be taken + // same as for multiple interactions, or be set separately. + useSamePTasMI = settingsPtr->flag("SpaceShower:samePTasMI"); + if (useSamePTasMI) { + pT0Ref = settingsPtr->parm("MultipleInteractions:pT0Ref"); + ecmRef = settingsPtr->parm("MultipleInteractions:ecmRef"); + ecmPow = settingsPtr->parm("MultipleInteractions:ecmPow"); + pTmin = settingsPtr->parm("MultipleInteractions:pTmin"); + } else { + pT0Ref = settingsPtr->parm("SpaceShower:pT0Ref"); + ecmRef = settingsPtr->parm("SpaceShower:ecmRef"); + ecmPow = settingsPtr->parm("SpaceShower:ecmPow"); + pTmin = settingsPtr->parm("SpaceShower:pTmin"); + } + + // Calculate nominal invariant mass of events. Set current pT0 scale. + sCM = m2( beamAPtr->p(), beamBPtr->p()); + eCM = sqrt(sCM); + pT0 = pT0Ref * pow(eCM / ecmRef, ecmPow); + + // Restrict pTmin to ensure that alpha_s(pTmin^2 + pT_0^2) does not blow up. + double pTminAbs = sqrtpos(pow2(LAMBDA3MARGIN) * Lambda3flav2 - pT0*pT0); + if (pTmin < pTminAbs) { + pTmin = pTminAbs; + ostringstream newPTmin; + newPTmin << fixed << setprecision(3) << pTmin; + infoPtr->errorMsg("Warning in SpaceShower::init: pTmin too low", + ", raised to " + newPTmin.str() ); + infoPtr->setTooLowPTmin(true); + } + + // Parameters of alphaEM generation. + alphaEMorder = settingsPtr->mode("SpaceShower:alphaEMorder"); + + // Initialize alphaEM generation. + alphaEM.init( alphaEMorder, settingsPtr); + + // Parameters of QED evolution. + pTminChgQ = settingsPtr->parm("SpaceShower:pTminchgQ"); + pTminChgL = settingsPtr->parm("SpaceShower:pTminchgL"); + + // Derived parameters of QCD evolution. + pT20 = pow2(pT0); + pT2min = pow2(pTmin); + pT2minChgQ = pow2(pTminChgQ); + pT2minChgL = pow2(pTminChgL); + + // Various other parameters. + doMEcorrections = settingsPtr->flag("SpaceShower:MEcorrections"); + doPhiPolAsym = settingsPtr->flag("SpaceShower:phiPolAsym"); + doPhiIntAsym = settingsPtr->flag("SpaceShower:phiIntAsym"); + strengthIntAsym = settingsPtr->parm("SpaceShower:strengthIntAsym"); + nQuarkIn = settingsPtr->mode("SpaceShower:nQuarkIn"); + + // Optional dampening at small pT's when large multiplicities. + enhanceScreening = settingsPtr->mode("MultipleInteractions:enhanceScreening"); + if (!useSamePTasMI) enhanceScreening = 0; + + // Possibility to allow user veto of emission step. + canVetoEmission = (userHooksPtr > 0) ? userHooksPtr->canVetoISREmission() + : false; + +} + +//-------------------------------------------------------------------------- + +// Find whether to limit maximum scale of emissions. +// Also allow for dampening at factorization or renormalization scale. + +bool SpaceShower::limitPTmax( Event& event, double Q2Fac, double Q2Ren) { + + // Find whether to limit pT. Begin by user-set cases. + bool dopTlimit = false; + if (pTmaxMatch == 1) dopTlimit = true; + else if (pTmaxMatch == 2) dopTlimit = false; + + // Look if any quark (u, d, s, c, b), gluon or photon in final state. + else { + for (int i = 5; i < event.size(); ++i) + if (event[i].status() != -21) { + int idAbs = event[i].idAbs(); + if (idAbs <= 5 || idAbs == 21 || idAbs == 22) dopTlimit = true; + } + } + + // Dampening at factorization or renormalization scale. + dopTdamp = false; + pT2damp = 0.; + if ( !dopTlimit && (pTdampMatch == 1 || pTdampMatch == 2) ) { + dopTdamp = true; + pT2damp = pow2(pTdampFudge) * ((pTdampMatch == 1) ? Q2Fac : Q2Ren); + } + + // Done. + return dopTlimit; + +} + +//-------------------------------------------------------------------------- + +// Prepare system for evolution; identify ME. +// Routine may be called after multiple interactions, for a new subystem. + +void SpaceShower::prepare( int iSys, Event& event, bool limitPTmaxIn) { + + // Find positions of incoming colliding partons. + int in1 = partonSystemsPtr->getInA(iSys); + int in2 = partonSystemsPtr->getInB(iSys); + + // Rescattered partons cannot radiate. + bool canRadiate1 = !(event[in1].isRescatteredIncoming()); + bool canRadiate2 = !(event[in2].isRescatteredIncoming()); + + // Reset dipole-ends list for first interaction. Also resonances. + if (iSys == 0) dipEnd.resize(0); + if (iSys == 0) idResFirst = 0; + if (iSys == 1) idResSecond = 0; + + // Find matrix element corrections for system. + int MEtype = findMEtype( iSys, event); + + // Maximum pT scale for dipole ends. + double pTmax1 = (limitPTmaxIn) ? event[in1].scale() : eCM; + double pTmax2 = (limitPTmaxIn) ? event[in2].scale() : eCM; + if (iSys == 0 && limitPTmaxIn) { + pTmax1 *= pTmaxFudge; + pTmax2 *= pTmaxFudge; + } else if (iSys > 0 && limitPTmaxIn) { + pTmax1 *= pTmaxFudgeMI; + pTmax2 *= pTmaxFudgeMI; + } + + // Find dipole ends for QCD radiation. + // Note: colour type can change during evolution, so book also if zero. + if (doQCDshower) { + int colType1 = event[in1].colType(); + if (canRadiate1) dipEnd.push_back( SpaceDipoleEnd( iSys, 1, + in1, in2, pTmax1, colType1, 0, MEtype, canRadiate2) ); + int colType2 = event[in2].colType(); + if (canRadiate2) dipEnd.push_back( SpaceDipoleEnd( iSys, 2, + in2, in1, pTmax2, colType2, 0, MEtype, canRadiate1) ); + } + + // Find dipole ends for QED radiation. + // Note: charge type can change during evolution, so book also if zero. + if (doQEDshowerByQ || doQEDshowerByL) { + int chgType1 = ( (event[in1].isQuark() && doQEDshowerByQ) + || (event[in1].isLepton() && doQEDshowerByL) ) + ? event[in1].chargeType() : 0; + // Special: photons have charge zero, but can evolve (only off Q for now) + if (event[in1].id() == 22 && doQEDshowerByQ) chgType1 = 22 ; + if (canRadiate1) dipEnd.push_back( SpaceDipoleEnd( iSys, -1, + in1, in2, pTmax1, 0, chgType1, MEtype, canRadiate2) ); + int chgType2 = ( (event[in2].isQuark() && doQEDshowerByQ) + || (event[in2].isLepton() && doQEDshowerByL) ) + ? event[in2].chargeType() : 0; + // Special: photons have charge zero, but can evolve (only off Q for now) + if (event[in2].id() == 22 && doQEDshowerByQ) chgType2 = 22 ; + if (canRadiate2) dipEnd.push_back( SpaceDipoleEnd( iSys, -2, + in2, in1, pTmax2, 0, chgType2, MEtype, canRadiate1) ); + + } + +} + +//-------------------------------------------------------------------------- + +// Select next pT in downwards evolution of the existing dipoles. + +double SpaceShower::pTnext( Event& event, double pTbegAll, double pTendAll, + int nRadIn) { + + // Current cm energy, in case it varies between events. + sCM = m2( beamAPtr->p(), beamBPtr->p()); + eCM = sqrt(sCM); + pTbegRef = pTbegAll; + + // Starting values: no radiating dipole found. + nRad = nRadIn; + double pT2sel = pow2(pTendAll); + iDipSel = 0; + iSysSel = 0; + dipEndSel = 0; + + // Loop over all possible dipole ends. + for (int iDipEnd = 0; iDipEnd < int(dipEnd.size()); ++iDipEnd) { + iDipNow = iDipEnd; + dipEndNow = &dipEnd[iDipEnd]; + iSysNow = dipEndNow->system; + dipEndNow->pT2 = 0.; + + // Check whether dipole end should be allowed to shower. + double pT2begDip = pow2( min( pTbegAll, dipEndNow->pTmax )); + if (pT2begDip > pT2sel + && ( dipEndNow->colType != 0 || dipEndNow->chgType != 0 ) ) { + double pT2endDip = 0.; + + // Determine lower cut for evolution, for QCD or QED (q or l). + if (dipEndNow->colType != 0) pT2endDip = max( pT2sel, pT2min ); + else if (abs(dipEndNow->chgType) != 3) pT2endDip + = max( pT2sel, pT2minChgQ ); + else pT2endDip = max( pT2sel, pT2minChgL ); + + // Find properties of dipole and radiating dipole end. + sideA = ( abs(dipEndNow->side) == 1 ); + BeamParticle& beamNow = (sideA) ? *beamAPtr : *beamBPtr; + BeamParticle& beamRec = (sideA) ? *beamBPtr : *beamAPtr; + iNow = beamNow[iSysNow].iPos(); + iRec = beamRec[iSysNow].iPos(); + idDaughter = beamNow[iSysNow].id(); + xDaughter = beamNow[iSysNow].x(); + x1Now = (sideA) ? xDaughter : beamRec[iSysNow].x(); + x2Now = (sideA) ? beamRec[iSysNow].x() : xDaughter; + + // Note dipole mass correction when recoiler is a rescatter. + m2Rec = (dipEndNow->normalRecoil) ? 0. : event[iRec].m2(); + m2Dip = x1Now * x2Now * sCM + m2Rec; + + // Now do evolution in pT2, for QCD or QED + if (pT2begDip > pT2endDip) { + if (dipEndNow->colType != 0) pT2nextQCD( pT2begDip, pT2endDip); + else pT2nextQED( pT2begDip, pT2endDip); + } + + // Update if found larger pT than current maximum. + if (dipEndNow->pT2 > pT2sel) { + pT2sel = dipEndNow->pT2; + iDipSel = iDipNow; + iSysSel = iSysNow; + dipEndSel = dipEndNow; + } + + // End loop over dipole ends. + } + } + + // Return nonvanishing value if found pT is bigger than already found. + return (dipEndSel == 0) ? 0. : sqrt(pT2sel); +} + +//-------------------------------------------------------------------------- + +// Evolve a QCD dipole end. + +void SpaceShower::pT2nextQCD( double pT2begDip, double pT2endDip) { + + // Some properties and kinematical starting values. + BeamParticle& beam = (sideA) ? *beamAPtr : *beamBPtr; + bool isGluon = (idDaughter == 21); + bool isValence = beam[iSysNow].isValence(); + int MEtype = dipEndNow->MEtype; + double pT2 = pT2begDip; + double xMaxAbs = beam.xMax(iSysNow); + double zMinAbs = xDaughter / xMaxAbs; + if (xMaxAbs < 0.) { + infoPtr->errorMsg("Warning in SpaceShower::pT2nextQCD: " + "xMaxAbs negative"); + return; + } + + // Starting values for handling of massive quarks (c/b), if any. + double idMassive = 0; + if ( abs(idDaughter) == 4 ) idMassive = 4; + if ( abs(idDaughter) == 5 ) idMassive = 5; + bool isMassive = (idMassive > 0); + double m2Massive = 0.; + double mRatio = 0.; + double zMaxMassive = 1.; + double m2Threshold = pT2; + + // Evolution below scale of massive quark or at large x is impossible. + if (isMassive) { + m2Massive = (idMassive == 4) ? m2c : m2b; + if (pT2 < HEAVYPT2EVOL * m2Massive) return; + mRatio = sqrt( m2Massive / m2Dip ); + zMaxMassive = (1. - mRatio) / ( 1. + mRatio * (1. - mRatio) ); + if (xDaughter > HEAVYXEVOL * zMaxMassive * xMaxAbs) return; + + // Find threshold scale below which only g -> Q + Qbar will be allowed. + m2Threshold = (idMassive == 4) ? min( pT2, CTHRESHOLD * m2c) + : min( pT2, BTHRESHOLD * m2b); + } + + // Variables used inside evolution loop. (Mainly dummy starting values.) + int nFlavour = 3; + double b0 = 4.5; + double Lambda2 = Lambda3flav2; + double pT2minNow = pT2endDip; + int idMother = 0; + int idSister = 0; + double z = 0.; + double zMaxAbs = 0.; + double zRootMax = 0.; + double zRootMin = 0.; + double g2gInt = 0.; + double q2gInt = 0.; + double q2qInt = 0.; + double g2qInt = 0.; + double g2Qenhance = 0.; + double xPDFdaughter = 0.; + double xPDFmother[21] = {0.}; + double xPDFgMother = 0.; + double xPDFmotherSum = 0.; + double kernelPDF = 0.; + double xMother = 0.; + double wt = 0.; + double Q2 = 0.; + double mSister = 0.; + double m2Sister = 0.; + double pT2corr = 0.; + double pT2PDF = pT2; + bool needNewPDF = true; + + // Begin evolution loop towards smaller pT values. + int loopTinyPDFdau = 0; + bool hasTinyPDFdau = false; + do { + wt = 0.; + + // Bad sign if repeated looping with small daughter PDF, so fail. + // (Example: if all PDF's = 0 below Q_0, except for c/b companion.) + if (hasTinyPDFdau) ++loopTinyPDFdau; + if (loopTinyPDFdau > MAXLOOPTINYPDF) { + infoPtr->errorMsg("Warning in SpaceShower::pT2nextQCD: " + "small daughter PDF"); + return; + } + + // Initialize integrals of splitting kernels and evaluate parton + // densities at the beginning. Reinitialize after long evolution + // in pT2 or when crossing c and b flavour thresholds. + if (needNewPDF || pT2 < EVALPDFSTEP * pT2PDF) { + pT2PDF = pT2; + hasTinyPDFdau = false; + + // Determine overestimated z range; switch at c and b masses. + if (pT2 > m2b) { + nFlavour = 5; + pT2minNow = m2b; + b0 = 23./6.; + Lambda2 = Lambda5flav2; + } else if (pT2 > m2c) { + nFlavour = 4; + pT2minNow = m2c; + b0 = 25./6.; + Lambda2 = Lambda4flav2; + } else { + nFlavour = 3; + pT2minNow = pT2endDip; + b0 = 27./6.; + Lambda2 = Lambda3flav2; + } + zMaxAbs = 1. - 0.5 * (pT2minNow / m2Dip) * + ( sqrt( 1. + 4. * m2Dip / pT2minNow ) - 1. ); + if (isMassive) zMaxAbs = min( zMaxAbs, zMaxMassive); + + // Go to another z range with lower mass scale if current is closed. + if (zMinAbs > zMaxAbs) { + if (nFlavour == 3 || (idMassive == 4 && nFlavour == 4) + || idMassive == 5) return; + pT2 = (nFlavour == 4) ? m2c : m2b; + continue; + } + + // Parton density of daughter at current scale. + xPDFdaughter = beam.xfISR(iSysNow, idDaughter, xDaughter, pT2); + if (xPDFdaughter < TINYPDF) { + xPDFdaughter = TINYPDF; + hasTinyPDFdau = true; + } + + // Integrals of splitting kernels for gluons: g -> g, q -> g. + if (isGluon) { + g2gInt = 6. * log(zMaxAbs * (1.-zMinAbs) + / (zMinAbs * (1.-zMaxAbs))); + if (doMEcorrections) g2gInt *= calcMEmax(MEtype, 21, 21); + q2gInt = (16./3.) * (1./sqrt(zMinAbs) - 1./sqrt(zMaxAbs)); + if (doMEcorrections) q2gInt *= calcMEmax(MEtype, 1, 21); + + // Parton density of potential quark mothers to a g. + xPDFmotherSum = 0.; + for (int i = -nQuarkIn; i <= nQuarkIn; ++i) { + if (i == 0) { + xPDFmother[10] = 0.; + } else { + xPDFmother[i+10] = beam.xfISR(iSysNow, i, xDaughter, pT2); + xPDFmotherSum += xPDFmother[i+10]; + } + } + + // Total QCD evolution coefficient for a gluon. + kernelPDF = g2gInt + q2gInt * xPDFmotherSum / xPDFdaughter; + + // For valence quark only need consider q -> q g branchings. + // Introduce an extra factor sqrt(z) to smooth bumps. + } else if (isValence) { + zRootMin = (1. + sqrt(zMinAbs)) / (1. - sqrt(zMinAbs)); + zRootMax = (1. + sqrt(zMaxAbs)) / (1. - sqrt(zMaxAbs)); + q2qInt = (8./3.) * log( zRootMax / zRootMin ); + if (doMEcorrections) q2qInt *= calcMEmax(MEtype, 1, 1); + g2qInt = 0.; + kernelPDF = q2qInt; + + // Integrals of splitting kernels for quarks: q -> q, g -> q. + } else { + q2qInt = (8./3.) * log( (1. - zMinAbs) / (1. - zMaxAbs) ); + if (doMEcorrections) q2qInt *= calcMEmax(MEtype, 1, 1); + g2qInt = 0.5 * (zMaxAbs - zMinAbs); + if (doMEcorrections) g2qInt *= calcMEmax(MEtype, 21, 1); + + // Increase estimated upper weight for g -> Q + Qbar. + if (isMassive) { + if (alphaSorder == 0) g2Qenhance = log(pT2/m2Massive) + / log(m2Threshold/m2Massive); + else { + double m2log = log( m2Massive / Lambda2); + g2Qenhance = log( log(pT2/Lambda2) / m2log ) + / log( log(m2Threshold/Lambda2) / m2log ); + } + g2qInt *= g2Qenhance; + } + + // Parton density of a potential gluon mother to a q. + xPDFgMother = beam.xfISR(iSysNow, 21, xDaughter, pT2); + + // Total QCD evolution coefficient for a quark. + kernelPDF = q2qInt + g2qInt * xPDFgMother / xPDFdaughter; + } + + // End evaluation of splitting kernels and parton densities. + needNewPDF = false; + } + if (kernelPDF < TINYKERNELPDF) return; + + // Pick pT2 (in overestimated z range), for one of three different cases. + // Assume form alphas(pT0^2 + pT^2) * dpT^2/(pT0^2 + pT^2). + double Q2alphaS; + + // Fixed alpha_strong. + if (alphaSorder == 0) { + pT2 = (pT2 + pT20) * pow( rndmPtr->flat(), + 1. / (alphaS2pi * kernelPDF)) - pT20; + + // First-order alpha_strong. + } else if (alphaSorder == 1) { + pT2 = Lambda2 * pow( (pT2 + pT20) / Lambda2, + pow(rndmPtr->flat(), b0 / kernelPDF) ) - pT20; + + // For second order reject by second term in alpha_strong expression. + } else { + do { + pT2 = Lambda2 * pow( (pT2 + pT20) / Lambda2, + pow(rndmPtr->flat(), b0 / kernelPDF) ) - pT20; + Q2alphaS = max(pT2 + pT20, pow2(LAMBDA3MARGIN) * Lambda3flav2); + } while (alphaS.alphaS2OrdCorr(Q2alphaS) < rndmPtr->flat() + && pT2 > pT2minNow); + } + + // Check for pT2 values that prompt special action. + + // If fallen into b threshold region, force g -> b + bbar. + if (idMassive == 5 && pT2 < m2Threshold) { + pT2nearQCDthreshold( beam, m2Massive, m2Threshold, xMaxAbs, + zMinAbs, zMaxMassive ); + return; + + // If crossed b threshold, continue evolution from this threshold. + } else if (nFlavour == 5 && pT2 < m2b) { + needNewPDF = true; + pT2 = m2b; + continue; + + // If fallen into c threshold region, force g -> c + cbar. + } else if (idMassive == 4 && pT2 < m2Threshold) { + pT2nearQCDthreshold( beam, m2Massive, m2Threshold, xMaxAbs, + zMinAbs, zMaxMassive ); + return; + + // If crossed c threshold, continue evolution from this threshold. + } else if (nFlavour == 4 && pT2 < m2c) { + needNewPDF = true; + pT2 = m2c; + continue; + + // Abort evolution if below cutoff scale, or below another branching. + } else if (pT2 < pT2endDip) return; + + // Select z value of branching to g, and corrective weight. + if (isGluon) { + // g -> g (+ g). + if (rndmPtr->flat() * kernelPDF < g2gInt) { + idMother = 21; + idSister = 21; + z = 1. / ( 1. + ((1. - zMinAbs) / zMinAbs) * pow( (zMinAbs * + (1. - zMaxAbs)) / (zMaxAbs * (1. - zMinAbs)), rndmPtr->flat() ) ); + wt = pow2( 1. - z * (1. - z)); + } else { + // q -> g (+ q): also select flavour. + double temp = xPDFmotherSum * rndmPtr->flat(); + idMother = -nQuarkIn - 1; + do { temp -= xPDFmother[(++idMother) + 10]; } + while (temp > 0. && idMother < nQuarkIn); + idSister = idMother; + z = (zMinAbs * zMaxAbs) / pow2( sqrt(zMinAbs) + rndmPtr->flat() + * ( sqrt(zMaxAbs)- sqrt(zMinAbs) )); + wt = 0.5 * (1. + pow2(1. - z)) * sqrt(z) + * xPDFdaughter / xPDFmother[idMother + 10]; + } + + // Select z value of branching to q, and corrective weight. + // Include massive kernel corrections for c and b quarks. + } else { + // q -> q (+ g). + if (isValence || rndmPtr->flat() * kernelPDF < q2qInt) { + idMother = idDaughter; + idSister = 21; + // Valence more peaked at large z. + if (isValence) { + double zTmp = zRootMin * pow(zRootMax / zRootMin, rndmPtr->flat() ); + z = pow2( (1. - zTmp) / (1. + zTmp) ); + } else { + z = 1. - (1. - zMinAbs) * pow( (1. - zMaxAbs) / (1. - zMinAbs), + rndmPtr->flat() ); + } + if (!isMassive) { + wt = 0.5 * (1. + pow2(z)); + } else { + wt = 0.5 * (1. + pow2(z) - z * pow2(1.-z) * m2Massive / pT2); + } + if (isValence) wt *= sqrt(z); + // g -> q (+ qbar). + } else { + idMother = 21; + idSister = - idDaughter; + z = zMinAbs + rndmPtr->flat() * (zMaxAbs - zMinAbs); + if (!isMassive) { + wt = (pow2(z) + pow2(1.-z)) * xPDFdaughter / xPDFgMother ; + } else { + wt = (pow2(z) + pow2(1.-z) + 2. * z * (1.-z) * m2Massive / pT2) + * xPDFdaughter / (xPDFgMother * g2Qenhance) ; + } + } + } + + // Derive Q2 and x of mother from pT2 and z. + Q2 = pT2 / (1.- z); + xMother = xDaughter / z; + // Correction to x for massive recoiler from rescattering. + if (!dipEndNow->normalRecoil) { + if (sideA) xMother += (m2Rec / (x2Now * sCM)) * (1. / z - 1.); + else xMother += (m2Rec / (x1Now * sCM)) * (1. / z - 1.); + } + if(xMother > xMaxAbs) { wt = 0.; continue; } + + // Forbidden emission if outside allowed z range for given pT2. + mSister = particleDataPtr->m0(idSister); + m2Sister = pow2(mSister); + pT2corr = Q2 - z * (m2Dip + Q2) * (Q2 + m2Sister) / m2Dip; + if(pT2corr < TINYPT2) { wt = 0.; continue; } + + // Optionally veto emissions not ordered in rapidity (= angle). + if ( doRapidityOrder && dipEndNow->nBranch > 0 + && pT2 > pow2( (1. - z) / (z * (1. - dipEndNow->zOld)) ) + * dipEndNow->pT2Old ) { wt = 0.; continue; } + + // If creating heavy quark by Q -> g + Q then next need g -> Q + Qbar. + // So minimum total mass2 is 4 * m2Sister, but use more to be safe. + if ( isGluon && ( abs(idMother) == 4 || abs(idMother) == 5 )) { + double m2QQsister = EXTRASPACEQ * 4. * m2Sister; + double pT2QQcorr = Q2 - z * (m2Dip + Q2) * (Q2 + m2QQsister) / m2Dip; + if(pT2QQcorr < TINYPT2) { wt = 0.; continue; } + } + + // Evaluation of ME correction. + if (doMEcorrections) wt *= calcMEcorr(MEtype, idMother, idDaughter, + m2Dip, z, Q2) / calcMEmax(MEtype, idMother, idDaughter); + + // Optional dampening of large pT values in first radiation. + if (dopTdamp && iSysNow == 0 && MEtype == 0 && nRad == 0) + wt *= pT2damp / (pT2 + pT2damp); + + // Idea suggested by Gosta Gustafson: increased screening in events + // with large activity can be simulated by pT0_eff = sqrt(n) * pT0. + if (enhanceScreening == 2) { + int nSysNow = infoPtr->nMI() + infoPtr->nISR() + 1; + double WTscreen = pow2( (pT2 + pT20) / (pT2 + nSysNow * pT20) ); + wt *= WTscreen; + } + + // Evaluation of new daughter and mother PDF's. + double xPDFdaughterNew = max ( TINYPDF, + beam.xfISR(iSysNow, idDaughter, xDaughter, pT2) ); + double xPDFmotherNew = beam.xfISR(iSysNow, idMother, xMother, pT2); + wt *= xPDFmotherNew / xPDFdaughterNew; + + // Check that valence step does not cause problem. + if (wt > 1.) infoPtr->errorMsg("Warning in SpaceShower::" + "pT2nextQCD: weight above unity"); + + // Iterate until acceptable pT (or have fallen below pTmin). + } while (wt < rndmPtr->flat()) ; + + // Save values for (so far) acceptable branching. + dipEndNow->store( idDaughter,idMother, idSister, x1Now, x2Now, m2Dip, + pT2, z, xMother, Q2, mSister, m2Sister, pT2corr); + +} + +//-------------------------------------------------------------------------- + +// Evolve a QCD dipole end near threshold, with g -> Q + Qbar enforced. +// Note: No explicit Sudakov factor formalism here. Instead use that +// df_Q(x, pT2) = (alpha_s/2pi) * (dT2/pT2) * ((gluon) * (splitting)). +// This implies that effects of Q -> Q + g are neglected in this range. + +void SpaceShower::pT2nearQCDthreshold( BeamParticle& beam, + double m2Massive, double m2Threshold, double xMaxAbs, + double zMinAbs, double zMaxMassive) { + + // Initial values, to be used in kinematics and weighting. + double Lambda2 = (abs(idDaughter) == 4) ? Lambda4flav2 : Lambda5flav2; + double logM2Lambda2 = log( m2Massive / Lambda2 ); + double xPDFmotherOld = beam.xfISR(iSysNow, 21, xDaughter, m2Threshold); + + // Variables used inside evolution loop. (Mainly dummy start values.) + int loop = 0; + double wt = 0.; + double pT2 = 0.; + double z = 0.; + double Q2 = 0.; + double pT2corr = 0.; + double xMother = 0.; + + // Begin loop over tries to find acceptable g -> Q + Qbar branching. + do { + wt = 0.; + + // Check that not caught in infinite loop with impossible kinematics. + if (++loop > 100) { + infoPtr->errorMsg("Error in SpaceShower::pT2nearQCDthreshold: " + "stuck in loop"); + return; + } + + // Pick dpT2/pT2 in range [m2Massive,thresholdRatio * m2Massive]. + pT2 = m2Massive * pow( m2Threshold / m2Massive, rndmPtr->flat() ); + + // Pick z flat in allowed range. + z = zMinAbs + rndmPtr->flat() * (zMaxMassive - zMinAbs); + + // Check that kinematically possible choice. + Q2 = pT2 / (1.-z) - m2Massive; + pT2corr = Q2 - z * (m2Dip + Q2) * (Q2 + m2Massive) / m2Dip; + if(pT2corr < TINYPT2) continue; + + // Correction factor for running alpha_s. ?? + wt = logM2Lambda2 / log( pT2 / Lambda2 ); + + // Correction factor for splitting kernel. + wt *= pow2(z) + pow2(1.-z) + 2. * z * (1.-z) * m2Massive / pT2; + + // x, including correction for massive recoiler from rescattering. + xMother = xDaughter / z; + if (!dipEndNow->normalRecoil) { + if (sideA) xMother += (m2Rec / (x2Now * sCM)) * (1. / z - 1.); + else xMother += (m2Rec / (x1Now * sCM)) * (1. / z - 1.); + } + if (xMother > xMaxAbs) { wt = 0.; continue; } + + // Correction factor for gluon density. + double xPDFmotherNew = beam.xfISR(iSysNow, 21, xMother, pT2); + wt *= xPDFmotherNew / xPDFmotherOld; + + // Iterate until acceptable pT and z. + } while (wt < rndmPtr->flat()) ; + + // Save values for (so far) acceptable branching. + double mSister = (abs(idDaughter) == 4) ? mc : mb; + dipEndNow->store( idDaughter, 21, -idDaughter, x1Now, x2Now, m2Dip, + pT2, z, xMother, Q2, mSister, pow2(mSister), pT2corr); + +} + +//-------------------------------------------------------------------------- + +// Evolve a QED dipole end. + +void SpaceShower::pT2nextQED( double pT2begDip, double pT2endDip) { + + // Type of dipole and starting values. + BeamParticle& beam = (sideA) ? *beamAPtr : *beamBPtr; + bool isLeptonBeam = beam.isLepton(); + int MEtype = dipEndNow->MEtype; + bool isPhoton = (idDaughter == 22); + double pT2 = pT2begDip; + double m2Lepton = (isLeptonBeam) ? pow2(beam.m()) : 0.; + if (isLeptonBeam && pT2begDip < m2Lepton) return; + + // Currently no f -> gamma branching implemented for lepton beams + if (isPhoton && isLeptonBeam) return; + + // alpha_em at maximum scale provides upper estimate. + double alphaEMmax = alphaEM.alphaEM(pT2begDip); + double alphaEM2pi = alphaEMmax / (2. * M_PI); + + // Maximum x of mother implies minimum z = xDaughter / xMother. + double xMaxAbs = (isLeptonBeam) ? LEPTONXMAX : beam.xMax(iSysNow); + double zMinAbs = xDaughter / xMaxAbs; + if (xMaxAbs < 0.) { + infoPtr->errorMsg("Warning in SpaceShower::pT2nextQED: " + "xMaxAbs negative"); + return; + } + + // Maximum z from minimum pT and, for lepton, from minimum x_gamma. + double zMaxAbs = 1. - 0.5 * (pT2endDip / m2Dip) * + ( sqrt( 1. + 4. * m2Dip / pT2endDip ) - 1. ); + if (isLeptonBeam) { + double zMaxLepton = xDaughter / (xDaughter + LEPTONXMIN); + if (zMaxLepton < zMaxAbs) zMaxAbs = zMaxLepton; + } + if (zMaxAbs < zMinAbs) return; + + // Variables used inside evolution loop. (Mainly dummy start values.) + int idMother = 0; + int idSister =22; + double z = 0.; + double xMother = 0.; + double wt = 0.; + double Q2 = 0.; + double mSister = 0.; + double m2Sister = 0.; + double pT2corr = 0.; + + // QED evolution of fermions + if (!isPhoton) { + + // Integrals of splitting kernels for fermions: f -> f. Use 1 + z^2 < 2. + // Ansatz f(z) = 2 / (1 - z), with + 2 / (z - xDaughter) for lepton. + double f2fInt = 0.; + double f2fIntA = 2. * log( (1. - zMinAbs) / (1. - zMaxAbs) ); + double f2fIntB = 0.; + if (isLeptonBeam) { + f2fIntB = 2. * log( (zMaxAbs - xDaughter) / (zMinAbs - xDaughter) ); + f2fInt = f2fIntA + f2fIntB; + } else f2fInt = pow2(dipEndNow->chgType / 3.) * f2fIntA; + + // Upper estimate for evolution equation, including fudge factor. + if (doMEcorrections) f2fInt *= calcMEmax(MEtype, 1, 1); + double kernelPDF = alphaEM2pi * f2fInt; + double fudge = (isLeptonBeam) ? LEPTONFUDGE * log(m2Dip/m2Lepton) : 1.; + kernelPDF *= fudge; + if (kernelPDF < TINYKERNELPDF) return; + + // Begin evolution loop towards smaller pT values. + do { + wt = 0.; + + // Pick pT2 (in overestimated z range). + // For l -> l gamma include extrafactor 1 / ln(pT2 / m2l) in evolution. + double shift = pow(rndmPtr->flat(), 1. / kernelPDF); + if (isLeptonBeam) pT2 = m2Lepton * pow( pT2 / m2Lepton, shift); + else pT2 = pT2 * shift; + + // Abort evolution if below cutoff scale, or below another branching. + if (pT2 < pT2endDip) return; + if (isLeptonBeam && pT2 < LEPTONPT2MIN * m2Lepton) return; + + // Select z value of branching f -> f + gamma, and corrective weight. + idMother = idDaughter; + wt = 0.5 * (1. + pow2(z)); + if (isLeptonBeam) { + if (f2fIntA > rndmPtr->flat() * (f2fIntA + f2fIntB)) { + z = 1. - (1. - zMinAbs) + * pow( (1. - zMaxAbs) / (1. - zMinAbs), rndmPtr->flat() ); + } else { + z = xDaughter + (zMinAbs - xDaughter) + * pow( (zMaxAbs - xDaughter) / (zMinAbs - xDaughter), + rndmPtr->flat() ); + } + wt *= (z - xDaughter) / (1. - xDaughter); + } else { + z = 1. - (1. - zMinAbs) + * pow( (1. - zMaxAbs) / (1. - zMinAbs), rndmPtr->flat() ); + } + + // Derive Q2 and x of mother from pT2 and z. + Q2 = pT2 / (1. - z); + xMother = xDaughter / z; + // Correction to x for massive recoiler from rescattering. + if (!dipEndNow->normalRecoil) { + if (sideA) xMother += (m2Rec / (x2Now * sCM)) * (1. / z - 1.); + else xMother += (m2Rec / (x1Now * sCM)) * (1. / z - 1.); + } + if(xMother > xMaxAbs) { wt = 0.; continue; } + + // Forbidden emission if outside allowed z range for given pT2. + mSister = 0.; + m2Sister = 0.; + pT2corr = Q2 - z * (m2Dip + Q2) * (Q2 + m2Sister) / m2Dip; + if(pT2corr < TINYPT2) { wt = 0.; continue; } + + // Correct by ln(pT2 / m2l) and fudge factor. + if (isLeptonBeam) wt *= log(pT2 / m2Lepton) / fudge; + + // Evaluation of ME correction. + if (doMEcorrections) wt *= calcMEcorr(MEtype, idMother, idDaughter, + m2Dip, z, Q2) / calcMEmax(MEtype, idMother, idDaughter); + + // Extra QED correction for f fbar -> W+- gamma. Debug?? + if (doMEcorrections && MEtype == 1 && idDaughter == idMother + && ( (iSysNow == 0 && idResFirst == 24) + || (iSysNow == 1 && idResSecond == 24) ) ) { + double tHe = -Q2; + double uHe = Q2 - m2Dip * (1. - z) / z; + double chg1 = abs(dipEndNow->chgType / 3.); + double chg2 = 1. - chg1; + wt *= pow2(chg1 * uHe - chg2 * tHe) + / ( (tHe + uHe) * (pow2(chg1) * uHe + pow2(chg2) * tHe) ); + } + + // Optional dampening of large pT values in first radiation. + if (dopTdamp && iSysNow == 0 && MEtype == 0 && nRad == 0) + wt *= pT2damp / (pT2 + pT2damp); + + // Correct to current value of alpha_EM. + double alphaEMnow = alphaEM.alphaEM(pT2); + wt *= (alphaEMnow / alphaEMmax); + + // Evaluation of new daughter and mother PDF's. + double xPDFdaughterNew = max ( TINYPDF, + beam.xfISR(iSysNow, idDaughter, xDaughter, pT2) ); + double xPDFmotherNew = beam.xfISR(iSysNow, idMother, xMother, pT2); + wt *= xPDFmotherNew / xPDFdaughterNew; + + // Iterate until acceptable pT (or have fallen below pTmin). + } while (wt < rndmPtr->flat()) ; + } + + // QED evolution of photons (so far only for hadron beams). + else { + + // Initial values + int nFlavour = 3; + double kernelPDF = 0.0; + double xPDFdaughter = 0.; + double xPDFmother[21] = {0.}; + double xPDFmotherSum = 0.0; + double pT2PDF = pT2; + double pT2minNow = pT2endDip; + bool needNewPDF = true; + + // Begin evolution loop towards smaller pT values. + int loopTinyPDFdau = 0; + bool hasTinyPDFdau = false; + do { + wt = 0.; + + // Bad sign if repeated looping with small daughter PDF, so fail. + if (hasTinyPDFdau) ++loopTinyPDFdau; + if (loopTinyPDFdau > MAXLOOPTINYPDF) { + infoPtr->errorMsg("Warning in SpaceShower::pT2nextQED: " + "small daughter PDF"); + return; + } + + // Initialize integrals of splitting kernels and evaluate parton + // densities at the beginning. Reinitialize after long evolution + // in pT2 or when crossing c and b flavour thresholds. + if (needNewPDF || pT2 < EVALPDFSTEP * pT2PDF) { + + pT2PDF = pT2; + hasTinyPDFdau = false; + + // Determine overestimated z range; switch at c and b masses. + if (pT2 > m2b && nQuarkIn >= 5) { + nFlavour = 5; + pT2minNow = m2b; + } else if (pT2 > m2c && nQuarkIn >= 4) { + nFlavour = 4; + pT2minNow = m2c; + } else { + nFlavour = 3; + pT2minNow = pT2endDip; + } + + // Compute upper z limit + zMaxAbs = 1. - 0.5 * (pT2minNow / m2Dip) * + ( sqrt( 1. + 4. * m2Dip / pT2minNow ) - 1. ); + + // Parton density of daughter at current scale. + xPDFdaughter = beam.xfISR(iSysNow, idDaughter, xDaughter, pT2); + if (xPDFdaughter < TINYPDF) { + xPDFdaughter = TINYPDF; + hasTinyPDFdau = true; + } + + // Integral over f -> gamma f splitting kernel. + // Normalized so: 4/3 aS/2pi P(z) -> eq^2 * aEM/2pi P(z). + // (Charge-weighting happens below.) + double q2gInt = 4. * (1./sqrt(zMinAbs) - 1./sqrt(zMaxAbs)); + + // Charge-weighted Parton density of potential quark mothers. + xPDFmotherSum = 0.; + for (int i = -nFlavour; i <= nFlavour; ++i) { + if (i == 0) { + xPDFmother[10] = 0.; + } else { + xPDFmother[i+10] = pow2((abs(i+1) % 2 + 1)/3.0) + * beam.xfISR(iSysNow, i, xDaughter, pT2); + xPDFmotherSum += xPDFmother[i+10]; + } + } + + // Total QED evolution coefficient for a photon. + kernelPDF = q2gInt * xPDFmotherSum / xPDFdaughter; + + // End evaluation of splitting kernels and parton densities. + needNewPDF = false; + } + if (kernelPDF < TINYKERNELPDF) return; + + // Select pT2 for next trial branching + pT2 *= pow( rndmPtr->flat(), 1. / (alphaEM2pi * kernelPDF)); + + // If crossed b threshold, continue evolution from this threshold. + if (nFlavour == 5 && pT2 < m2b) { + needNewPDF = true; + pT2 = m2b; + continue; + } + + // If crossed c threshold, continue evolution from this threshold. + else if (nFlavour == 4 && pT2 < m2c) { + needNewPDF = true; + pT2 = m2c; + continue; + } + + // Abort evolution if below cutoff scale, or below another branching. + else if (pT2 < pT2endDip) return; + + // Select flavour for trial branching + double temp = xPDFmotherSum * rndmPtr->flat(); + idMother = -nQuarkIn - 1; + do { + temp -= xPDFmother[(++idMother) + 10]; + } while (temp > 0. && idMother < nQuarkIn); + + // Sister is same as mother, but can have m2 > 0 + idSister = idMother; + mSister = particleDataPtr->m0(idSister); + m2Sister = pow2(mSister); + + // Select z for trial branching + z = (zMinAbs * zMaxAbs) / pow2( sqrt(zMinAbs) + rndmPtr->flat() + * ( sqrt(zMaxAbs)- sqrt(zMinAbs) )); + + // Trial weight: splitting kernel + wt = 0.5 * (1. + pow2(1. - z)) * sqrt(z); + + // Trial weight: running alpha_EM + double alphaEMnow = alphaEM.alphaEM(pT2); + wt *= (alphaEMnow / alphaEMmax); + + // Derive Q2 and x of mother from pT2 and z + Q2 = pT2 / (1. - z); + xMother = xDaughter / z; + // Correction to x for massive recoiler from rescattering. + if (!dipEndNow->normalRecoil) { + if (sideA) xMother += (m2Rec / (x2Now * sCM)) * (1. / z - 1.); + else xMother += (m2Rec / (x1Now * sCM)) * (1. / z - 1.); + } + + // Compute pT2corr + pT2corr = Q2 - z * (m2Dip + Q2) * (Q2 + m2Sister) / m2Dip; + if(pT2corr < TINYPT2) { wt = 0.; continue; } + + // If creating heavy quark by Q -> gamma + Q then next need g -> Q + Qbar. + // So minimum total mass2 is 4 * m2Sister, but use more to be safe. + if ( abs(idMother) == 4 || abs(idMother) == 5 ) { + double m2QQsister = EXTRASPACEQ * 4. * m2Sister; + double pT2QQcorr = Q2 - z * (m2Dip + Q2) * (Q2 + m2QQsister) / m2Dip; + if(pT2QQcorr < TINYPT2) { wt = 0.; continue; } + } + + // Optional dampening of large pT values in first radiation. + if (dopTdamp && iSysNow == 0 && MEtype == 0 && nRad == 0) + wt *= pT2damp / (pT2 + pT2damp); + + // Evaluation of new daughter PDF + double xPDFdaughterNew = beam.xfISR(iSysNow, idDaughter, xDaughter, pT2); + if (xPDFdaughterNew < TINYPDF) { + xPDFdaughterNew = TINYPDF; + } + + // Evaluation of new charge-weighted mother PDF + double xPDFmotherNew = pow2( (abs(idMother+1) % 2 + 1)/3.0 ) + * beam.xfISR(iSysNow, idMother, xMother, pT2); + + // Trial weight: divide out old pdf ratio + wt *= xPDFdaughter / xPDFmother[idMother + 10]; + + // Trial weight: new pdf ratio + wt *= xPDFmotherNew / xPDFdaughterNew; + + // Debug information. + if (DEBUG) cout << " Trial weight is : " << wt << "\n pT2 = " + << pT2 << " z = " << z << " alpha/alphahat = " << alphaEMnow + << "/" << alphaEMmax << " idMother = " << idMother + << " xPDFd/xPDFm = " << xPDFdaughter << "/" << xPDFmother[idMother+10] + << " xPDFmNew/xPDFdNew " << xPDFmotherNew << "/" << xPDFdaughterNew + << " pT2damp = " << pT2damp << " Q2 = " << Q2 << " pT2corr = " + << pT2corr << endl; + + // Iterate until acceptable pT (or have fallen below pTmin). + } while (wt < rndmPtr->flat()) ; + } + + // Save values for (so far) acceptable branching. + dipEndNow->store( idDaughter, idMother, idSister, x1Now, x2Now, m2Dip, + pT2, z, xMother, Q2, mSister, m2Sister, pT2corr); + +} + +//-------------------------------------------------------------------------- + +// Kinematics of branching. +// Construct mother -> daughter + sister, with recoiler on other side. + +bool SpaceShower::branch( Event& event) { + + // Side on which branching occured. + int side = abs(dipEndSel->side); + double sideSign = (side == 1) ? 1. : -1.; + + // Read in flavour and colour variables. + int iDaughter = partonSystemsPtr->getInA(iSysSel); + int iRecoiler = partonSystemsPtr->getInB(iSysSel); + if (side == 2) swap(iDaughter, iRecoiler); + int idDaughterNow = dipEndSel->idDaughter; + int idMother = dipEndSel->idMother; + int idSister = dipEndSel->idSister; + int colDaughter = event[iDaughter].col(); + int acolDaughter = event[iDaughter].acol(); + + // Recoil parton may be rescatterer, requiring special processing. + bool normalRecoil = dipEndSel->normalRecoil; + int iRecoilMother = event[iRecoiler].mother1(); + + // Read in kinematical variables. + double x1 = dipEndSel->x1; + double x2 = dipEndSel->x2; + double xMo = dipEndSel->xMo; + double m2 = dipEndSel->m2Dip; + double m = sqrt(m2); + double pT2 = dipEndSel->pT2; + double z = dipEndSel->z; + double Q2 = dipEndSel->Q2; + double mSister = dipEndSel->mSister; + double m2Sister = dipEndSel->m2Sister; + double pT2corr = dipEndSel->pT2corr; + double x1New = (side == 1) ? xMo : x1; + double x2New = (side == 2) ? xMo : x2; + + // Rescatter: kinematics may fail; use the rescatterFail flag to tell + // parton level to try again. + rescatterFail = false; + + // Construct kinematics of mother, sister and recoiler in old rest frame. + // Normally both mother and recoiler are taken massless. + double eNewRec, pzNewRec, pTbranch, pzMother; + if (normalRecoil) { + eNewRec = 0.5 * (m2 + Q2) / m; + pzNewRec = -sideSign * eNewRec; + pTbranch = sqrt(pT2corr) * m2 / ( z * (m2 + Q2) ); + pzMother = sideSign * 0.5 * m * ( (m2 - Q2) / ( z * (m2 + Q2) ) + + (Q2 + m2Sister) / m2 ); + // More complicated kinematics when recoiler not massless. May fail. + } else { + m2Rec = event[iRecoiler].m2(); + double s1Tmp = m2 + Q2 - m2Rec; + double s3Tmp = m2 / z - m2Rec; + double r1Tmp = sqrt(s1Tmp * s1Tmp + 4. * Q2 * m2Rec); + eNewRec = 0.5 * (m2 + m2Rec + Q2) / m; + pzNewRec = -sideSign * 0.5 * r1Tmp / m; + double pT2br = Q2 * s3Tmp * (m2 / z - m2 - Q2) + - m2Sister * s1Tmp * s3Tmp - m2Rec * pow2(Q2 + m2Sister); + if (pT2br <= 0.) return false; + pTbranch = sqrt(pT2br) / r1Tmp; + pzMother = sideSign * (m * s3Tmp + - eNewRec * (m2 / z - Q2 - m2Rec - m2Sister)) / r1Tmp; + } + // Common final kinematics steps for both normal and rescattering. + double eMother = sqrt( pow2(pTbranch) + pow2(pzMother) ); + double pzSister = pzMother + pzNewRec; + double eSister = sqrt( pow2(pTbranch) + pow2(pzSister) + m2Sister ); + Vec4 pMother( pTbranch, 0., pzMother, eMother ); + Vec4 pSister( pTbranch, 0., pzSister, eSister ); + Vec4 pNewRec( 0., 0., pzNewRec, eNewRec ); + + // Current event and subsystem size. + int eventSizeOld = event.size(); + int systemSizeOld = partonSystemsPtr->sizeAll(iSysSel); + + // Save properties to be restored in case of user-hook veto of emission. + int ev1dau1V = event[1].daughter1(); + int ev2dau1V = event[2].daughter1(); + vector statusV, mother1V, mother2V, daughter1V, daughter2V; + if (canVetoEmission) { + for ( int iCopy = 0; iCopy < systemSizeOld; ++iCopy) { + int iOldCopy = partonSystemsPtr->getAll(iSysSel, iCopy); + statusV.push_back( event[iOldCopy].status()); + mother1V.push_back( event[iOldCopy].mother1()); + mother2V.push_back( event[iOldCopy].mother2()); + daughter1V.push_back( event[iOldCopy].daughter1()); + daughter2V.push_back( event[iOldCopy].daughter2()); + } + } + + // Take copy of existing system, to be given modified kinematics. + // Incoming negative status. Rescattered also negative, but after copy. + for ( int iCopy = 0; iCopy < systemSizeOld; ++iCopy) { + int iOldCopy = partonSystemsPtr->getAll(iSysSel, iCopy); + int statusOld = event[iOldCopy].status(); + int statusNew = (iOldCopy == iDaughter + || iOldCopy == iRecoiler) ? statusOld : 44; + int iNewCopy = event.copy(iOldCopy, statusNew); + if (statusOld < 0) event[iNewCopy].statusNeg(); + } + + // Define colour flow in branching. + // Default corresponds to f -> f + gamma. + int colMother = colDaughter; + int acolMother = acolDaughter; + int colSister = 0; + int acolSister = 0; + if (idSister == 22) ; + // q -> q + g and 50% of g -> g + g; need new colour. + else if (idSister == 21 && ( (idMother > 0 && idMother < 9) + || (idMother == 21 && rndmPtr->flat() < 0.5) ) ) { + colMother = event.nextColTag(); + colSister = colMother; + acolSister = colDaughter; + // qbar -> qbar + g and other 50% of g -> g + g; need new colour. + } else if (idSister == 21) { + acolMother = event.nextColTag(); + acolSister = acolMother; + colSister = acolDaughter; + // q -> g + q. + } else if (idDaughterNow == 21 && idMother > 0) { + colMother = colDaughter; + acolMother = 0; + colSister = acolDaughter; + // qbar -> g + qbar + } else if (idDaughterNow == 21) { + acolMother = acolDaughter; + colMother = 0; + acolSister = colDaughter; + // g -> q + qbar. + } else if (idDaughterNow > 0 && idDaughterNow < 9) { + acolMother = event.nextColTag(); + acolSister = acolMother; + // g -> qbar + q. + } else if (idDaughterNow < 0 && idDaughterNow > -9) { + colMother = event.nextColTag(); + colSister = colMother; + // q -> gamma + q. + } else if (idDaughterNow == 22 && idMother > 0) { + colMother = event.nextColTag(); + colSister = colMother; + // qbar -> gamma + qbar. + } else if (idDaughterNow == 22) { + acolMother = event.nextColTag(); + acolSister = acolMother; + } + + // Indices of partons involved. Add new sister. + int iMother = eventSizeOld + side - 1; + int iNewRecoiler = eventSizeOld + 2 - side; + int iSister = event.append( idSister, 43, iMother, 0, 0, 0, + colSister, acolSister, pSister, mSister, sqrt(pT2) ); + + // References to the partons involved. + Particle& daughter = event[iDaughter]; + Particle& mother = event[iMother]; + Particle& newRecoiler = event[iNewRecoiler]; + Particle& sister = event.back(); + + // Replace old by new mother; update new recoiler. + mother.id( idMother ); + mother.status( -41); + mother.cols( colMother, acolMother); + mother.p( pMother); + newRecoiler.status( (normalRecoil) ? -42 : -46 ); + newRecoiler.p( pNewRec); + if (!normalRecoil) newRecoiler.m( event[iRecoiler].m() ); + + // Update mother and daughter pointers; also for beams. + daughter.mothers( iMother, 0); + mother.daughters( iSister, iDaughter); + if (iSysSel == 0) { + event[1].daughter1( (side == 1) ? iMother : iNewRecoiler ); + event[2].daughter1( (side == 2) ? iMother : iNewRecoiler ); + } + + // Initially select phi angle of branching at random. + double phi = 2. * M_PI * rndmPtr->flat(); + + // Evaluate coefficient of azimuthal asymmetry from gluon polarization. + findAsymPol( event, dipEndSel); + int iFinPol = dipEndSel->iFinPol; + double cPol = dipEndSel->asymPol; + double phiPol = (iFinPol == 0) ? 0. : event[iFinPol].phi(); + + // If interference: try to match sister (anti)colour to final state. + int iFinInt = 0; + double cInt = 0.; + double phiInt = 0.; + if (doPhiIntAsym) { + for (int i = 0; i < partonSystemsPtr->sizeOut(iSysSel); ++ i) { + int iOut = partonSystemsPtr->getOut(iSysSel, i); + if ( (acolSister != 0 && event[iOut].col() == acolSister) + || (colSister != 0 && event[iOut].acol() == colSister) ) + iFinInt = iOut; + } + if (iFinInt != 0) { + double theFin = event[iFinInt].theta(); + if (side == 2) theFin = M_PI - theFin; + double theSis = pSister.theta(); + if (side == 2) theSis = M_PI - theSis; + cInt = strengthIntAsym * 2. * theSis * theFin + / (pow2(theSis) + pow2(theFin)); + phiInt = event[iFinInt].phi(); + } + } + + // Bias phi distribution for polarization and interference. + if (iFinPol != 0 || iFinInt != 0) { + double cPhiPol, cPhiInt, weight; + do { + phi = 2. * M_PI * rndmPtr->flat(); + weight = 1.; + if (iFinPol !=0 ) { + cPhiPol = cos(phi - phiPol); + weight *= ( 1. + cPol * (2. * pow2(cPhiPol) - 1.) ) + / ( 1. + abs(cPol) ); + } + if (iFinInt !=0 ) { + cPhiInt = cos(phi - phiInt); + weight *= (1. - cInt) * (1. - cInt * cPhiInt) + / (1. + pow2(cInt) - 2. * cInt * cPhiInt); + } + } while (weight < rndmPtr->flat()); + } + + // Find boost to old rest frame, and include rotation -phi. + RotBstMatrix Mtot; + if (normalRecoil) Mtot.bst(0., 0., (x2 - x1) / (x1 + x2) ); + else if (side == 1) + Mtot.toCMframe( event[iDaughter].p(), event[iRecoiler].p() ); + else Mtot.toCMframe( event[iRecoiler].p(), event[iDaughter].p() ); + Mtot.rot(0., -phi); + + // Find boost from old rest frame to event cm frame. + RotBstMatrix MfromRest; + // The boost to the new rest frame. + Vec4 sumNew = pMother + pNewRec; + double betaX = sumNew.px() / sumNew.e(); + double betaZ = sumNew.pz() / sumNew.e(); + MfromRest.bst( -betaX, 0., -betaZ); + // Alignment of radiator + recoiler to +- z axis, and rotation +phi. + // Note: with spacelike (E < 0) recoiler p'_x_mother < 0 can happen! + pMother.rotbst(MfromRest); + double theta = pMother.theta(); + if (pMother.px() < 0.) theta = -theta; + if (side == 2) theta += M_PI; + MfromRest.rot(-theta, phi); + // Boost to radiator + recoiler in event cm frame. + if (normalRecoil) { + MfromRest.bst( 0., 0., (x1New - x2New) / (x1New + x2New) ); + } else if (side == 1) { + Vec4 pMotherWanted( 0., 0., 0.5 * eCM * x1New, 0.5 * eCM * x1New); + MfromRest.fromCMframe( pMotherWanted, event[iRecoiler].p() ); + + } else { + Vec4 pMotherWanted( 0., 0., -0.5 * eCM * x2New, 0.5 * eCM * x2New); + MfromRest.fromCMframe( event[iRecoiler].p(), pMotherWanted ); + } + Mtot.rotbst(MfromRest); + + // Perform cumulative rotation/boost operation. + // Mother, recoiler and sister from old rest frame to event cm frame. + mother.rotbst(MfromRest); + newRecoiler.rotbst(MfromRest); + sister.rotbst(MfromRest); + // The rest from (and to) event cm frame. + for ( int i = eventSizeOld + 2; i < eventSizeOld + systemSizeOld; ++i) + event[i].rotbst(Mtot); + + // Allow veto of branching. If so restore event record to before emission. + if ( canVetoEmission + && userHooksPtr->doVetoISREmission(eventSizeOld, event) ) { + event.popBack( event.size() - eventSizeOld); + event[1].daughter1( ev1dau1V); + event[2].daughter1( ev2dau1V); + for ( int iCopy = 0; iCopy < systemSizeOld; ++iCopy) { + int iOldCopy = partonSystemsPtr->getAll(iSysSel, iCopy); + event[iOldCopy].status( statusV[iCopy]); + event[iOldCopy].mothers( mother1V[iCopy], mother2V[iCopy]); + event[iOldCopy].daughters( daughter1V[iCopy], daughter2V[iCopy]); + } + return false; + } + + // Update list of partons in system; adding newly produced one. + partonSystemsPtr->setInA(iSysSel, eventSizeOld); + partonSystemsPtr->setInB(iSysSel, eventSizeOld + 1); + for (int iCopy = 2; iCopy < systemSizeOld; ++iCopy) + partonSystemsPtr->setOut(iSysSel, iCopy - 2, eventSizeOld + iCopy); + partonSystemsPtr->addOut(iSysSel, eventSizeOld + systemSizeOld); + partonSystemsPtr->setSHat(iSysSel, m2 / z); + + // Update info on radiating dipole ends (QCD or QED). + for (int iDip = 0; iDip < int(dipEnd.size()); ++iDip) + if ( dipEnd[iDip].system == iSysSel) { + if (abs(dipEnd[iDip].side) == side) { + dipEnd[iDip].iRadiator = iMother; + dipEnd[iDip].iRecoiler = iNewRecoiler; + if (dipEnd[iDip].side > 0) + dipEnd[iDip].colType = mother.colType(); + else { + dipEnd[iDip].chgType = 0; + if ( (mother.isQuark() && doQEDshowerByQ) + || (mother.isLepton() && doQEDshowerByL) ) + dipEnd[iDip].chgType = mother.chargeType(); + } + // Kill ME corrections after first emission. + dipEnd[iDip].MEtype = 0; + + // Update info on recoiling dipole ends (QCD or QED). + } else { + dipEnd[iDip].iRadiator = iNewRecoiler; + dipEnd[iDip].iRecoiler = iMother; + } + } + + // Update info on beam remnants. + BeamParticle& beamNow = (side == 1) ? *beamAPtr : *beamBPtr; + double xNew = (side == 1) ? x1New : x2New; + beamNow[iSysSel].update( iMother, idMother, xNew); + // Redo choice of companion kind whenever new flavour. + if (idMother != idDaughterNow) { + beamNow.xfISR( iSysSel, idMother, xNew, pT2); + beamNow.pickValSeaComp(); + } + BeamParticle& beamRec = (side == 1) ? *beamBPtr : *beamAPtr; + beamRec[iSysSel].iPos( iNewRecoiler); + + // Store branching values of current dipole. (For rapidity ordering.) + ++dipEndSel->nBranch; + dipEndSel->pT2Old = pT2; + dipEndSel->zOld = z; + + // Update history if recoiler rescatters. + if (!normalRecoil) + event[iRecoilMother].daughters( iNewRecoiler, iNewRecoiler); + + // Start list of rescatterers that force changed kinematics. + vector iRescatterer; + for ( int i = 0; i < systemSizeOld - 2; ++i) { + int iOutNew = partonSystemsPtr->getOut( iSysSel, i); + if (!event[iOutNew].isFinal()) iRescatterer.push_back(iOutNew); + } + + // Start iterate over list of such rescatterers. + int iRescNow = -1; + while (++iRescNow < int(iRescatterer.size())) { + + // Identify partons that induce or are affected by rescatter shift. + // In following Old is before change of kinematics, New after, + // Out scatterer in outstate and In in instate of another system. + // Daughter sequence is (iOutOld ->) iOutNew -> iInNew -> iInOld. + int iOutNew = iRescatterer[iRescNow]; + int iInOld = event[iOutNew].daughter1(); + int iSysResc = partonSystemsPtr->getSystemOf(iInOld, true); + + // Copy incoming partons of rescattered system and hook them up. + int iOldA = partonSystemsPtr->getInA(iSysResc); + int iOldB = partonSystemsPtr->getInB(iSysResc); + bool rescSideA = event[iOldA].isRescatteredIncoming(); + int statusNewA = (rescSideA) ? -45 : -42; + int statusNewB = (rescSideA) ? -42 : -45; + int iNewA = event.copy(iOldA, statusNewA); + int iNewB = event.copy(iOldB, statusNewB); + + // Copy outgoing partons of rescattered system and hook them up. + int eventSize = event.size(); + int sizeOutAB = partonSystemsPtr->sizeOut(iSysResc); + int iOldAB, statusOldAB, iNewAB; + for (int iOutAB = 0; iOutAB < sizeOutAB; ++iOutAB) { + iOldAB = partonSystemsPtr->getOut(iSysResc, iOutAB); + statusOldAB = event[iOldAB].status(); + iNewAB = event.copy(iOldAB, 44); + // Status could be negative for parton that rescatters in its turn. + if (statusOldAB < 0) { + event[iNewAB].statusNeg(); + iRescatterer.push_back(iNewAB); + } + } + + // Hook up new outgoing with new incoming parton. + int iInNew = (rescSideA) ? iNewA : iNewB; + event[iOutNew].daughters( iInNew, iInNew); + event[iInNew].mothers( iOutNew, iOutNew); + + // Rescale recoiling incoming parton for correct invariant mass. + event[iInNew].p( event[iOutNew].p() ); + double momFac = (rescSideA) + ? event[iInOld].pPos() / event[iInNew].pPos() + : event[iInOld].pNeg() / event[iInNew].pNeg(); + int iInRec = (rescSideA) ? iNewB : iNewA; + + // Rescatter: A previous boost may cause the light cone momentum of a + // rescattered parton to change sign. If this happens, tell + // parton level to try again. + if (momFac < 0.0) { + infoPtr->errorMsg("Warning in SpaceShower::branch: " + "change in lightcone momentum sign; retrying parton level"); + rescatterFail = true; + return false; + } + + event[iInRec].rescale4( momFac); + + // Boost outgoing partons to new frame of incoming. + RotBstMatrix MmodResc; + MmodResc.toCMframe( event[iOldA].p(), event[iOldB].p()); + MmodResc.fromCMframe(event[iNewA].p(), event[iNewB].p()); + for (int iOutAB = 0; iOutAB < sizeOutAB; ++iOutAB) + event[eventSize + iOutAB].rotbst(MmodResc); + + // Update list of partons in system. + partonSystemsPtr->setInA(iSysResc, iNewA); + partonSystemsPtr->setInB(iSysResc, iNewB); + for (int iCopy = 0; iCopy < sizeOutAB; ++iCopy) + partonSystemsPtr->setOut(iSysResc, iCopy, eventSize + iCopy); + + // Update info on radiating dipole ends (QCD or QED). + for (int iDip = 0; iDip < int(dipEnd.size()); ++iDip) + if ( dipEnd[iDip].system == iSysResc) { + bool sideAnow = (abs(dipEnd[iDip].side) == 1); + dipEnd[iDip].iRadiator = (sideAnow) ? iNewA : iNewB; + dipEnd[iDip].iRecoiler = (sideAnow) ? iNewB : iNewA; + } + + // Update info on beam remnants. + BeamParticle& beamResc = (rescSideA) ? *beamAPtr : *beamBPtr; + beamResc[iSysResc].iPos( iInNew); + beamResc[iSysResc].p( event[iInNew].p() ); + beamResc[iSysResc].scaleX( 1. / momFac ); + BeamParticle& beamReco = (rescSideA) ? *beamBPtr : *beamAPtr; + beamReco[iSysResc].iPos( iInRec); + beamReco[iSysResc].scaleX( momFac); + + // End iterate over list of rescatterers. + } + + // Check that beam momentum not used up by rescattered-system boosts. + if (beamAPtr->xMax(-1) < 0.0 || beamBPtr->xMax(-1) < 0.0) { + infoPtr->errorMsg("Warning in SpaceShower::branch: " + "used up beam momentum; retrying parton level"); + rescatterFail = true; + return false; + } + + // Done without any errors. + return true; + +} + +//-------------------------------------------------------------------------- + +// Find class of ME correction. + +int SpaceShower::findMEtype( int iSys, Event& event) { + + // Default values and no action. + int MEtype = 0; + if (!doMEcorrections) ; + + // Identify systems producing a single resonance. + else if (partonSystemsPtr->sizeOut( iSys) == 1) { + int idIn1 = event[partonSystemsPtr->getInA(iSys)].id(); + int idIn2 = event[partonSystemsPtr->getInA(iSys)].id(); + int idRes = event[partonSystemsPtr->getOut(iSys, 0)].id(); + if (iSys == 0) idResFirst = abs(idRes); + if (iSys == 1) idResSecond = abs(idRes); + + // f + fbar -> vector boson. + if ( (idRes == 23 || abs(idRes) == 24 || idRes == 32 + || idRes == 33 || abs(idRes) == 34 || abs(idRes) == 41) + && abs(idIn1) < 20 && abs(idIn2) < 20 ) MEtype = 1; + + // g + g, gamma + gamma -> Higgs boson. + if ( (idRes == 25 || idRes == 35 || idRes == 36) + && ( ( idIn1 == 21 && idIn2 == 21 ) + || ( idIn1 == 22 && idIn2 == 22 ) ) ) MEtype = 2; + + // f + fbar -> Higgs boson. + if ( (idRes == 25 || idRes == 35 || idRes == 36) + && abs(idIn1) < 20 && abs(idIn2) < 20 ) MEtype = 3; + } + + // Done. + return MEtype; + +} + +//-------------------------------------------------------------------------- + +// Provide maximum of expected ME weight; for preweighting of evolution. + +double SpaceShower::calcMEmax( int MEtype, int idMother, int idDaughterIn) { + + // Currently only one non-unity case: g(gamma) f -> V f'. + if (MEtype == 1 && idMother > 20 && idDaughterIn < 20) return 3.; + return 1.; + +} + +//-------------------------------------------------------------------------- + +// Provide actual ME weight for current branching. +// Note: currently ME corrections are only allowed for first branching +// on each side, so idDaughter is essentially known and checks overkill. + +double SpaceShower::calcMEcorr(int MEtype, int idMother, int idDaughterIn, + double M2, double z, double Q2) { + + // Convert to Mandelstam variables. Sometimes may need to swap later. + double sH = M2 / z; + double tH = -Q2; + double uH = Q2 - M2 * (1. - z) / z; + int idMabs = abs(idMother); + int idDabs = abs(idDaughterIn); + + // Corrections for f + fbar -> s-channel vector boson. + if (MEtype == 1) { + if (idMabs < 20 && idDabs < 20) { + return (tH*tH + uH*uH + 2. * M2 * sH) / (sH*sH + M2*M2); + } else if (idDabs < 20) { + // g(gamma) f -> V f': -Q2 = (p_g - p_f')^2 in PS while + // tHat = (p_f - p_f')^2 in ME so need to swap tHat <-> uHat. + swap( tH, uH); + return (sH*sH + uH*uH + 2. * M2 * tH) / (pow2(sH - M2) + M2*M2); + } + + // Corrections for g + g -> Higgs boson. + } else if (MEtype == 2) { + if (idMabs < 20 && idDabs > 20) { + return (sH*sH + uH*uH) / (sH*sH + pow2(sH - M2)); + } else if (idDabs > 20) { + return 0.5 * (pow4(sH) + pow4(tH) + pow4(uH) + pow4(M2)) + / pow2(sH*sH - M2 * (sH - M2)); + } + + // Corrections for f + fbar -> Higgs boson (f = b mainly). + } else if (MEtype == 3) { + if (idMabs < 20 && idDabs < 20) { + // The PS and ME answers agree for f fbar -> H g/gamma. + return 1.; + } else if (idDabs < 20) { + // Need to swap tHat <-> uHat, cf. vector-boson production above. + swap( tH, uH); + return (sH*sH + uH*uH + 2. * (M2 - uH) * (M2 - sH)) + / (pow2(sH - M2) + M2*M2); + } + } + + return 1.; + +} + +//-------------------------------------------------------------------------- + +// Find coefficient of azimuthal asymmetry from gluon polarization. + +void SpaceShower::findAsymPol( Event& event, SpaceDipoleEnd* dip) { + + // Default is no asymmetry. Only gluons are studied. + dip->iFinPol = 0.; + dip->asymPol = 0.; + int iRad = dip->iRadiator; + if (!doPhiPolAsym || dip->idDaughter != 21) return; + + // Check if granddaughter in final state of hard scattering. + // (May need to trace across carbon copies to find granddaughters.) + // If so, only accept 2 -> 2 scatterings with gg or qq in final state. + int iGrandD1 = event[iRad].daughter1(); + int iGrandD2 = event[iRad].daughter2(); + bool traceCopy = false; + do { + traceCopy = false; + if (iGrandD1 > 0 && iGrandD2 == iGrandD1) { + iGrandD1 = event[iGrandD2].daughter1(); + iGrandD2 = event[iGrandD2].daughter2(); + traceCopy = true; + } + } while (traceCopy); + int statusGrandD1 = event[ iGrandD1 ].statusAbs(); + bool isHardProc = (statusGrandD1 == 23 || statusGrandD1 == 33); + if (isHardProc) { + if (iGrandD2 != iGrandD1 + 1) return; + if (event[iGrandD1].isGluon() && event[iGrandD2].isGluon()); + else if (event[iGrandD1].isQuark() && event[iGrandD2].isQuark()); + else return; + } + dip->iFinPol = iGrandD1; + + // Coefficient from gluon production. + if (dip->idMother == 21) dip->asymPol = pow2( (1. - dip->z) + / (1. - dip->z * (1. - dip->z) ) ); + else dip->asymPol = 2. * (1. - dip->z) / (1. + pow2(1. - dip->z) ); + + // Coefficients from gluon decay. Put z = 1/2 for hard process. + double zDau = (isHardProc) ? 0.5 : dip->zOld; + if (event[iGrandD1].isGluon()) dip->asymPol *= pow2( (1. - zDau) + / (1. - zDau * (1. - zDau) ) ); + else dip->asymPol *= -2. * zDau *( 1. - zDau ) + / (1. - 2. * zDau * (1. - zDau) ); + +} + +//-------------------------------------------------------------------------- + +// Print the list of dipoles. + +void SpaceShower::list(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA SpaceShower Dipole Listing -------------- \n" + << "\n i syst side rad rec pTmax col chg ME rec \n" + << fixed << setprecision(3); + + // Loop over dipole list and print it. + for (int i = 0; i < int(dipEnd.size()); ++i) + os << setw(5) << i << setw(6) << dipEnd[i].system + << setw(6) << dipEnd[i].side << setw(6) << dipEnd[i].iRadiator + << setw(6) << dipEnd[i].iRecoiler << setw(12) << dipEnd[i].pTmax + << setw(5) << dipEnd[i].colType << setw(5) << dipEnd[i].chgType + << setw(5) << dipEnd[i].MEtype << setw(4) + << dipEnd[i].normalRecoil << "\n"; + + // Done. + os << "\n -------- End PYTHIA SpaceShower Dipole Listing ----------" + << endl; + + +} + +//========================================================================== + +} // end namespace Pythia8 + diff --git a/PYTHIA8/pythia8140/src/StandardModel.cxx b/PYTHIA8/pythia8140/src/StandardModel.cxx new file mode 100644 index 00000000000..d8b97119ad6 --- /dev/null +++ b/PYTHIA8/pythia8140/src/StandardModel.cxx @@ -0,0 +1,490 @@ +// StandardModel.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the AlphaStrong class. + +#include "StandardModel.h" + +namespace Pythia8 { + +//========================================================================== + +// The AlphaStrong class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Number of iterations to determine Lambda from given alpha_s. +const int AlphaStrong::NITER = 10; + +// Masses: m_c, m_b, m_Z. Used for flavour thresholds and normalization scale. +const double AlphaStrong::MC = 1.5; +const double AlphaStrong::MB = 4.8; +const double AlphaStrong::MZ = 91.188; + +// Always evaluate running alpha_s above Lambda3 to avoid disaster. +// Safety margin picked to freeze roughly for alpha_s = 10. +const double AlphaStrong::SAFETYMARGIN1 = 1.07; +const double AlphaStrong::SAFETYMARGIN2 = 1.33; + +//-------------------------------------------------------------------------- + +// Initialize alpha_strong calculation by finding Lambda values etc. + +void AlphaStrong::init( double valueIn, int orderIn) { + + // Order of alpha_s evaluation. + valueRef = valueIn; + order = max( 0, min( 2, orderIn ) ); + + // Fix alpha_s. + if (order == 0) { + Lambda3Save = Lambda4Save = Lambda5Save = scale2Min = 0.; + + // First order alpha_s: match at flavour thresholds. + } else if (order == 1) { + Lambda5Save = MZ * exp( -6. * M_PI / (23. * valueRef) ); + Lambda4Save = Lambda5Save * pow(MB/Lambda5Save, 2./25.); + Lambda3Save = Lambda4Save * pow(MC/Lambda4Save, 2./27.); + scale2Min = pow2(SAFETYMARGIN1 * Lambda3Save); + + // Second order alpha_s: iterative match at flavour thresholds. + } else { + double b15 = 348. / 529.; + double b14 = 462. / 625.; + double b13 = 64. / 81.; + double b25 = 224687. / 242208.; + double b24 = 548575. / 426888.; + double b23 = 938709. / 663552.; + double logScale, loglogScale, correction, valueIter; + + // Find Lambda_5 at m_Z. + Lambda5Save = MZ * exp( -6. * M_PI / (23. * valueRef) ); + for (int iter = 0; iter < NITER; ++iter) { + logScale = 2. * log(MZ/Lambda5Save); + loglogScale = log(logScale); + correction = 1. - b15 * loglogScale / logScale + + pow2(b15 / logScale) * (pow2(loglogScale - 0.5) + b25 - 1.25); + valueIter = valueRef / correction; + Lambda5Save = MZ * exp( -6. * M_PI / (23. * valueIter) ); + } + + // Find Lambda_4 at m_b. + double logScaleB = 2. * log(MB/Lambda5Save); + double loglogScaleB = log(logScaleB); + double valueB = 12. * M_PI / (23. * logScaleB) + * (1. - b15 * loglogScaleB / logScaleB + + pow2(b15 / logScaleB) * (pow2(loglogScaleB - 0.5) + b25- 1.25) ); + Lambda4Save = Lambda5Save; + for (int iter = 0; iter < NITER; ++iter) { + logScale = 2. * log(MB/Lambda4Save); + loglogScale = log(logScale); + correction = 1. - b14 * loglogScale / logScale + + pow2(b14 / logScale) * (pow2(loglogScale - 0.5) + b24 - 1.25); + valueIter = valueB / correction; + Lambda4Save = MB * exp( -6. * M_PI / (25. * valueIter) ); + } + + // Find Lambda_3 at m_c. + double logScaleC = 2. * log(MC/Lambda4Save); + double loglogScaleC = log(logScaleC); + double valueC = 12. * M_PI / (25. * logScaleC) + * (1. - b14 * loglogScaleC / logScaleC + + pow2(b14 / logScaleC) * (pow2(loglogScaleC - 0.5) + b24 - 1.25) ); + Lambda3Save = Lambda4Save; + for (int iter = 0; iter < NITER; ++iter) { + logScale = 2. * log(MC/Lambda3Save); + loglogScale = log(logScale); + correction = 1. - b13 * loglogScale / logScale + + pow2(b13 / logScale) * (pow2(loglogScale - 0.5) + b23 - 1.25); + valueIter = valueC / correction; + Lambda3Save = MC * exp( -6. * M_PI / (27. * valueIter) ); + } + scale2Min = pow2(SAFETYMARGIN2 * Lambda3Save); + } + + // Save squares of mass and Lambda values as well. + mc2 = pow2(MC); + mb2 = pow2(MB); + Lambda3Save2 = pow2(Lambda3Save); + Lambda4Save2 = pow2(Lambda4Save); + Lambda5Save2 = pow2(Lambda5Save); + valueNow = valueIn; + scale2Now = MZ * MZ; + isInit = true; + +} + +//-------------------------------------------------------------------------- + +// Calculate alpha_s value + +double AlphaStrong::alphaS( double scale2) { + + // Check for initialization and ensure minimal scale2 value. + if (!isInit) return 0.; + if (scale2 < scale2Min) scale2 = scale2Min; + + // If equal to old scale then same answer. + if (scale2 == scale2Now && (order < 2 || lastCallToFull)) return valueNow; + scale2Now = scale2; + lastCallToFull = true; + + // Fix alpha_s. + if (order == 0) { + valueNow = valueRef; + + // First order alpha_s: differs by mass region. + } else if (order == 1) { + if (scale2 > mb2) + valueNow = 12. * M_PI / (23. * log(scale2/Lambda5Save2)); + else if (scale2 > mc2) + valueNow = 12. * M_PI / (25. * log(scale2/Lambda4Save2)); + else valueNow = 12. * M_PI / (27. * log(scale2/Lambda3Save2)); + + // Second order alpha_s: differs by mass region. + } else { + double Lambda2, b0, b1, b2; + if (scale2 > mb2) { + Lambda2 = Lambda5Save2; + b0 = 23.; + b1 = 348. / 529.; + b2 = 224687. / 242208.; + } else if (scale2 > mc2) { + Lambda2 = Lambda4Save2; + b0 = 25.; + b1 = 462. / 625.; + b2 = 548575. / 426888.; + } else { + Lambda2 = Lambda3Save2; + b0 = 27.; + b1 = 64. / 81.; + b2 = 938709. / 663552.; + } + double logScale = log(scale2/Lambda2); + double loglogScale = log(logScale); + valueNow = 12. * M_PI / (b0 * logScale) + * ( 1. - b1 * loglogScale / logScale + + pow2(b1 / logScale) * (pow2(loglogScale - 0.5) + b2 - 1.25) ); + } + + // Done. + return valueNow; + +} + +//-------------------------------------------------------------------------- + +// Calculate alpha_s value, but only use up to first-order piece. +// (To be combined with alphaS2OrdCorr.) + +double AlphaStrong::alphaS1Ord( double scale2) { + + // Check for initialization and ensure minimal scale2 value. + if (!isInit) return 0.; + if (scale2 < scale2Min) scale2 = scale2Min; + + // If equal to old scale then same answer. + if (scale2 == scale2Now && (order < 2 || !lastCallToFull)) return valueNow; + scale2Now = scale2; + lastCallToFull = false; + + // Fix alpha_S. + if (order == 0) { + valueNow = valueRef; + + // First/second order alpha_s: differs by mass region. + } else { + if (scale2 > mb2) + valueNow = 12. * M_PI / (23. * log(scale2/Lambda5Save2)); + else if (scale2 > mc2) + valueNow = 12. * M_PI / (25. * log(scale2/Lambda4Save2)); + else valueNow = 12. * M_PI / (27. * log(scale2/Lambda3Save2)); + } + + // Done. + return valueNow; +} + +//-------------------------------------------------------------------------- + +// Calculates the second-order extra factor in alpha_s. +// (To be combined with alphaS1Ord.) + +double AlphaStrong::alphaS2OrdCorr( double scale2) { + + // Check for initialization and ensure minimal scale2 value. + if (!isInit) return 1.; + if (scale2 < scale2Min) scale2 = scale2Min; + + // Only meaningful for second order calculations. + if (order < 2) return 1.; + + // Second order correction term: differs by mass region. + double Lambda2, b0, b1, b2; + if (scale2 > mb2) { + Lambda2 = Lambda5Save2; + b0 = 23.; + b1 = 348. / 529.; + b2 = 224687. / 242208.; + } else if (scale2 > mc2) { + Lambda2 = Lambda4Save2; + b0 = 25.; + b1 = 462. / 625.; + b2 = 548575. / 426888.; + } else { + Lambda2 = Lambda3Save2; + b0 = 27.; + b1 = 64. / 81.; + b2 = 938709. / 663552.; + } + double logScale = log(scale2/Lambda2); + double loglogScale = log(logScale); + return ( 1. - b1 * loglogScale / logScale + + pow2(b1 / logScale) * (pow2(loglogScale - 0.5) + b2 - 1.25) ); + +} + +//========================================================================== + +// The AlphaEM class. + +//-------------------------------------------------------------------------- + +// Definitions of static variables. + +// Z0 mass. Used for normalization scale. +const double AlphaEM::MZ = 91.188; + +// Effective thresholds for electron, muon, light quarks, tau+c, b. +const double AlphaEM::Q2STEP[5] = {0.26e-6, 0.011, 0.25, 3.5, 90.}; + +// Running coefficients are sum charge2 / 3 pi in pure QED, here slightly +// enhanced for quarks to approximately account for QCD corrections. +const double AlphaEM::BRUNDEF[5] = {0.1061, 0.2122, 0.460, 0.700, 0.725}; + +//-------------------------------------------------------------------------- + +// Initialize alpha_EM calculation. + +void AlphaEM::init(int orderIn, Settings* settingsPtr) { + + // Order. Read in alpha_EM value at 0 and m_Z, and mass of Z. + order = orderIn; + alpEM0 = settingsPtr->parm("StandardModel:alphaEM0"); + alpEMmZ = settingsPtr->parm("StandardModel:alphaEMmZ"); + mZ2 = MZ * MZ; + + // AlphaEM values at matching scales and matching b value. + if (order <= 0) return; + for (int i = 0; i < 5; ++i) bRun[i] = BRUNDEF[i]; + + // Step down from mZ to tau/charm threshold. + alpEMstep[4] = alpEMmZ / ( 1. + alpEMmZ * bRun[4] + * log(mZ2 / Q2STEP[4]) ); + alpEMstep[3] = alpEMstep[4] / ( 1. - alpEMstep[4] * bRun[3] + * log(Q2STEP[3] / Q2STEP[4]) ); + + // Step up from me to light-quark threshold. + alpEMstep[0] = alpEM0; + alpEMstep[1] = alpEMstep[0] / ( 1. - alpEMstep[0] * bRun[0] + * log(Q2STEP[1] / Q2STEP[0]) ); + alpEMstep[2] = alpEMstep[1] / ( 1. - alpEMstep[1] * bRun[1] + * log(Q2STEP[2] / Q2STEP[1]) ); + + // Fit b in range between light-quark and tau/charm to join smoothly. + bRun[2] = (1./alpEMstep[3] - 1./alpEMstep[2]) + / log(Q2STEP[2] / Q2STEP[3]); + +} + +//-------------------------------------------------------------------------- + +// Calculate alpha_EM value + +double AlphaEM::alphaEM( double scale2) { + + // Fix alphaEM; for order = -1 fixed at m_Z. + if (order == 0) return alpEM0; + if (order < 0) return alpEMmZ; + + // Running alphaEM. + for (int i = 4; i >= 0; --i) if (scale2 > Q2STEP[i]) + return alpEMstep[i] / (1. - bRun[i] * alpEMstep[i] + * log(scale2 / Q2STEP[i]) ); + return alpEM0; + +} + +//========================================================================== + +// The CoupSM class. + +//-------------------------------------------------------------------------- + +// Definitions of static variables: charges and axial couplings. +const double CoupSM::efSave[20] = { 0., -1./3., 2./3., -1./3., 2./3., -1./3., + 2./3., -1./3., 2./3., 0., 0., -1., 0., -1., 0., -1., 0., -1., 0., 0.}; +const double CoupSM::afSave[20] = { 0., -1., 1., -1., 1., -1., 1., -1., 1., + 0., 0., -1., 1., -1., 1., -1., 1., -1., 1., 0.}; + +//-------------------------------------------------------------------------- + +// Initialize electroweak mixing angle and couplings, and CKM matrix elements. + +void CoupSM::init(Settings& settings, Rndm* rndmPtrIn) { + + // Store input pointer; + rndmPtr = rndmPtrIn; + + // Initialize the local AlphaStrong instance. + double alphaSvalue = settings.parm("SigmaProcess:alphaSvalue"); + int alphaSorder = settings.mode("SigmaProcess:alphaSorder"); + alphaSlocal.init( alphaSvalue, alphaSorder); + + // Initialize the local AlphaEM instance. + int order = settings.mode("SigmaProcess:alphaEMorder"); + alphaEMlocal.init( order, &settings); + + // Read in electroweak mixing angle. + s2tW = settings.parm("StandardModel:sin2thetaW"); + c2tW = 1. - s2tW; + s2tWbar = settings.parm("StandardModel:sin2thetaWbar"); + + // Initialize electroweak couplings. + for (int i = 0; i < 20; ++i) { + vfSave[i] = afSave[i] - 4. * s2tWbar * efSave[i]; + lfSave[i] = afSave[i] - 2. * s2tWbar * efSave[i]; + rfSave[i] = - 2. * s2tWbar * efSave[i]; + ef2Save[i] = pow2(efSave[i]); + vf2Save[i] = pow2(vfSave[i]); + af2Save[i] = pow2(afSave[i]); + efvfSave[i] = efSave[i] * vfSave[i]; + vf2af2Save[i] = vf2Save[i] + af2Save[i]; + } + + // Read in CKM matrix element values and store them. + VCKMsave[1][1] = settings.parm("StandardModel:Vud"); + VCKMsave[1][2] = settings.parm("StandardModel:Vus"); + VCKMsave[1][3] = settings.parm("StandardModel:Vub"); + VCKMsave[2][1] = settings.parm("StandardModel:Vcd"); + VCKMsave[2][2] = settings.parm("StandardModel:Vcs"); + VCKMsave[2][3] = settings.parm("StandardModel:Vcb"); + VCKMsave[3][1] = settings.parm("StandardModel:Vtd"); + VCKMsave[3][2] = settings.parm("StandardModel:Vts"); + VCKMsave[3][3] = settings.parm("StandardModel:Vtb"); + + // Also allow for the potential existence of a fourth generation. + VCKMsave[1][4] = settings.parm("FourthGeneration:VubPrime"); + VCKMsave[2][4] = settings.parm("FourthGeneration:VcbPrime"); + VCKMsave[3][4] = settings.parm("FourthGeneration:VtbPrime"); + VCKMsave[4][1] = settings.parm("FourthGeneration:VtPrimed"); + VCKMsave[4][2] = settings.parm("FourthGeneration:VtPrimes"); + VCKMsave[4][3] = settings.parm("FourthGeneration:VtPrimeb"); + VCKMsave[4][4] = settings.parm("FourthGeneration:VtPrimebPrime"); + + // Calculate squares of matrix elements. + for(int i = 1; i < 5; ++i) for(int j = 1; j < 5; ++j) + V2CKMsave[i][j] = pow2(VCKMsave[i][j]); + + // Sum VCKM^2_out sum for given incoming flavour, excluding top as partner. + V2CKMout[1] = V2CKMsave[1][1] + V2CKMsave[2][1]; + V2CKMout[2] = V2CKMsave[1][1] + V2CKMsave[1][2] + V2CKMsave[1][3]; + V2CKMout[3] = V2CKMsave[1][2] + V2CKMsave[2][2]; + V2CKMout[4] = V2CKMsave[2][1] + V2CKMsave[2][2] + V2CKMsave[2][3]; + V2CKMout[5] = V2CKMsave[1][3] + V2CKMsave[2][3]; + V2CKMout[6] = V2CKMsave[3][1] + V2CKMsave[3][2] + V2CKMsave[3][3]; + V2CKMout[7] = V2CKMsave[1][4] + V2CKMsave[2][4]; + V2CKMout[8] = V2CKMsave[4][1] + V2CKMsave[4][2] + V2CKMsave[4][3]; + for (int i = 11; i <= 18; ++i) V2CKMout[i] = 1.; + +} + +//-------------------------------------------------------------------------- + +// Return CKM value for incoming flavours (sign irrelevant). + +double CoupSM::VCKMid(int id1, int id2) { + + // Use absolute sign (want to cover both f -> f' W and f fbar' -> W). + int id1Abs = abs(id1); + int id2Abs = abs(id2); + if (id1Abs == 0 || id2Abs == 0 || (id1Abs + id2Abs)%2 != 1) return 0.; + + // Ensure proper order before reading out from VCKMsave or lepton match. + if (id1Abs%2 == 1) swap(id1Abs, id2Abs); + if (id1Abs <= 8 && id2Abs <= 8) return VCKMsave[id1Abs/2][(id2Abs + 1)/2]; + if ( (id1Abs == 12 || id1Abs == 14 || id1Abs == 16 || id1Abs == 18) + && id2Abs == id1Abs - 1 ) return 1.; + + // No more valid cases. + return 0.; + +} + +//-------------------------------------------------------------------------- + +// Return squared CKM value for incoming flavours (sign irrelevant). + +double CoupSM::V2CKMid(int id1, int id2) { + + // Use absolute sign (want to cover both f -> f' W and f fbar' -> W). + int id1Abs = abs(id1); + int id2Abs = abs(id2); + if (id1Abs == 0 || id2Abs == 0 || (id1Abs + id2Abs)%2 != 1) return 0.; + + // Ensure proper order before reading out from V2CKMsave or lepton match. + if (id1Abs%2 == 1) swap(id1Abs, id2Abs); + if (id1Abs <= 8 && id2Abs <= 8) return V2CKMsave[id1Abs/2][(id2Abs + 1)/2]; + if ( (id1Abs == 12 || id1Abs == 14 || id1Abs == 16 || id1Abs == 18) + && id2Abs == id1Abs - 1 ) return 1.; + + // No more valid cases. + return 0.; + +} + +//-------------------------------------------------------------------------- + +// Pick an outgoing flavour for given incoming one, given CKM mixing. + +int CoupSM::V2CKMpick(int id) { + + // Initial values. + int idIn = abs(id); + int idOut = 0; + + // Quarks: need to make random choice. + if (idIn >= 1 && idIn <= 8) { + double V2CKMrndm = rndmPtr->flat() * V2CKMout[idIn]; + if (idIn == 1) idOut = (V2CKMrndm < V2CKMsave[1][1]) ? 2 : 4; + else if (idIn == 2) idOut = (V2CKMrndm < V2CKMsave[1][1]) ? 1 + : ( (V2CKMrndm < V2CKMsave[1][1] + V2CKMsave[1][2]) ? 3 : 5 ); + else if (idIn == 3) idOut = (V2CKMrndm < V2CKMsave[1][2]) ? 2 : 4; + else if (idIn == 4) idOut = (V2CKMrndm < V2CKMsave[2][1]) ? 1 + : ( (V2CKMrndm < V2CKMsave[2][1] + V2CKMsave[2][2]) ? 3 : 5 ); + else if (idIn == 5) idOut = (V2CKMrndm < V2CKMsave[1][3]) ? 2 : 4; + else if (idIn == 6) idOut = (V2CKMrndm < V2CKMsave[3][1]) ? 1 + : ( (V2CKMrndm < V2CKMsave[3][1] + V2CKMsave[3][2]) ? 3 : 5 ); + else if (idIn == 7) idOut = (V2CKMrndm < V2CKMsave[1][4]) ? 2 : 4; + else if (idIn == 8) idOut = (V2CKMrndm < V2CKMsave[4][1]) ? 1 + : ( (V2CKMrndm < V2CKMsave[4][1] + V2CKMsave[4][2]) ? 3 : 5 ); + + // Leptons: unambiguous. + } else if (idIn >= 11 && idIn <= 18) { + if (idIn%2 == 1) idOut = idIn + 1; + else idOut = idIn - 1; + } + + // Done. Return with sign. + return ( (id > 0) ? idOut : -idOut ); + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/StringFragmentation.cxx b/PYTHIA8/pythia8140/src/StringFragmentation.cxx new file mode 100644 index 00000000000..fba1c22e33e --- /dev/null +++ b/PYTHIA8/pythia8140/src/StringFragmentation.cxx @@ -0,0 +1,1220 @@ +// StringFragmentation.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the StringEnd and +// StringFragmentation classes. + +#include "StringFragmentation.h" + +namespace Pythia8 { + +//========================================================================== + +// The StringEnd class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. + +// Avoid unphysical solutions to equation system. +const double StringEnd::TINY = 1e-6; + +// Assume two (eX, eY) regions are related if pT2 differs by less. +const double StringEnd::PT2SAME = 0.01; + +//-------------------------------------------------------------------------- + +// Set up initial endpoint values from input. + +void StringEnd::setUp(bool fromPosIn, int iEndIn, int idOldIn, int iMaxIn, + double pxIn, double pyIn, double GammaIn, double xPosIn, double xNegIn) { + + // Simple transcription from input. + fromPos = fromPosIn; + iEnd = iEndIn; + iMax = iMaxIn; + flavOld = FlavContainer(idOldIn); + pxOld = pxIn; + pyOld = pyIn; + GammaOld = GammaIn; + iPosOld = (fromPos) ? 0 : iMax; + iNegOld = (fromPos) ? iMax : 0; + xPosOld = xPosIn; + xNegOld = xNegIn; + +} + +//-------------------------------------------------------------------------- + +// Fragment off one hadron from the string system, in flavour and pT. + +void StringEnd::newHadron() { + + // Pick new flavour and form a new hadron. + do { + flavNew = flavSelPtr->pick( flavOld); + idHad = flavSelPtr->combine( flavOld, flavNew); + } while (idHad == 0); + + // Pick its transverse momentum. + pair pxy = pTSelPtr->pxy(); + pxNew = pxy.first; + pyNew = pxy.second; + pxHad = pxOld + pxNew; + pyHad = pyOld + pyNew; + + // Pick its mass and thereby define its transverse mass. + mHad = particleDataPtr->mass(idHad); + mT2Had = pow2(mHad) + pow2(pxHad) + pow2(pyHad); + +} + +//-------------------------------------------------------------------------- + +// Fragment off one hadron from the string system, in momentum space, +// by taking steps from positive end. + +Vec4 StringEnd::kinematicsHadron( StringSystem& system) { + + // Pick fragmentation step z and calculate new Gamma. + zHad = zSelPtr->zFrag( flavOld.id, flavNew.id, mT2Had); + GammaNew = (1. - zHad) * (GammaOld + mT2Had / zHad); + + // Set up references that are direction-neutral; + // ...Dir for direction of iteration and ...Inv for its inverse. + int& iDirOld = (fromPos) ? iPosOld : iNegOld; + int& iInvOld = (fromPos) ? iNegOld : iPosOld; + int& iDirNew = (fromPos) ? iPosNew : iNegNew; + int& iInvNew = (fromPos) ? iNegNew : iPosNew; + double& xDirOld = (fromPos) ? xPosOld : xNegOld; + double& xInvOld = (fromPos) ? xNegOld : xPosOld; + double& xDirNew = (fromPos) ? xPosNew : xNegNew; + double& xInvNew = (fromPos) ? xNegNew : xPosNew; + double& xDirHad = (fromPos) ? xPosHad : xNegHad; + double& xInvHad = (fromPos) ? xNegHad : xPosHad; + + // Start search for new breakup in the old region. + iDirNew = iDirOld; + iInvNew = iInvOld; + Vec4 pTNew; + + // Each step corresponds to trying a new string region. + for (int iStep = 0; ; ++iStep) { + + // Referance to current string region. + StringRegion& region = system.region( iPosNew, iNegNew); + + // Now begin special section for rapid processing of low region. + if (iStep == 0 && iPosOld + iNegOld == iMax) { + + // A first step within a low region is easy. + if (mT2Had < zHad * xDirOld * (1. - xInvOld) * region.w2) { + + // Translate into x coordinates. + xDirHad = zHad * xDirOld; + xInvHad = mT2Had / (xDirHad * region.w2); + xDirNew = xDirOld - xDirHad; + xInvNew = xInvOld + xInvHad; + + // Find and return four-momentum of the produced particle. + return region.pHad( xPosHad, xNegHad, pxHad, pyHad); + + // A first step out of a low region also OK, if there are more regions. + // Negative energy signals failure, i.e. in last region. + } else { + --iInvNew; + if (iInvNew < 0) return Vec4(0., 0., 0., -1.); + + // Momentum taken by stepping out of region. Continue to next region. + xInvHad = 1. - xInvOld; + xDirHad = 0.; + pSoFar = region.pHad( xPosHad, xNegHad, pxOld, pyOld); + continue; + } + + // Else, for first step, take into account starting pT. + } else if (iStep == 0) { + pSoFar = region.pHad( 0., 0., pxOld, pyOld); + pTNew = region.pHad( 0., 0., pxNew, pyNew); + } + + // Now begin normal treatment of nontrivial regions. + // Set up four-vectors in a region not visited before. + if (!region.isSetUp) region.setUp( + system.regionLowPos(iPosNew).pPos, + system.regionLowNeg(iNegNew).pNeg, true); + + // If new region is vanishingly small, continue immediately to next. + // Negative energy signals failure to do this, i.e. moved too low. + if (region.isEmpty) { + xDirHad = (iDirNew == iDirOld) ? xDirOld : 1.; + xInvHad = 0.; + pSoFar += region.pHad( xPosHad, xNegHad, 0., 0.); + ++iDirNew; + if (iDirNew + iInvNew > iMax) return Vec4(0., 0., 0., -1.); + continue; + } + + // Reexpress pTNew w.r.t. base vectors in new region, if possible. + // Recall minus sign from normalization e_x^2 = e_y^2 = -1. + double pxNewTemp = -pTNew * region.eX; + double pyNewTemp = -pTNew * region.eY; + if (abs( pxNewTemp * pxNewTemp + pyNewTemp * pyNewTemp + - pxNew * pxNew - pyNew * pyNew) < PT2SAME) { + pxNew = pxNewTemp; + pyNew = pyNewTemp; + } + + // Four-momentum taken so far, including new pT. + Vec4 pTemp = pSoFar + region.pHad( 0., 0., pxNew, pyNew); + + // Derive coefficients for m2 expression. + // cM2 * x+ + cM3 * x- + cM4 * x+ * x- = m^2 - cM1; + double cM1 = pTemp.m2Calc(); + double cM2 = 2. * (pTemp * region.pPos); + double cM3 = 2. * (pTemp * region.pNeg); + double cM4 = region.w2; + if (!fromPos) swap( cM2, cM3); + + // Derive coefficients for Gamma expression. + // cGam2 * x+ + cGam3 * x- + cGam4 * x+ * x- = Gamma_new - cGam1; + double cGam1 = 0.; + double cGam2 = 0.; + double cGam3 = 0.; + double cGam4 = 0.; + for (int iInv = iInvNew; iInv <= iMax - iDirNew; ++iInv) { + double xInv = 1.; + if (iInv == iInvNew) xInv = (iInvNew == iInvOld) ? xInvOld : 0.; + for (int iDir = iDirNew; iDir <= iMax - iInv; ++iDir) { + double xDir = (iDir == iDirOld) ? xDirOld : 1.; + int iPos = (fromPos) ? iDir : iInv; + int iNeg = (fromPos) ? iInv : iDir; + StringRegion& regionGam = system.region( iPos, iNeg); + if (!regionGam.isSetUp) regionGam.setUp( + system.regionLowPos(iPos).pPos, + system.regionLowNeg(iNeg).pNeg, true); + double w2 = regionGam.w2; + cGam1 += xDir * xInv * w2; + if (iDir == iDirNew) cGam2 -= xInv * w2; + if (iInv == iInvNew) cGam3 += xDir * w2; + if (iDir == iDirNew && iInv == iInvNew) cGam4 -= w2; + } + } + + // Solve (m2, Gamma) equation system => r2 * x-^2 + r1 * x- + r0 = 0. + double cM0 = pow2(mHad) - cM1; + double cGam0 = GammaNew - cGam1; + double r2 = cM3 * cGam4 - cM4 * cGam3; + double r1 = cM4 * cGam0 - cM0 * cGam4 + cM3 * cGam2 - cM2 * cGam3; + double r0 = cM2 * cGam0 - cM0 * cGam2; + double root = sqrtpos( r1*r1 - 4. * r2 * r0 ); + if (abs(r2) < TINY || root < TINY) return Vec4(0., 0., 0., -1.); + xInvHad = 0.5 * (root / abs(r2) - r1 / r2); + xDirHad = (cM0 - cM3 * xInvHad) / (cM2 + cM4 * xInvHad); + + // Define position of new trial vertex. + xDirNew = (iDirNew == iDirOld) ? xDirOld - xDirHad : 1. - xDirHad; + xInvNew = (iInvNew == iInvOld) ? xInvOld + xInvHad : xInvHad; + + // Step up to new region if new x- > 1. + if (xInvNew > 1.) { + xInvHad = (iInvNew == iInvOld) ? 1. - xInvOld : 1.; + xDirHad = 0.; + pSoFar += region.pHad( xPosHad, xNegHad, 0., 0.); + --iInvNew; + if (iInvNew < 0) return Vec4(0., 0., 0., -1.); + continue; + + // Step down to new region if new x+ < 0. + } else if (xDirNew < 0.) { + xDirHad = (iDirNew == iDirOld) ? xDirOld : 1.; + xInvHad = 0.; + pSoFar += region.pHad( xPosHad, xNegHad, 0., 0.); + ++iDirNew; + if (iDirNew + iInvNew > iMax) return Vec4(0., 0., 0., -1.); + continue; + } + + // Else we have found the correct region, and can return four-momentum. + return pSoFar + region.pHad( xPosHad, xNegHad, pxNew, pyNew); + + // End of "infinite" loop of stepping to new region. + } + +} + +//-------------------------------------------------------------------------- + +// Update string end information after a hadron has been removed. + +void StringEnd::update() { + + flavOld.anti(flavNew); + iPosOld = iPosNew; + iNegOld = iNegNew; + pxOld = -pxNew; + pyOld = -pyNew; + GammaOld = GammaNew; + xPosOld = xPosNew; + xNegOld = xNegNew; + +} + +//========================================================================== + +// The StringFragmentation class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Maximum number of tries to (flavour-, energy) join the two string ends. +const int StringFragmentation::NTRYFLAV = 10; +const int StringFragmentation::NTRYJOIN = 25; + +// The last few times gradually increase the stop mass to make it easier. +const int StringFragmentation::NSTOPMASS = 10; +const double StringFragmentation::FACSTOPMASS = 1.05; + +// For closed string, pick a Gamma by taking a step with fictitious mass. +const double StringFragmentation::CLOSEDM2MAX = 25.; +const double StringFragmentation::CLOSEDM2FRAC = 0.1; + +// Do not allow too large argument to exp function. +const double StringFragmentation::EXPMAX = 50.; + +// Matching criterion that p+ and p- not the same (can happen in gg loop). +const double StringFragmentation::MATCHPOSNEG = 1e-6; + +// For pull on junction, do not trace too far down each leg. +const double StringFragmentation::EJNWEIGHTMAX = 10.; + +// Iterate junction rest frame boost until convergence or too many tries. +const double StringFragmentation::CONVJNREST = 1e-5; +const int StringFragmentation::NTRYJNREST = 20; + +// Fail and try again when two legs combined to diquark (3 loops). +const int StringFragmentation::NTRYJNMATCH = 20; + +// Consider junction-leg parton as massless if m2 tiny. +const double StringFragmentation::M2MAXJRF = 1e-4; + +// Iterate junction rest frame equation until convergence or too many tries. +const double StringFragmentation::CONVJRFEQ = 1e-12; +const int StringFragmentation::NTRYJRFEQ = 40; + +//-------------------------------------------------------------------------- + +// Initialize and save pointers. + +void StringFragmentation::init(Info* infoPtrIn, Settings& settings, + ParticleData* particleDataPtrIn, Rndm* rndmPtrIn, StringFlav* flavSelPtrIn, + StringPT* pTSelPtrIn, StringZ* zSelPtrIn) { + + // Save pointers. + infoPtr = infoPtrIn; + particleDataPtr = particleDataPtrIn; + rndmPtr = rndmPtrIn; + flavSelPtr = flavSelPtrIn; + pTSelPtr = pTSelPtrIn; + zSelPtr = zSelPtrIn; + + // Initialize the StringFragmentation class. + stopMass = settings.parm("StringFragmentation:stopMass"); + stopNewFlav = settings.parm("StringFragmentation:stopNewFlav"); + stopSmear = settings.parm("StringFragmentation:stopSmear"); + eNormJunction = settings.parm("StringFragmentation:eNormJunction"); + eBothLeftJunction + = settings.parm("StringFragmentation:eBothLeftJunction"); + eMaxLeftJunction + = settings.parm("StringFragmentation:eMaxLeftJunction"); + eMinLeftJunction + = settings.parm("StringFragmentation:eMinLeftJunction"); + + // Initialize the b parameter of the z spectrum, used when joining jets. + bLund = settings.parm("StringZ:bLund"); + + // Initialize the hadrons instance of an event record. + hadrons.init( "(string fragmentation)", particleDataPtr); + + // Send on pointers to the two StringEnd instances. + posEnd.init( particleDataPtr, flavSelPtr, pTSelPtr, zSelPtr); + negEnd.init( particleDataPtr, flavSelPtr, pTSelPtr, zSelPtr); + +} + +//-------------------------------------------------------------------------- + +// Perform the fragmentation. + +bool StringFragmentation::fragment( int iSub, ColConfig& colConfig, + Event& event) { + + // Find partons and their total four-momentum. + iParton = colConfig[iSub].iParton; + iPos = iParton[0]; + if (iPos < 0) iPos = iParton[1]; + int idPos = event[iPos].id(); + iNeg = iParton.back(); + int idNeg = event[iNeg].id(); + pSum = colConfig[iSub].pSum; + + // Reset the local event record. + hadrons.clear(); + + // For closed gluon string: pick first breakup region. + isClosed = colConfig[iSub].isClosed; + if (isClosed) iParton = findFirstRegion(iParton, event); + + // For junction topology: fragment off two of the string legs. + // Then iParton overwritten to remaining leg + leftover diquark. + pJunctionHadrons = 0.; + hasJunction = colConfig[iSub].hasJunction; + if (hasJunction && !fragmentToJunction(event)) return false; + int junctionHadrons = hadrons.size(); + if (hasJunction) { + idPos = event[ iParton[0] ].id(); + idNeg = event.back().id(); + pSum -= pJunctionHadrons; + } + + // Set up kinematics of string evolution ( = motion). + system.setUp(iParton, event); + stopMassNow = stopMass; + + // Fallback loop, when joining in the middle fails. Bailout if stuck. + for ( int iTry = 0; ; ++iTry) { + if (iTry > NTRYJOIN) { + infoPtr->errorMsg("Error in StringFragmentation::fragment: " + "stuck in joining"); + if (hasJunction) event.popBack(1); + return false; + } + + // After several failed tries gradually allow larger stop mass. + if (iTry > NTRYJOIN - NSTOPMASS) stopMassNow *= FACSTOPMASS; + + // Set up flavours of two string ends, and reset other info. + setStartEnds(idPos, idNeg, system); + pRem = pSum; + + // Begin fragmentation loop, interleaved from the two ends. + bool fromPos; + for ( ; ; ) { + + // Take a step either from the positive or the negative end. + fromPos = (rndmPtr->flat() < 0.5); + StringEnd& nowEnd = (fromPos) ? posEnd : negEnd; + + // Construct trial hadron and check that energy remains. + nowEnd.newHadron(); + if ( energyUsedUp(fromPos) ) break; + + // Construct kinematics of the new hadron and store it. + Vec4 pHad = nowEnd.kinematicsHadron(system); + int statusHad = (fromPos) ? 83 : 84; + hadrons.append( nowEnd.idHad, statusHad, iPos, iNeg, + 0, 0, 0, 0, pHad, nowEnd.mHad); + if (pHad.e() < 0.) break; + + // Update string end and remaining momentum. + nowEnd.update(); + pRem -= pHad; + + // End of fragmentation loop. + } + + // When done, join in the middle. If this works, then really done. + if ( finalTwo(fromPos) ) break; + + // Else remove produced particles (except from first two junction legs) + // and start all over. + int newHadrons = hadrons.size() - junctionHadrons; + hadrons.popBack(newHadrons); + } + + // Junctions: remove fictitious end, restore original parton list + if (hasJunction) { + event.popBack(1); + iParton = colConfig[iSub].iParton; + } + + // Store the hadrons in the normal event record, ordered from one end. + store(event); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Find region where to put first string break for closed gluon loop. + +vector StringFragmentation::findFirstRegion(vector& iPartonIn, + Event& event) { + + // Evaluate mass-squared for all adjacent gluon pairs. + vector m2Pair; + double m2Sum = 0.; + int size = iPartonIn.size(); + for (int i = 0; i < size; ++i) { + double m2Now = 0.5 * event[ iPartonIn[i] ].p() + * event[ iPartonIn[(i + 1)%size] ].p(); + m2Pair.push_back(m2Now); + m2Sum += m2Now; + } + + // Pick breakup region with probability proportional to mass-squared. + double m2Reg = m2Sum * rndmPtr->flat(); + int iReg = -1; + do m2Reg -= m2Pair[++iReg]; + while (m2Reg > 0. && iReg < size - 1); + + // Create reordered parton list, with breakup string region duplicated. + vector iPartonOut; + for (int i = 0; i < size + 2; ++i) + iPartonOut.push_back( iPartonIn[(i + iReg)%size] ); + + // Done. + return iPartonOut; + +} + +//-------------------------------------------------------------------------- + +// Set flavours and momentum position for initial string endpoints. + +void StringFragmentation::setStartEnds( int idPos, int idNeg, + StringSystem systemNow) { + + // Variables characterizing string endpoints: defaults for open string. + double px = 0.; + double py = 0.; + double Gamma = 0.; + double xPosFromPos = 1.; + double xNegFromPos = 0.; + double xPosFromNeg = 0.; + double xNegFromNeg = 1.; + + // For closed gluon loop need to pick an initial flavour. + if (isClosed) { + do { + int idTry = flavSelPtr->pickLightQ(); + FlavContainer flavTry(idTry, 1); + flavTry = flavSelPtr->pick( flavTry); + flavTry = flavSelPtr->pick( flavTry); + idPos = flavTry.id; + idNeg = -idPos; + } while (idPos == 0); + + // Also need pT and breakup vertex position in region. + pair pxy = pTSelPtr->pxy(); + px = pxy.first; + py = pxy.second; + double m2Region = systemNow.regionLowPos(0).w2; + double m2Temp = min( CLOSEDM2MAX, CLOSEDM2FRAC * m2Region); + do { + double zTemp = zSelPtr->zFrag( idPos, idNeg, m2Temp); + xPosFromPos = 1. - zTemp; + xNegFromPos = m2Temp / (zTemp * m2Region); + } while (xNegFromPos > 1.); + Gamma = xPosFromPos * xNegFromPos * m2Region; + xPosFromNeg = xPosFromPos; + xNegFromNeg = xNegFromPos; + } + + // Initialize two string endpoints. + posEnd.setUp( true, iPos, idPos, systemNow.iMax, px, py, + Gamma, xPosFromPos, xNegFromPos); + negEnd.setUp( false, iNeg, idNeg, systemNow.iMax, -px, -py, + Gamma, xPosFromNeg, xNegFromNeg); + + // For closed gluon loop can allow popcorn on one side but not both. + if (isClosed) { + flavSelPtr->assignPopQ(posEnd.flavOld); + flavSelPtr->assignPopQ(negEnd.flavOld); + if (rndmPtr->flat() < 0.5) posEnd.flavOld.nPop = 0; + else negEnd.flavOld.nPop = 0; + posEnd.flavOld.rank = 1; + negEnd.flavOld.rank = 1; + } + + // Done. + +} + +//-------------------------------------------------------------------------- + +// Check remaining energy-momentum whether it is OK to continue. + +bool StringFragmentation::energyUsedUp(bool fromPos) { + + // If remaining negative energy then abort right away. + if (pRem.e() < 0.) return true; + + // Calculate W2_minimum and done if remaining W2 is below it. + double wMin = stopMassNow + + particleDataPtr->constituentMass(posEnd.flavOld.id) + + particleDataPtr->constituentMass(negEnd.flavOld.id); + if (fromPos) wMin += stopNewFlav + * particleDataPtr->constituentMass(posEnd.flavNew.id); + else wMin += stopNewFlav + * particleDataPtr->constituentMass(negEnd.flavNew.id); + wMin *= 1. + (2. * rndmPtr->flat() - 1.) * stopSmear; + w2Rem = pRem.m2Calc(); + if (w2Rem < pow2(wMin)) return true; + + // Else still enough energy left to continue iteration. + return false; + +} + +//-------------------------------------------------------------------------- + +// Produce the final two partons to complete the system. + +bool StringFragmentation::finalTwo(bool fromPos) { + + // Check whether we went too far in p+-. + if (pRem.e() < 0. || w2Rem < 0. || (hadrons.size() > 0 + && hadrons.back().e() < 0.) ) return false; + if ( posEnd.iPosOld > negEnd.iPosOld || negEnd.iNegOld > posEnd.iNegOld) + return false; + if ( posEnd.iPosOld == negEnd.iPosOld && posEnd.xPosOld < negEnd.xPosOld) + return false; + if ( posEnd.iNegOld == negEnd.iNegOld && posEnd.xNegOld > negEnd.xNegOld) + return false; + + // Construct the final hadron from the leftover flavours. + // Impossible to join two diquarks. Also break if stuck for other reason. + FlavContainer flav1 = (fromPos) ? posEnd.flavNew.anti() : posEnd.flavOld; + FlavContainer flav2 = (fromPos) ? negEnd.flavOld : negEnd.flavNew.anti(); + if (abs(flav1.id) > 8 && abs(flav2.id) > 8) return false; + int idHad; + for (int iTry = 0; iTry < NTRYFLAV; ++iTry) { + idHad = flavSelPtr->combine( flav1, flav2); + if (idHad != 0) break; + } + if (idHad == 0) return false; + + // Store the final particle and its new pT, and construct its mass. + if (fromPos) { + negEnd.idHad = idHad; + negEnd.pxNew = -posEnd.pxNew; + negEnd.pyNew = -posEnd.pyNew; + negEnd.mHad = particleDataPtr->mass(idHad); + } else { + posEnd.idHad = idHad; + posEnd.pxNew = -negEnd.pxNew; + posEnd.pyNew = -negEnd.pyNew; + posEnd.mHad = particleDataPtr->mass(idHad); + } + + // String region in which to do the joining. + StringRegion region = finalRegion(); + if (region.isEmpty) return false; + + // Project remaining momentum along longitudinal and transverse directions. + region.project( pRem); + double pxRem = region.px() - posEnd.pxOld - negEnd.pxOld; + double pyRem = region.py() - posEnd.pyOld - negEnd.pyOld; + double xPosRem = region.xPos(); + double xNegRem = region.xNeg(); + + // Share extra pT kick evenly between final two hadrons. + posEnd.pxOld += 0.5 * pxRem; + posEnd.pyOld += 0.5 * pyRem; + negEnd.pxOld += 0.5 * pxRem; + negEnd.pyOld += 0.5 * pyRem; + + // Construct new pT and mT of the final two particles. + posEnd.pxHad = posEnd.pxOld + posEnd.pxNew; + posEnd.pyHad = posEnd.pyOld + posEnd.pyNew; + posEnd.mT2Had = pow2(posEnd.mHad) + pow2(posEnd.pxHad) + + pow2(posEnd.pyHad); + negEnd.pxHad = negEnd.pxOld + negEnd.pxNew; + negEnd.pyHad = negEnd.pyOld + negEnd.pyNew; + negEnd.mT2Had = pow2(negEnd.mHad) + pow2(negEnd.pxHad) + + pow2(negEnd.pyHad); + + // Construct remaining system transverse mass. + double wT2Rem = w2Rem + pow2( posEnd.pxHad + negEnd.pxHad) + + pow2( posEnd.pyHad + negEnd.pyHad); + + // Check that kinematics possible. + if ( sqrt(wT2Rem) < sqrt(posEnd.mT2Had) + sqrt(negEnd.mT2Had) ) + return false; + double lambda2 = pow2( wT2Rem - posEnd.mT2Had - negEnd.mT2Had) + - 4. * posEnd.mT2Had * negEnd.mT2Had; + if (lambda2 <= 0.) return false; + + // Construct kinematics, as viewed in the transverse rest frame. + double lambda = sqrt(lambda2); + double probReverse = 1. / (1. + exp( min( EXPMAX, bLund * lambda) ) ); + double xpzPos = 0.5 * lambda/ wT2Rem; + if (probReverse > rndmPtr->flat()) xpzPos = -xpzPos; + double xmDiff = (posEnd.mT2Had - negEnd.mT2Had) / wT2Rem; + double xePos = 0.5 * (1. + xmDiff); + double xeNeg = 0.5 * (1. - xmDiff ); + + // Translate this into kinematics in the string frame. + Vec4 pHadPos = region.pHad( (xePos + xpzPos) * xPosRem, + (xePos - xpzPos) * xNegRem, posEnd.pxHad, posEnd.pyHad); + Vec4 pHadNeg = region.pHad( (xeNeg - xpzPos) * xPosRem, + (xeNeg + xpzPos) * xNegRem, negEnd.pxHad, negEnd.pyHad); + + // Add produced particles to the event record. + hadrons.append( posEnd.idHad, 83, posEnd.iEnd, negEnd.iEnd, + 0, 0, 0, 0, pHadPos, posEnd.mHad); + hadrons.append( negEnd.idHad, 84, posEnd.iEnd, negEnd.iEnd, + 0, 0, 0, 0, pHadNeg, negEnd.mHad); + + // It worked. + return true; + +} + +//-------------------------------------------------------------------------- + +// Construct a special joining region for the final two hadrons. + +StringRegion StringFragmentation::finalRegion() { + + // Simple case when both string ends are in the same region. + if (posEnd.iPosOld == negEnd.iPosOld && posEnd.iNegOld == negEnd.iNegOld) + return system.region( posEnd.iPosOld, posEnd.iNegOld); + + // Start out with empty region. (Empty used for error returns.) + StringRegion region; + + // Add up all remaining p+. + Vec4 pPosJoin; + if ( posEnd.iPosOld == negEnd.iPosOld) { + double xPosJoin = posEnd.xPosOld - negEnd.xPosOld; + if (xPosJoin < 0.) return region; + pPosJoin = system.regionLowPos(posEnd.iPosOld).pHad( xPosJoin, 0., 0., 0.); + } else { + for (int iPosNow = posEnd.iPosOld; iPosNow <= negEnd.iPosOld; ++iPosNow) { + if (iPosNow == posEnd.iPosOld) pPosJoin + += system.regionLowPos(iPosNow).pHad( posEnd.xPosOld, 0., 0., 0.); + else if (iPosNow == negEnd.iPosOld) pPosJoin + += system.regionLowPos(iPosNow).pHad( 1. - negEnd.xPosOld, 0., 0., 0.); + else pPosJoin += system.regionLowPos(iPosNow).pHad( 1., 0., 0., 0.); + } + } + + // Add up all remaining p-. + Vec4 pNegJoin; + if ( negEnd.iNegOld == posEnd.iNegOld) { + double xNegJoin = negEnd.xNegOld - posEnd.xNegOld; + if (xNegJoin < 0.) return region; + pNegJoin = system.regionLowNeg(negEnd.iNegOld).pHad( 0., xNegJoin, 0., 0.); + } else { + for (int iNegNow = negEnd.iNegOld; iNegNow <= posEnd.iNegOld; ++iNegNow) { + if (iNegNow == negEnd.iNegOld) pNegJoin + += system.regionLowNeg(iNegNow).pHad( 0., negEnd.xNegOld, 0., 0.); + else if (iNegNow == posEnd.iNegOld) pNegJoin + += system.regionLowNeg(iNegNow).pHad( 0., 1. - posEnd.xNegOld, 0., 0.); + else pNegJoin += system.regionLowNeg(iNegNow).pHad( 0., 1., 0., 0.); + } + } + + // For a closed gluon loop pPosJoin == pNegJoin and the above does not work. + // So reshuffle; "perfect" for g g systems, OK in general. + Vec4 pTest = pPosJoin - pNegJoin; + if ( abs(pTest.px()) + abs(pTest.py()) + abs(pTest.pz()) + abs(pTest.e()) + < MATCHPOSNEG * (pPosJoin.e() + pNegJoin.e()) ) { + Vec4 delta + = system.regionLowPos(posEnd.iPosOld + 1).pHad( 1., 0., 0., 0.) + - system.regionLowNeg(negEnd.iNegOld + 1).pHad( 0., 1., 0., 0.); + pPosJoin -= delta; + pNegJoin += delta; + } + + // Construct a new region from remaining p+ and p-. + region.setUp( pPosJoin, pNegJoin); + if (region.isEmpty) return region; + + // Project the existing pTold vectors onto the new directions. + Vec4 pTposOld = system.region( posEnd.iPosOld, posEnd.iNegOld).pHad( + 0., 0., posEnd.pxOld, posEnd.pyOld); + region.project( pTposOld); + posEnd.pxOld = region.px(); + posEnd.pyOld = region.py(); + Vec4 pTnegOld = system.region( negEnd.iPosOld, negEnd.iNegOld).pHad( + 0., 0., negEnd.pxOld, negEnd.pyOld); + region.project( pTnegOld); + negEnd.pxOld = region.px(); + negEnd.pyOld = region.py(); + + // Done. + return region; + +} + +//-------------------------------------------------------------------------- + +// Store the hadrons in the normal event record, ordered from one end. + +void StringFragmentation::store(Event& event) { + + // Starting position. + int iFirst = event.size(); + + // Copy straight over from first two junction legs. + if (hasJunction) { + for (int i = 0; i < hadrons.size(); ++i) + if (hadrons[i].status() == 85 || hadrons[i].status() == 86) + event.append( hadrons[i] ); + } + + // Loop downwards, copying all from the positive end. + for (int i = 0; i < hadrons.size(); ++i) + if (hadrons[i].status() == 83) event.append( hadrons[i] ); + + // Loop upwards, copying all from the negative end. + for (int i = hadrons.size() - 1; i >= 0 ; --i) + if (hadrons[i].status() == 84) event.append( hadrons[i] ); + int iLast = event.size() - 1; + + // Set decay vertex when this is displaced. + if (event[posEnd.iEnd].hasVertex()) { + Vec4 vDec = event[posEnd.iEnd].vDec(); + for (int i = iFirst; i <= iLast; ++i) event[i].vProd( vDec ); + } + + // Set lifetime of hadrons. + for (int i = iFirst; i <= iLast; ++i) + event[i].tau( event[i].tau0() * rndmPtr->exp() ); + + // Mark original partons as hadronized and set their daughter range. + for (int i = 0; i < int(iParton.size()); ++i) + if (iParton[i] >= 0) { + event[ iParton[i] ].statusNeg(); + event[ iParton[i] ].daughters(iFirst, iLast); + } + +} + +//-------------------------------------------------------------------------- + +// Fragment off two of the string legs in to a junction. + +bool StringFragmentation::fragmentToJunction(Event& event) { + + // Identify range of partons on the three legs. + // (Each leg begins with an iParton[i] = -(10 + 10*junctionNuber + leg), + // and partons then appear ordered from the junction outwards.) + int legBeg[3], legEnd[3]; + int leg = -1; + for (int i = 0; i < int(iParton.size()); ++i) { + if (iParton[i] < 0) legBeg[++leg] = i + 1; + else legEnd[leg] = i; + } + + // Iterate from system rest frame towards the junction rest frame (JRF). + RotBstMatrix MtoJRF, Mstep; + MtoJRF.bstback(pSum); + Vec4 pWTinJRF[3]; + int iter = 0; + double errInCM = 0.; + do { + ++iter; + + // Find weighted sum of momenta on the three sides of the junction. + for (leg = 0; leg < 3; ++ leg) { + pWTinJRF[leg] = 0.; + double eWeight = 0.; + for (int i = legBeg[leg]; i <= legEnd[leg]; ++i) { + Vec4 pTemp = event[ iParton[i] ].p(); + pTemp.rotbst(MtoJRF); + pWTinJRF[leg] += pTemp * exp(-eWeight); + eWeight += pTemp.e() / eNormJunction; + if (eWeight > EJNWEIGHTMAX) break; + } + } + + // Store original deviation from 120 degree topology. + if (iter == 1) errInCM = pow2(costheta(pWTinJRF[0], pWTinJRF[1]) + 0.5) + + pow2(costheta(pWTinJRF[0], pWTinJRF[2]) + 0.5) + + pow2(costheta(pWTinJRF[1], pWTinJRF[2]) + 0.5); + + // Find new JRF from the set of weighted momenta. + Mstep = junctionRestFrame( pWTinJRF[0], pWTinJRF[1], pWTinJRF[2]); + // Fortran code will not take full step after the first few + // iterations. How implement this in terms of an M matrix?? + MtoJRF.rotbst( Mstep ); + } while (iter < 3 || (Mstep.deviation() > CONVJNREST && iter < NTRYJNREST) ); + + // If final deviation from 120 degrees is bigger than in CM then revert. + double errInJRF = pow2(costheta(pWTinJRF[0], pWTinJRF[1]) + 0.5) + + pow2(costheta(pWTinJRF[0], pWTinJRF[2]) + 0.5) + + pow2(costheta(pWTinJRF[1], pWTinJRF[2]) + 0.5); + if (errInJRF > errInCM) { + infoPtr->errorMsg("Warning in StringFragmentation::fragmentTo" + "Junction: bad convergence junction rest frame"); + MtoJRF.reset(); + MtoJRF.bstback(pSum); + } + + // Opposite operation: boost from JRF to original system. + RotBstMatrix MfromJRF = MtoJRF; + MfromJRF.invert(); + + // Sum leg four-momenta in original frame and in JRF. + Vec4 pInLeg[3], pInJRF[3]; + for (leg = 0; leg < 3; ++leg) { + pInLeg[leg] = 0.; + for (int i = legBeg[leg]; i <= legEnd[leg]; ++i) + pInLeg[leg] += event[ iParton[i] ].p(); + pInJRF[leg] = pInLeg[leg]; + pInJRF[leg].rotbst(MtoJRF); + } + + // Pick the two legs with lowest energy in JRF. + int legMin = (pInJRF[0].e() < pInJRF[1].e()) ? 0 : 1; + int legMax = 1 - legMin; + if (pInJRF[2].e() < min(pInJRF[0].e(), pInJRF[1].e()) ) legMin = 2; + else if (pInJRF[2].e() > max(pInJRF[0].e(), pInJRF[1].e()) ) legMax = 2; + int legMid = 3 - legMin - legMax; + + // Save info on which status codes belong with the three legs. + int iJunction = (-iParton[0]) / 10 - 1; + event.statusJunction( iJunction, legMin, 85); + event.statusJunction( iJunction, legMid, 86); + event.statusJunction( iJunction, legMax, 83); + + // Temporarily copy the partons on the low-energy legs, into the JRF, + // in reverse order, so (anti)quark leg end first. + vector iPartonMin; + for (int i = legEnd[legMin]; i >= legBeg[legMin]; --i) { + int iNew = event.append( event[ iParton[i] ] ); + event[iNew].rotbst(MtoJRF); + iPartonMin.push_back( iNew ); + } + vector iPartonMid; + for (int i = legEnd[legMid]; i >= legBeg[legMid]; --i) { + int iNew = event.append( event[ iParton[i] ] ); + event[iNew].rotbst(MtoJRF); + iPartonMid.push_back( iNew ); + } + + // Find final weighted sum of momenta on each of the two legs. + double eWeight = 0.; + pWTinJRF[legMin] = 0.; + for (int i = iPartonMin.size() - 1; i >= 0; --i) { + pWTinJRF[legMin] += event[ iPartonMin[i] ].p() * exp(-eWeight); + eWeight += event[ iPartonMin[i] ].e() / eNormJunction; + if (eWeight > EJNWEIGHTMAX) break; + } + eWeight = 0.; + pWTinJRF[legMid] = 0.; + for (int i = iPartonMid.size() - 1; i >= 0; --i) { + pWTinJRF[legMid] += event[ iPartonMid[i] ].p() * exp(-eWeight); + eWeight += event[ iPartonMid[i] ].e() / eNormJunction; + if (eWeight > EJNWEIGHTMAX) break; + } + + // Define fictitious opposing partons in JRF and store as string ends. + Vec4 pOppose = pWTinJRF[legMin]; + pOppose.flip3(); + int idOppose = (rndmPtr->flat() > 0.5) ? 2 : 1; + if (event[ iPartonMin[0] ].col() > 0) idOppose = -idOppose; + int iOppose = event.append( idOppose, 77, 0, 0, 0, 0, 0, 0, + pOppose, 0.); + iPartonMin.push_back( iOppose); + pOppose = pWTinJRF[legMid]; + pOppose.flip3(); + idOppose = (rndmPtr->flat() > 0.5) ? 2 : 1; + if (event[ iPartonMid[0] ].col() > 0) idOppose = -idOppose; + iOppose = event.append( idOppose, 77, 0, 0, 0, 0, 0, 0, + pOppose, 0.); + iPartonMid.push_back( iOppose); + + // Set up kinematics of string evolution in low-energy temporary systems. + systemMin.setUp(iPartonMin, event); + systemMid.setUp(iPartonMid, event); + + // Outer fallback loop, when too little energy left for third leg. + int idMin = 0; + int idMid = 0; + Vec4 pDiquark; + for ( int iTryOuter = 0; ; ++iTryOuter) { + + // Middle fallback loop, when much unused energy in leg remnants. + double eLeftMin = 0.; + double eLeftMid = 0.; + for ( int iTryMiddle = 0; ; ++iTryMiddle) { + + // Loop over the two lowest-energy legs. + for (int legLoop = 0; legLoop < 2; ++ legLoop) { + int legNow = (legLoop == 0) ? legMin : legMid; + + // Read in properties specific to this leg. + StringSystem& systemNow = (legLoop == 0) ? systemMin : systemMid; + int idPos = (legLoop == 0) ? event[ iPartonMin[0] ].id() + : event[ iPartonMid[0] ].id(); + idOppose = (legLoop == 0) ? event[ iPartonMin.back() ].id() + : event[ iPartonMid.back() ].id(); + double eInJRF = pInJRF[legNow].e(); + int statusHad = (legLoop == 0) ? 85 : 86; + + // Inner fallback loop, when a diquark comes in to junction. + double eUsed = 0.; + for ( int iTryInner = 0; ; ++iTryInner) { + if (iTryInner > NTRYJNMATCH) { + infoPtr->errorMsg("Error in StringFragmentation::fragment" + "ToJunction: caught in junction flavour loop"); + event.popBack( iPartonMin.size() + iPartonMid.size() ); + return false; + } + + // Set up two string ends, and begin fragmentation loop. + setStartEnds(idPos, idOppose, systemNow); + eUsed = 0.; + int nHadrons = 0; + bool noNegE = true; + for ( ; ; ++nHadrons) { + + // Construct trial hadron from positive end. + posEnd.newHadron(); + Vec4 pHad = posEnd.kinematicsHadron(systemNow); + + // Negative energy signals failure in construction. + if (pHad.e() < 0. ) { noNegE = false; break; } + + // Break if passed system midpoint ( = junction) in energy. + if (eUsed + pHad.e() > eInJRF) break; + + // Else construct kinematics of the new hadron and store it. + hadrons.append( posEnd.idHad, statusHad, iPos, iNeg, + 0, 0, 0, 0, pHad, posEnd.mHad); + + // Update string end and remaining momentum. + posEnd.update(); + eUsed += pHad.e(); + } + + // End of fragmentation loop. Inner loopback if ends on a diquark. + if ( noNegE && abs(posEnd.flavOld.id) < 10 ) break; + hadrons.popBack(nHadrons); + } + + // End of one-leg fragmentation. Store end quark and remnant energy. + if (legNow == legMin) { + idMin = posEnd.flavOld.id; + eLeftMin = eInJRF - eUsed; + } else { + idMid = posEnd.flavOld.id; + eLeftMid = eInJRF - eUsed; + } + } + + // End of both-leg fragmentation. Middle loopback if too much energy left. + double eTrial = eBothLeftJunction + rndmPtr->flat() * eMaxLeftJunction; + if (iTryMiddle > NTRYJNMATCH + || ( min( eLeftMin, eLeftMid) < eBothLeftJunction + && max( eLeftMin, eLeftMid) < eTrial ) ) break; + hadrons.clear(); + } + + // Boost hadrons away from the JRF to the original frame. + for (int i = 0; i < hadrons.size(); ++i) { + hadrons[i].rotbst(MfromJRF); + // Recalculate energy to compensate for numerical precision loss + // in iterative calculation of MfromJRF. + hadrons[i].e( hadrons[i].eCalc() ); + pJunctionHadrons += hadrons[i].p(); + } + + // Outer loopback if too little energy left in third leg. + pDiquark = pInLeg[legMin] + pInLeg[legMid] - pJunctionHadrons; + double m2Left = m2( pInLeg[legMax], pDiquark); + if (iTryOuter > NTRYJNMATCH + || m2Left > eMinLeftJunction * pInLeg[legMax].e() ) break; + hadrons.clear(); + pJunctionHadrons = 0.; + } + + // Now found solution; no more loopback. Remove temporary parton copies. + event.popBack( iPartonMin.size() + iPartonMid.size() ); + + // Construct and store an effective diquark string end from the + // two remnant quark ends, for temporary usage. + int idDiquark = flavSelPtr->makeDiquark( idMin, idMid); + double mDiquark = pDiquark.mCalc(); + int iDiquark = event.append( idDiquark, 78, 0, 0, 0, 0, 0, 0, + pDiquark, mDiquark); + + // Find the partons on the last leg, again in reverse order. + vector iPartonMax; + for (int i = legEnd[legMax]; i >= legBeg[legMax]; --i) + iPartonMax.push_back( iParton[i] ); + iPartonMax.push_back( iDiquark ); + + // Modify parton list to remaining leg + remnant of the first two. + iParton = iPartonMax; + + // Done. + return true; +} + +//-------------------------------------------------------------------------- + +// Find the boost matrix to the rest frame of a junction, +// given the three respective endpoint four-momenta. + +RotBstMatrix StringFragmentation::junctionRestFrame(Vec4& p0, Vec4& p1, + Vec4& p2) { + + // Calculate masses and other invariants. + Vec4 pSumJun = p0 + p1 + p2; + double sHat = pSumJun.m2Calc(); + double pp[3][3]; + pp[0][0] = p0.m2Calc(); + pp[1][1] = p1.m2Calc(); + pp[2][2] = p2.m2Calc(); + pp[0][1] = pp[1][0] = p0 * p1; + pp[0][2] = pp[2][0] = p0 * p2; + pp[1][2] = pp[2][1] = p1 * p2; + + // Requirement (eiMax)_j = pi*pj/mj < (eiMax)_k = pi*pk/mk, used below, + // here rewritten as pi*pj * mk < pi*pk * mj and squared. + double eMax01 = pow2(pp[0][1]) * pp[2][2]; + double eMax02 = pow2(pp[0][2]) * pp[1][1]; + double eMax12 = pow2(pp[1][2]) * pp[0][0]; + + // Initially pick i to be the most massive parton. but allow other tries. + int i = (pp[1][1] > pp[0][0]) ? 1 : 0; + if (pp[2][2] > max(pp[0][0], pp[1][1])) i = 2; + int j, k; + double ei = 0.; + double ej = 0.; + double ek = 0.; + for (int iTry = 0; iTry < 3; ++iTry) { + + // Pick j to give minimal eiMax, and k the third vector. + if (i == 0) j = (eMax02 < eMax01) ? 2 : 1; + else if (i == 1) j = (eMax12 < eMax01) ? 2 : 0; + else j = (eMax12 < eMax02) ? 1 : 0; + k = 3 - i - j; + + // Alternative names according to i, j, k conventions. + double m2i = pp[i][i]; + double m2j = pp[j][j]; + double m2k = pp[k][k]; + double pipj = pp[i][j]; + double pipk = pp[i][k]; + double pjpk = pp[j][k]; + + // Trivial to find new parton energies if all three partons are massless. + if (m2i < M2MAXJRF) { + ei = sqrt( 2. * pipk * pipj / (3. * pjpk) ); + ej = sqrt( 2. * pjpk * pipj / (3. * pipk) ); + ek = sqrt( 2. * pipk * pjpk / (3. * pipj) ); + + // Else find three-momentum range for parton i and values at extremes. + } else { + // Minimum when i is at rest. + double piMin = 0.; + double eiMin = sqrt(m2i); + double ejMin = pipj / eiMin; + double ekMin = pipk / eiMin; + double pjMin = sqrtpos( ejMin*ejMin - m2j ); + double pkMin = sqrtpos( ekMin*ekMin - m2k ); + double fMin = ejMin * ekMin + 0.5 * pjMin * pkMin - pjpk; + // Maximum estimated when j + k is at rest, alternatively j at rest. + double eiMax = (pipj + pipk) / sqrt(m2j + m2k + 2. * pjpk); + if (m2j > M2MAXJRF) eiMax = min( eiMax, pipj / sqrt(m2j) ); + double piMax = sqrtpos( eiMax*eiMax - m2i ); + double temp = eiMax*eiMax - 0.25 *piMax*piMax; + double pjMax = (eiMax * sqrtpos( pipj*pipj - m2j * temp ) + - 0.5 * piMax * pipj) / temp; + double pkMax = (eiMax * sqrtpos( pipk*pipk - m2k * temp ) + - 0.5 * piMax * pipk) / temp; + double ejMax = sqrt(pjMax*pjMax + m2j); + double ekMax = sqrt(pkMax*pkMax + m2k); + double fMax = ejMax * ekMax + 0.5 * pjMax * pkMax - pjpk; + + // If unexpected values at upper endpoint then pick another parton. + if (fMax > 0.) { + int iPrel = (i + 1)%3; + if (pp[iPrel][iPrel] > M2MAXJRF) {i = iPrel; continue;} + ++iTry; + iPrel = (i + 2)%3; + if (iTry < 3 && pp[iPrel][iPrel] > M2MAXJRF) {i = iPrel; continue;} + } + + // Start binary + linear search to find solution inside range. + int iterMin = 0; + int iterMax = 0; + double pi = 0.5 * (piMin + piMax); + for (int iter = 0; iter < NTRYJRFEQ; ++iter) { + + // Derive momentum of other two partons and distance to root. + ei = sqrt(pi*pi + m2i); + temp = ei*ei - 0.25 * pi*pi; + double pj = (ei * sqrtpos( pipj*pipj - m2j * temp ) + - 0.5 * pi * pipj) / temp; + double pk = (ei * sqrtpos( pipk*pipk - m2k * temp ) + - 0.5 * pi * pipk) / temp; + ej = sqrt(pj*pj + m2j); + ek = sqrt(pk*pk + m2k); + double fNow = ej * ek + 0.5 * pj * pk - pjpk; + + // Replace lower or upper bound by new value. + if (fNow > 0.) { ++iterMin; piMin = pi; fMin = fNow;} + else {++iterMax; piMax = pi; fMax = fNow;} + + // Pick next i momentum to explore, hopefully closer to root. + if (2 * iter < NTRYJRFEQ + && (iterMin < 2 || iterMax < 2 || 4 * iter < NTRYJRFEQ)) + { pi = 0.5 * (piMin + piMax); continue;} + if (fMin < 0. || fMax > 0. || abs(fNow) < CONVJRFEQ * sHat) break; + pi = piMin + (piMax - piMin) * fMin / (fMin - fMax); + } + + // If arrived here then either succeeded or exhausted possibilities. + } break; + } + + // Now we know the energies in the junction rest frame. + double eNew[3]; eNew[i] = ei; eNew[j] = ej; eNew[k] = ek; + + // Boost (copy of) partons to their rest frame. + RotBstMatrix Mmove; + Vec4 p0cm = p0; + Vec4 p1cm = p1; + Vec4 p2cm = p2; + Mmove.bstback(pSumJun); + p0cm.rotbst(Mmove); + p1cm.rotbst(Mmove); + p2cm.rotbst(Mmove); + + // Construct difference vectors and the boost to junction rest frame. + Vec4 pDir01 = p0cm / p0cm.e() - p1cm / p1cm.e(); + Vec4 pDir02 = p0cm / p0cm.e() - p2cm / p2cm.e(); + double pDiff01 = pDir01.pAbs2(); + double pDiff02 = pDir02.pAbs2(); + double pDiff0102 = dot3(pDir01, pDir02); + double eDiff01 = eNew[0] / p0cm.e() - eNew[1] / p1cm.e(); + double eDiff02 = eNew[0] / p0cm.e() - eNew[2] / p2cm.e(); + double denom = pDiff01 * pDiff02 - pDiff0102*pDiff0102; + double coef01 = (eDiff01 * pDiff02 - eDiff02 * pDiff0102) / denom; + double coef02 = (eDiff02 * pDiff01 - eDiff01 * pDiff0102) / denom; + Vec4 vJunction = coef01 * pDir01 + coef02 * pDir02; + vJunction.e( sqrt(1. + vJunction.pAbs2()) ); + + // Add two boosts, giving final result. + Mmove.bst(vJunction); + return Mmove; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/SusyCouplings.cxx b/PYTHIA8/pythia8140/src/SusyCouplings.cxx new file mode 100644 index 00000000000..beee5eda727 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SusyCouplings.cxx @@ -0,0 +1,765 @@ +// SusyCouplings.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Peter Skands, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the +// supersymmetric couplings class. + +#include "SusyCouplings.h" + +namespace Pythia8 { + +//========================================================================== + +// The CoupSUSY class. + +//-------------------------------------------------------------------------- + +// Constants: could be changed here if desired, but normally should not. +// These are of technical nature, as described for each. + +// Allow verbose printout for debug purposes. +const bool CoupSUSY::DEBUG = false; + +//-------------------------------------------------------------------------- + +// Initialize SM+SUSY couplings (only performed once). + +void CoupSUSY::init (SusyLesHouches* slhaPtrIn, Settings* settingsPtrIn, + ParticleData* particleDataPtrIn, CoupSM* coupSMPtrIn) { + + // Save pointers.. + slhaPtr = slhaPtrIn; + settingsPtr = settingsPtrIn; + particleDataPtr = particleDataPtrIn; + coupSMPtr = coupSMPtrIn; + + // Is NMSSM switched on? + isNMSSM = (slhaPtr->modsel(3) != 1 ? false : true); + settingsPtr->flag("SLHA:NMSSM",isNMSSM); + int nNeut = (isNMSSM ? 5 : 4); + int nChar = 2; + + // Initialize pole masses + mZpole = particleDataPtr->m0(23); + wZpole = particleDataPtr->mWidth(23); + mWpole = particleDataPtr->m0(24); + wWpole = particleDataPtr->mWidth(24); + + // Running masses and weak mixing angle + // (default to pole values if no running available) + mW = mWpole; + mZ = mZpole; + sin2W = 1.0 - pow(mW/mZ,2); + + if (slhaPtr->gauge.exists(1) && slhaPtr->gauge.exists(2) + && slhaPtr->hmix.exists(3)) { + double gp=slhaPtr->gauge(1); + double g =slhaPtr->gauge(2); + double v =slhaPtr->hmix(3); + mW = g * v / 2.0; + mZ = sqrt(pow(gp,2)+pow(g,2)) * v / 2.0; + double tan2W = pow2(gp)/pow2(g); + if (DEBUG) cout << " tan2W = " << tan2W << endl; + sin2W = pow2(gp)/(pow2(g)+pow2(gp)); + } + sinW = sqrt(sin2W); + cosW = sqrt(1.0-sin2W); + + // Tan(beta) + // By default, use the running one in HMIX (if not found, use MINPAR) + tanb = slhaPtr->hmix.exists(2) ? slhaPtr->hmix(2) : slhaPtr->minpar(3); + cosb = sqrt( 1.0 / (1.0 + tanb*tanb) ); + sinb = sqrt(max(0.0,1.0-cosb*cosb)); + + // tmp : verbose output + if (DEBUG) { + cout << " sin2W(Q) = " << sin2W << " mW(Q) = " << mW + << " mZ(Q) = " << mZ << endl; + cout << " vev(Q) = " << slhaPtr->hmix(3) << " tanb(Q) = " << tanb + << endl; + for (int i=1;i<=3;i++) { + for (int j=1;j<=3;j++) { + cout << " VCKM [" << i << "][" << j << "] = " + << scientific << setw(10) << coupSMPtr->VCKMgen(i,j) << endl; + } + } + } + + // Shorthand for squark mixing matrices + SusyLesHouches::matrixblock<6> Ru(slhaPtr->usqmix); + SusyLesHouches::matrixblock<6> Rd(slhaPtr->dsqmix); + SusyLesHouches::matrixblock<6> imRu(slhaPtr->imusqmix); + SusyLesHouches::matrixblock<6> imRd(slhaPtr->imusqmix); + + // Construct ~g couplings + for (int i=1 ; i<=6 ; i++) { + for (int j=1 ; j<=3 ; j++) { + LsddG[i][j] = complex( Rd(i,j) , imRd(i,j)); + RsddG[i][j] = complex(-Rd(i,j+3), -imRd(i,j+3)); + LsuuG[i][j] = complex( Ru(i,j) , imRu(i,j)); + RsuuG[i][j] = complex(-Ru(i,j+3), -imRu(i,j+3)); + } + } + + // Construct qqZ couplings + for (int i=1 ; i<=6 ; i++) { + + // q[i] q[i] Z (def with extra factor 2 compared to [Okun]) + LqqZ[i] = coupSMPtr->af(i) - 2.0*coupSMPtr->ef(i)*sin2W ; + RqqZ[i] = - 2.0*coupSMPtr->ef(i)*sin2W ; + + // tmp: verbose output + if (DEBUG) { + cout << " LqqZ [" << i << "][" << i << "] = " + << scientific << setw(10) << LqqZ[i] + << " RqqZ [" << i << "][" << i << "] = " + << scientific << setw(10) << RqqZ[i] << endl; + } + } + + // Construct ~q~qZ couplings + for (int i=1 ; i<=6 ; i++) { + + // Squarks can have off-diagonal couplings as well + for (int j=1 ; j<=6 ; j++) { + + // ~d[i] ~d[j] Z + LsdsdZ[i][j] = 0.0; + RsdsdZ[i][j] = 0.0; + for (int k=1;k<=3;k++) { + complex Rdik = complex(Rd(i,k), imRd(i,k) ); + complex Rdjk = complex(Rd(j,k), imRd(j,k) ); + complex Rdik3 = complex(Rd(i,k+3),imRd(i,k+3)); + complex Rdjk3 = complex(Rd(j,k+3),imRd(j,k+3)); + LsdsdZ[i][j] += LqqZ[1] * (Rdik*conj(Rdjk)); + RsdsdZ[i][j] += RqqZ[1] * (Rdik3*conj(Rdjk3)); + } + + // ~u[i] ~u[j] Z + LsusuZ[i][j] = 0.0; + RsusuZ[i][j] = 0.0; + for (int k=1;k<=3;k++) { + complex Ruik = complex(Ru(i,k) ,imRu(i,k) ); + complex Rujk = complex(Ru(j,k) ,imRu(j,k) ); + complex Ruik3 = complex(Ru(i,k+3),imRu(i,k+3)); + complex Rujk3 = complex(Ru(j,k+3),imRu(j,k+3)); + LsusuZ[i][j] += LqqZ[2] * (Ruik*conj(Rujk)); + RsusuZ[i][j] += RqqZ[2] * (Ruik3*conj(Rujk3)); + } + + // tmp: verbose output + if (DEBUG) { + if (max(abs(LsdsdZ[i][j]),abs(RsdsdZ[i][j])) > 1e-6) { + cout << " LsdsdZ[" << i << "][" << j << "] = " + << scientific << setw(10) << LsdsdZ[i][j] + << " RsdsdZ[" << i << "][" << j << "] = " + << scientific << setw(10) << RsdsdZ[i][j] << endl; + } + if (max(abs(LsusuZ[i][j]),abs(RsusuZ[i][j]))> 1e-6) { + cout << " LsusuZ[" << i << "][" << j << "] = " + << scientific << setw(10) << LsusuZ[i][j] + << " RsusuZ[" << i << "][" << j << "] = " + << scientific << setw(10) << RsusuZ[i][j] << endl; + } + } + + } + + } + + // Construct udW couplings + + // Loop over up [i] and down [j] quark generation + for (int i=1;i<=3;i++) { + for (int j=1;j<=3;j++) { + + // CKM matrix (use Pythia one if no SLHA) + // (NB: could also try input one if no running one found, but + // would then need to compute from Wolfenstein) + complex Vij=coupSMPtr->VCKMgen(i,j); + if (slhaPtr->vckm.exists()) { + Vij=complex(slhaPtr->vckm(i,j),slhaPtr->imvckm(i,j)); + } + + // u[i] d[j] W + LudW[i][j] = sqrt(2.0) * cosW * Vij; + RudW[i][j] = 0.0; + + // tmp: verbose output + if (DEBUG) { + cout << " LudW [" << i << "][" << j << "] = " + << scientific << setw(10) << LudW[i][j] + << " RudW [" << i << "][" << j << "] = " + << scientific << setw(10) << RudW[i][j] << endl; + } + } + } + + // Construct ~u~dW couplings + + // Loop over ~u[k] and ~d[l] flavours + for (int k=1;k<=6;k++) { + for (int l=1;l<=6;l++) { + + LsusdW[k][l]=0.0; + RsusdW[k][l]=0.0; + + // Loop over u[i] and d[j] flavours + for (int i=1;i<=3;i++) { + for (int j=1;j<=3;j++) { + + // CKM matrix (use Pythia one if no SLHA) + // (NB: could also try input one if no running one found, but + // would then need to compute from Wolfenstein) + complex Vij=coupSMPtr->VCKMgen(i,j); + if (slhaPtr->vckm.exists()) { + Vij=complex(slhaPtr->vckm(i,j),slhaPtr->imvckm(i,j)); + } + + // ~u[k] ~d[l] W (add one term for each quark flavour i,j) + complex Ruki = complex(Ru(k,i),imRu(k,i)); + complex Rdlj = complex(Rd(l,j),imRd(l,j)); + LsusdW[k][l] += sqrt(2.0) * cosW * Vij * Ruki * conj(Rdlj); + RsusdW[k][l] += 0.0; + + } + } + + // tmp: verbose output + if (DEBUG) { + if (max(abs(LsusdW[k][l]),abs(RsusdW[k][l]))> 1e-6) { + cout << " LsusdW[" << k << "][" << l << "] = " + << scientific << setw(10) << LsusdW[k][l] + << " RsusdW[" << k << "][" << l << "] = " + << scientific << setw(10) << RsusdW[k][l] << endl; + } + } + + } + } + + // Now we come to the ones with really many indices + + // Construct ~chi0 couplings (allow for 5 neutralinos in NMSSM) + for (int i=1;i<=nNeut;i++) { + + // Ni1, Ni2, Ni3, Ni4, Ni5 + complex ni1,ni2,ni3,ni4,ni5; + if (not isNMSSM) { + ni1=complex( slhaPtr->nmix(i,1), slhaPtr->imnmix(i,1) ); + ni2=complex( slhaPtr->nmix(i,2), slhaPtr->imnmix(i,2) ); + ni3=complex( slhaPtr->nmix(i,3), slhaPtr->imnmix(i,3) ); + ni4=complex( slhaPtr->nmix(i,4), slhaPtr->imnmix(i,4) ); + ni5=complex( 0.0, 0.0); + } else { + ni1=complex( slhaPtr->nmnmix(i,1), slhaPtr->imnmnmix(i,1) ); + ni2=complex( slhaPtr->nmnmix(i,2), slhaPtr->imnmnmix(i,2) ); + ni3=complex( slhaPtr->nmnmix(i,3), slhaPtr->imnmnmix(i,3) ); + ni4=complex( slhaPtr->nmnmix(i,4), slhaPtr->imnmnmix(i,4) ); + ni5=complex( slhaPtr->nmnmix(i,5), slhaPtr->imnmnmix(i,5) ); + } + + // Change to positive mass convention + complex iRot( 0., 1.); + if (slhaPtr->mass(idNeut(i)) < 0.) { + ni1 *= iRot; + ni2 *= iRot; + ni3 *= iRot; + ni4 *= iRot; + ni5 *= iRot; + } + + // ~chi0 [i] ~chi0 [j] Z : loop over [j] + for (int j=1; j<=nNeut; j++) { + + // neutralino [j] higgsino components + complex nj3, nj4; + if (not isNMSSM) { + nj3=complex( slhaPtr->nmix(j,3), slhaPtr->imnmix(j,3) ); + nj4=complex( slhaPtr->nmix(j,4), slhaPtr->imnmix(j,4) ); + } else { + nj3=complex( slhaPtr->nmnmix(j,3), slhaPtr->imnmnmix(j,3) ); + nj4=complex( slhaPtr->nmnmix(j,4), slhaPtr->imnmnmix(j,4) ); + } + // Change to positive mass convention + if (slhaPtr->mass(idNeut(j)) < 0.) { + nj3 *= iRot; + nj4 *= iRot; + } + + // ~chi0 [i] ~chi0 [j] Z : couplings + OLpp[i][j] = -0.5 * ni3 * conj(nj3) + 0.5 * ni4 * conj(nj4); + ORpp[i][j] = 0.5 * conj(ni3) * nj3 - 0.5 * conj(ni4) * nj4; + + // tmp: verbose output + if (DEBUG) { + cout << " OL'' [" << i << "][" << j << "] = " + << scientific << setw(10) << OLpp[i][j] + << " OR'' [" << i << "][" << j << "] = " + << scientific << setw(10) << ORpp[i][j] << endl; + } + + } + + // ~chi0 [i] ~chi+ [j] W : loop over [j] + for (int j=1; j<=nChar; j++) { + + // Chargino mixing + complex uj1, uj2, vj1, vj2; + uj1=complex( slhaPtr->umix(j,1), slhaPtr->imumix(j,1) ); + uj2=complex( slhaPtr->umix(j,2), slhaPtr->imumix(j,2) ); + vj1=complex( slhaPtr->vmix(j,1), slhaPtr->imvmix(j,1) ); + vj2=complex( slhaPtr->vmix(j,2), slhaPtr->imvmix(j,2) ); + + // ~chi0 [i] ~chi+ [j] W : couplings + OL[i][j] = -1.0/sqrt(2.0)*ni4*conj(vj2)+ni2*conj(vj1); + OR[i][j] = 1.0/sqrt(2.0)*conj(ni3)*uj2+conj(ni2)*uj1; + + // tmp: verbose output + if (DEBUG) { + cout << " OL [" << i << "][" << j << "] = " + << scientific << setw(10) << OL[i][j] + << " OR [" << i << "][" << j << "] = " + << scientific << setw(10) << OR[i][j] << endl; + } + } + + // Charges + double ed = -1.0/3.0; + double T3d = -0.5; + double eu = 2.0/3.0; + double T3u = 0.5; + + // Loop over quark [k] generation + for (int k=1;k<=3;k++) { + + // Set quark masses + // Initial guess 0,0,0,mc,mb,mt with the latter from the PDT + double mu = particleDataPtr->m0(2*k); + double md = particleDataPtr->m0(2*k-1); + if (k == 1) { mu=0.0 ; md=0.0; } + if (k == 2) { md=0.0 ; mu=0.0; } + + // Compute running mass from Yukawas and vevs if possible. + if (slhaPtr->yd.exists() && slhaPtr->hmix.exists(3)) { + double ykk=slhaPtr->yd(k,k); + double v1=slhaPtr->hmix(3)/sqrt(1+pow(tanb,2)); + if (ykk > 0.0) md = ykk * v1 / sqrt(2.0) ; + } + if (slhaPtr->yu.exists() && slhaPtr->hmix.exists(3)) { + double ykk=slhaPtr->yu(k,k); + double v2=slhaPtr->hmix(3)/sqrt(1.0+1.0/pow(tanb,2)); + if (ykk > 0.0) mu = ykk * v2 / sqrt(2.0) ; + } + + // tmp: verbose output + if (DEBUG) { + cout << " Gen = " << k << " mu = " << mu << " md = " << md + << " yUU,DD = " << slhaPtr->yu(k,k) << "," + << slhaPtr->yd(k,k) << endl; + } + + // Loop over squark [j] flavour + for (int j=1;j<=6;j++) { + + // Squark mixing + complex Rdjk = complex(Rd(j,k), imRd(j,k) ); + complex Rdjk3 = complex(Rd(j,k+3),imRd(j,k+3)); + complex Rujk = complex(Ru(j,k), imRu(j,k) ); + complex Rujk3 = complex(Ru(j,k+3),imRu(j,k+3)); + + // ~d[j] d[k] ~chi0[i] + double rt2 = sqrt(2.0); + LsddX[j][k][i] = ((ed-T3d)*sinW/cosW*ni1 + T3d*ni2)*conj(Rdjk)/rt2 + + md*ni3*conj(Rdjk3)/2.0/rt2/mW/cosb; + RsddX[j][k][i] = -ed*sinW/cosW*conj(ni1)*conj(Rdjk3)/rt2 + + md*conj(ni3)*conj(Rdjk)/2.0/rt2/mW/cosb; + + // ~u[j] u[k] ~chi0[i] + LsuuX[j][k][i] = ((eu-T3u)*sinW/cosW*ni1 + T3u*ni2)*conj(Rujk)/rt2 + + mu*ni4*conj(Rujk3)/2.0/rt2/mW/sinb; + RsuuX[j][k][i] = -eu*sinW/cosW*conj(ni1)*conj(Rujk3)/rt2 + + mu*conj(ni4)*conj(Rujk)/2.0/rt2/mW/sinb; + + if (DEBUG) { + if (abs(LsddX[j][k][i]) > 1e-6) { + // tmp: verbose output + cout << " LsddX[" << j << "][" << k << "][" << i << "] = " + << scientific << setw(10) << LsddX[j][k][i] << endl; + } + if (abs(RsddX[j][k][i]) > 1e-6) { + // tmp: verbose output + cout << " RsddX[" << j << "][" << k << "][" << i << "] = " + << scientific << setw(10) << RsddX[j][k][i] << endl; + } + if (abs(LsuuX[j][k][i]) > 1e-6) { + // tmp: verbose output + cout << " LsuuX[" << j << "][" << k << "][" << i << "] = " + << scientific << setw(10) << LsuuX[j][k][i] << endl; + } + if (abs(RsuuX[j][k][i]) > 1e-6) { + // tmp: verbose output + cout << " RsuuX[" << j << "][" << k << "][" << i << "] = " + << scientific << setw(10) << RsuuX[j][k][i] << endl; + } + } + } + + } + + } + + // Construct ~chi+ couplings + for (int i=1;i<=nChar;i++) { + + // Ui1, Ui2, Vi1, Vi2 + complex ui1,ui2,vi1,vi2; + ui1=complex( slhaPtr->umix(i,1), slhaPtr->imumix(i,1) ); + ui2=complex( slhaPtr->umix(i,2), slhaPtr->imumix(i,2) ); + vi1=complex( slhaPtr->vmix(i,1), slhaPtr->imvmix(i,1) ); + vi2=complex( slhaPtr->vmix(i,2), slhaPtr->imvmix(i,2) ); + + // ~chi+ [i] ~chi- [j] Z : loop over [j] + for (int j=1; j<=nChar; j++) { + + // Chargino mixing + complex uj1, uj2, vj1, vj2; + uj1=complex( slhaPtr->umix(j,1), slhaPtr->imumix(j,1) ); + uj2=complex( slhaPtr->umix(j,2), slhaPtr->imumix(j,2) ); + vj1=complex( slhaPtr->vmix(j,1), slhaPtr->imvmix(j,1) ); + vj2=complex( slhaPtr->vmix(j,2), slhaPtr->imvmix(j,2) ); + + // ~chi+ [i] ~chi- [j] Z : couplings + OLp[i][j] = -vi1*conj(vj1) - 0.5*vi2*conj(vj2) + + ( (i == j) ? sin2W : 0.0); + ORp[i][j] = -conj(ui1)*uj1 - 0.5*conj(ui2)*uj2 + + ( (i == j) ? sin2W : 0.0); + + if (DEBUG) { + // tmp: verbose output + cout << " OL' [" << i << "][" << j << "] = " + << scientific << setw(10) << OLp[i][j] + << " OR' [" << i << "][" << j << "] = " + << scientific << setw(10) << ORp[i][j] << endl; + } + } + + // Loop over quark [l] flavour + for (int l=1;l<=3;l++) { + + // Set quark [l] masses + // Initial guess 0,0,0,mc,mb,mt with the latter from the PDT + double mul = particleDataPtr->m0(2*l); + double mdl = particleDataPtr->m0(2*l-1); + if (l == 1) { mul=0.0 ; mdl=0.0; } + if (l == 2) { mdl=0.0 ; mul=0.0; } + + // Compute running mass from Yukawas and vevs if possible. + if (slhaPtr->yd.exists() && slhaPtr->hmix.exists(3)) { + double yll=slhaPtr->yd(l,l); + double v1=slhaPtr->hmix(3)/sqrt(1+pow(tanb,2)); + if (yll > 0.0) mdl = yll * v1 / sqrt(2.0) ; + } + if (slhaPtr->yu.exists() && slhaPtr->hmix.exists(3)) { + double yll=slhaPtr->yu(l,l); + double v2=slhaPtr->hmix(3)/sqrt(1.0+1.0/pow(tanb,2)); + if (yll > 0.0) mul = yll * v2 / sqrt(2.0) ; + } + + // Loop over squark [j] flavour + for (int j=1;j<=6;j++) { + + // Loop over off-diagonal quark [k] generation + for (int k=1;k<=3;k++) { + + // Set quark [k] masses + // Initial guess 0,0,0,0,mb,mt with the latter from the PDT + double muk = particleDataPtr->m0(2*k); + double mdk = particleDataPtr->m0(2*k-1); + if (k == 1) { muk=0.0 ; mdk=0.0; } + if (k == 2) { mdk=0.0 ; muk=0.0; } + + // Compute running mass from Yukawas and vevs if possible. + if (slhaPtr->yd.exists() && slhaPtr->hmix.exists(3)) { + double ykk=slhaPtr->yd(k,k); + double v1=slhaPtr->hmix(3)/sqrt(1+pow(tanb,2)); + if (ykk > 0.0) mdk = ykk * v1 / sqrt(2.0) ; + } + if (slhaPtr->yu.exists() && slhaPtr->hmix.exists(3)) { + double ykk=slhaPtr->yu(k,k); + double v2=slhaPtr->hmix(3)/sqrt(1.0+1.0/pow(tanb,2)); + if (ykk > 0.0) muk = ykk * v2 / sqrt(2.0) ; + } + + // CKM matrix (use Pythia one if no SLHA) + // (NB: could also try input one if no running one found, but + // would then need to compute from Wolfenstein) + complex Vlk=coupSMPtr->VCKMgen(l,k); + complex Vkl=coupSMPtr->VCKMgen(k,l); + if (slhaPtr->vckm.exists()) { + Vlk=complex(slhaPtr->vckm(l,k),slhaPtr->imvckm(l,k)); + Vkl=complex(slhaPtr->vckm(k,l),slhaPtr->imvckm(k,l)); + } + + // Squark mixing + complex Rdjk = complex(Rd(j,k), imRd(j,k) ); + complex Rdjk3 = complex(Rd(j,k+3),imRd(j,k+3)); + complex Rujk = complex(Ru(j,k), imRu(j,k) ); + complex Rujk3 = complex(Ru(j,k+3),imRu(j,k+3)); + + // sqrt(2) + double rt2 = sqrt(2.0); + + // ~d[j] u[l] ~chi+[i] + LsduX[j][l][i] += 0.5*(ui1*conj(Rdjk) + - mdk*ui2*conj(Rdjk3)/rt2/mW/cosb)*Vlk; + RsduX[j][l][i] -= 0.5*mul*conj(vi2)*Vlk*Rdjk/rt2/mW/sinb; + + // ~u[j] d[l] ~chi+[i] + LsudX[j][l][i] += 0.5*(vi1*conj(Rujk) + - muk*vi2*conj(Rujk3)/rt2/mW/sinb)*conj(Vkl); + RsudX[j][l][i] -= 0.5*mdl*conj(ui2)*conj(Vkl)*conj(Rujk)/rt2/mW/cosb; + + } + + if (DEBUG) { + if (max(abs(LsduX[j][l][i]),abs(RsduX[j][l][i])) > 1e-6) { + // tmp: verbose output + cout << " LsduX[" << j << "][" << l << "][" << i << "] = " + << scientific << setw(10) << LsduX[j][l][i]; + cout << " RsduX[" << j << "][" << l << "][" << i << "] = " + << scientific << setw(10) << RsduX[j][l][i] << endl; + } + if (max(abs(LsudX[j][l][i]),abs(RsudX[j][l][i])) > 1e-6) { + // tmp: verbose output + cout << " LsudX[" << j << "][" << l << "][" << i << "] = " + << scientific << setw(10) << LsudX[j][l][i]; + cout << " RsudX[" << j << "][" << l << "][" << i << "] = " + << scientific << setw(10) << RsudX[j][l][i] << endl; + } + } + + } + + + } + + } + + // SLHA2 compatibility + // Check whether scalar particle masses are ordered + bool orderedQ = true; + bool orderedL = true; + for (int j=1;j<=5;j++) { + if (particleDataPtr->m0(idSlep(j+1)) < particleDataPtr->m0(idSlep(j))) + orderedL = false; + if (particleDataPtr->m0(idSup(j+1)) < particleDataPtr->m0(idSup(j))) + orderedQ = false; + if (particleDataPtr->m0(idSdown(j+1)) m0(idSdown(j))) + orderedQ = false; + } + + // If ordered, change sparticle labels to mass-ordered enumeration + for (int i=1;i<=6;i++) { + ostringstream indx; + indx << i; + string uName = "~u_"+indx.str(); + string dName = "~d_"+indx.str(); + string lName = "~e_"+indx.str(); + ParticleDataEntry* pdePtr; + if (orderedQ) { + pdePtr = particleDataPtr->particleDataEntryPtr(idSup(i)); + pdePtr->setNames(uName,uName+"bar"); + pdePtr = particleDataPtr->particleDataEntryPtr(idSdown(i)); + pdePtr->setNames(dName,dName+"bar"); + } + if (orderedL) { + pdePtr = particleDataPtr->particleDataEntryPtr(idSlep(i)); + pdePtr->setNames(lName,lName+"bar"); + } + } + + // Let everyone know we are ready + isInit = true; + +} + +//-------------------------------------------------------------------------- + +// Return neutralino flavour codes. + +int CoupSUSY::idNeut(int idChi) { + int id = 0; + if (idChi == 1) id = 1000022; + else if (idChi == 2) id = 1000023; + else if (idChi == 3) id = 1000025; + else if (idChi == 4) id = 1000035; + else if (idChi == 5) id = 1000045; + return id; +} + +//-------------------------------------------------------------------------- + +// Return chargino flavour codes. + +int CoupSUSY::idChar(int idChi) { + int id = 0; + if (idChi == 1) id = 1000024; + else if (idChi == -1) id = -1000024; + else if (idChi == 2) id = 1000037; + else if (idChi == -2) id = -1000037; + return id; +} + +//-------------------------------------------------------------------------- + +// Return sup flavour codes. + +int CoupSUSY::idSup(int iSup) { + int id = 0; + int sgn = ( iSup > 0 ) ? 1 : -1; + iSup = abs(iSup); + if (iSup == 1) id = 1000002; + else if (iSup == 2) id = 1000004; + else if (iSup == 3) id = 1000006; + else if (iSup == 4) id = 2000002; + else if (iSup == 5) id = 2000004; + else if (iSup == 6) id = 2000006; + return sgn*id; +} + +//-------------------------------------------------------------------------- + +// Return sdown flavour codes + +int CoupSUSY::idSdown(int iSdown) { + int id = 0; + int sgn = ( iSdown > 0 ) ? 1 : -1; + iSdown = abs(iSdown); + if (iSdown == 1) id = 1000001; + else if (iSdown == 2) id = 1000003; + else if (iSdown == 3) id = 1000005; + else if (iSdown == 4) id = 2000001; + else if (iSdown == 5) id = 2000003; + else if (iSdown == 6) id = 2000005; + return sgn*id; +} + +//-------------------------------------------------------------------------- + +// Function to return slepton flavour codes + +int CoupSUSY::idSlep(int iSlep) { + int id = 0; + int sgn = ( iSlep > 0 ) ? 1 : -1; + iSlep = abs(iSlep); + if (iSlep == 1) id = 1000011; + else if (iSlep == 2) id = 1000013; + else if (iSlep == 3) id = 1000015; + else if (iSlep == 4) id = 2000011; + else if (iSlep == 5) id = 2000013; + else if (iSlep == 6) id = 2000015; + return sgn*id; +} + +//-------------------------------------------------------------------------- + +// Return a particle name, given the PDG code. + +string CoupSUSY::getName(int pdgCode) { + + // Absolute value and corresponding SM code + int codeA = abs(pdgCode); + int idSM = codeA % 1000000; + + // Name + string name; + + // Flag to indicate whether SLHA1 or SLHA2 + bool slha1 = false; + + // SM particles + if (codeA == idSM) { + // Neutrinos + if (!slhaPtr->upmns.exists()) slha1=true; + if (codeA == 12) name = (slha1) ? "nu_e" : "nu_1"; + if (codeA == 14) name = (slha1) ? "nu_mu" : "nu_2"; + if (codeA == 16) name = (slha1) ? "nu_tau" : "nu_3"; + } + + // Squarks + else if ( idSM <= 6) { + // up squarks + if (idSM % 2 == 0) { + // If SLHA1, return old PDG names + if (slhaPtr->stopmix.exists()) slha1 = true; + if (codeA == 1000002) name = (slha1) ? "~u_L" : "~u_1"; + if (codeA == 1000004) name = (slha1) ? "~c_L" : "~u_2"; + if (codeA == 1000006) name = (slha1) ? "~t_1" : "~u_3"; + if (codeA == 2000002) name = (slha1) ? "~u_R" : "~u_4"; + if (codeA == 2000004) name = (slha1) ? "~c_R" : "~u_5"; + if (codeA == 2000006) name = (slha1) ? "~t_2" : "~u_6"; + } + // down squarks + else { + // If SLHA1, return old PDG names + if (slhaPtr->sbotmix.exists()) slha1 = true; + if (codeA == 1000001) name = (slha1) ? "~d_L" : "~d_1"; + if (codeA == 1000003) name = (slha1) ? "~s_L" : "~d_2"; + if (codeA == 1000005) name = (slha1) ? "~b_1" : "~d_3"; + if (codeA == 2000001) name = (slha1) ? "~d_R" : "~d_4"; + if (codeA == 2000003) name = (slha1) ? "~s_R" : "~d_5"; + if (codeA == 2000005) name = (slha1) ? "~b_2" : "~d_6"; + } + if (pdgCode < 0) name += "bar"; + } + + // Sleptons + else if ( idSM <= 19 ) { + + // Sneutrinos + if (idSM % 2 == 0) { + // If SLHA1, return old PDG names + if (slhaPtr->staumix.exists()) slha1 = true; + if (codeA == 1000012) name = (slha1) ? "~nu_eL" : "~nu_1"; + if (codeA == 1000014) name = (slha1) ? "~nu_muL" : "~nu_2"; + if (codeA == 1000016) name = (slha1) ? "~nu_tauL" : "~nu_3"; + if (codeA == 2000012) name = (slha1) ? "~nu_eR" : "~nu_4"; + if (codeA == 2000014) name = (slha1) ? "~nu_muR" : "~nu_5"; + if (codeA == 2000016) name = (slha1) ? "~nu_tauR" : "~nu_6"; + if (pdgCode < 0) name += "bar"; + } + // charged sleptons + else { + // If SLHA1, return old PDG names + if (slhaPtr->staumix.exists()) slha1 = true; + if (codeA == 1000011) name = (slha1) ? "~e_L" : "~e_1"; + if (codeA == 1000013) name = (slha1) ? "~mu_L" : "~e_2"; + if (codeA == 1000015) name = (slha1) ? "~tau_1" : "~e_3"; + if (codeA == 2000011) name = (slha1) ? "~e_R" : "~e_4"; + if (codeA == 2000013) name = (slha1) ? "~mu_R" : "~e_5"; + if (codeA == 2000015) name = (slha1) ? "~tau_2" : "~e_6"; + if (pdgCode < 0) name += "-"; + else name += "+"; + } + } + + else if (codeA == 1000021) name = "~g"; + else if (codeA == 1000022) name = "~chi_10"; + else if (codeA == 1000023) name = "~chi_20"; + else if (codeA == 1000024) name = (pdgCode > 0) ? "~chi_1+" : "~chi_1-"; + else if (codeA == 1000025) name = "~chi_30"; + else if (codeA == 1000035) name = "~chi_40"; + else if (codeA == 1000037) name = (pdgCode > 0) ? "~chi_2+" : "~chi_2-"; + + return name; + +} + +//========================================================================== + +} // end namespace Pythia8 + + diff --git a/PYTHIA8/pythia8140/src/SusyLesHouches.cxx b/PYTHIA8/pythia8140/src/SusyLesHouches.cxx new file mode 100644 index 00000000000..b8bc5ba52d5 --- /dev/null +++ b/PYTHIA8/pythia8140/src/SusyLesHouches.cxx @@ -0,0 +1,1253 @@ +// SusyLesHouches.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Peter Skands, Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +#include "SusyLesHouches.h" + +//========================================================================== + +// Main routine to read in SLHA and LHEF+SLHA files + +int SusyLesHouches::readFile(string slhaFileIn, int verboseIn) { + + // Copy inputs to local + slhaFile = slhaFileIn; + verbose = verboseIn; + + // Check that input file is OK. + int iFailFile=0; + const char* cstring = slhaFile.c_str(); + ifstream file(cstring); + if (!file.good()) { + message(2,"readFile",slhaFile+" not found",0); + return -1; + slhaRead=false; + } + + if (verbose >= 3) message(0,"readFile","parsing "+slhaFile,0); + + // Array of particles read in. + vector idRead; + + //Initial values for read-in variables. + slhaRead=true; + lhefRead=false; + lhefSlha=false; + bool foundSlhaTag = false; + bool xmlComment = false; + bool decayPrinted = false; + string line=""; + string blockIn=""; + string decay=""; + string comment=""; + string blockName=""; + string nameNow=""; + int idNow=0; + double width=0.0; + + //Initialize line counter + int iLine=0; + + // Read in one line at a time. + while ( getline(file, line) ) { + iLine++; + + //Rewrite string in lowercase + for (unsigned int i=0;i") != string::npos) { + xmlComment = false; + } + else if (xmlComment) continue; + else if (line.find(" SLHA2 interoperability + //Note: the mass basis is NOT mass-ordered in SLHA1, so be careful! + //Here, the mass basis is hence by PDG code, not by mass-ordered value. + + if (stopmix.exists() && ! usqmix.exists() ) { + //1000002 = ~uL, 1000004 = ~cL, 2000002 = ~uR, 2000004 = ~cR + usqmix.set(1,1, 1.0); + usqmix.set(2,2, 1.0); + usqmix.set(4,4, 1.0); + usqmix.set(5,5, 1.0); + //Fill (1000006,2000006) sector from stopmix + usqmix.set(3,3, stopmix(1,1)); + usqmix.set(3,6, stopmix(1,2)); + usqmix.set(6,3, stopmix(2,1)); + usqmix.set(6,6, stopmix(2,2)); + }; + if (sbotmix.exists() && ! dsqmix.exists() ) { + //1000001 = ~dL, 1000003 = ~sL, 2000001 = ~dR, 2000003 = ~sR + dsqmix.set(1,1, 1.0); + dsqmix.set(2,2, 1.0); + dsqmix.set(4,4, 1.0); + dsqmix.set(5,5, 1.0); + //Fill (1000005,2000005) sector from sbotmix + dsqmix.set(3,3, sbotmix(1,1)); + dsqmix.set(3,6, sbotmix(1,2)); + dsqmix.set(6,3, sbotmix(2,1)); + dsqmix.set(6,6, sbotmix(2,2)); + }; + if (staumix.exists() && ! selmix.exists() ) { + //1000011 = ~eL, 1000013 = ~muL, 2000011 = ~eR, 2000013 = ~muR + selmix.set(1,1, 1.0); + selmix.set(2,2, 1.0); + selmix.set(4,4, 1.0); + selmix.set(5,5, 1.0); + //Fill (1000015,2000015) sector from staumix + selmix.set(3,3, staumix(1,1)); + selmix.set(3,6, staumix(1,2)); + selmix.set(6,3, staumix(2,1)); + selmix.set(6,6, staumix(2,2)); + }; + if (! snumix.exists() && ! snsmix.exists()) { + //1000012 = ~nu_e, 1000014 = ~nu_mu, 1000016 = ~nu_tau + snumix.set(1,1, 1.0); + snumix.set(2,2, 1.0); + snumix.set(3,3, 1.0); + }; + + // Step 4) Check unitarity/orthogonality of mixing matrices + + //NMIX + if (nmix.exists()) { + for (int i=1;i<=4;i++) { + double cn1=0.0; + double cn2=0.0; + for (int j=1;j<=4;j++) { + cn1 += pow(nmix(i,j),2); + cn2 += pow(nmix(j,i),2); + } + if (abs(1.0-cn1) > 1e-3 || abs(1.0-cn2) > 1e-3) { + ifail=2; + message(2,"checkSpectrum","inconsistent normalization of NMIX",0); + } + } + } + + //VMIX, UMIX + if (vmix.exists() && umix.exists()) { + for (int i=1;i<=2;i++) { + double cu1=0.0; + double cu2=0.0; + double cv1=0.0; + double cv2=0.0; + for (int j=1;j<=2;j++) { + cu1 += pow(umix(i,j),2); + cu2 += pow(umix(j,i),2); + cv1 += pow(vmix(i,j),2); + cv2 += pow(vmix(j,i),2); + } + if (abs(1.0-cu1) > 1e-3 || abs(1.0-cu2) > 1e-3) { + ifail=2; + message(2,"checkSpectrum","inconsistent normalization of UMIX",0); + } + if (abs(1.0-cv1) > 1e-3 || abs(1.0-cv2) > 1e-3) { + ifail=2; + message(2,"checkSpectrum","inconsistent normalization of VMIX",0); + } + } + + } + + //STOPMIX, SBOTMIX + if (stopmix.exists() && sbotmix.exists()) { + for (int i=1;i<=2;i++) { + double ct1=0.0; + double ct2=0.0; + double cb1=0.0; + double cb2=0.0; + for (int j=1;j<=2;j++) { + ct1 += pow(stopmix(i,j),2); + ct2 += pow(stopmix(j,i),2); + cb1 += pow(sbotmix(i,j),2); + cb2 += pow(sbotmix(j,i),2); + } + if (abs(1.0-ct1) > 1e-3 || abs(1.0-ct2) > 1e-3) { + ifail=2; + message(2,"checkSpectrum","inconsistent normalization of STOPMIX",0); + } + if (abs(1.0-cb1) > 1e-3 || abs(1.0-cb2) > 1e-3) { + ifail=2; + message(2,"checkSpectrum","inconsistent normalization of SBOTMIX",0); + } + } + } + + //STAUMIX + if (staumix.exists()) { + for (int i=1;i<=2;i++) { + double ct1=0.0; + double ct2=0.0; + for (int j=1;j<=2;j++) { + ct1 += pow(staumix(i,j),2); + ct2 += pow(staumix(j,i),2); + } + if (abs(1.0-ct1) > 1e-3 || abs(1.0-ct2) > 1e-3) { + ifail=2; + message(2,"checkSpectrum","inconsistent normalization of STAUMIX",0); + } + } + } + + //NMSSM: + if (modsel(3) == 1) { + //NMNMIX + if ( nmnmix.exists() ) { + for (int i=1;i<=5;i++) { + double cn1=0.0; + double cn2=0.0; + for (int j=1;j<=4;j++) { + cn1 += pow(nmnmix(i,j),2); + cn2 += pow(nmnmix(j,i),2); + } + if (abs(1.0-cn1) > 1e-3 || abs(1.0-cn2) > 1e-3) { + ifail=max(ifail,2); + message(2,"checkSpectrum","inconsistent normalization of NMNMIX",0); + } + } + } + else { + ifail=-1; + message(1,"checkSpectrum","MODSEL 3 = 1 (NMSSM) but no NMNMIX found",0); + } + //NMAMIX + if ( nmamix.exists() ) { + for (int i=1;i<=2;i++) { + double cn1=0.0; + for (int j=1;j<=3;j++) { + cn1 += pow(nmamix(i,j),2); + } + if (abs(1.0-cn1) > 1e-3) { + ifail=max(ifail,2); + message(2,"checkSpectrum","inconsistent normalization of NMAMIX",0); + } + } + } + else { + ifail=-1; + message(1,"checkSpectrum","MODSEL 3 = 1 (NMSSM) but no NMAMIX found",0); + } + //NMHMIX + if ( nmhmix.exists() ) { + for (int i=1;i<=3;i++) { + double cn1=0.0; + double cn2=0.0; + for (int j=1;j<=3;j++) { + cn1 += pow(nmhmix(i,j),2); + cn2 += pow(nmhmix(j,i),2); + } + if (abs(1.0-cn1) > 1e-3 || abs(1.0-cn2) > 1e-3) { + ifail=max(ifail,2); + message(2,"checkSpectrum","inconsistent normalization of NMHMIX",0); + } + } + } + else { + ifail=-1; + message(1,"checkSpectrum","MODSEL 3 = 1 (NMSSM) but no NMHMIX found",0); + } + //NMSSMRUN + if (! nmssmrun.exists() ) { + ifail=-1; + message(2,"checkSpectrum","MODSEL 3 = 1 (NMSSM) but no NMSSMRUN found", + 0); + } + } + + //Check for documentation + if (slhaRead && ! spinfo.exists(1)) spinfo.set(1,"unknown"); + if (slhaRead && ! spinfo.exists(2)) spinfo.set(2,"unknown"); + if (! slhaRead && ! spinfo.exists(1)) { + spinfo.set(1,"DEFAULT"); + spinfo.set(2,"n/a"); + } + + //Give status + if (ifail >= 2) + message(0,"checkSpectrum","one or more serious problems were found"); + + //Print Footer + printFooter(); + + //Return + return ifail; +} + +//-------------------------------------------------------------------------- + +// Check consistency of decay tables + +int SusyLesHouches::checkDecays() { + + if (! headerPrinted) printHeader(); + int iFailDecays=0; + + // Loop over all particles read in + for (int i = 0; i < int(decays.size()); ++i) { + + // Shorthand + decayTable decTab = decays[i]; + int idRes = decTab.getId(); + double width = decTab.getWidth(); + if (width <= 0.0 || decTab.size() == 0) continue; + + // Check sum of branching ratios and phase spaces + double sum = 0.0; + double absSum = 0.0; + int decSize = decTab.size(); + for (int j = 0; j < decSize; ++j) { + + double brat = decTab.getBrat(j); + + // Check phase space + if (abs(brat) > 0.0) { + vector idDa = decTab.getIdDa(j); + double massSum=abs(mass(idRes)); + for (int k=0; k"; + for (int jDa=0; jDa 1e-6) { + message(1,"checkDecays","sum(BR) != 1"); + cout << " | offending particle: "< 2 * pTmin * sqrt(1/XMARGIN), +// i.e. will become problem roughly for E_CM > 10^6 GeV. +const double TimeShower::XMARGIN = 1e-12; +const double TimeShower::XMARGINCOMB = 1e-4; + +// Lower limit on PDF value in order to avoid division by zero. +const double TimeShower::TINYPDF = 1e-10; + +// Big starting value in search for smallest invariant-mass pair. +const double TimeShower::LARGEM2 = 1e20; + +// In g -> q qbar or gamma -> f fbar require m2_pair > this * m2_q/f. +const double TimeShower::THRESHM2 = 4.004; + +// Never pick pT so low that alphaS is evaluated too close to Lambda_3. +const double TimeShower::LAMBDA3MARGIN = 1.1; + +// Rescatter: rescattering + ISR + FSR + primordial kT can lead to +// systems not locally conserving momentum. +// Fix up momentum in intermediate systems with rescattering +const bool TimeShower::FIXRESCATTER = true; +// Veto negative energies when using FIXRESCATTER option. +const bool TimeShower::VETONEGENERGY = false; +// Do not allow too large time- or spacelike virtualities in fixing-up. +const double TimeShower::MAXVIRTUALITYFRACTION = 0.5; +// Do not allow too large negative spacelike energy in system rest frame. +const double TimeShower::MAXNEGENERGYFRACTION = 0.7; + +//-------------------------------------------------------------------------- + +// Initialize alphaStrong, alphaEM and related pTmin parameters. + +void TimeShower::init( BeamParticle* beamAPtrIn, + BeamParticle* beamBPtrIn) { + + // Store input pointers for future use. + beamAPtr = beamAPtrIn; + beamBPtr = beamBPtrIn; + + // Main flags. + doQCDshower = settingsPtr->flag("TimeShower:QCDshower"); + doQEDshowerByQ = settingsPtr->flag("TimeShower:QEDshowerByQ"); + doQEDshowerByL = settingsPtr->flag("TimeShower:QEDshowerByL"); + doQEDshowerByGamma = settingsPtr->flag("TimeShower:QEDshowerByGamma"); + doMEcorrections = settingsPtr->flag("TimeShower:MEcorrections"); + doPhiPolAsym = settingsPtr->flag("TimeShower:phiPolAsym"); + doInterleave = settingsPtr->flag("TimeShower:interleave"); + allowBeamRecoil = settingsPtr->flag("TimeShower:allowBeamRecoil"); + dampenBeamRecoil = settingsPtr->flag("TimeShower:dampenBeamRecoil"); + + // Matching in pT of hard interaction or MI to shower evolution. + pTmaxMatch = settingsPtr->mode("TimeShower:pTmaxMatch"); + pTdampMatch = settingsPtr->mode("TimeShower:pTdampMatch"); + pTmaxFudge = settingsPtr->parm("TimeShower:pTmaxFudge"); + pTmaxFudgeMI = settingsPtr->parm("TimeShower:pTmaxFudgeMI"); + pTdampFudge = settingsPtr->parm("TimeShower:pTdampFudge"); + + // Charm and bottom mass thresholds. + mc = particleDataPtr->m0(4); + mb = particleDataPtr->m0(5); + m2c = mc * mc; + m2b = mb * mb; + + // Parameters of alphaStrong generation . + alphaSvalue = settingsPtr->parm("TimeShower:alphaSvalue"); + alphaSorder = settingsPtr->mode("TimeShower:alphaSorder"); + alphaS2pi = 0.5 * alphaSvalue / M_PI; + + // Initialize alphaStrong generation. + alphaS.init( alphaSvalue, alphaSorder); + + // Lambda for 5, 4 and 3 flavours. + Lambda3flav = alphaS.Lambda3(); + Lambda4flav = alphaS.Lambda4(); + Lambda5flav = alphaS.Lambda5(); + Lambda5flav2 = pow2(Lambda5flav); + Lambda4flav2 = pow2(Lambda4flav); + Lambda3flav2 = pow2(Lambda3flav); + + // Parameters of QCD evolution. Warn if pTmin must be raised. + nGluonToQuark = settingsPtr->mode("TimeShower:nGluonToQuark"); + pTcolCutMin = settingsPtr->parm("TimeShower:pTmin"); + if (pTcolCutMin > LAMBDA3MARGIN * Lambda3flav) + pTcolCut = pTcolCutMin; + else { + pTcolCut = LAMBDA3MARGIN * Lambda3flav; + ostringstream newPTcolCut; + newPTcolCut << fixed << setprecision(3) << pTcolCut; + infoPtr->errorMsg("Warning in TimeShower::init: pTmin too low", + ", raised to " + newPTcolCut.str() ); + infoPtr->setTooLowPTmin(true); + } + pT2colCut = pow2(pTcolCut); + + // Parameters of alphaEM generation . + alphaEMorder = settingsPtr->mode("TimeShower:alphaEMorder"); + + // Initialize alphaEM generation. + alphaEM.init( alphaEMorder, settingsPtr); + + // Parameters of QED evolution. + nGammaToQuark = settingsPtr->mode("TimeShower:nGammaToQuark"); + nGammaToLepton = settingsPtr->mode("TimeShower:nGammaToLepton"); + pTchgQCut = settingsPtr->parm("TimeShower:pTminChgQ"); + pT2chgQCut = pow2(pTchgQCut); + pTchgLCut = settingsPtr->parm("TimeShower:pTminChgL"); + pT2chgLCut = pow2(pTchgLCut); + mMaxGamma = settingsPtr->parm("TimeShower:mMaxGamma"); + m2MaxGamma = pow2(mMaxGamma); + + // Consisteny check for gamma -> f fbar variables. + if (nGammaToQuark <= 0 && nGammaToLepton <= 0) doQEDshowerByGamma = false; + + // Fraction and colour factor of gluon emission off onium octat state. + octetOniumFraction = settingsPtr->parm("TimeShower:octetOniumFraction"); + octetOniumColFac = settingsPtr->parm("TimeShower:octetOniumColFac"); + + // Z0 properties needed for gamma/Z0 mixing. + mZ = particleDataPtr->m0(23); + gammaZ = particleDataPtr->mWidth(23); + thetaWRat = 1. / (16. * coupSMPtr->sin2thetaW() + * coupSMPtr->cos2thetaW()); + + // May have to fix up recoils related to rescattering. + allowRescatter = settingsPtr->flag("PartonLevel:MI") + && settingsPtr->flag("MultipleInteractions:allowRescatter"); + + // Hidden Valley scenario with further shower activity. + doHVshower = settingsPtr->flag("HiddenValley:FSR"); + nCHV = settingsPtr->mode("HiddenValley:Ngauge"); + alphaHVfix = settingsPtr->parm("HiddenValley:alphaFSR"); + pThvCut = settingsPtr->parm("HiddenValley:pTminFSR"); + pT2hvCut = pThvCut * pThvCut; + CFHV = (nCHV == 1) ? 1. : (nCHV * nCHV - 1.)/(2. * nCHV); + + // Possibility to allow user veto of emission step. + canVetoEmission = (userHooksPtr > 0) ? userHooksPtr->canVetoFSREmission() + : false; + +} + +//-------------------------------------------------------------------------- + +// Find whether to limit maximum scale of emissions. +// Also allow for dampening at factorization or renormalization scale. + +bool TimeShower::limitPTmax( Event& event, double Q2Fac, double Q2Ren) { + + // Find whether to limit pT. Begin by user-set cases. + bool dopTlimit = false; + if (pTmaxMatch == 1) dopTlimit = true; + else if (pTmaxMatch == 2) dopTlimit = false; + + // Look if any quark (u, d, s, c, b), gluon or photon in final state. + else { + for (int i = 5; i < event.size(); ++i) + if (event[i].status() != -21) { + int idAbs = event[i].idAbs(); + if (idAbs <= 5 || idAbs == 21 || idAbs == 22) dopTlimit = true; + } + } + + // Dampening at factorization or renormalization scale. + dopTdamp = false; + pT2damp = 0.; + if ( !dopTlimit && (pTdampMatch == 1 || pTdampMatch == 2) ) { + dopTdamp = true; + pT2damp = pow2(pTdampFudge) * ((pTdampMatch == 1) ? Q2Fac : Q2Ren); + } + + // Done. + return dopTlimit; + +} + +//-------------------------------------------------------------------------- + +// Top-level routine to do a full time-like shower in resonance decay. + +int TimeShower::shower( int iBeg, int iEnd, Event& event, double pTmax, + int nBranchMax) { + + // Add new system, automatically with two empty beam slots. + int iSys = partonSystemsPtr->addSys(); + + // Loop over allowed range to find all final-state particles. + Vec4 pSum; + for (int i = iBeg; i <= iEnd; ++i) if (event[i].isFinal()) { + partonSystemsPtr->addOut( iSys, i); + pSum += event[i].p(); + } + partonSystemsPtr->setSHat( iSys, pSum.m2Calc() ); + + // Let prepare routine do the setup. + prepare( iSys, event, true); + + // Begin evolution down in pT from hard pT scale. + int nBranch = 0; + pTLastBranch = 0.; + do { + double pTtimes = pTnext( event, pTmax, 0.); + + // Do a final-state emission (if allowed). + if (pTtimes > 0.) { + if (branch( event)) { + ++nBranch; + pTLastBranch = pTtimes; + } + pTmax = pTtimes; + } + + // Keep on evolving until nothing is left to be done. + else pTmax = 0.; + } while (pTmax > 0. && (nBranchMax <= 0 || nBranch < nBranchMax)); + + // Return number of emissions that were performed. + return nBranch; + +} + +//-------------------------------------------------------------------------- + +// Prepare system for evolution; identify ME. + +void TimeShower::prepare( int iSys, Event& event, bool limitPTmaxIn) { + + // Reset dipole-ends list for first interaction and for resonance decays. + int iInA = partonSystemsPtr->getInA(iSys); + int iInB = partonSystemsPtr->getInB(iSys); + if (iSys == 0 || iInA == 0) dipEnd.resize(0); + int dipEndSizeBeg = dipEnd.size(); + + // Loop through final state of system to find possible dipole ends. + for (int i = 0; i < partonSystemsPtr->sizeOut(iSys); ++i) { + int iRad = partonSystemsPtr->getOut( iSys, i); + if (event[iRad].isFinal() && event[iRad].scale() > 0.) { + + // Identify colour octet onium state. Check whether QCD shower allowed. + int idRad = event[iRad].id(); + int idRadAbs = abs(idRad); + bool isOctetOnium + = ( idRad == 9900441 || idRad == 9900443 || idRad == 9910441 + || idRad == 9900551 || idRad == 9900553 || idRad == 9910551 ); + bool doQCD = doQCDshower; + if (doQCD && isOctetOnium) + doQCD = (rndmPtr->flat() < octetOniumFraction); + + // Find dipole end formed by colour index. + int colTag = event[iRad].col(); + if (doQCD && colTag > 0) setupQCDdip( iSys, i, colTag, 1, event, + isOctetOnium, limitPTmaxIn); + + // Find dipole end formed by anticolour index. + int acolTag = event[iRad].acol(); + if (doQCD && acolTag > 0) setupQCDdip( iSys, i, acolTag, -1, event, + isOctetOnium, limitPTmaxIn); + + // Find "charge-dipole" and "photon-dipole" ends. + int chgType = event[iRad].chargeType(); + bool doChgDip = (chgType != 0) + && ( ( doQEDshowerByQ && event[iRad].isQuark() ) + || ( doQEDshowerByL && event[iRad].isLepton() ) ); + int gamType = (idRad == 22) ? 1 : 0; + bool doGamDip = (gamType == 1) && doQEDshowerByGamma; + if (doChgDip || doGamDip) setupQEDdip( iSys, i, chgType, gamType, + event, limitPTmaxIn); + + // Find Hidden Valley dipole ends. + bool isHVrad = (idRadAbs > 4900000 && idRadAbs < 4900007) + || (idRadAbs > 4900010 && idRadAbs < 4900017) + || idRadAbs == 4900101; + if (doHVshower && isHVrad) setupHVdip( iSys, i, event, limitPTmaxIn); + + // End loop over system final state. Have now found the dipole ends. + } + } + + // Loop through dipole ends to find matrix element corrections. + for (int iDip = dipEndSizeBeg; iDip < int(dipEnd.size()); ++iDip) + findMEtype( event, dipEnd[iDip]); + + // Update dipole list after a multiple interactions rescattering. + if (iSys > 0 && ( (iInA > 0 && event[iInA].status() == -34) + || (iInB > 0 && event[iInB].status() == -34) ) ) + rescatterUpdate( iSys, event); + +} + +//-------------------------------------------------------------------------- + +// Update dipole list after a multiple interactions rescattering. +void TimeShower::rescatterUpdate( int iSys, Event& event) { + + // Loop over two incoming partons in system; find their rescattering mother. + // (iOut is outgoing from old system, = incoming iIn of rescattering system.) + for (int iResc = 0; iResc < 2; ++iResc) { + int iIn = (iResc == 0) ? partonSystemsPtr->getInA(iSys) + : partonSystemsPtr->getInB(iSys); + if (iIn == 0 || event[iIn].status() != -34) continue; + int iOut = event[iIn].mother1(); + + // Loop over all dipoles. + int dipEndSize = dipEnd.size(); + for (int iDip = 0; iDip < dipEndSize; ++iDip) { + TimeDipoleEnd& dipNow = dipEnd[iDip]; + + // Kill dipoles where rescattered parton is radiator. + if (dipNow.iRadiator == iOut) { + dipNow.colType = 0; + dipNow.chgType = 0; + dipNow.gamType = 0; + continue; + } + // No matrix element for dipoles between scatterings. + if (dipNow.iMEpartner == iOut) { + dipNow.MEtype = 0; + dipNow.iMEpartner = -1; + } + + // Update dipoles where outgoing rescattered parton is recoiler. + if (dipNow.iRecoiler == iOut) { + int iRad = dipNow.iRadiator; + + // Colour dipole: recoil in final state, initial state or new + if (dipNow.colType > 0) { + int colTag = event[iRad].col(); + bool done = false; + for (int i = 0; i < partonSystemsPtr->sizeOut(iSys); ++i) { + int iRecNow = partonSystemsPtr->getOut( iSys, i); + if (event[iRecNow].acol() == colTag) { + dipNow.iRecoiler = iRecNow; + dipNow.systemRec = iSys; + dipNow.MEtype = 0; + done = true; + break; + } + } + if (!done) { + int iIn2 = (iResc == 0) ? partonSystemsPtr->getInB(iSys) + : partonSystemsPtr->getInA(iSys); + if (event[iIn2].col() == colTag) { + dipNow.iRecoiler = iIn2; + dipNow.systemRec = iSys; + dipNow.MEtype = 0; + int isrType = event[iIn2].mother1(); + // This line in case mother is a rescattered parton. + while (isrType > 2 + beamOffset) + isrType = event[isrType].mother1(); + if (isrType > 2) isrType -= beamOffset; + dipNow.isrType = isrType; + done = true; + } + } + // If above options failed, then create new dipole + if (!done) { + int iRadNow = partonSystemsPtr->getIndexOfOut(dipNow.system, iRad); + if (iRadNow != -1) + setupQCDdip(dipNow.system, iRadNow, event[iRad].col(), 1, + event, dipNow.isOctetOnium, true); + else + infoPtr->errorMsg("Warning in TimeShower::rescatterUpdate: " + "failed to locate radiator in system"); + + dipNow.colType = 0; + dipNow.chgType = 0; + dipNow.gamType = 0; + + infoPtr->errorMsg("Warning in TimeShower::rescatterUpdate: " + "failed to locate new recoiling colour partner"); + } + + // Anticolour dipole: recoil in final state, initial state or new + } else if (dipNow.colType < 0) { + int acolTag = event[iRad].acol(); + bool done = false; + for (int i = 0; i < partonSystemsPtr->sizeOut(iSys); ++i) { + int iRecNow = partonSystemsPtr->getOut( iSys, i); + if (event[iRecNow].col() == acolTag) { + dipNow.iRecoiler = iRecNow; + dipNow.systemRec = iSys; + dipNow.MEtype = 0; + done = true; + break; + } + } + if (!done) { + int iIn2 = (iResc == 0) ? partonSystemsPtr->getInB(iSys) + : partonSystemsPtr->getInA(iSys); + if (event[iIn2].acol() == acolTag) { + dipNow.iRecoiler = iIn2; + dipNow.systemRec = iSys; + dipNow.MEtype = 0; + int isrType = event[iIn2].mother1(); + // This line in case mother is a rescattered parton. + while (isrType > 2 + beamOffset) + isrType = event[isrType].mother1(); + if (isrType > 2) isrType -= beamOffset; + dipNow.isrType = isrType; + done = true; + } + } + // If above options failed, then create new dipole + if (!done) { + int iRadNow = partonSystemsPtr->getIndexOfOut(dipNow.system, iRad); + if (iRadNow != -1) + setupQCDdip(dipNow.system, iRadNow, event[iRad].acol(), -1, + event, dipNow.isOctetOnium, true); + else + infoPtr->errorMsg("Warning in TimeShower::rescatterUpdate: " + "failed to locate radiator in system"); + + dipNow.colType = 0; + dipNow.chgType = 0; + dipNow.gamType = 0; + + infoPtr->errorMsg("Warning in TimeShower::rescatterUpdate: " + "failed to locate new recoiling colour partner"); + } + + // Charge or photon dipoles: same flavour in final or initial state. + } else if (dipNow.chgType != 0 || dipNow.gamType != 0) { + int idTag = event[dipNow.iRecoiler].id(); + bool done = false; + for (int i = 0; i < partonSystemsPtr->sizeOut(iSys); ++i) { + int iRecNow = partonSystemsPtr->getOut( iSys, i); + if (event[iRecNow].id() == idTag) { + dipNow.iRecoiler = iRecNow; + dipNow.systemRec = iSys; + dipNow.MEtype = 0; + done = true; + break; + } + } + if (!done) { + int iIn2 = (iResc == 0) ? partonSystemsPtr->getInB(iSys) + : partonSystemsPtr->getInA(iSys); + if (event[iIn2].id() == -idTag) { + dipNow.iRecoiler = iIn2; + dipNow.systemRec = iSys; + dipNow.MEtype = 0; + int isrType = event[iIn2].mother1(); + // This line in case mother is a rescattered parton. + while (isrType > 2 + beamOffset) + isrType = event[isrType].mother1(); + if (isrType > 2) isrType -= beamOffset; + dipNow.isrType = isrType; + done = true; + } + } + // If above options failed, then create new dipole + if (!done) { + int iRadNow = partonSystemsPtr->getIndexOfOut(dipNow.system, iRad); + if (iRadNow != -1) + setupQEDdip(dipNow.system, iRadNow, dipNow.chgType, + dipNow.gamType, event, true); + else + infoPtr->errorMsg("Warning in TimeShower::rescatterUpdate: " + "failed to locate radiator in system"); + + dipNow.colType = 0; + dipNow.chgType = 0; + dipNow.gamType = 0; + + infoPtr->errorMsg("Warning in TimeShower::rescatterUpdate: " + "failed to locate new recoiling charge partner"); + } + } + } + + // End of loop over dipoles and two incoming sides. + } + } + +} + +//-------------------------------------------------------------------------- + +// Update dipole list after each ISR emission (so not used for resonances). + +void TimeShower::update( int iSys, Event& event) { + + // Start list of rescatterers that gave further changed systems in ISR. + vector iRescatterer; + + // Find new and old positions of incoming partons in the system. + vector iNew, iOld; + iNew.push_back( partonSystemsPtr->getInA(iSys) ); + iOld.push_back( event[iNew[0]].daughter2() ); + iNew.push_back( partonSystemsPtr->getInB(iSys) ); + iOld.push_back( event[iNew[1]].daughter2() ); + + // Ditto for outgoing partons, except the newly created one. + int sizeOut = partonSystemsPtr->sizeOut(iSys) - 1; + for (int i = 0; i < sizeOut; ++i) { + int iNow = partonSystemsPtr->getOut(iSys, i); + iNew.push_back( iNow ); + iOld.push_back( event[iNow].mother1() ); + // Add non-final to list of rescatterers. + if (!event[iNow].isFinal()) iRescatterer.push_back( iNow ); + } + int iNewNew = partonSystemsPtr->getOut(iSys, sizeOut); + + // Swap beams to let 0 be side on which branching occured. + if (event[iNew[0]].status() != -41) { + swap( iNew[0], iNew[1]); + swap( iOld[0], iOld[1]); + } + + // Loop over all dipole ends belonging to the system + // or to the recoil system, if different. + for (int iDip = 0; iDip < int(dipEnd.size()); ++iDip) + if (dipEnd[iDip].system == iSys || dipEnd[iDip].systemRec == iSys) { + TimeDipoleEnd& dipNow = dipEnd[iDip]; + + // Replace radiator (always in final state so simple). + for (int i = 2; i < 2 + sizeOut; ++i) + if (dipNow.iRadiator == iOld[i]) { + dipNow.iRadiator = iNew[i]; + break; + } + + // Replace ME partner (always in final state, if exists, so simple). + for (int i = 2; i < 2 + sizeOut; ++i) + if (dipNow.iMEpartner == iOld[i]) { + dipNow.iMEpartner = iNew[i]; + break; + } + + // Recoiler: by default pick old one, only moved. Note excluded beam. + int iRec = 0; + if (dipNow.systemRec == iSys) { + for (int i = 1; i < 2 + sizeOut; ++i) + if (dipNow.iRecoiler == iOld[i]) { + iRec = iNew[i]; + break; + } + + // QCD recoiler: check if colour hooks up with new final parton. + if ( dipNow.colType > 0 + && event[dipNow.iRadiator].col() == event[iNewNew].acol() ) { + iRec = iNewNew; + dipNow.isrType = 0; + } + if ( dipNow.colType < 0 + && event[dipNow.iRadiator].acol() == event[iNewNew].col() ) { + iRec = iNewNew; + dipNow.isrType = 0; + } + + // QCD recoiler: check if colour hooks up with new beam parton. + if ( iRec == 0 && dipNow.colType > 0 + && event[dipNow.iRadiator].col() == event[iNew[0]].col() ) + iRec = iNew[0]; + if ( iRec == 0 && dipNow.colType < 0 + && event[dipNow.iRadiator].acol() == event[iNew[0]].acol() ) + iRec = iNew[0]; + + // QED/photon recoiler: either to new particle or remains to beam. + if ( iRec == 0 && (dipNow.chgType != 0 || dipNow.gamType != 0) ) { + if ( event[iNew[0]].chargeType() == 0 ) { + iRec = iNewNew; + dipNow.isrType = 0; + } else { + iRec = iNew[0]; + } + } + + // Recoiler in another system: keep it as is. + } else iRec = dipNow.iRecoiler; + + // Done. Kill dipole if failed to find new recoiler. + dipNow.iRecoiler = iRec; + if ( iRec == 0 && (dipNow.colType != 0 || dipNow.chgType != 0 + || dipNow.gamType != 0) ) { + dipNow.colType = 0; + dipNow.chgType = 0; + dipNow.gamType = 0; + infoPtr->errorMsg("Error in TimeShower::update: " + "failed to locate new recoiling partner"); + } + } + + // Find new dipole end formed by colour index. + int colTag = event[iNewNew].col(); + if (doQCDshower && colTag > 0) + setupQCDdip( iSys, sizeOut, colTag, 1, event, false, true); + + // Find new dipole end formed by anticolour index. + int acolTag = event[iNewNew].acol(); + if (doQCDshower && acolTag > 0) + setupQCDdip( iSys, sizeOut, acolTag, -1, event, false, true); + + // Find new "charge-dipole" and "photon-dipole" ends. + int chgType = event[iNewNew].chargeType(); + bool doChgDip = (chgType != 0) + && ( ( doQEDshowerByQ && event[iNewNew].isQuark() ) + || ( doQEDshowerByL && event[iNewNew].isLepton() ) ); + int gamType = (event[iNewNew].id() == 22) ? 1 : 0; + bool doGamDip = (gamType == 1) && doQEDshowerByGamma; + if (doChgDip || doGamDip) + setupQEDdip( iSys, sizeOut, chgType, gamType, event, true); + + // Start iterate over list of rescatterers - may be empty. + int iRescNow = -1; + while (++iRescNow < int(iRescatterer.size())) { + + // Identify systems that rescatterers belong to. + int iOutNew = iRescatterer[iRescNow]; + int iInNew = event[iOutNew].daughter1(); + int iSysResc = partonSystemsPtr->getSystemOf(iInNew, true); + + // Find new and old positions of incoming partons in the system. + iNew.resize(0); + iOld.resize(0); + iNew.push_back( partonSystemsPtr->getInA(iSysResc) ); + iOld.push_back( event[iNew[0]].daughter1() ); + iNew.push_back( partonSystemsPtr->getInB(iSysResc) ); + iOld.push_back( event[iNew[1]].daughter1() ); + + // Ditto for outgoing partons. + sizeOut = partonSystemsPtr->sizeOut(iSysResc); + for (int i = 0; i < sizeOut; ++i) { + int iNow = partonSystemsPtr->getOut(iSysResc, i); + iNew.push_back( iNow ); + iOld.push_back( event[iNow].mother1() ); + // Add non-final to list of rescatterers. + if (!event[iNow].isFinal()) iRescatterer.push_back( iNow ); + } + + // Loop over all dipole ends belonging to the system + // or to the recoil system, if different. + for (int iDip = 0; iDip < int(dipEnd.size()); ++iDip) + if (dipEnd[iDip].system == iSysResc + || dipEnd[iDip].systemRec == iSysResc) { + TimeDipoleEnd& dipNow = dipEnd[iDip]; + + // Replace radiator (always in final state so simple). + for (int i = 2; i < 2 + sizeOut; ++i) + if (dipNow.iRadiator == iOld[i]) { + dipNow.iRadiator = iNew[i]; + break; + } + + // Replace ME partner (always in final state, if exists, so simple). + for (int i = 2; i < 2 + sizeOut; ++i) + if (dipNow.iMEpartner == iOld[i]) { + dipNow.iMEpartner = iNew[i]; + break; + } + + // Replace recoiler. + for (int i = 0; i < 2 + sizeOut; ++i) + if (dipNow.iRecoiler == iOld[i]) { + dipNow.iRecoiler = iNew[i]; + break; + } + } + + // End iterate over list of rescatterers. + } + +} + +//-------------------------------------------------------------------------- + +// Setup a dipole end for a QCD colour charge. + +void TimeShower::setupQCDdip( int iSys, int i, int colTag, int colSign, + Event& event, bool isOctetOnium, bool limitPTmaxIn) { + + // Initial values. Find if allowed to hook up beams. + int iRad = partonSystemsPtr->getOut(iSys, i); + int iRec = 0; + int sizeAllA = partonSystemsPtr->sizeAll(iSys); + int sizeOut = partonSystemsPtr->sizeOut(iSys); + int sizeAll = ( allowBeamRecoil ) ? sizeAllA : sizeOut; + int sizeIn = sizeAll - sizeOut; + int sizeInA = sizeAllA - sizeIn - sizeOut; + int iOffset = i + sizeAllA - sizeOut; + bool otherSystemRec = false; + bool allowInitial = (partonSystemsPtr->hasInAB(iSys)) ? true : false; + + // Colour: other end by same index in beam or opposite in final state. + // Exclude rescattered incoming and not final outgoing. + if (colSign > 0) + for (int j = 0; j < sizeAll; ++j) if (j + sizeInA != iOffset) { + int iRecNow = partonSystemsPtr->getAll(iSys, j + sizeInA); + if ( ( j < sizeIn && event[iRecNow].col() == colTag + && !event[iRecNow].isRescatteredIncoming() ) + || ( j >= sizeIn && event[iRecNow].acol() == colTag + && event[iRecNow].isFinal() ) ) { + iRec = iRecNow; + break; + } + } + + // Anticolour: other end by same index in beam or opposite in final state. + // Exclude rescattered incoming and not final outgoing. + if (colSign < 0) + for (int j = 0; j < sizeAll; ++j) if (j + sizeInA != iOffset) { + int iRecNow = partonSystemsPtr->getAll(iSys, j + sizeInA); + if ( ( j < sizeIn && event[iRecNow].acol() == colTag + && !event[iRecNow].isRescatteredIncoming() ) + || ( j >= sizeIn && event[iRecNow].col() == colTag + && event[iRecNow].isFinal() ) ) { + iRec = iRecNow; + break; + } + } + + // Resonance decays (= no instate), without a junction colour: + // other end to nearest recoiler in same system final state, + // by (p_i + p_j)^2 - (m_i + m_j)^2 = 2 (p_i p_j - m_i m_j). + if (iRec == 0 && !allowInitial) { + bool hasJunction = false; + for (int iJun = 0; iJun < event.sizeJunction(); ++ iJun) + for (int iLeg = 0; iLeg < 3; ++iLeg) + if (event.endColJunction( iJun, iLeg) == colTag) hasJunction = true; + if (!hasJunction) { + double ppMin = LARGEM2; + for (int j = 0; j < sizeOut; ++j) if (j != i) { + int iRecNow = partonSystemsPtr->getOut(iSys, j); + if (!event[iRecNow].isFinal()) continue; + double ppNow = event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m(); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + } + } + } + } + + // If no success then look for matching (anti)colour anywhere in final state. + if ( iRec == 0 || (!doInterleave && !event[iRec].isFinal()) ) { + iRec = 0; + for (int j = 0; j < event.size(); ++j) if (event[j].isFinal()) + if ( (colSign > 0 && event[j].acol() == colTag) + || (colSign < 0 && event[j].col() == colTag) ) { + iRec = j; + otherSystemRec = true; + break; + } + + // If no success then look for match to non-rescattered in initial state. + if (iRec == 0 && allowInitial) { + for (int iSysR = 0; iSysR < partonSystemsPtr->sizeSys(); ++iSysR) + if (iSysR != iSys) { + int j = partonSystemsPtr->getInA(iSysR); + if (j > 0 && event[j].isRescatteredIncoming()) j = 0; + if (j > 0 && ( (colSign > 0 && event[j].col() == colTag) + || (colSign < 0 && event[j].acol() == colTag) ) ) { + iRec = j; + otherSystemRec = true; + break; + } + j = partonSystemsPtr->getInB(iSysR); + if (j > 0 && event[j].isRescatteredIncoming()) j = 0; + if (j > 0 && ( (colSign > 0 && event[j].col() == colTag) + || (colSign < 0 && event[j].acol() == colTag) ) ) { + iRec = j; + otherSystemRec = true; + break; + } + } + } + + // For junction pick any of other leg as recoiler. Note colour sign. + if (iRec == 0) { + for (int iJun = 0; iJun < event.sizeJunction(); ++ iJun) + for (int iLeg = 0; iLeg < 3; ++iLeg) + if (event.endColJunction( iJun, iLeg) == colTag) { + int iLegRec = iLeg + 1 + int(2. * rndmPtr->flat()); + if (iLegRec >= 3) iLegRec -= 3; + int colTagRec = event.endColJunction( iJun, iLegRec); + for (int j = 0; j < event.size(); ++j) if (event[j].isFinal()) + if ( (colSign > 0 && event[j].col() == colTagRec) + || (colSign < 0 && event[j].acol() == colTagRec) ) { + iRec = j; + otherSystemRec = true; + break; + } + } + } + } + + // If fail, then other end to nearest recoiler in same system final state, + // by (p_i + p_j)^2 - (m_i + m_j)^2 = 2 (p_i p_j - m_i m_j). + if (iRec == 0) { + double ppMin = LARGEM2; + for (int j = 0; j < sizeOut; ++j) if (j != i) { + int iRecNow = partonSystemsPtr->getOut(iSys, j); + if (!event[iRecNow].isFinal()) continue; + double ppNow = event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m(); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + } + } + } + + // If fail, then other end to nearest recoiler in any system final state, + // by (p_i + p_j)^2 - (m_i + m_j)^2 = 2 (p_i p_j - m_i m_j). + if (iRec == 0) { + double ppMin = LARGEM2; + for (int iRecNow = 0; iRecNow < event.size(); ++iRecNow) + if (iRecNow != iRad && event[iRecNow].isFinal()) { + double ppNow = event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m(); + if (ppNow < ppMin) { + iRec = iRecNow; + otherSystemRec = true; + ppMin = ppNow; + } + } + } + + // Store dipole colour end. + if (iRec > 0) { + // Max scale either by parton scale or by half dipole mass. + double pTmax = event[iRad].scale(); + if (limitPTmaxIn) { + if (iSys == 0) pTmax *= pTmaxFudge; + if (iSys > 0 && sizeIn > 0) pTmax *= pTmaxFudgeMI; + } else pTmax = 0.5 * m( event[iRad], event[iRec]); + int colType = (event[iRad].id() == 21) ? 2 * colSign : colSign; + int isrType = (event[iRec].isFinal()) ? 0 : event[iRec].mother1(); + // This line in case mother is a rescattered parton. + while (isrType > 2 + beamOffset) isrType = event[isrType].mother1(); + if (isrType > 2) isrType -= beamOffset; + dipEnd.push_back( TimeDipoleEnd( iRad, iRec, pTmax, + colType, 0, 0, isrType, iSys, -1, -1, isOctetOnium) ); + + // If hooked up with other system then find which. + if (otherSystemRec) { + int systemRec = partonSystemsPtr->getSystemOf(iRec, true); + if (systemRec >= 0) dipEnd.back().systemRec = systemRec; + dipEnd.back().MEtype = 0; + } + } else { + infoPtr->errorMsg("Error in TimeShower::setupQCDdip: " + "failed to locate any recoiling partner"); + } + +} + +//-------------------------------------------------------------------------- + +// Setup a dipole end for a QED colour charge or a photon. +// No failsafe choice of recoiler, so gradually widen search. + +void TimeShower::setupQEDdip( int iSys, int i, int chgType, int gamType, + Event& event, bool limitPTmaxIn) { + + // Initial values. Find if allowed to hook up beams. + int iRad = partonSystemsPtr->getOut(iSys, i); + int idRad = event[iRad].id(); + int iRec = 0; + int sizeAllA = partonSystemsPtr->sizeAll(iSys); + int sizeOut = partonSystemsPtr->sizeOut(iSys); + int sizeAll = ( allowBeamRecoil ) ? sizeAllA : sizeOut; + int sizeIn = sizeAll - sizeOut; + int sizeInA = sizeAllA - sizeIn - sizeOut; + int iOffset = i + sizeAllA - sizeOut; + double ppMin = LARGEM2; + bool hasRescattered = false; + bool otherSystemRec = false; + + // Find nearest same- (opposide-) flavour recoiler in initial (final) + // state of same system, excluding rescattered (in or out) partons. + // Also find if system is involved in rescattering. + // Note: (p_i + p_j)2 - (m_i + m_j)2 = 2 (p_i p_j - m_i m_j). + for (int j = 0; j < sizeAll; ++j) if (j + sizeInA != iOffset) { + int iRecNow = partonSystemsPtr->getAll(iSys, j + sizeInA); + if ( (j < sizeIn && !event[iRecNow].isRescatteredIncoming()) + || (j >= sizeIn && event[iRecNow].isFinal()) ) { + if ( (j < sizeIn && event[iRecNow].id() == idRad) + || (j >= sizeIn && event[iRecNow].id() == -idRad) ) { + double ppNow = event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m(); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + } + } + } else hasRescattered = true; + } + + // If rescattering then find nearest opposite-flavour recoiler + // anywhere in final state. + if (iRec == 0 && hasRescattered) { + for (int iRecNow = 0; iRecNow < event.size(); ++iRecNow) + if (event[iRecNow].id() == -idRad && event[iRecNow].isFinal()) { + double ppNow = event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m(); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + otherSystemRec = true; + } + } + } + + // Find nearest recoiler in same system, charge-squared-weighted, + // including initial state, but excluding rescatterer. + if (iRec == 0) + for (int j = 0; j < sizeAll; ++j) if (j + sizeInA != iOffset) { + int iRecNow = partonSystemsPtr->getAll(iSys, j + sizeInA); + int chgTypeRecNow = event[iRecNow].chargeType(); + if (chgTypeRecNow == 0) continue; + if ( (j < sizeIn && !event[iRecNow].isRescatteredIncoming()) + || (j >= sizeIn && event[iRecNow].isFinal()) ) { + double ppNow = (event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m()) + / pow2(chgTypeRecNow); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + } + } + } + + // If rescattering then find nearest recoiler in the final state, + // charge-squared-weighted. + if (iRec == 0 && hasRescattered) { + for (int iRecNow = 0; iRecNow < event.size(); ++iRecNow) + if (iRecNow != iRad && event[iRecNow].isFinal()) { + int chgTypeRecNow = event[iRecNow].chargeType(); + if (chgTypeRecNow != 0 && event[iRecNow].isFinal()) { + double ppNow = (event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m()) + / pow2(chgTypeRecNow); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + otherSystemRec = true; + } + } + } + } + + // Find any nearest recoiler in final state of same system. + if (iRec == 0) + for (int j = 0; j < sizeOut; ++j) if (j != i) { + int iRecNow = partonSystemsPtr->getOut(iSys, j); + double ppNow = event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m(); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + } + } + + // Find any nearest recoiler in final state. + if (iRec == 0) + for (int iRecNow = 0; iRecNow < event.size(); ++iRecNow) + if (iRecNow != iRad && event[iRecNow].isFinal()) { + double ppNow = event[iRecNow].p() * event[iRad].p() + - event[iRecNow].m() * event[iRad].m(); + if (ppNow < ppMin) { + iRec = iRecNow; + ppMin = ppNow; + otherSystemRec = true; + } + } + + // Fill charge-dipole or photon-dipole end. + if (iRec > 0) { + // Max scale either by parton scale or by half dipole mass. + double pTmax = event[iRad].scale(); + if (limitPTmaxIn) { + if (iSys == 0) pTmax *= pTmaxFudge; + if (iSys > 0 && sizeIn > 0) pTmax *= pTmaxFudgeMI; + } else pTmax = 0.5 * m( event[iRad], event[iRec]); + int isrType = (event[iRec].isFinal()) ? 0 : event[iRec].mother1(); + // This line in case mother is a rescattered parton. + while (isrType > 2 + beamOffset) isrType = event[isrType].mother1(); + if (isrType > 2) isrType -= beamOffset; + dipEnd.push_back( TimeDipoleEnd(iRad, iRec, pTmax, + 0, chgType, gamType, isrType, iSys, -1) ); + + // If hooked up with other system then find which. + if (otherSystemRec) { + int systemRec = partonSystemsPtr->getSystemOf(iRec); + if (systemRec >= 0) dipEnd.back().systemRec = systemRec; + dipEnd.back().MEtype = 0; + } + + // Failure to find other end of dipole. + } else { + infoPtr->errorMsg("Error in TimeShower::setupQEDdip: " + "failed to locate any recoiling partner"); + } + +} + +//-------------------------------------------------------------------------- + +// Setup a dipole end for a Hidden Valley colour charge. + +void TimeShower::setupHVdip( int iSys, int i, Event& event, + bool limitPTmaxIn) { + + // Initial values. + int iRad = partonSystemsPtr->getOut(iSys, i); + int iRec = 0; + int idRad = event[iRad].id(); + int sizeOut = partonSystemsPtr->sizeOut(iSys); + + // Hidden Valley colour positive for positive id, and vice versa. + // Find opposte HV colour in final state of same system. + for (int j = 0; j < sizeOut; ++j) if (j != i) { + int iRecNow = partonSystemsPtr->getOut(iSys, j); + int idRec = event[iRecNow].id(); + if ( (abs(idRec) > 4900000 && abs(idRec) < 4900017) + && idRad * idRec < 0) { + iRec = iRecNow; + break; + } + } + + // Else find heaviest other final-state in same system. + // (Intended for decays; should mainly be two-body so unique.) + double mMax = -sqrt(LARGEM2); + if (iRec == 0) + for (int j = 0; j < sizeOut; ++j) if (j != i) { + int iRecNow = partonSystemsPtr->getOut(iSys, j); + if (event[iRecNow].m() > mMax) { + iRec = iRecNow; + mMax = event[iRecNow].m(); + } + } + + // Set up dipole end, or report failure. + if (iRec > 0) { + // Max scale either by parton scale or by half dipole mass. + double pTmax = event[iRad].scale(); + if (limitPTmaxIn) { + if (iSys == 0) pTmax *= pTmaxFudge; + } else pTmax = 0.5 * m( event[iRad], event[iRec]); + int colvType = (event[iRad].id() > 0) ? 1 : -1; + dipEnd.push_back( TimeDipoleEnd( iRad, iRec, pTmax, 0, 0, 0, 0, + iSys, -1, -1, false, true, colvType) ); + } else infoPtr->errorMsg("Error in TimeShower::setupHVdip: " + "failed to locate any recoiling partner"); + +} + +//-------------------------------------------------------------------------- + +// Select next pT in downwards evolution of the existing dipoles. + +double TimeShower::pTnext( Event& event, double pTbegAll, double pTendAll) { + + // Begin loop over all possible radiating dipole ends. + dipSel = 0; + iDipSel = -1; + double pT2sel = pTendAll * pTendAll; + for (int iDip = 0; iDip < int(dipEnd.size()); ++iDip) { + TimeDipoleEnd& dip = dipEnd[iDip]; + + // Dipole properties. (Could partly be moved up to prepare??) + dip.mRad = event[dip.iRadiator].m(); + dip.m2Rad = pow2(dip.mRad); + dip.mRec = event[dip.iRecoiler].m(); + dip.m2Rec = pow2(dip.mRec); + dip.mDip = m( event[dip.iRadiator], event[dip.iRecoiler] ); + dip.m2Dip = pow2(dip.mDip); + + // Find maximum evolution scale for dipole. + dip.m2DipCorr = pow2(dip.mDip - dip.mRec) - dip.m2Rad; + double pTbegDip = min( pTbegAll, dip.pTmax ); + double pT2begDip = min( pow2(pTbegDip), 0.25 * dip.m2DipCorr); + + // Do QCD, QED or HV evolution if it makes sense. + dip.pT2 = 0.; + if (pT2begDip > pT2sel) { + if (dip.colType != 0) + pT2nextQCD(pT2begDip, pT2sel, dip, event); + else if (dip.chgType != 0 || dip.gamType != 0) + pT2nextQED(pT2begDip, pT2sel, dip, event); + else if (dip.colvType != 0) + pT2nextHV(pT2begDip, pT2sel, dip, event); + + // Update if found larger pT than current maximum. + if (dip.pT2 > pT2sel) { + pT2sel = dip.pT2; + dipSel = &dip; + iDipSel = iDip; + } + } + } + + // Return nonvanishing value if found pT bigger than already found. + return (dipSel == 0) ? 0. : sqrt(pT2sel); + +} + +//-------------------------------------------------------------------------- + +// Evolve a QCD dipole end. + +void TimeShower::pT2nextQCD(double pT2begDip, double pT2sel, + TimeDipoleEnd& dip, Event& event) { + + // Lower cut for evolution. Return if no evolution range. + double pT2endDip = max( pT2sel, pT2colCut ); + if (pT2begDip < pT2endDip) return; + + // Upper estimate for matrix element weighting and colour factor. + // Special cases for triplet recoiling against gluino and octet onia. + // Note that g -> g g and g -> q qbar are split on two sides. + int colTypeAbs = abs(dip.colType); + double wtPSglue = 2.; + double colFac = (colTypeAbs == 1) ? 4./3. : 3./2.; + if (dip.MEgluinoRec) colFac = 3.; + if (dip.isOctetOnium) colFac *= 0.5 * octetOniumColFac; + double wtPSqqbar = (colTypeAbs == 2) ? 0.25 * nGluonToQuark : 0.; + + // Variables used inside evolution loop. (Mainly dummy start values.) + dip.pT2 = pT2begDip; + int nFlavour = 3; + double zMinAbs = 0.5; + double pT2min = pT2endDip; + double b0 = 4.5; + double Lambda2 = Lambda3flav2; + double emitCoefGlue = 0.; + double emitCoefQqbar = 0.; + double emitCoefTot = 0.; + double wt = 0.; + bool mustFindRange = true; + + // Begin evolution loop towards smaller pT values. + do { + + // Initialize evolution coefficients at the beginning and + // reinitialize when crossing c and b flavour thresholds. + if (mustFindRange) { + + // Determine overestimated z range; switch at c and b masses. + if (dip.pT2 > m2b) { + nFlavour = 5; + pT2min = m2b; + b0 = 23./6.; + Lambda2 = Lambda5flav2; + } else if (dip.pT2 > m2c) { + nFlavour = 4; + pT2min = m2c; + b0 = 25./6.; + Lambda2 = Lambda4flav2; + } else { + nFlavour = 3; + pT2min = pT2endDip; + b0 = 27./6.; + Lambda2 = Lambda3flav2; + } + zMinAbs = 0.5 - sqrtpos( 0.25 - pT2min / dip.m2DipCorr ); + if (zMinAbs < SIMPLIFYROOT) zMinAbs = pT2min / dip.m2DipCorr; + + // Find emission coefficients for X -> X g and g -> q qbar. + emitCoefGlue = wtPSglue * colFac * log(1. / zMinAbs - 1.); + emitCoefTot = emitCoefGlue; + if (colTypeAbs == 2 && event[dip.iRadiator].id() == 21) { + emitCoefQqbar = wtPSqqbar * (1. - 2. * zMinAbs); + emitCoefTot += emitCoefQqbar; + } + + // Initialization done for current range. + mustFindRange = false; + } + + // Pick pT2 (in overestimated z range) for fixed alpha_strong. + if (alphaSorder == 0) { + dip.pT2 = dip.pT2 * pow( rndmPtr->flat(), + 1. / (alphaS2pi * emitCoefTot) ); + + // Ditto for first-order alpha_strong. + } else if (alphaSorder == 1) { + dip.pT2 = Lambda2 * pow( dip.pT2 / Lambda2, + pow( rndmPtr->flat(), b0 / emitCoefTot) ); + + // For second order reject by second term in alpha_strong expression. + } else { + do dip.pT2 = Lambda2 * pow( dip.pT2 / Lambda2, + pow( rndmPtr->flat(), b0 / emitCoefTot) ); + while (alphaS.alphaS2OrdCorr(dip.pT2) < rndmPtr->flat() + && dip.pT2 > pT2min); + } + wt = 0.; + + // If crossed c or b thresholds: continue evolution from threshold. + if (nFlavour == 5 && dip.pT2 < m2b) { + mustFindRange = true; + dip.pT2 = m2b; + } else if ( nFlavour == 4 && dip.pT2 < m2c) { + mustFindRange = true; + dip.pT2 = m2c; + + // Abort evolution if below cutoff scale, or below another branching. + } else { + if ( dip.pT2 < pT2endDip) { dip.pT2 = 0.; return; } + + // Pick kind of branching: X -> X g or g -> q qbar. + dip.flavour = 21; + dip.mFlavour = 0.; + if (colTypeAbs == 2 && emitCoefQqbar > rndmPtr->flat() + * emitCoefTot) dip.flavour = 0; + + // Pick z: either dz/(1-z) or flat dz. + if (dip.flavour == 21) { + dip.z = 1. - zMinAbs * pow( 1. / zMinAbs - 1., rndmPtr->flat() ); + } else { + dip.z = zMinAbs + (1. - 2. * zMinAbs) * rndmPtr->flat(); + } + + // Do not accept branching if outside allowed z range. + double zMin = 0.5 - sqrtpos( 0.25 - dip.pT2 / dip.m2DipCorr ); + if (zMin < SIMPLIFYROOT) zMin = dip.pT2 / dip.m2DipCorr; + dip.m2 = dip.m2Rad + dip.pT2 / (dip.z * (1. - dip.z)); + if (dip.z > zMin && dip.z < 1. - zMin + && dip.m2 * dip.m2Dip < dip.z * (1. - dip.z) + * pow2(dip.m2Dip + dip.m2 - dip.m2Rec) ) { + + // Flavour choice for g -> q qbar. + if (dip.flavour == 0) { + dip.flavour = min(5, 1 + int(nGluonToQuark * rndmPtr->flat())); + dip.mFlavour = particleDataPtr->m0(dip.flavour); + } + + // No z weight, except threshold, if to do ME corrections later on. + if (dip.MEtype > 0) { + wt = 1.; + if (dip.flavour < 10 && dip.m2 < THRESHM2 * pow2(dip.mFlavour)) + wt = 0.; + + // z weight for X -> X g. + } else if (dip.flavour == 21 && colTypeAbs == 1) { + wt = (1. + pow2(dip.z)) / wtPSglue; + } else if (dip.flavour == 21) { + wt = (1. + pow3(dip.z)) / wtPSglue; + + // z weight for g -> q qbar. + } else { + double beta = sqrtpos( 1. - 4. * pow2(dip.mFlavour) / dip.m2 ); + wt = beta * ( pow2(dip.z) + pow2(1. - dip.z) ); + } + + // Suppression factors for dipole to beam remnant. + if (dip.isrType != 0) { + BeamParticle& beam = (dip.isrType == 1) ? *beamAPtr : *beamBPtr; + int iSysRec = dip.systemRec; + double xOld = beam[iSysRec].x(); + double xNew = xOld * (1. + (dip.m2 - dip.m2Rad) / + (dip.m2Dip - dip.m2Rad)); + double xMaxAbs = beam.xMax(iSysRec); + if (xMaxAbs < 0.) { + infoPtr->errorMsg("Warning in TimeShower::pT2nextQCD: " + "xMaxAbs negative"); + return; + } + + // Firstly reduce by PDF ratio. + if (xNew > xMaxAbs) wt = 0.; + else { + int idRec = event[dip.iRecoiler].id(); + double pdfOld = max ( TINYPDF, + beam.xfISR( iSysRec, idRec, xOld, dip.pT2) ); + double pdfNew = beam.xfISR( iSysRec, idRec, xNew, dip.pT2); + wt *= min( 1., pdfNew / pdfOld); + } + + // Secondly optionally reduce by 4 pT2_hard / (4 pT2_hard + m2). + if (dampenBeamRecoil) { + double pTpT = sqrt(event[dip.iRadiator].pT2() * dip.pT2); + wt *= pTpT / (pTpT + dip.m2); + } + } + } + } + + // Iterate until acceptable pT (or have fallen below pTmin). + } while (wt < rndmPtr->flat()); + +} + +//-------------------------------------------------------------------------- + +// Evolve a QED dipole end, either charged or photon. + +void TimeShower::pT2nextQED(double pT2begDip, double pT2sel, + TimeDipoleEnd& dip, Event& event) { + + // Lower cut for evolution. Return if no evolution range. + double pT2chgCut = (dip.chgType != 0 && abs(dip.chgType) != 3) + ? pT2chgQCut : pT2chgLCut; + double pT2endDip = max( pT2sel, pT2chgCut ); + if (pT2begDip < pT2endDip) return; + + // Emission of photon or photon branching. + bool hasCharge = (dip.chgType != 0); + + // Default values. + double wtPSgam = 0.; + double chg2Sum = 0.; + double chg2SumL = 0.; + double chg2SumQ = 0.; + double zMinAbs = 0.; + double emitCoefTot = 0.; + + // alpha_em at maximum scale provides upper estimate. + double alphaEMmax = alphaEM.alphaEM(pT2begDip); + double alphaEM2pi = alphaEMmax / (2. * M_PI); + + // Emission: upper estimate for matrix element weighting; charge factor. + if (hasCharge) { + wtPSgam = 2.; + double chg2 = pow2(dip.chgType / 3.); + + // Determine overestimated z range. Find evolution coefficient. + zMinAbs = 0.5 - sqrtpos( 0.25 - pT2endDip / dip.m2DipCorr ); + if (zMinAbs < SIMPLIFYROOT) zMinAbs = pT2endDip / dip.m2DipCorr; + emitCoefTot = alphaEM2pi * chg2 * wtPSgam * log(1. / zMinAbs - 1.); + + // Branching: sum of squared charge factors for lepton and quark daughters. + } else { + chg2SumL = max(0, min(3, nGammaToLepton)); + if (nGammaToQuark > 4) chg2SumQ = 11. / 9.; + else if (nGammaToQuark > 3) chg2SumQ = 10. / 9.; + else if (nGammaToQuark > 2) chg2SumQ = 6. / 9.; + else if (nGammaToQuark > 1) chg2SumQ = 5. / 9.; + else if (nGammaToQuark > 0) chg2SumQ = 1. / 9.; + + // Total sum of squared charge factors. Find evolution coefficient. + chg2Sum = chg2SumL + 3. * chg2SumQ; + emitCoefTot = alphaEM2pi * chg2Sum; + } + + // Variables used inside evolution loop. + dip.pT2 = pT2begDip; + double wt; + + // Begin evolution loop towards smaller pT values. + do { + + // Pick pT2 (in overestimated z range). + dip.pT2 = dip.pT2 * pow(rndmPtr->flat(), 1. / emitCoefTot); + wt = 0.; + + // Abort evolution if below cutoff scale, or below another branching. + if ( dip.pT2 < pT2endDip) { dip.pT2 = 0.; return; } + + // Pick z according to dz/(1-z) or flat. + if (hasCharge) dip.z = 1. - zMinAbs + * pow( 1. / zMinAbs - 1., rndmPtr->flat() ); + else dip.z = rndmPtr->flat(); + + // Do not accept branching if outside allowed z range. + double zMin = 0.5 - sqrtpos( 0.25 - dip.pT2 / dip.m2DipCorr ); + if (zMin < SIMPLIFYROOT) zMin = dip.pT2 / dip.m2DipCorr; + dip.m2 = dip.m2Rad + dip.pT2 / (dip.z * (1. - dip.z)); + if (dip.z > zMin && dip.z < 1. - zMin + && dip.m2 * dip.m2Dip < dip.z * (1. - dip.z) + * pow2(dip.m2Dip + dip.m2 - dip.m2Rec) + // For gamma -> f fbar also impose maximum mass. + && (hasCharge || dip.m2 < m2MaxGamma) ) { + + // Photon emission: unique flavour choice. + if (hasCharge) { + dip.flavour = 22; + dip.mFlavour = 0.; + + // Photon branching: either lepton or quark flavour choice. + } else { + if (rndmPtr->flat() * chg2Sum < chg2SumL) + dip.flavour = 9 + 2 * min(3, 1 + int(chg2SumL * rndmPtr->flat())); + else { + double rndmQ = 9. * chg2SumQ * rndmPtr->flat(); + if (rndmQ < 1.) dip.flavour = 1; + else if (rndmQ < 5.) dip.flavour = 2; + else if (rndmQ < 6.) dip.flavour = 3; + else if (rndmQ < 10.) dip.flavour = 4; + else dip.flavour = 5; + } + dip.mFlavour = particleDataPtr->m0(dip.flavour); + } + + + // No z weight, except threshold, if to do ME corrections later on. + if (dip.MEtype > 0) { + wt = 1.; + if (dip.flavour < 20 && dip.m2 < THRESHM2 * pow2(dip.mFlavour)) + wt = 0.; + + // z weight for X -> X gamma. + } else if (hasCharge) { + wt = (1. + pow2(dip.z)) / wtPSgam; + + // z weight for gamma -> f fbar. + } else { + double beta = sqrtpos( 1. - 4. * pow2(dip.mFlavour) / dip.m2 ); + wt = beta * ( pow2(dip.z) + pow2(1. - dip.z) ); + } + + // Correct to current value of alpha_EM. + double alphaEMnow = alphaEM.alphaEM(dip.pT2); + wt *= (alphaEMnow / alphaEMmax); + + // Suppression factors for dipole to beam remnant. + if (dip.isrType != 0) { + BeamParticle& beam = (dip.isrType == 1) ? *beamAPtr : *beamBPtr; + int iSys = dip.system; + double xOld = beam[iSys].x(); + double xNew = xOld * (1. + (dip.m2 - dip.m2Rad) / + (dip.m2Dip - dip.m2Rad)); + double xMaxAbs = beam.xMax(iSys); + if (xMaxAbs < 0.) { + infoPtr->errorMsg("Warning in TimeShower::pT2nextQED: " + "xMaxAbs negative"); + return; + } + + // Firstly reduce by PDF ratio. + if (xNew > xMaxAbs) wt = 0.; + else { + int idRec = event[dip.iRecoiler].id(); + double pdfOld = max ( TINYPDF, + beam.xfISR( iSys, idRec, xOld, dip.pT2) ); + double pdfNew = beam.xfISR( iSys, idRec, xNew, dip.pT2); + wt *= min( 1., pdfNew / pdfOld); + } + + // Secondly optionally reduce by 4 pT2_hard / (4 pT2_hard + m2). + if (dampenBeamRecoil) { + double pT24 = 4. * event[dip.iRadiator].pT2(); + wt *= pT24 / (pT24 + dip.m2); + } + } + } + + // Iterate until acceptable pT (or have fallen below pTmin). + } while (wt < rndmPtr->flat()); + +} + +//-------------------------------------------------------------------------- + +// Evolve a Hidden Valley dipole end. + +void TimeShower::pT2nextHV(double pT2begDip, double pT2sel, + TimeDipoleEnd& dip, Event& ) { + + // Lower cut for evolution. Return if no evolution range. + double pT2endDip = max( pT2sel, pT2hvCut ); + if (pT2begDip < pT2endDip) return; + + // C_F * alpha_HV/2 pi. + int colvTypeAbs = abs(dip.colvType); + double colvFac = (colvTypeAbs == 1) ? CFHV : 0.5 * nCHV; + double alphaHV2pi = colvFac * (alphaHVfix / (2. * M_PI)); + + // Determine overestimated z range. Find evolution coefficient. + double zMinAbs = 0.5 - sqrtpos( 0.25 - pT2endDip / dip.m2DipCorr ); + if (zMinAbs < SIMPLIFYROOT) zMinAbs = pT2endDip / dip.m2DipCorr; + double emitCoefTot = alphaHV2pi * 2. * log(1. / zMinAbs - 1.); + + // Variables used inside evolution loop. + dip.pT2 = pT2begDip; + double wt; + + // Begin evolution loop towards smaller pT values. + do { + + // Pick pT2 (in overestimated z range). + dip.pT2 = dip.pT2 * pow(rndmPtr->flat(), 1. / emitCoefTot); + wt = 0.; + + // Abort evolution if below cutoff scale, or below another branching. + if ( dip.pT2 < pT2endDip) { dip.pT2 = 0.; return; } + + // Pick z according to dz/(1-z). + dip.z = 1. - zMinAbs * pow( 1. / zMinAbs - 1., rndmPtr->flat() ); + + // Do not accept branching if outside allowed z range. + double zMin = 0.5 - sqrtpos( 0.25 - dip.pT2 / dip.m2DipCorr ); + if (zMin < SIMPLIFYROOT) zMin = dip.pT2 / dip.m2DipCorr; + dip.m2 = dip.m2Rad + dip.pT2 / (dip.z * (1. - dip.z)); + if (dip.z > zMin && dip.z < 1. - zMin + && dip.m2 * dip.m2Dip < dip.z * (1. - dip.z) + * pow2(dip.m2Dip + dip.m2 - dip.m2Rec) ) { + + // HV gamma or gluon emission: unique flavour choice. + dip.flavour = (nCHV == 1) ? 4900022 : 4900021; + dip.mFlavour = 0.; + + // No z weight, except threshold, if to do ME corrections later on. + if (dip.MEtype > 0) wt = 1.; + + // z weight for X -> X g_HV. + else if (colvTypeAbs == 1) wt = (1. + pow2(dip.z)) / 2.; + else wt = (1. + pow3(dip.z)) / 2.; + } + + // Iterate until acceptable pT (or have fallen below pTmin). + } while (wt < rndmPtr->flat()); + +} + +//-------------------------------------------------------------------------- + +// ME corrections and kinematics that may give failure. +// Notation: radBef, recBef = radiator, recoiler before emission, +// rad, rec, emt = radiator, recoiler, emitted efter emission. +// (rad, emt distinguished by colour flow for g -> q qbar.) + +bool TimeShower::branch( Event& event, bool isInterleaved) { + + // Find initial particles in dipole branching. + int iRadBef = dipSel->iRadiator; + int iRecBef = dipSel->iRecoiler; + Particle& radBef = event[iRadBef]; + Particle& recBef = event[iRecBef]; + + // Default flavours and colour tags for new particles in dipole branching. + int idRad = radBef.id(); + int idEmt = dipSel->flavour; + int colRad = radBef.col(); + int acolRad = radBef.acol(); + int colEmt = 0; + int acolEmt = 0; + iSysSel = dipSel->system; + int iSysSelRec = dipSel->systemRec; + + // Default OK for photon, photon_HV or gluon_HV emission. + if (dipSel->flavour == 22 || dipSel->flavour == 4900021 + || dipSel->flavour == 4900022) { + // New colour tag required for gluon emission. + } else if (dipSel->flavour == 21 && dipSel->colType > 0) { + colEmt = colRad; + colRad = event.nextColTag(); + acolEmt = colRad; + } else if (dipSel->flavour == 21) { + acolEmt = acolRad; + acolRad = event.nextColTag(); + colEmt = acolRad; + // New flavours for g -> q qbar; split colours. + } else if (dipSel->colType > 0) { + idEmt = dipSel->flavour ; + idRad = -idEmt; + colEmt = colRad; + colRad = 0; + } else if (dipSel->colType < 0) { + idEmt = -dipSel->flavour ; + idRad = -idEmt; + acolEmt = acolRad; + acolRad = 0; + // New flavours for gamma -> f fbar, and maybe also colours. + } else if (dipSel->gamType == 1 && rndmPtr->flat() > 0.5) { + idEmt = -dipSel->flavour ; + idRad = -idEmt; + if (idRad < 10) colRad = event.nextColTag(); + acolEmt = colRad; + } else if (dipSel->gamType == 1) { + idEmt = dipSel->flavour ; + idRad = -idEmt; + if (idEmt < 10) colEmt = event.nextColTag(); + acolRad = colEmt; + } + + // Construct kinematics in dipole rest frame: + // begin simple (like g -> g g). + double eRadPlusEmt = 0.5 * (dipSel->m2Dip + dipSel->m2 - dipSel->m2Rec) + / dipSel->mDip; + double e2RadPlusEmt = pow2(eRadPlusEmt); + double pzRadPlusEmt = 0.5 * sqrtpos( pow2(dipSel->m2Dip - dipSel->m2 + - dipSel->m2Rec) - 4. * dipSel->m2 * dipSel->m2Rec ) / dipSel->mDip; + double pT2corr = dipSel->m2 * (e2RadPlusEmt * dipSel->z * (1. - dipSel->z) + - 0.25 * dipSel->m2) / pow2(pzRadPlusEmt); + double pTcorr = sqrtpos( pT2corr ); + double pzRad = (e2RadPlusEmt * dipSel->z - 0.5 * dipSel->m2) + / pzRadPlusEmt; + double pzEmt = (e2RadPlusEmt * (1. - dipSel->z) - 0.5 * dipSel->m2) + / pzRadPlusEmt; + double mRad = dipSel->mRad; + double mEmt = 0.; + + // Kinematics reduction for q -> q g/gamma/g_HV when m_q > 0. + if (abs(dipSel->colType) == 1 || dipSel->chgType != 0 + || abs(dipSel->colvType) == 1) { + pTcorr *= 1. - dipSel->m2Rad / dipSel->m2; + pzRad += pzEmt * dipSel->m2Rad / dipSel->m2; + pzEmt *= 1. - dipSel->m2Rad / dipSel->m2; + // Kinematics reduction for g -> q qbar or gamma -> f fbar when m_f > 0; + } else if (abs(dipSel->flavour) < 20) { + mEmt = dipSel->mFlavour; + mRad = mEmt; + double beta = sqrtpos( 1. - 4. * pow2(mEmt) / dipSel->m2 ); + pTcorr *= beta; + pzRad = 0.5 * ( (1. + beta) * pzRad + (1. - beta) * pzEmt ); + pzEmt = pzRadPlusEmt - pzRad; + } + + // Find rest frame and angles of original dipole. + RotBstMatrix M; + M.fromCMframe(radBef.p(), recBef.p()); + + // Evaluate coefficient of azimuthal asymmetry from gluon polarization. + findAsymPol( event, dipSel); + + // Begin construction of new dipole kinematics: pick azimuthal angle. + Vec4 pRad, pEmt, pRec; + double wtPhi = 1.; + do { + double phi = 2. * M_PI * rndmPtr->flat(); + + // Define kinematics of branching in dipole rest frame. + pRad = Vec4( pTcorr * cos(phi), pTcorr * sin(phi), pzRad, + sqrt( pow2(pTcorr) + pow2(pzRad) + pow2(mRad) ) ); + pEmt = Vec4( -pRad.px(), -pRad.py(), pzEmt, + sqrt( pow2(pTcorr) + pow2(pzEmt) + pow2(mEmt) ) ); + pRec = Vec4( 0., 0., -pzRadPlusEmt, sqrt( pow2(pzRadPlusEmt) + + dipSel->m2Rec ) ); + + // Rotate and boost dipole products to the event frame. + pRad.rotbst(M); + pEmt.rotbst(M); + pRec.rotbst(M); + + // Azimuthal phi weighting: loop to new phi value if required. + if (dipSel->asymPol != 0.) { + Vec4 pRadBef = event[iRadBef].p(); + Vec4 pAunt = event[dipSel->iAunt].p(); + double cosPhi = cosphi( pRad, pAunt, pRadBef ); + wtPhi = ( 1. + dipSel->asymPol * (2. * pow2(cosPhi) - 1.) ) + / ( 1. + abs(dipSel->asymPol) ); + } + } while (wtPhi < rndmPtr->flat()) ; + + // Kinematics when recoiler is initial-state parton. + int isrTypeNow = dipSel->isrType; + if (isrTypeNow != 0) pRec = 2. * recBef.p() - pRec; + + // Define new particles from dipole branching. + double pTsel = sqrt(dipSel->pT2); + Particle rad = Particle(idRad, 51, iRadBef, 0, 0, 0, + colRad, acolRad, pRad, mRad, pTsel); + Particle emt = Particle(idEmt, 51, iRadBef, 0, 0, 0, + colEmt, acolEmt, pEmt, mEmt, pTsel); + + // Recoiler either in final or in initial state + Particle rec = (isrTypeNow == 0) + ? Particle(recBef.id(), 52, iRecBef, iRecBef, 0, 0, + recBef.col(), recBef.acol(), pRec, dipSel->mRec, pTsel) + : Particle(recBef.id(), -53, 0, 0, iRecBef, iRecBef, + recBef.col(), recBef.acol(), pRec, 0., 0.); + + // ME corrections can lead to branching being rejected. + if (dipSel->MEtype > 0) { + Particle& partner = (dipSel->iMEpartner == iRecBef) + ? rec : event[dipSel->iMEpartner]; + if ( findMEcorr( dipSel, rad, partner, emt) < rndmPtr->flat() ) + return false; + } + + // Rescatter: if the recoiling partner is not in the same system + // as the radiator, fix up intermediate systems (can lead + // to emissions being vetoed) + if (allowRescatter && FIXRESCATTER && isInterleaved + && iSysSel != iSysSelRec) { + Vec4 pNew = rad.p() + emt.p(); + if (!rescatterPropagateRecoil(event, pNew)) return false; + } + + // Save properties to be restored in case of user-hook veto of emission. + int eventSizeOld = event.size(); + int iRadStatusV = event[iRadBef].status(); + int iRadDau1V = event[iRadBef].daughter1(); + int iRadDau2V = event[iRadBef].daughter2(); + int iRecStatusV = event[iRecBef].status(); + int iRecMot1V = event[iRecBef].mother1(); + int iRecMot2V = event[iRecBef].mother2(); + int iRecDau1V = event[iRecBef].daughter1(); + int iRecDau2V = event[iRecBef].daughter2(); + int beamOff1 = 1 + beamOffset; + int beamOff2 = 2 + beamOffset; + int ev1Dau1V = event[beamOff1].daughter1(); + int ev2Dau1V = event[beamOff2].daughter1(); + + // Put new particles into the event record. + int iRad = event.append(rad); + int iEmt = event.append(emt); + int iRec = event.append(rec); + + // Mark original dipole partons as branched and set daughters/mothers. + event[iRadBef].statusNeg(); + event[iRadBef].daughters( iRad, iEmt); + if (isrTypeNow == 0) { + event[iRecBef].statusNeg(); + event[iRecBef].daughters( iRec, iRec); + } else { + event[iRecBef].mothers( iRec, iRec); + event[iRec].mothers( iRecMot1V, iRecMot2V); + if (iRecMot1V == beamOff1) event[beamOff1].daughter1( iRec); + if (iRecMot1V == beamOff2) event[beamOff2].daughter1( iRec); + } + + // Allow veto of branching. If so restore event record to before emission. + if ( canVetoEmission + && userHooksPtr->doVetoFSREmission(eventSizeOld, event) ) { + event.popBack( event.size() - eventSizeOld); + event[iRadBef].status( iRadStatusV); + event[iRadBef].daughters( iRadDau1V, iRadDau2V); + if (isrTypeNow == 0) { + event[iRecBef].status( iRecStatusV); + event[iRecBef].daughters( iRecDau1V, iRecDau2V); + } else { + event[iRecBef].mothers( iRecMot1V, iRecMot2V); + if (iRecMot1V == beamOff1) event[beamOff1].daughter1( ev1Dau1V); + if (iRecMot1V == beamOff2) event[beamOff2].daughter1( ev2Dau1V); + } + return false; + } + + // For initial-state recoiler also update beam and sHat info. + if (isrTypeNow != 0) { + BeamParticle& beamRec = (isrTypeNow == 1) ? *beamAPtr : *beamBPtr; + double xOld = beamRec[iSysSelRec].x(); + double xRec = 2. * pRec.e() / (beamAPtr->e() + beamBPtr->e()); + beamRec[iSysSelRec].iPos( iRec); + beamRec[iSysSelRec].x( xRec); + partonSystemsPtr->setSHat( iSysSelRec, + partonSystemsPtr->getSHat(iSysSelRec) * xRec / xOld); + } + + // Photon emission: update to new dipole ends; add new photon "dipole". + if (dipSel->flavour == 22) { + dipSel->iRadiator = iRad; + dipSel->iRecoiler = iRec; + dipSel->pTmax = pTsel; + if (doQEDshowerByGamma) dipEnd.push_back( TimeDipoleEnd(iEmt, iRad, + pTsel, 0, 0, 1, 0, iSysSel, 0)); + + // Gluon emission: update both dipole ends and add two new ones. + } else if (dipSel->flavour == 21) { + dipSel->iRadiator = iRad; + dipSel->iRecoiler = iEmt; + dipSel->systemRec = iSysSel; + dipSel->isrType = 0; + dipSel->pTmax = pTsel; + for (int i = 0; i < int(dipEnd.size()); ++i) { + if (dipEnd[i].iRadiator == iRecBef && dipEnd[i].iRecoiler == iRadBef + && dipEnd[i].colType != 0) { + dipEnd[i].iRadiator = iRec; + dipEnd[i].iRecoiler = iEmt; + // Strive to match colour to anticolour inside closed system. + if (dipEnd[i].colType * dipSel->colType > 0) + dipEnd[i].iRecoiler = iRad; + dipEnd[i].pTmax = pTsel; + } + } + int colType = (dipSel->colType > 0) ? 2 : -2 ; + dipEnd.push_back( TimeDipoleEnd(iEmt, iRec, pTsel, + colType, 0, 0, isrTypeNow, iSysSel, 0)); + dipEnd.back().systemRec = iSysSelRec; + dipEnd.push_back( TimeDipoleEnd(iEmt, iRad, pTsel, + -colType, 0, 0, 0, iSysSel, 0)); + + // Gluon branching to q qbar: update current dipole and other of gluon. + } else if (dipSel->colType != 0) { + for (int i = 0; i < int(dipEnd.size()); ++i) { + // Strive to match colour to anticolour inside closed system. + if ( dipEnd[i].iRecoiler == iRadBef + && dipEnd[i].colType * dipSel->colType < 0 ) + dipEnd[i].iRecoiler = iEmt; + + if (dipEnd[i].iRadiator == iRadBef && abs(dipEnd[i].colType) == 2) { + dipEnd[i].colType /= 2; + + if (dipEnd[i].system != dipEnd[i].systemRec) continue; + + // Note: gluino -> quark + squark gives a deeper radiation dip than + // the more obvious alternative photon decay, so is more realistic. + dipEnd[i].MEtype = 66; + if (&dipEnd[i] == dipSel) dipEnd[i].iMEpartner = iRad; + else dipEnd[i].iMEpartner = iEmt; + } + } + dipSel->iRadiator = iEmt; + dipSel->iRecoiler = iRec; + dipSel->pTmax = pTsel; + + // Gluon branching to q qbar: also add two charge dipole ends. + // Note: gluino -> quark + squark gives a deeper radiation dip than + // the more obvious alternative photon decay, so is more realistic. + if (doQEDshowerByQ) { + int chgType = event[iRad].chargeType(); + dipEnd.push_back( TimeDipoleEnd(iRad, iEmt, pTsel, + 0, chgType, 0, 0, iSysSel, 66, iEmt)); + dipEnd.push_back( TimeDipoleEnd(iEmt, iRad, pTsel, + 0, -chgType, 0, 0, iSysSel, 66, iRad)); + } + + // Photon branching to f fbar: inactivate photon "dipole"; + // optionally add new charge and colour dipole ends. + } else if (dipSel->gamType != 0) { + dipSel->gamType = 0; + int chgType = event[iRad].chargeType(); + int colType = event[iRad].colType(); + // MEtype = 102 for charge in vector decay. + if ( chgType != 0 && ( ( doQEDshowerByQ && colType != 0 ) + || ( doQEDshowerByL && colType == 0 ) ) ) { + dipEnd.push_back( TimeDipoleEnd(iRad, iEmt, pTsel, + 0, chgType, 0, 0, iSysSel, 102, iEmt)); + dipEnd.push_back( TimeDipoleEnd(iEmt, iRad, pTsel, + 0, -chgType, 0, 0, iSysSel, 102, iRad)); + } + // MEtype = 11 for colour in vector decay. + if (colType != 0 && doQCDshower) { + dipEnd.push_back( TimeDipoleEnd(iRad, iEmt, pTsel, + colType, 0, 0, 0, iSysSel, 11, iEmt)); + dipEnd.push_back( TimeDipoleEnd(iEmt, iRad, pTsel, + -colType, 0, 0, 0, iSysSel, 11, iRad)); + } + + // Photon_HV emission: update to new dipole ends. + } else if (dipSel->flavour == 4900022) { + dipSel->iRadiator = iRad; + dipSel->iRecoiler = iRec; + dipSel->pTmax = pTsel; + + // Gluon_HV emission: update to new dipole ends. + } else if (dipSel->flavour == 4900021) { + dipSel->iRadiator = iRad; + dipSel->iRecoiler = iEmt; + dipSel->pTmax = pTsel; + for (int i = 0; i < int(dipEnd.size()); ++i) + if (dipEnd[i].iRadiator == iRecBef && dipEnd[i].iRecoiler == iRadBef + && dipEnd[i].isHiddenValley) { + dipEnd[i].iRadiator = iRec; + dipEnd[i].iRecoiler = iEmt; + dipEnd[i].pTmax = pTsel; + } + int colvType = (dipSel->colvType > 0) ? 2 : -2 ; + dipEnd.push_back( TimeDipoleEnd(iEmt, iRec, pTsel, + 0, 0, 0, isrTypeNow, iSysSel, 0, -1, false, true, colvType) ); + dipEnd.back().systemRec = iSysSelRec; + dipEnd.push_back( TimeDipoleEnd(iEmt, iRad, pTsel, + 0, 0, 0, 0, iSysSel, 0, -1, false, true, -colvType) ); + } + + // Copy or set lifetime for new final state. + if (event[iRad].id() == event[iRadBef].id()) { + event[iRad].tau( event[iRadBef].tau() ); + } else { + event[iRad].tau( event[iRad].tau0() * rndmPtr->exp() ); + event[iEmt].tau( event[iEmt].tau0() * rndmPtr->exp() ); + } + event[iRec].tau( event[iRecBef].tau() ); + + // Now update other dipoles that also involved the radiator or recoiler. + for (int i = 0; i < int(dipEnd.size()); ++i) { + if (dipEnd[i].iRadiator == iRadBef) dipEnd[i].iRadiator = iRad; + if (dipEnd[i].iRadiator == iRecBef) dipEnd[i].iRadiator = iRec; + if (dipEnd[i].iRecoiler == iRadBef) dipEnd[i].iRecoiler = iRad; + if (dipEnd[i].iRecoiler == iRecBef) dipEnd[i].iRecoiler = iRec; + if (dipEnd[i].iMEpartner == iRadBef) dipEnd[i].iMEpartner = iRad; + if (dipEnd[i].iMEpartner == iRecBef) dipEnd[i].iMEpartner = iRec; + } + + // Finally update the list of all partons in all systems. + partonSystemsPtr->replace(iSysSel, iRadBef, iRad); + partonSystemsPtr->addOut(iSysSel, iEmt); + partonSystemsPtr->replace(iSysSelRec, iRecBef, iRec); + + // Done. + return true; + +} + +//-------------------------------------------------------------------------- + +// Rescatter: If a dipole stretches between two different systems, those +// systems will no longer locally conserve momentum. These +// imbalances become problematic when ISR or primordial kT +// is switched on as these steps involve Lorentz boosts. +// +// 'rescatterPropagateRecoil' tries to fix momentum in all +// systems by propogating recoil momentum through all +// intermediate systems. As the momentum transfer is already +// defined, this can lead to internal lines gaining a +// virtuality. + +// Useful definitions for a pair of integers and a vector of pairs +typedef pair < int, int > pairInt; +typedef vector < pairInt > vectorPairInt; + +//-------------------------------------------------------------------------- + +// findParentSystems +// Utility routine to find all parent systems of a given system +// Returns a vector of pairs of integers with: +// a) The system index, including the starting system (negative +// if (b) points to a parent system, positive if (b) points +// to a daughter system +// b) The event record index that is the path out of the system +// (if forwards == false, this is an incoming parton to the +// system, and is +ve if side A or -ve if side B, +// if forwards == true, this is an outgoing parton from the +// system). +// Returns as empty vector on failure +// Note: this assumes single rescattering only and therefore only +// one possible parent system + +inline vectorPairInt findParentSystems(const int sys, + Event& event, PartonSystems* partonSystemsPtr, bool forwards) { + + vectorPairInt parentSystems; + parentSystems.reserve(10); + + int iSysCur = sys; + while (true) { + // Get two incoming partons + int iInA = partonSystemsPtr->getInA(iSysCur); + int iInB = partonSystemsPtr->getInB(iSysCur); + + // Check if either of these links to another system + int iIn = 0; + if (event[iInA].isRescatteredIncoming()) iIn = iInA; + if (event[iInB].isRescatteredIncoming()) iIn = -iInB; + + // Save the current system to the vector + parentSystems.push_back( pairInt(-iSysCur, iIn) ); + if (iIn == 0) break; + + int iInAbs = abs(iIn); + int iMother = event[iInAbs].mother1(); + iSysCur = partonSystemsPtr->getSystemOf(iMother); + if (iSysCur == -1) { + parentSystems.clear(); + break; + } + } // while (true) + + // If forwards is set, change all event record indices to go to daughter + // systems rather than parent systems + if (forwards) { + vectorPairInt::reverse_iterator rit; + for (rit = parentSystems.rbegin(); rit < (parentSystems.rend() - 1); + ++rit) { + pairInt &cur = *rit; + pairInt &next = *(rit + 1); + cur.first = -cur.first; + cur.second = (next.second < 0) ? -event[abs(next.second)].mother1() : + event[abs(next.second)].mother1(); + } + } + + return parentSystems; +} + +//-------------------------------------------------------------------------- + +// rescatterPropagateRecoil +// Fix up momentum in all intermediate systems when radiator and recoiler +// systems are different. The strategy is to look at all parent systems +// from the radiator system and the recoiler system and find where they +// intersect. + +bool TimeShower::rescatterPropagateRecoil( Event& event, Vec4& pNew) { + + // Some useful variables for later + int iRadBef = dipSel->iRadiator; + iSysSel = dipSel->system; + int iSysSelRec = dipSel->systemRec; + Vec4 pImbal = pNew - event[iRadBef].p(); + + // Store changes locally at first in case we veto the branching + // eventMod stores index into the event record and new 4-vector + vector < pair < int, Vec4 > > eventMod; + eventMod.reserve(10); + // systemMod stores system index (iSys) and system-parton index (iMem) + // iMem >= 0 - index into outgoing partons (iOut) + // iMem == -1 - incoming A + // iMem == -2 - incoming B + vectorPairInt systemMod; + systemMod.reserve(10); + + // Find all parent systems from radiating and recoiling systems + vectorPairInt radParent = findParentSystems(iSysSel, event, + partonSystemsPtr, false); + vectorPairInt recParent = findParentSystems(iSysSelRec, event, + partonSystemsPtr, true); + if (radParent.size() == 0 || recParent.size() == 0) { + // This should never happen + infoPtr->errorMsg("Error in TimeShower::rescatterPropagateRecoil: " + "couldn't find parent system; branching vetoed"); + return false; + } + // Find the system that connects radiating and recoiling system + bool foundPath = false; + unsigned int iRadP = 0; + unsigned int iRecP = 0; + for (iRadP = 0; iRadP < radParent.size(); iRadP++) { + for (iRecP = 0; iRecP < recParent.size(); iRecP++) + if (abs(radParent[iRadP].first) == abs(recParent[iRecP].first)) { + foundPath = true; + break; + } + if (foundPath) break; + } + if (!foundPath) { + // Can fail e.g. for QED dipoles where there is no connection + // between radiator and recoiler systems + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "couldn't find recoil path; branching vetoed"); + return false; + } + + // Join together to form complete path from radiating system + // to recoiling system + vectorPairInt path; + if (radParent.size() > 1) + path.assign(radParent.begin(), radParent.begin() + iRadP); + if (recParent.size() > 1) + path.insert(path.end(), recParent.rend() - iRecP - 1, + recParent.rend() - 1); + + // Follow the path fixing up momenta as we go + for (unsigned int i = 0; i < path.size(); i++) { + // Line out of the current system + bool isIncoming = (path[i].first < 0) ? true : false; + int iSysCur = abs(path[i].first); + bool isIncomingA = (path[i].second > 0) ? true : false; + int iLink = abs(path[i].second); + + int iMemCur; + if (isIncoming) iMemCur = (isIncomingA) ? -1 : -2; + else { + iMemCur = -1; + for (int j = 0; j < partonSystemsPtr->sizeOut(iSysCur); j++) + if (partonSystemsPtr->getOut(iSysCur, j) == iLink) { + iMemCur = j; + break; + } + if (iMemCur == -1) { + // This should never happen + infoPtr->errorMsg("Error in TimeShower::rescatterPropagateRecoil: " + "couldn't find parton system; branching vetoed"); + return false; + } + } + + Vec4 pMod = (isIncoming) ? event[iLink].p() + pImbal : + event[iLink].p() - pImbal; + eventMod.push_back(pair (iLink, pMod)); + systemMod.push_back(pairInt(iSysCur, iMemCur)); + + // Calculate sHat of iSysCur + int iInCurA = partonSystemsPtr->getInA(iSysCur); + int iInCurB = partonSystemsPtr->getInB(iSysCur); + Vec4 pTotCur = event[iInCurA].p() + event[iInCurB].p(); + + // If iMemCur is -1 or -2, then we must have changed the sHat of iSysCur + if (iMemCur < 0) pTotCur += (isIncoming) ? pImbal : -pImbal; + double sHatCur = pTotCur.m2Calc(); + + // The fixed-up incoming and outgoing partons should not have + // too large a virtuality in relation to the system mass-square. + if (abs(pMod.m2Calc()) > MAXVIRTUALITYFRACTION * sHatCur) { + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "virtuality much larger than sHat; branching vetoed"); + return false; + } + + // Outgoing ones should also not have too large negative energy + // in the rest frame of the system. + if (!isIncoming && pMod * pTotCur < -MAXNEGENERGYFRACTION * sHatCur) { + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "rest frame energy too negative; branching vetoed"); + return false; + } + + // Veto negative sHat. + if (sHatCur < 0.0) { + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "sHat became negative; branching vetoed"); + return false; + } + + // Line into the new current system + iLink = (isIncoming) ? event[iLink].mother1() : + event[iLink].daughter1(); + iSysCur = partonSystemsPtr->getSystemOf(iLink, true); + + if (!isIncoming) iMemCur = (isIncomingA) ? -1 : -2; + else { + iMemCur = -1; + for (int j = 0; j < partonSystemsPtr->sizeOut(iSysCur); j++) + if (partonSystemsPtr->getOut(iSysCur, j) == iLink) { + iMemCur = j; + break; + } + if (iMemCur == -1) { + // This should never happen + infoPtr->errorMsg("Error in TimeShower::rescatterPropagateRecoil: " + "couldn't find parton system; branching vetoed"); + return false; + } + } + + pMod = (isIncoming) ? event[iLink].p() + pImbal : + event[iLink].p() - pImbal; + eventMod.push_back(pair (iLink, pMod)); + systemMod.push_back(pairInt(iSysCur, iMemCur)); + + // Calculate sHat of iSysCur + iInCurA = partonSystemsPtr->getInA(iSysCur); + iInCurB = partonSystemsPtr->getInB(iSysCur); + pTotCur = event[iInCurA].p() + event[iInCurB].p(); + + // If iMemCur is -1 or -2, then we must have changed the sHat of iSysCur + if (iMemCur < 0) pTotCur += (isIncoming) ? pImbal : -pImbal; + sHatCur = pTotCur.m2Calc(); + + // The fixed-up incoming and outgoing partons should not have + // too large a virtuality in relation to the system mass-square. + if (abs(pMod.m2Calc()) > MAXVIRTUALITYFRACTION * sHatCur) { + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "virtuality much larger than sHat; branching vetoed"); + return false; + } + + // Outgoing ones should also not have too large negative energy + // in the rest frame of the system. + if (!isIncoming && pMod * pTotCur < -MAXNEGENERGYFRACTION * sHatCur) { + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "rest frame energy too negative; branching vetoed"); + return false; + } + + // Veto negative sHat + if (sHatCur < 0.0) { + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "sHat became negative; branching vetoed"); + return false; + } + + // Do negative energy veto + if (VETONEGENERGY && pMod.e() < 0.0) { + infoPtr->errorMsg("Warning in TimeShower::rescatterPropagateRecoil: " + "energy became negative; branching vetoed"); + return false; + } + + } // for (unsigned int i = 0; i < path.size(); i++) + + // If no vetos by this point, apply the changes to the event record + // An incoming particle with changed momentum is given status code -54, + // an outgoing particle with changed momentum is given status code -55 + for (unsigned int i = 0; i < eventMod.size(); i++) { + int idx = eventMod[i].first; + Vec4 &pMod = eventMod[i].second; + int iSys = systemMod[i].first; + int iMem = systemMod[i].second; + + // If incoming to a process then set the copy to be the mother + if (event[idx].isRescatteredIncoming()) { + int mother1 = event[idx].mother1(); + idx = event.copy(idx, -54); + event[mother1].daughters(idx, idx); + + // Update beam information if necessary + double eCM = sqrt(m2( beamAPtr->p(), beamBPtr->p())); + if (iMem == -1) { + partonSystemsPtr->setInA(iSys, idx); + (*beamAPtr)[iSys].x((pMod.e() + pMod.pz()) / eCM); + (*beamAPtr)[iSys].m(pMod.mCalc()); + (*beamAPtr)[iSys].p(pMod); + (*beamAPtr)[iSys].iPos(idx); + } else if (iMem == -2) { + partonSystemsPtr->setInB(iSys, idx); + (*beamBPtr)[iSys].x((pMod.e() - pMod.pz()) / eCM); + (*beamBPtr)[iSys].m(pMod.mCalc()); + (*beamBPtr)[iSys].p(pMod); + (*beamBPtr)[iSys].iPos(idx); + } else { + // This should never happen + infoPtr->errorMsg("Error in TimeShower::rescatterPropagateRecoil: " + "internal bookeeping error"); + } + + // Otherwise set the new event record entry to be the daughter + } else { + int daughter1 = event[idx].daughter1(); + idx = event.copy(idx, 55); + event[idx].statusNeg(); + event[daughter1].mothers(idx, idx); + + partonSystemsPtr->setOut(iSys, iMem, idx); + } + + event[idx].p( eventMod[i].second ); + event[idx].m( event[idx].mCalc() ); + } + + return true; +} + + +//-------------------------------------------------------------------------- + +// Find class of QCD ME correction. +// MEtype classification follow codes in Norrbin article, +// additionally -1 = try to find type, 0 = no ME corrections. +// Warning: not yet tried out to do a correct assignment in +// arbitrary multiparton configurations! ?? + +void TimeShower::findMEtype( Event& event, TimeDipoleEnd& dip) { + + // Initial value. Mark if no ME corrections to be applied. + bool setME = true; + if (!doMEcorrections) setME = false; + + // No ME corrections in 2 -> n processes. + int iMother = event[dip.iRadiator].mother1(); + int iMother2 = event[dip.iRadiator].mother2(); + if (iMother2 != iMother && iMother2 != 0) setME = false; + if (event[dip.iRecoiler].mother1() != iMother) setME = false; + if (event[dip.iRecoiler].mother2() != iMother2) setME = false; + + // No ME corrections for recoiler in initial state. + if (event[dip.iRecoiler].status() < 0) setME = false; + + // No ME corrections for recoiler not in same system + if (dip.system != dip.systemRec) setME = false; + + // Done if no ME to be set. + if (!setME) { + dip.MEtype = 0; + return; + } + + // If no ME partner set, assume it is the recoiler. + if (dip.iMEpartner < 0) dip.iMEpartner = dip.iRecoiler; + + // Now begin processing of colour dipole, including Hidden Valley. + if (dip.colType != 0 || dip.colvType != 0) { + bool isHiddenColour = (dip.colvType != 0); + + // Find daughter types (may or may not be used later on). + int idDau1 = event[dip.iRadiator].id(); + int idDau2 = event[dip.iMEpartner].id(); + int dau1Type = findMEparticle(idDau1, isHiddenColour); + int dau2Type = findMEparticle(idDau2, isHiddenColour); + int minDauType = min(dau1Type, dau2Type); + int maxDauType = max(dau1Type, dau2Type); + + // Reorder dipole ends in kinematics. Split ME expression in two sides. + dip.MEorder = (dau2Type >= dau1Type); + dip.MEsplit = (maxDauType <= 6); + dip.MEgluinoRec = false; + + // If type already set (or set not to have) then done. + if (minDauType == 0 && dip.MEtype < 0) dip.MEtype = 0; + if (dip.MEtype >= 0) return; + dip.MEtype = 0; + + // For H -> gg -> ggg we found that DGLAP kernels do better than eikonal. + if (dau1Type == 4 && dau2Type == 4) return; + + // Find mother type. + int idMother = 0; + if ( event[dip.iRecoiler].mother1() == iMother && iMother >= 0) + idMother = event[iMother].id(); + int motherType = (idMother != 0) + ? findMEparticle(idMother, isHiddenColour) : 0; + + // When a mother if not known then use colour and spin content to guess. + if (motherType == 0) { + int col1 = event[dip.iRadiator].col(); + int acol1 = event[dip.iRadiator].acol(); + int col2 = event[dip.iMEpartner].col(); + int acol2 = event[dip.iMEpartner].acol(); + // spinT = 0/1 = integer or half-integer. + int spinT = ( event[dip.iRadiator].spinType() + + event[dip.iMEpartner].spinType() )%2; + // Colour singlet mother. + if ( col1 == acol2 && acol1 == col2 ) + motherType = (spinT == 0) ? 7 : 9; + // Colour octet mother. + else if ( (col1 == acol2 && acol1 != 0 && col2 != 0) + || (acol1 == col2 && col1 != 0 && acol2 != 0) ) + motherType = (spinT == 0) ? 4 : 5; + // Colour triplet mother. + else if ( (col1 == acol2 && acol1 != col2) + || (acol1 == col2 && col1 != acol2) ) + motherType = (spinT == 0) ? 2 : 1; + // If no colours are matched then cannot have common mother, so done. + else return; + } + + // Now start from default, which is eikonal ME corrections, + // and try to find matching ME cases below. + int MEkind = 0; + int MEcombi = 4; + dip.MEmix = 0.5; + + // Triplet recoiling against gluino needs enhanced radiation + // to match to matrix elements. + dip.MEgluinoRec = (dau1Type >= 1 && dau1Type <= 3 && dau2Type == 5); + + // Vector/axial vector -> q + qbar. + if (minDauType == 1 && maxDauType == 1 && + (motherType == 4 || motherType == 7) ) { + MEkind = 2; + if (idMother == 21 || idMother == 22) MEcombi = 1; + else if (idMother == 23 || idDau1 + idDau2 == 0) { + MEcombi = 3; + dip.MEmix = gammaZmix( event, iMother, dip.iRadiator, dip.iRecoiler ); + } + else if (idMother == 24) MEcombi = 4; + } + // For chi -> chi q qbar, use V/A -> q qbar as first approximation. + else if (minDauType == 1 && maxDauType == 1 && motherType == 9) + MEkind = 2; + + // q -> q + V. + else if (minDauType == 1 && maxDauType == 7 && motherType == 1) + MEkind = 3; + if (idDau1 == 22 || idDau2 == 22) MEcombi = 1; + + // Scalar/pseudoscalar -> q + qbar; q -> q + S. + else if (minDauType == 1 && maxDauType == 1 && motherType == 8) { + MEkind = 4; + if (idMother == 25 || idMother == 35 || idMother == 37) MEcombi = 1; + else if (idMother == 36) MEcombi = 2; + } + else if (minDauType == 1 && maxDauType == 8 && motherType == 1) + MEkind = 5; + + // V -> ~q + ~qbar; ~q -> ~q + V; S -> ~q + ~qbar; ~q -> ~q + S. + else if (minDauType == 2 && maxDauType == 2 && (motherType == 4 + || motherType == 7) ) MEkind = 6; + else if (minDauType == 2 && (maxDauType == 4 || maxDauType == 7) + && motherType == 2) MEkind = 7; + else if (minDauType == 2 && maxDauType == 2 && motherType == 8) + MEkind = 8; + else if (minDauType == 2 && maxDauType == 8 && motherType == 2) + MEkind = 9; + + // chi -> q + ~qbar; ~q -> q + chi; q -> ~q + chi. + else if (minDauType == 1 && maxDauType == 2 && motherType == 9) + MEkind = 10; + else if (minDauType == 1 && maxDauType == 9 && motherType == 2) + MEkind = 11; + else if (minDauType == 2 && maxDauType == 9 && motherType == 1) + MEkind = 12; + + // ~g -> q + ~qbar; ~q -> q + ~g; q -> ~q + ~g. + else if (minDauType == 1 && maxDauType == 2 && motherType == 5) + MEkind = 13; + else if (minDauType == 1 && maxDauType == 5 && motherType == 2) + MEkind = 14; + else if (minDauType == 2 && maxDauType == 5 && motherType == 1) + MEkind = 15; + + // In cases where coloured spin 1 particle involved use spin 0. + // V_coloured -> q + l. + else if (minDauType == 1 && maxDauType == 9 && motherType == 3) + MEkind = 11; + // q -> V_coloured + l; + else if (minDauType == 3 && maxDauType == 9 && motherType == 1) + MEkind = 12; + + // g (+V, S) -> ~g + ~g (eikonal approximation). + else if (minDauType == 5 && maxDauType == 5) MEkind = 16; + + // Save ME type and gamma_5 admixture. + dip.MEtype = 5 * MEkind + MEcombi; + + // Now begin processing of charge dipole - still primitive. + } else if (dip.chgType != 0) { + + // Set defaults for QED case; then possibly done. + dip.MEorder = true; + dip.MEsplit = true; + if (dip.MEtype >= 0) return; + + // So far only ME corrections for q qbar or l lbar. + int idDau1 = event[dip.iRadiator].id(); + int idDau2 = event[dip.iMEpartner].id(); + if (abs(idDau1) < 9 && abs(idDau2) < 9 && idDau1 * idDau2 < 0) ; + else if (abs(idDau1) > 10 && abs(idDau1) < 19 && abs(idDau2) > 10 + && abs(idDau2) < 19 && idDau1 * idDau2 < 0) ; + else { dip.MEtype = 0; return; } + + // Distinguish charge sum != 0 or = 0; in latter assume vector source. + dip.MEtype = 101; + if (idDau1 + idDau2 == 0) dip.MEtype = 102; + dip.MEmix = 1.; + } + +} + +//-------------------------------------------------------------------------- + +// Find type of particle for ME type: 0 = unknown, 1 = quark, 2 = squark, +// 3 = spare triplet, 4 = gluon, 5 = gluino, 6 = spare octet, +// 7 = vector boson, 8 = colourless scalar, 9 = colourless spin 1/2. + +int TimeShower::findMEparticle( int id, bool isHiddenColour) { + + // find colour and spin of particle. + int type = 0; + int colType = abs(particleDataPtr->colType(id)); + int spinType = particleDataPtr->spinType(id); + + // For hidden valley particle treat HV colour as normal one. + // Note: no need to assign gv/gammav since not in ME. + if (isHiddenColour) { + colType = 0; + int idAbs = abs(id); + if ( (idAbs > 4900000 && idAbs < 4900007) + || (idAbs > 4900010 && idAbs < 4900017) + || idAbs == 4900101) colType = 1; + } + + // Find particle type from colour and spin. + if (colType == 1 && spinType == 2) type = 1; + else if (colType == 1 && spinType == 1) type = 2; + else if (colType == 1) type = 3; + else if (colType == 2 && spinType == 3) type = 4; + else if (colType == 2 && spinType == 2) type = 5; + else if (colType == 2) type = 6; + else if (colType == 0 && spinType == 3) type = 7; + else if (colType == 0 && spinType == 1) type = 8; + else if (colType == 0 && spinType == 2) type = 9; + + // Done. + return type; + +} + +//-------------------------------------------------------------------------- + +// Find mixture of V and A in gamma/Z: energy- and flavour-dependent. + +double TimeShower::gammaZmix( Event& event, int iRes, int iDau1, int iDau2) { + + // Try to identify initial flavours; use e+e- as default. + int idIn1 = -11; + int idIn2 = 11; + int iIn1 = (iRes >= 0) ? event[iRes].mother1() : -1; + int iIn2 = (iRes >= 0) ? event[iRes].mother2() : -1; + if (iIn1 >=0) idIn1 = event[iIn1].id(); + if (iIn2 >=0) idIn2 = event[iIn1].id(); + + // In processes f + g/gamma -> f + Z only need find one fermion. + if (idIn1 == 21 || idIn1 == 22) idIn1 = -idIn2; + if (idIn2 == 21 || idIn2 == 22) idIn2 = -idIn1; + + // Initial flavours and couplings; return if don't make sense. + if (idIn1 + idIn2 != 0 ) return 0.5; + int idInAbs = abs(idIn1); + if (idInAbs == 0 || idInAbs > 18 ) return 0.5; + double ei = coupSMPtr->ef(idInAbs); + double vi = coupSMPtr->vf(idInAbs); + double ai = coupSMPtr->af(idInAbs); + + // Final flavours and couplings; return if don't make sense. + if (event[iDau1].id() + event[iDau2].id() != 0) return 0.5; + int idOutAbs = abs(event[iDau1].id()); + if (idOutAbs == 0 || idOutAbs >18 ) return 0.5; + double ef = coupSMPtr->ef(idOutAbs); + double vf = coupSMPtr->vf(idOutAbs); + double af = coupSMPtr->af(idOutAbs); + + // Calculate prefactors for interference and resonance part. + Vec4 psum = event[iDau1].p() + event[iDau2].p(); + double sH = psum.m2Calc(); + double intNorm = 2. * thetaWRat * sH * (sH - mZ*mZ) + / ( pow2(sH - mZ*mZ) + pow2(sH * gammaZ / mZ) ); + double resNorm = pow2(thetaWRat * sH) + / ( pow2(sH - mZ*mZ) + pow2(sH * gammaZ / mZ) ); + + // Calculate vector and axial expressions and find mix. + double vect = ei*ei * ef*ef + ei*vi * intNorm * ef*vf + + (vi*vi + ai*ai) * resNorm * vf*vf; + double axiv = (vi*vi + ai*ai) * resNorm * af*af; + return vect / (vect + axiv); +} + +//-------------------------------------------------------------------------- + +// Set up to calculate QCD ME correction with calcMEcorr. +// Normally for primary particles, but also from g/gamma -> f fbar. + +double TimeShower::findMEcorr(TimeDipoleEnd* dip, Particle& rad, + Particle& partner, Particle& emt) { + + // Initial values and matrix element kind. + double wtME = 1.; + double wtPS = 1.; + int MEkind = dip->MEtype / 5; + int MEcombi = dip->MEtype % 5; + + // Construct ME variables. + Vec4 sum = rad.p() + partner.p() + emt.p(); + double eCMME = sum.mCalc(); + double x1 = 2. * (sum * rad.p()) / pow2(eCMME); + double x2 = 2. * (sum * partner.p()) / pow2(eCMME); + double r1 = rad.m() / eCMME; + double r2 = partner.m() / eCMME; + + // Derived ME variables, suitably protected. + double x1minus = max(XMARGIN, 1. + r1*r1 - r2*r2 - x1); + double x2minus = max(XMARGIN, 1. + r2*r2 - r1*r1 - x2) ; + double x3 = max(XMARGIN, 2. - x1 - x2); + + // Begin processing of QCD dipoles. + if (dip->colType !=0 || dip->colvType != 0) { + + // Evaluate normal ME, for proper order of particles. + if (dip->MEorder) + wtME = calcMEcorr(MEkind, MEcombi, dip->MEmix, x1, x2, r1, r2); + else wtME = calcMEcorr(MEkind, MEcombi, dip->MEmix, x2, x1, r2, r1); + + // Split up total ME when two radiating particles. + if (dip->MEsplit) wtME = wtME * x1minus / x3; + + // Evaluate shower rate to be compared with. + wtPS = 2. / ( x3 * x2minus ); + if (dip->MEgluinoRec) wtPS *= 9./4.; + + // For generic charge combination currently only massless expression. + // (Masses included only to respect phase space boundaries.) + } else if (dip->chgType !=0 && dip->MEtype == 101) { + double chg1 = particleDataPtr->charge(rad.id()); + double chg2 = particleDataPtr->charge(partner.id()); + wtME = (x1*x1 + x2*x2) * pow2( chg1 * x1minus / x3 + - chg2 * x2minus / x3 ); + wtPS = 2. * ( chg1*chg1 * x1minus / x3 + chg2*chg2 * x2minus / x3 ); + + // For flavour neutral system assume vector source and include masses. + } else if (dip->chgType !=0 && dip->MEtype == 102) { + wtME = calcMEcorr(2, 1, dip->MEmix, x1, x2, r1, r2) * x1minus / x3; + wtPS = 2. / ( x3 * x2minus ); + } + if (wtME > wtPS) infoPtr->errorMsg("Warning in TimeShower::findMEcorr: " + "ME weight above PS one"); + + // Return ratio of actual ME to assumed PS rate of emission. + return wtME / wtPS; +} + +//-------------------------------------------------------------------------- + +// Matrix elements for gluon (or photon) emission from +// a two-body state; to be used by the parton shower routine. +// Here x_i = 2 E_i/E_cm, r_i = m_i/E_cm and +// 1/sigma_0 d(sigma)/d(x_1)d(x_2) = (alpha-strong/2 pi) * C_F * (this), +// i.e. normalization is such that one recovers the familiar +// (x_1^2 + x_2^2)/((1-x_1)*(1-x_2)) for the massless case. +// Coupling structure: +// kind = 1 : eikonal soft-gluon expression (spin-independent) +// = 2 : V -> q qbar (V = vector/axial vector colour singlet) +// = 3 : q -> q V +// = 4 : S -> q qbar (S = scalar/pseudoscalar colour singlet) +// = 5 : q -> q S +// = 6 : V -> ~q ~qbar (~q = squark) +// = 7 : ~q -> ~q V +// = 8 : S -> ~q ~qbar +// = 9 : ~q -> ~q S +// = 10 : chi -> q ~qbar (chi = neutralino/chargino) +// = 11 : ~q -> q chi +// = 12 : q -> ~q chi +// = 13 : ~g -> q ~qbar +// = 14 : ~q -> q ~g +// = 15 : q -> ~q ~g +// = 16 : (9/4)*(eikonal) for gg -> ~g ~g +// Note that the order of the decay products is important. +// combi = 1 : pure non-gamma5, i.e. vector/scalar/... +// = 2 : pure gamma5, i.e. axial vector/pseudoscalar/.... +// = 3 : mixture mix*(combi=1) + (1-mix)*(combi=2) +// = 4 : mixture (combi=1) +- (combi=2) + +double TimeShower::calcMEcorr( int kind, int combiIn, double mixIn, + double x1, double x2, double r1, double r2) { + + // Frequent variable combinations. + double x3 = 2. - x1 - x2; + double x1s = x1 * x1; + double x2s = x2 * x2; + double x3s = x3 * x3; + double x1c = x1 * x1s; + double x2c = x2 * x2s; + double x3c = x3 * x3s; + double r1s = r1 * r1; + double r2s = r2 * r2; + double r1c = r1 * r1s; + double r2c = r2 * r2s; + double r1q = r1s * r1s; + double r2q = r2s * r2s; + double prop1 = 1. + r1s - r2s - x1; + double prop2 = 1. + r2s - r1s - x2; + double prop1s = prop1 * prop1; + double prop2s = prop2 * prop2; + double prop12 = prop1 * prop2; + double prop13 = prop1 * x3; + double prop23 = prop2 * x3; + + // Check input values. Return zero outside allowed phase space. + if (x1 - 2.*r1 < XMARGIN || prop1 < XMARGIN) return 0.; + if (x2 - 2.*r2 < XMARGIN || prop2 < XMARGIN) return 0.; + if (x1 + x2 - 1. - pow2(r1+r2) < XMARGIN) return 0.; + // Note: equivalent rewritten form 4. * ( (1. - x1) * (1. - x2) + // * (1. - r1s - r2s - x3) + r1s * (1. - x2s - x3) + r2s + // * (1. - x1s - x3) - pow2(r1s - r2s) ) gives abot same result. + if ( (x1s - 4.*r1s) * (x2s - 4.*r2s) + - pow2( 2. * (1. - x1 - x2 + r1s + r2s) + x1*x2 ) + < XMARGIN * (XMARGINCOMB + r1 + r2) ) return 0.; + + // Initial values; phase space. + int combi = max(1, min(4, combiIn) ); + double mix = max(0., min(1., mixIn) ); + bool isSet1 = false; + bool isSet2 = false; + bool isSet4 = false; + double ps = sqrtpos( pow2(1. - r1*r1 - r2*r2) - pow2(2. * r1 * r2) ); + double rLO = 0., rFO = 0., rLO1 = 0., rFO1 = 0., rLO2 = 0., + rFO2 = 0., rLO4 = 0., rFO4 = 0.; + double offset = 0; + + // Select which kind of ME to use. + switch (kind) { + + // case 1 is equal to default, i.e. eikonal expression. + + // V -> q qbar (V = gamma*/Z0/W+-/...). + case 2: + if (combi == 1 || combi == 3) { + rLO1 = ps*(2.-r1s-r1q+6.*r1*r2-r2s+2.*r1s*r2s-r2q)/2.; + rFO1 = -(3.+6.*r1s+r1q-6.*r1*r2+6.*r1c*r2-2.*r2s-6.*r1s*r2s + +6.*r1*r2c+r2q-3.*x1+6.*r1*r2*x1+2.*r2s*x1+x1s-2.*r1s*x1s + +3.*r1s*x3+6.*r1*r2*x3-r2s*x3-2.*x1*x3-5.*r1s*x1*x3 + +r2s*x1*x3+x1s*x3-3.*x3s-3.*r1s*x3s+r2s*x3s + +2.*x1*x3s+x3c-x2) + /prop2s + -2.*(-3.+r1s-6.*r1*r2+6.*r1c*r2+3.*r2s-4.*r1s*r2s + +6.*r1*r2c+2.*x1+3.*r1s*x1+r2s*x1-x1s-r1s*x1s + -r2s*x1s+4.*x3+2.*r1s*x3+3.*r1*r2*x3-r2s*x3-3.*x1*x3 + -2.*r1s*x1*x3+x1s*x3-x3s-r1s*x3s+r1*r2*x3s+x1*x3s) + /prop12 + -(-1.+2.*r1s+r1q+6.*r1*r2+6.*r1c*r2-2.*r2s-6.*r1s*r2s + +6.*r1*r2c+r2q-x1-2.*r1s*x1-6.*r1*r2*x1+8.*r2s*x1+x1s + -2.*r2s*x1s-r1s*x3+r2s*x3-r1s*x1*x3+r2s*x1*x3+x1s*x3+x2) + /prop1s; + rFO1 = rFO1/2.; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(2.-r1s-r1q-6.*r1*r2-r2s+2.*r1s*r2s-r2q)/2.; + rFO2 = -(3.+6.*r1s+r1q+6.*r1*r2-6.*r1c*r2-2.*r2s-6.*r1s*r2s + -6.*r1*r2c+r2q-3.*x1-6.*r1*r2*x1+2.*r2s*x1+x1s-2.*r1s*x1s + +3.*r1s*x3-6.*r1*r2*x3-r2s*x3-2.*x1*x3-5.*r1s*x1*x3 + +r2s*x1*x3+x1s*x3-3.*x3s-3.*r1s*x3s+r2s*x3s+2.*x1*x3s+x3c-x2) + /prop2s + -2.*(-3+r1s+6.*r1*r2-6.*r1c*r2+3.*r2s-4.*r1s*r2s-6.*r1*r2c + +2.*x1+3.*r1s*x1+r2s*x1-x1s-r1s*x1s-r2s*x1s+4.*x3+2.*r1s*x3 + -3.*r1*r2*x3-r2s*x3-3.*x1*x3-2.*r1s*x1*x3+x1s*x3-x3s-r1s*x3s + -r1*r2*x3s+x1*x3s) + /prop12 + -(-1.+2.*r1s+r1q-6.*r1*r2-6.*r1c*r2-2.*r2s-6.*r1s*r2s + -6.*r1*r2c+r2q-x1-2.*r1s*x1+6.*r1*r2*x1+8.*r2s*x1+x1s + -2.*r2s*x1s-r1s*x3+r2s*x3-r1s*x1*x3+r2s*x1*x3+x1s*x3+x2) + /prop1s; + rFO2 = rFO2/2.; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(2.-r1s-r1q-r2s+2.*r1s*r2s-r2q)/2.; + rFO4 = (1.-r1q+6.*r1s*r2s-r2q+x1+3.*r1s*x1-9.*r2s*x1-3.*x1s + -r1s*x1s+3.*r2s*x1s+x1c-x2-r1s*x2+r2s*x2-r1s*x1*x2+r2s*x1*x2 + +x1s*x2) + /prop1s + -2.*(1.+r1s+r2s-4.*r1s*r2s+r1s*x1+2.*r2s*x1-x1s-r2s*x1s + +2.*r1s*x2+r2s*x2-3.*x1*x2+x1s*x2-x2s-r1s*x2s+x1*x2s) + /prop12 + +(1.-r1q+6.*r1s*r2s-r2q-x1+r1s*x1-r2s*x1+x2-9.*r1s*x2 + +3.*r2s*x2+r1s*x1*x2-r2s*x1*x2-3.*x2s+3.*r1s*x2s-r2s*x2s + +x1*x2s+x2c) + /prop2s; + rFO4 = rFO4/2.; + isSet4 = true; + } + break; + + // q -> q V. + case 3: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.-2.*r1s+r1q+r2s-6.*r1*r2s+r1s*r2s-2.*r2q); + rFO1 = -2.*(-1.+r1-2.*r1s+2.*r1c-r1q+pow5(r1)-r2s+r1*r2s + -5.*r1s*r2s+r1c*r2s-2.*r1*r2q+2.*x1-2.*r1*x1+2.*r1s*x1 + -2.*r1c*x1+2.*r2s*x1+5.*r1*r2s*x1+r1s*r2s*x1+2.*r2q*x1 + -x1s+r1*x1s-r2s*x1s+3.*x2+4.*r1s*x2+r1q*x2+2.*r2s*x2 + +2.*r1s*r2s*x2-4.*x1*x2-2.*r1s*x1*x2-r2s*x1*x2+x1s*x2 + -2.*x2s-2.*r1s*x2s+x1*x2s) + /prop23 + +(2.*r2s+6.*r1*r2s-6.*r1s*r2s+6.*r1c*r2s+2.*r2q+6.*r1*r2q + -r2s*x1+r1s*r2s*x1-r2q*x1+x2-r1q*x2-3.*r2s*x2-6.*r1*r2s*x2 + +9.*r1s*r2s*x2-2.*r2q*x2-x1*x2+r1s*x1*x2-x2s-3.*r1s*x2s + +2.*r2s*x2s+x1*x2s) + /prop2s + +(-4.-8.*r1s-4.*r1q+4.*r2s-4.*r1s*r2s+8.*r2q+9.*x1+10.*r1s*x1 + +r1q*x1-3.*r2s*x1+6.*r1*r2s*x1+r1s*r2s*x1-2.*r2q*x1-6.*x1s- + 2.*r1s*x1s+x1c+7.*x2+8.*r1s*x2+r1q*x2-7.*r2s*x2+6.*r1*r2s*x2 + +r1s*r2s*x2-2.*r2q*x2-9.*x1*x2-3.*r1s*x1*x2+2.*r2s*x1*x2 + +2.*x1s*x2-3.*x2s-r1s*x2s+2.*r2s*x2s+x1*x2s) + /x3s; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.-2.*r1s+r1q+r2s+6.*r1*r2s+r1s*r2s-2.*r2q); + rFO2 = 2*(1.+r1+2.*r1s+2.*r1c+r1q+pow5(r1)+r2s+r1*r2s + +5.*r1s*r2s+r1c*r2s-2.*r1*r2q-2.*x1-2.*r1*x1-2.*r1s*x1 + -2.*r1c*x1-2.*r2s*x1+5.*r1*r2s*x1-r1s*r2s*x1-2.*r2q*x1+x1s + +r1*x1s+r2s*x1s-3.*x2-4.*r1s*x2-r1q*x2-2.*r2s*x2 + -2.*r1s*r2s*x2+4.*x1*x2+2.*r1s*x1*x2+r2s*x1*x2-x1s*x2 + +2.*x2s+2.*r1s*x2s-x1*x2s) + /prop23 + +(2.*r2s-6.*r1*r2s-6.*r1s*r2s-6.*r1c*r2s+2.*r2q-6.*r1*r2q + -r2s*x1+r1s*r2s*x1-r2q*x1+x2-r1q*x2-3.*r2s*x2+6.*r1*r2s*x2 + +9.*r1s*r2s*x2-2.*r2q*x2-x1*x2+r1s*x1*x2-x2s-3.*r1s*x2s + +2.*r2s*x2s+x1*x2s) + /prop2s + +(-4.-8.*r1s-4.*r1q+4.*r2s-4.*r1s*r2s+8.*r2q+9.*x1+10.*r1s*x1 + +r1q*x1-3.*r2s*x1-6.*r1*r2s*x1+r1s*r2s*x1-2.*r2q*x1-6.*x1s + -2.*r1s*x1s+x1c+7.*x2+8.*r1s*x2+r1q*x2-7.*r2s*x2-6.*r1*r2s*x2 + +r1s*r2s*x2-2.*r2q*x2-9.*x1*x2-3.*r1s*x1*x2+2.*r2s*x1*x2 + +2.*x1s*x2-3.*x2s-r1s*x2s+2.*r2s*x2s+x1*x2s) + /x3s; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.-2.*r1s+r1q+r2s+r1s*r2s-2.*r2q); + rFO4 = 2*(1.+2.*r1s+r1q+r2s+5.*r1s*r2s-2.*x1-2.*r1s*x1 + -2.*r2s*x1-r1s*r2s*x1-2.*r2q*x1+x1s+r2s*x1s-3.*x2-4.*r1s*x2 + -r1q*x2-2.*r2s*x2-2.*r1s*r2s*x2+4.*x1*x2+2.*r1s*x1*x2+r2s*x1*x2 + -x1s*x2+2.*x2s+2.*r1s*x2s-x1*x2s) + /prop23 + +(2.*r2s-6.*r1s*r2s+2.*r2q-r2s*x1+r1s*r2s*x1-r2q*x1+x2-r1q*x2 + -3.*r2s*x2+9.*r1s*r2s*x2-2.*r2q*x2-x1*x2+r1s*x1*x2-x2s-3.*r1s*x2s + +2.*r2s*x2s+x1*x2s) + /prop2s + +(-4.-8.*r1s-4.*r1q+4.*r2s-4.*r1s*r2s+8.*r2q+9.*x1+10.*r1s*x1 + +r1q*x1-3.*r2s*x1+r1s*r2s*x1-2.*r2q*x1-6.*x1s-2.*r1s*x1s+x1c + +7.*x2+8.*r1s*x2+r1q*x2-7.*r2s*x2+r1s*r2s*x2-2.*r2q*x2-9.*x1*x2 + -3.*r1s*x1*x2+2.*r2s*x1*x2+2.*x1s*x2-3.*x2s-r1s*x2s+2.*r2s*x2s + +x1*x2s) + /x3s; + isSet4 = true; + } + break; + + // S -> q qbar (S = h0/H0/A0/H+-/...). + case 4: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.-r1s-r2s-2.*r1*r2); + rFO1 = -(-1.+r1q-2.*r1*r2-2.*r1c*r2-6.*r1s*r2s-2.*r1*r2c+r2q+x1 + -r1s*x1+2.*r1*r2*x1+3.*r2s*x1+x2+r1s*x2-r2s*x2-x1*x2) + /prop1s + -2.*(r1s+r1q-2.*r1c*r2+r2s-6.*r1s*r2s-2.*r1*r2c+r2q-r1s*x1 + +r1*r2*x1+2.*r2s*x1+2.*r1s*x2+r1*r2*x2-r2s*x2-x1*x2) + /prop12 + -(-1.+r1q-2.*r1*r2-2.*r1c*r2-6.*r1s*r2s-2.*r1*r2c+r2q+x1-r1s*x1 + +r2s*x1+x2+3.*r1s*x2+2.*r1*r2*x2-r2s*x2-x1*x2) + /prop2s; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.-r1s-r2s+2.*r1*r2); + rFO2 = -(-1.+r1q+2.*r1*r2+2.*r1c*r2-6.*r1s*r2s+2.*r1*r2c+r2q+x1 + -r1s*x1-2.*r1*r2*x1+3.*r2s*x1+x2+r1s*x2-r2s*x2-x1*x2) + /prop1s + -(-1.+r1q+2.*r1*r2+2.*r1c*r2-6.*r1s*r2s+2.*r1*r2c+r2q+x1 + -r1s*x1+r2s*x1+x2+3.*r1s*x2-2.*r1*r2*x2-r2s*x2-x1*x2) + /prop2s + +2.*(-r1s-r1q-2.*r1c*r2-r2s+6.*r1s*r2s-2.*r1*r2c-r2q+r1s*x1 + +r1*r2*x1-2.*r2s*x1-2.*r1s*x2+r1*r2*x2+r2s*x2+x1*x2) + /prop12; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.-r1s-r2s); + rFO4 = -(-1.+r1q-6.*r1s*r2s+r2q+x1-r1s*x1+3.*r2s*x1+x2 + +r1s*x2-r2s*x2-x1*x2) + /prop1s + -2.*(r1s+r1q+r2s-6.*r1s*r2s+r2q-r1s*x1 + +2.*r2s*x1+2.*r1s*x2-r2s*x2-x1*x2) + /prop12 + -(-1.+r1q-6.*r1s*r2s+r2q+x1-r1s*x1+r2s*x1 + +x2+3.*r1s*x2-r2s*x2-x1*x2) + /prop2s; + isSet4 = true; + } + break; + + // q -> q S. + case 5: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.+r1s-r2s+2.*r1); + rFO1 = (4.-4.*r1s+4.*r2s-3.*x1-2.*r1*x1+r1s*x1-r2s*x1-5.*x2 + -2.*r1*x2+r1s*x2-r2s*x2+x1*x2+x2s) + /x3s + -2.*(3.-r1-5.*r1s-r1c+3.*r2s+r1*r2s-2.*x1-r1*x1 + +r1s*x1-4.*x2+2.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop23 + +(2.-2.*r1-6.*r1s-2.*r1c+2.*r2s-2.*r1*r2s-x1+r1s*x1 + -r2s*x1-3.*x2+2.*r1*x2+3.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop2s; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.+r1s-r2s-2.*r1); + rFO2 = (4.-4.*r1s+4.*r2s-3.*x1+2.*r1*x1+r1s*x1-r2s*x1-5.*x2 + +2.*r1*x2+r1s*x2-r2s*x2+x1*x2+x2s) + /x3s + -2.*(3.+r1-5.*r1s+r1c+3.*r2s-r1*r2s-2.*x1+r1*x1 + +r1s*x1-4.*x2+2.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop23 + +(2.+2.*r1-6.*r1s+2.*r1c+2.*r2s+2.*r1*r2s-x1+r1s*x1 + -r2s*x1-3.*x2-2.*r1*x2+3.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop2s; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.+r1s-r2s); + rFO4 = (4.-4.*r1s+4.*r2s-3.*x1+r1s*x1-r2s*x1-5.*x2+r1s*x2 + -r2s*x2+x1*x2+x2s) + /x3s + -2.*(3.-5.*r1s+3.*r2s-2.*x1+r1s*x1-4.*x2+2.*r1s*x2 + -r2s*x2+x1*x2+x2s) + /prop23 + +(2.-6.*r1s+2.*r2s-x1+r1s*x1-r2s*x1-3.*x2+3.*r1s*x2 + -r2s*x2+x1*x2+x2s) + /prop2s; + isSet4 = true; + } + break; + + // V -> ~q ~qbar (~q = squark). + case 6: + rLO1 = ps*(1.-2.*r1s+r1q-2.*r2s-2.*r1s*r2s+r2q); + rFO1 = 2.*3.+(1.+r1s+r2s-x1)*(4.*r1s-x1s) + /prop1s + +2.*(-1.-3.*r1s-r2s+x1+x1s*0.5+x2-x1*x2*0.5) + /prop1 + +(1.+r1s+r2s-x2)*(4.*r2s-x2s) + /prop2s + +2.*(-1.-r1s-3.*r2s+x1+x2-x1*x2*0.5+x2s*0.5) + /prop2 + -(-4.*r1s-4.*r1q-4.*r2s-8.*r1s*r2s-4.*r2q+2.*x1+6.*r1s*x1 + +6.*r2s*x1-2.*x1s+2.*x2+6.*r1s*x2+6.*r2s*x2-4.*x1*x2 + -2.*r1s*x1*x2-2.*r2s*x1*x2+x1s*x2-2.*x2s+x1*x2s) + /prop12; + isSet1 = true; + break; + + // ~q -> ~q V. + case 7: + rLO1 = ps*(1.-2.*r1s+r1q-2.*r2s-2.*r1s*r2s+r2q); + rFO1 = 16.*r2s-8.*(4.*r2s+2.*r2s*x1+x2+r1s*x2+r2s*x2-x1*x2 + -2.*x2s) + /(3.*prop2) + +8.*(1.+r1s+r2s-x2)*(4.*r2s-x2s) + /(3.*prop2s) + +8.*(x1+x2)*(-1.-2.*r1s-r1q-2.*r2s+2.*r1s*r2s-r2q+2.*x1 + +2.*r1s*x1+2.*r2s*x1-x1s+2.*x2+2.*r1s*x2+2.*r2s*x2-2.*x1*x2-x2s) + /(3.*x3s) + +8.*(-1.-r1s+r2s-x1)*(2.*r2s*x1+x2+r1s*x2+r2s*x2-x1*x2-x2s) + /(3.*prop2*x3) + -8.*(1.+2.*r1s+r1q+2.*r2s-2.*r1s*r2s+r2q-2.*x1-2.*r1s*x1 + -4.*r2s*x1+x1s-3.*x2-3.*r1s*x2-3.*r2s*x2+3.*x1*x2+2.*x2s) + /(3.*x3); + rFO1 = 3.*rFO1/8.; + isSet1 = true; + break; + + // S -> ~q ~qbar. + case 8: + rLO1 = ps; + rFO1 = (-1.-2.*r1s-r1q-2.*r2s+2.*r1s*r2s-r2q+2.*x1+2.*r1s*x1 + +2.*r2s*x1-x1s-r2s*x1s+2.*x2+2.*r1s*x2+2.*r2s*x2-3.*x1*x2 + -r1s*x1*x2-r2s*x1*x2+x1s*x2-x2s-r1s*x2s+x1*x2s) + /(prop1s*prop2s); + rFO1 = 2.*rFO1; + isSet1 = true; + break; + + // ~q -> ~q S. + case 9: + rLO1 = ps; + rFO1 = (-1.-r1s-r2s+x2) + /prop2s + +(1.+r1s-r2s+x1) + /prop23 + -(x1+x2) + /x3s; + isSet1 = true; + break; + + // chi -> q ~qbar (chi = neutralino/chargino). + case 10: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.+r1s-r2s+2.*r1); + rFO1 = (2.*r1+x1)*(-1.-r1s-r2s+x1) + /prop1s + +2.*(-1.-r1s-2.*r1c-r2s-2.*r1*r2s+3.*x1*0.5+r1*x1 + -r1s*x1*0.5-r2s*x1*0.5+x2+r1*x2+r1s*x2-x1*x2*0.5) + /prop12 + +(2.-2.*r1-6.*r1s-2.*r1c+2.*r2s-2.*r1*r2s-x1+r1s*x1 + -r2s*x1-3.*x2+2.*r1*x2+3.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop2s; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.-2.*r1+r1s-r2s); + rFO2 = (2.*r1-x1)*(1.+r1s+r2s-x1) + /prop1s + +2.*(-1.-r1s+2.*r1c-r2s+2.*r1*r2s+3.*x1*0.5-r1*x1 + -r1s*x1*0.5-r2s*x1*0.5+x2-r1*x2+r1s*x2-x1*x2*0.5) + /prop12 + +(2.+2.*r1-6.*r1s+2.*r1c+2.*r2s+2.*r1*r2s-x1+r1s*x1 + -r2s*x1-3.*x2-2.*r1*x2+3.*r1s*x2-r2s*x2+x1*x2+x2s)/ + prop2s; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.+r1s-r2s); + rFO4 = x1*(-1.-r1s-r2s+x1) + /prop1s + +2.*(-1.-r1s-r2s+3.*x1*0.5-r1s*x1*0.5-r2s*x1*0.5 + +x2+r1s*x2-x1*x2*0.5) + /prop12 + +(2.-6.*r1s+2.*r2s-x1+r1s*x1-r2s*x1-3.*x2+3.*r1s*x2 + -r2s*x2+x1*x2+x2s) + /prop2s; + isSet4 = true; + } + break; + + // ~q -> q chi. + case 11: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.-pow2(r1+r2)); + rFO1 = (1.+r1s+2.*r1*r2+r2s-x1-x2)*(x1+x2) + /x3s + -(-1.+r1q-2.*r1*r2-2.*r1c*r2-6.*r1s*r2s-2.*r1*r2c+r2q+x1 + -r1s*x1+r2s*x1+x2+3.*r1s*x2+2.*r1*r2*x2-r2s*x2-x1*x2) + /prop2s + +(-1.-2.*r1s-r1q-2.*r1*r2-2.*r1c*r2+2.*r1*r2c+r2q+x1+r1s*x1 + -2.*r1*r2*x1-3.*r2s*x1+2.*r1s*x2-2.*r2s*x2+x1*x2+x2s) + /prop23; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.-pow2(r1-r2)); + rFO2 = (1.+r1s-2.*r1*r2+r2s-x1-x2)*(x1+x2) + /x3s + -(-1.+r1q+2.*r1*r2+2.*r1c*r2-6.*r1s*r2s+2.*r1*r2c+r2q+x1 + -r1s*x1+r2s*x1+x2+3.*r1s*x2-2.*r1*r2*x2-r2s*x2-x1*x2) + /prop2s + +(-1.-2.*r1s-r1q+2.*r1*r2+2.*r1c*r2-2.*r1*r2c+r2q+x1+r1s*x1 + +2.*r1*r2*x1-3.*r2s*x1+2.*r1s*x2-2.*r2s*x2+x1*x2+x2s) + /prop23; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.-r1s-r2s); + rFO4 = (1.+r1s+r2s-x1-x2)*(x1+x2) + /x3s + -(-1.+r1q-6.*r1s*r2s+r2q+x1-r1s*x1+r2s*x1+x2 + +3.*r1s*x2-r2s*x2-x1*x2) + /prop2s + +(-1.-2.*r1s-r1q+r2q+x1+r1s*x1-3.*r2s*x1 + +2.*r1s*x2-2.*r2s*x2+x1*x2+x2s) + /prop23; + isSet4 = true; + } + break; + + // q -> ~q chi. + case 12: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.-r1s+r2s+2.*r2); + rFO1 = (2.*r2+x2)*(-1.-r1s-r2s+x2) + /prop2s + +(4.+4.*r1s-4.*r2s-5.*x1-r1s*x1-2.*r2*x1+r2s*x1+x1s + -3.*x2-r1s*x2-2.*r2*x2+r2s*x2+x1*x2) + /x3s + +2.*(-1.-r1s+r2+r1s*r2-r2s-r2c+x1+r2*x1+r2s*x1+2.*x2 + +r1s*x2-x1*x2*0.5-x2s*0.5) + /prop23; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.-r1s+r2s-2.*r2); + rFO2 = (2.*r2-x2)*(1.+r1s+r2s-x2) + /prop2s + +(4.+4.*r1s-4.*r2s-5.*x1-r1s*x1+2.*r2*x1+r2s*x1+x1s + -3.*x2-r1s*x2+2.*r2*x2+r2s*x2+x1*x2) + /x3s + +2.*(-1.-r1s-r2-r1s*r2-r2s+r2c+x1-r2*x1+r2s*x1+2.*x2 + +r1s*x2-x1*x2*0.5-x2s*0.5) + /prop23; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.-r1s+r2s); + rFO4 = x2*(-1.-r1s-r2s+x2) + /prop2s + +(4.+4.*r1s-4.*r2s-5.*x1-r1s*x1+r2s*x1+x1s + -3.*x2-r1s*x2+r2s*x2+x1*x2) + /x3s + +2.*(-1.-r1s-r2s+x1+r2s*x1+2.*x2 + +r1s*x2-x1*x2*0.5-x2s*0.5) + /prop23; + isSet4 = true; + } + break; + + // ~g -> q ~qbar. + case 13: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.+r1s-r2s+2.*r1); + rFO1 = 4.*(2.*r1+x1)*(-1.-r1s-r2s+x1) + /(3.*prop1s) + -(-1.-r1s-2.*r1c-r2s-2.*r1*r2s+3.*x1*0.5+r1*x1-r1s*x1*0.5 + -r2s*x1*0.5+x2+r1*x2+r1s*x2-x1*x2*0.5) + /(3.*prop12) + +3.*(-1.+r1-r1s-r1c-r2s+r1*r2s+2.*x1+r2s*x1-x1s*0.5+x2+r1*x2 + +r1s*x2-x1*x2*0.5) + /prop13 + +3.*(4.-4.*r1s+4.*r2s-3.*x1-2.*r1*x1+r1s*x1-r2s*x1-5.*x2 + -2.*r1*x2+r1s*x2-r2s*x2+x1*x2+x2s) + /x3s + -3.*(3.-r1-5.*r1s-r1c+3.*r2s+r1*r2s-2.*x1-r1*x1+r1s*x1 + -4.*x2+2.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop23 + +4.*(2.-2.*r1-6.*r1s-2.*r1c+2.*r2s-2.*r1*r2s-x1+r1s*x1-r2s*x1 + -3.*x2+2.*r1*x2+3.*r1s*x2-r2s*x2+x1*x2+x2s) + /(3.*prop2s); + rFO1 = 3.*rFO1/4.; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.+r1s-r2s-2.*r1); + rFO2 = 4.*(2.*r1-x1)*(1.+r1s+r2s-x1) + /(3.*prop1s) + +3.*(-1.-r1-r1s+r1c-r2s-r1*r2s+2.*x1+r2s*x1-x1s*0.5 + +x2-r1*x2+r1s*x2-x1*x2*0.5) + /prop13 + +(2.+2.*r1s-4.*r1c+2.*r2s-4.*r1*r2s-3.*x1+2.*r1*x1 + +r1s*x1+r2s*x1-2.*x2+2.*r1*x2-2.*r1s*x2+x1*x2) + /(6.*prop12) + +3.*(4.-4.*r1s+4.*r2s-3.*x1+2.*r1*x1+r1s*x1-r2s*x1-5.*x2 + +2.*r1*x2+r1s*x2-r2s*x2+x1*x2+x2s) + /x3s + -3.*(3.+r1-5.*r1s+r1c+3.*r2s-r1*r2s-2.*x1+r1*x1+r1s*x1-4.*x2 + +2.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop23 + +4.*(2.+2.*r1-6.*r1s+2.*r1c+2.*r2s+2.*r1*r2s-x1+r1s*x1-r2s*x1 + -3.*x2-2.*r1*x2+3.*r1s*x2-r2s*x2+x1*x2+x2s) + /(3.*prop2s); + rFO2 = 3.*rFO2/4.; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.+r1s-r2s); + rFO4 = 8.*x1*(-1.-r1s-r2s+x1) + /(3.*prop1s) + +6.*(-1-r1s-r2s+2.*x1+r2s*x1-x1s*0.5+x2+r1s*x2-x1*x2*0.5) + /prop13 + +(2.+2.*r1s+2.*r2s-3.*x1+r1s*x1+r2s*x1-2.*x2-2.*r1s*x2+x1*x2) + /(3.*prop12) + +6.*(4.-4.*r1s+4.*r2s-3.*x1+r1s*x1-r2s*x1-5.*x2+r1s*x2-r2s*x2 + +x1*x2+x2s) + /x3s + -6.*(3.-5.*r1s+3.*r2s-2.*x1+r1s*x1-4.*x2+2.*r1s*x2-r2s*x2+x1*x2+x2s) + /prop23 + +8.*(2.-6.*r1s+2.*r2s-x1+r1s*x1-r2s*x1-3.*x2+3.*r1s*x2-r2s*x2 + +x1*x2+x2s) + /(3.*prop2s); + rFO4 = 3.*rFO4/8.; + isSet4 = true; + } + break; + + // ~q -> q ~g. + case 14: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.-r1s-r2s-2.*r1*r2); + rFO1 = 64.*(1.+r1s+2.*r1*r2+r2s-x1-x2)*(x1+x2) + /(9.*x3s) + -16.*(-1.+r1q-2.*r1*r2-2.*r1c*r2-6.*r1s*r2s-2.*r1*r2c+r2q + +x1-r1s*x1+2.*r1*r2*x1+3.*r2s*x1+x2+r1s*x2-r2s*x2-x1*x2) + /prop1s + -16.*(r1s+r1q-2.*r1c*r2+r2s-6.*r1s*r2s-2.*r1*r2c+r2q-r1s*x1 + +r1*r2*x1+2.*r2s*x1+2.*r1s*x2+r1*r2*x2-r2s*x2-x1*x2) + /prop12 + -64.*(-1.+r1q-2.*r1*r2-2.*r1c*r2-6.*r1s*r2s-2.*r1*r2c+r2q+x1 + -r1s*x1+r2s*x1+x2+3.*r1s*x2+2.*r1*r2*x2-r2s*x2-x1*x2) + /(9.*prop2s) + +8.*(-1.+r1q-2.*r1*r2+2.*r1c*r2-2.*r2s-2.*r1*r2c-r2q-2.*r1s*x1 + +2.*r2s*x1+x1s+x2-3.*r1s*x2-2.*r1*r2*x2+r2s*x2+x1*x2) + /prop13 + -8.*(-1.-2.*r1s-r1q-2.*r1*r2-2.*r1c*r2+2.*r1*r2c+r2q+x1+r1s*x1 + -2.*r1*r2*x1-3.*r2s*x1+2.*r1s*x2-2.*r2s*x2+x1*x2+x2s) + /(9.*prop23); + rFO1 = 9.*rFO1/64.; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.-r1s-r2s+2.*r1*r2); + rFO2 = 64.*(1.+r1s-2.*r1*r2+r2s-x1-x2)*(x1+x2) + /(9.*x3s) + -16.*(-1.+r1q+2.*r1*r2+2.*r1c*r2-6.*r1s*r2s+2.*r1*r2c+r2q+x1 + -r1s*x1-2.*r1*r2*x1+3.*r2s*x1+x2+r1s*x2-r2s*x2-x1*x2) + /prop1s + -64.*(-1.+r1q+2.*r1*r2+2.*r1c*r2-6.*r1s*r2s+2.*r1*r2c+r2q+x1 + -r1s*x1+r2s*x1+x2+3.*r1s*x2-2.*r1*r2*x2-r2s*x2-x1*x2) + /(9.*prop2s) + +16.*(-r1s-r1q-2.*r1c*r2-r2s+6.*r1s*r2s-2.*r1*r2c-r2q+r1s*x1 + +r1*r2*x1-2.*r2s*x1-2.*r1s*x2+r1*r2*x2+r2s*x2+x1*x2) + /prop12 + +8.*(-1.+r1q+2.*r1*r2-2.*r1c*r2-2.*r2s+2.*r1*r2c-r2q-2.*r1s*x1 + +2.*r2s*x1+x1s+x2-3.*r1s*x2+2.*r1*r2*x2+r2s*x2+x1*x2) + /prop13 + -8.*(-1.-2.*r1s-r1q+2.*r1*r2+2.*r1c*r2-2.*r1*r2c+r2q+x1+r1s*x1+ + 2.*r1*r2*x1-3.*r2s*x1+2.*r1s*x2-2.*r2s*x2+x1*x2+x2s) + /(9.*prop23); + rFO2 = 9.*rFO2/64.; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.-r1s-r2s); + rFO4 = 128.*(1.+r1s+r2s-x1-x2)*(x1+x2) + /(9.*x3s) + -32*(-1.+r1q-6.*r1s*r2s+r2q+x1-r1s*x1+3.*r2s*x1+x2 + +r1s*x2-r2s*x2-x1*x2) + /prop1s + -32.*(r1s+r1q+r2s-6.*r1s*r2s+r2q-r1s*x1+2.*r2s*x1+2.*r1s*x2 + -r2s*x2-x1*x2) + /prop12 + -128.*(-1.+r1q-6.*r1s*r2s+r2q+x1-r1s*x1+r2s*x1+x2+3.*r1s*x2 + -r2s*x2-x1*x2) + /(9.*prop2s) + +16.*(-1.+r1q-2.*r2s-r2q-2.*r1s*x1+2.*r2s*x1+x1s + +x2-3.*r1s*x2+r2s*x2+x1*x2) + /prop13 + -16.*(-1.-2.*r1s-r1q+r2q+x1+r1s*x1-3.*r2s*x1 + +2.*r1s*x2-2.*r2s*x2+x1*x2+x2s) + /(9.*prop23); + rFO4 = 9.*rFO4/128.; + isSet4 = true; + } + break; + + // q -> ~q ~g. + case 15: + if (combi == 1 || combi == 3) { + rLO1 = ps*(1.-r1s+r2s+2.*r2); + rFO1 = 32*(2.*r2+x2)*(-1.-r1s-r2s+x2) + /(9.*prop2s) + +8.*(-1.-r1s-2.*r1s*r2-r2s-2.*r2c+x1+r2*x1+r2s*x1 + +3.*x2*0.5-r1s*x2*0.5+r2*x2-r2s*x2*0.5-x1*x2*0.5) + /prop12 + +8.*(2.+2.*r1s-2.*r2-2.*r1s*r2-6.*r2s-2.*r2c-3.*x1-r1s*x1 + +2.*r2*x1+3.*r2s*x1+x1s-x2-r1s*x2+r2s*x2+x1*x2) + /prop1s + +32.*(4.+4.*r1s-4.*r2s-5.*x1-r1s*x1-2.*r2*x1+r2s*x1+x1s + -3.*x2-r1s*x2-2.*r2*x2+r2s*x2+x1*x2) + /(9.*x3s) + -8.*(3.+3.*r1s-r2+r1s*r2-5.*r2s-r2c-4.*x1-r1s*x1 + +2.*r2s*x1+x1s-2.*x2-r2*x2+r2s*x2+x1*x2) + /prop13 + -8.*(-1.-r1s+r2+r1s*r2-r2s-r2c+x1+r2*x1+r2s*x1+2.*x2+r1s*x2 + -x1*x2*0.5-x2s*0.5) + /(9.*prop23); + rFO1 = 9.*rFO1/32.; + isSet1 = true; + } + if (combi == 2 || combi == 3) { + rLO2 = ps*(1.-r1s+r2s-2.*r2); + rFO2 = 32*(2.*r2-x2)*(1.+r1s+r2s-x2) + /(9.*prop2s) + +8.*(-1.-r1s+2.*r1s*r2-r2s+2.*r2c+x1-r2*x1+r2s*x1 + +3.*x2*0.5-r1s*x2*0.5-r2*x2-r2s*x2*0.5-x1*x2*0.5) + /prop12 + +8.*(2.+2.*r1s+2.*r2+2.*r1s*r2-6.*r2s+2.*r2c-3.*x1-r1s*x1 + -2.*r2*x1+3.*r2s*x1+x1s-x2-r1s*x2+r2s*x2+x1*x2) + /prop1s + -8.*(3.+3.*r1s+r2-r1s*r2-5.*r2s+r2c-4.*x1-r1s*x1+2.*r2s*x1+x1s + -2.*x2+r2*x2+r2s*x2+x1*x2) + /prop13 + +32*(4.+4.*r1s-4.*r2s-5.*x1-r1s*x1+2.*r2*x1+r2s*x1 + +x1s-3.*x2-r1s*x2+2.*r2*x2+r2s*x2+x1*x2) + /(9.*x3s) + -8.*(-1.-r1s-r2-r1s*r2-r2s+r2c+x1-r2*x1+r2s*x1+2.*x2+r1s*x2 + -x1*x2*0.5-x2s*0.5) + /(9.*prop23); + rFO2 = 9.*rFO2/32.; + isSet2 = true; + } + if (combi == 4) { + rLO4 = ps*(1.-r1s+r2s); + rFO4 = 64.*x2*(-1.-r1s-r2s+x2) + /(9.*prop2s) + +16.*(-1.-r1s-r2s+x1+r2s*x1+3.*x2*0.5-r1s*x2*0.5 + -r2s*x2*0.5-x1*x2*0.5) + /prop12 + -16.*(3.+3.*r1s-5.*r2s-4.*x1-r1s*x1+2.*r2s*x1+x1s-2.*x2+r2s*x2 + +x1*x2) + /prop13 + +64.*(4.+4.*r1s-4.*r2s-5.*x1-r1s*x1+r2s*x1+x1s-3.*x2 + -r1s*x2+r2s*x2+x1*x2) + /(9.*x3s) + +16.*(2.+2.*r1s-6.*r2s-3.*x1-r1s*x1+3.*r2s*x1+x1s + -x2-r1s*x2+r2s*x2+x1*x2) + /prop1s + -16.*(-1.-r1s-r2s+x1+r2s*x1+2.*x2+r1s*x2-x1*x2*0.5-x2s*0.5) + /(9.*prop23); + rFO4 = 9.*rFO4/64.; + isSet4 = true; + } + break; + + // g -> ~g ~g. Use (9/4)*eikonal. May be changed in the future. + case 16: + rLO = ps; + if (combi == 2) offset = x3s; + else if (combi == 3) offset = mix * x3s; + else if (combi == 4) offset = 0.5 * x3s; + rFO = ps * 4.5 * ( (x1+x2-1.+offset-r1s-r2s)/prop12 + - r1s/prop2s - r2s/prop1s ); + break; + + // Eikonal expression for kind == 1; also acts as default. + default: + rLO = ps; + if (combi == 2) offset = x3s; + else if (combi == 3) offset = mix * x3s; + else if (combi == 4) offset = 0.5 * x3s; + rFO = ps * 2. * ( (x1+x2-1.+offset-r1s-r2s)/prop12 + - r1s/prop2s - r2s/prop1s ); + break; + + // End of ME cases. + } + + // Find relevant leading and first order expressions. + if (combi == 1 && isSet1) { + rLO = rLO1; + rFO = rFO1; } + else if (combi == 2 && isSet2) { + rLO = rLO2; + rFO = rFO2; } + else if (combi == 3 && isSet1 && isSet2) { + rLO = mix * rLO1 + (1.-mix) * rLO2; + rFO = mix * rFO1 + (1.-mix) * rFO2; } + else if (isSet4) { + rLO = rLO4; + rFO = rFO4; } + else if (combi == 4 && isSet1 && isSet2) { + rLO = 0.5 * (rLO1 + rLO2); + rFO = 0.5 * (rFO1 + rFO2); } + else if (isSet1) { + rLO = rLO1; + rFO = rFO1; } + + // Return ratio of first to leading order cross section. + return rFO / rLO; +} + +//-------------------------------------------------------------------------- + +// Find coefficient of azimuthal asymmetry from gluon polarization. + +void TimeShower::findAsymPol( Event& event, TimeDipoleEnd* dip) { + + // Default is no asymmetry. Only gluons are studied. + dip->asymPol = 0.; + dip->iAunt = 0; + int iRad = dip->iRadiator; + if (!doPhiPolAsym || event[iRad].id() != 21) return; + + // Trace grandmother via possibly intermediate recoil copies. + int iMother = event.iTopCopy(iRad); + int iGrandM = event[iMother].mother1(); + + // If grandmother in initial state of hard scattering, + // then only keep gg and qq initial states. + int statusGrandM = event[iGrandM].status(); + bool isHardProc = (statusGrandM == -21 || statusGrandM == -31); + if (isHardProc) { + if (event[iGrandM + 1].status() != statusGrandM) return; + if (event[iGrandM].isGluon() && event[iGrandM + 1].isGluon()); + else if (event[iGrandM].isQuark() && event[iGrandM + 1].isQuark()); + else return; + } + + // Set aunt by history or, for hard scattering, by colour flow. + if (isHardProc) dip->iAunt = dip->iRecoiler; + else dip->iAunt = (event[iGrandM].daughter1() == iMother) + ? event[iGrandM].daughter2() : event[iGrandM].daughter1(); + + // Coefficient from gluon production (approximate z by energy). + // For hard process arbitrarily put z = 1/2. + double zProd = (isHardProc) ? 0.5 : event[iRad].e() + / (event[iRad].e() + event[dip->iAunt].e()); + if (event[iGrandM].isGluon()) dip->asymPol = pow2( (1. - zProd) + / (1. - zProd * (1. - zProd) ) ); + else dip->asymPol = 2. * (1. - zProd) / (1. + pow2(1. - zProd) ); + + // Coefficients from gluon decay. + if (dip->flavour == 21) dip->asymPol *= pow2( (1. - dip->z) + / (1. - dip->z * (1. - dip->z) ) ); + else dip->asymPol *= -2. * dip->z *( 1. - dip->z ) + / (1. - 2. * dip->z * (1. - dip->z) ); + +} + +//-------------------------------------------------------------------------- + +// Print the list of dipoles. + +void TimeShower::list(ostream& os) const { + + // Header. + os << "\n -------- PYTHIA TimeShower Dipole Listing ----------------" + << "--------------------------------------------- \n \n i rad" + << " rec pTmax col chg gam oni hv isr sys sysR typ" + << "e MErec mix ord spl ~gR \n" << fixed << setprecision(3); + + // Loop over dipole list and print it. + for (int i = 0; i < int(dipEnd.size()); ++i) + os << setw(5) << i << setw(7) << dipEnd[i].iRadiator + << setw(7) << dipEnd[i].iRecoiler << setw(12) << dipEnd[i].pTmax + << setw(5) << dipEnd[i].colType << setw(5) << dipEnd[i].chgType + << setw(5) << dipEnd[i].gamType << setw(5) << dipEnd[i].isOctetOnium + << setw(5) << dipEnd[i].isHiddenValley << setw(5) << dipEnd[i].isrType + << setw(5) << dipEnd[i].system << setw(5) << dipEnd[i].systemRec + << setw(5) << dipEnd[i].MEtype << setw(7) << dipEnd[i].iMEpartner + << setw(8) << dipEnd[i].MEmix << setw(5) << dipEnd[i].MEorder + << setw(5) << dipEnd[i].MEsplit << setw(5) << dipEnd[i].MEgluinoRec + << "\n"; + + // Done. + os << "\n -------- End PYTHIA TimeShower Dipole Listing ------------" + << "---------------------------------------------" << endl; + +} + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/src/UserHooks.cxx b/PYTHIA8/pythia8140/src/UserHooks.cxx new file mode 100644 index 00000000000..c7f521c87eb --- /dev/null +++ b/PYTHIA8/pythia8140/src/UserHooks.cxx @@ -0,0 +1,203 @@ +// UserHooks.cc is a part of the PYTHIA event generator. +// Copyright (C) 2010 Torbjorn Sjostrand. +// PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. +// Please respect the MCnet Guidelines, see GUIDELINES for details. + +// Function definitions (not found in the header) for the UserHooks class. + +#include "UserHooks.h" + +namespace Pythia8 { + +//========================================================================== + +// The UserHooks class. + +//-------------------------------------------------------------------------- + +// multiplySigmaBy allows the user to introduce a multiplicative factor +// that modifies the cross section of a hard process. Since it is called +// from before the event record is generated in full, the normal analysis +// does not work. The code here provides a rather extensive summary of +// which methods actually do work. It is a convenient starting point for +// writing your own derived routine. + +double UserHooks::multiplySigmaBy( const SigmaProcess* sigmaProcessPtr, + const PhaseSpace* phaseSpacePtr, bool inEvent) { + + // Process code, necessary when some to be treated differently. + //int code = sigmaProcessPtr->code(); + + // Final multiplicity, i.e. whether 2 -> 1 or 2 -> 2. + //int nFinal = sigmaProcessPtr->nFinal(); + + // Incoming x1 and x2 to the hard collision, and factorization scale. + //double x1 = phaseSpacePtr->x1(); + //double x2 = phaseSpacePtr->x2(); + //double Q2Fac = sigmaProcessPtr->Q2Fac(); + + // Renormalization scale and assumed alpha_strong and alpha_EM. + //double Q2Ren = sigmaProcessPtr->Q2Ren(); + //double alphaS = sigmaProcessPtr->alphaSRen(); + //double alphaEM = sigmaProcessPtr->alphaEMRen(); + + // Subprocess mass-square. + //double sHat = phaseSpacePtr->sHat(); + + // Now methods only relevant for 2 -> 2. + //if (nFinal == 2) { + + // Mandelstam variables and hard-process pT. + //double tHat = phaseSpacePtr->tHat(); + //double uHat = phaseSpacePtr->uHat(); + //double pTHat = phaseSpacePtr->pTHat(); + + // Masses of the final-state particles. (Here 0 for light quarks.) + //double m3 = sigmaProcessPtr->m(3); + //double m4 = sigmaProcessPtr->m(4); + //} + + // Dummy statement to avoid compiler warnings. + return ((inEvent && sigmaProcessPtr->code() == 0 + && phaseSpacePtr->sHat() < 0.) ? 0. : 1.); + +} + +//-------------------------------------------------------------------------- + +// omitResonanceDecays omits resonance decay chains from process record. + +void UserHooks::omitResonanceDecays(const Event& process) { + + // Reset work event to be empty + workEvent.clear(); + + // Loop through all partons. Beam particles should be copied. + for (int i = 0; i < process.size(); ++i) { + bool doCopy = false; + bool isFinal = false; + if (i < 3) doCopy = true; + + // Daughters of beams should be copied. + else { + int iMother = process[i].mother1(); + if (iMother == 1 || iMother == 2) doCopy = true; + + // Granddaughters of beams should be copied and are final. + else if (iMother > 2) { + int iGrandMother = process[iMother].mother1(); + if (iGrandMother == 1 || iGrandMother == 2) { + doCopy = true; + isFinal = true; + } + } + } + + // Do copying and modify status/daughters of final. + if (doCopy) { + int iNew = workEvent.append( process[i]); + if (isFinal) { + workEvent[iNew].statusPos(); + workEvent[iNew].daughters( 0, 0); + } + } + } + +} + +//-------------------------------------------------------------------------- + +// subEvent extracts currently resolved partons in the hard process. + +void UserHooks::subEvent(const Event& event, bool isHardest) { + + // Reset work event to be empty. + workEvent.clear(); + + // Find which subsystem to study. + int iSys = 0; + if (!isHardest) iSys = partonSystemsPtr->sizeSys() - 1; + + // Loop through all the final partons of the given subsystem. + for (int i = 0; i < partonSystemsPtr->sizeOut(iSys); ++i) { + int iOld = partonSystemsPtr->getOut( iSys, i); + + // Copy partons to work event. + int iNew = workEvent.append( event[iOld]); + + // No mothers. Position in full event as daughters. + workEvent[iNew].mothers( 0, 0); + workEvent[iNew].daughters( iOld, iOld); + } + +} + +//========================================================================== + +// The SuppressSmallPT class, derived from UserHooks. + +//-------------------------------------------------------------------------- + +// Modify event weight at the trial level, before selection. + +double SuppressSmallPT::multiplySigmaBy( const SigmaProcess* sigmaProcessPtr, + const PhaseSpace* phaseSpacePtr, bool ) { + + // Need to initialize first time this method is called. + if (!isInit) { + + // Calculate pT0 as for multiple interactions. + // Fudge factor allows offset relative to MI framework. + double eCM = phaseSpacePtr->ecm(); + double pT0Ref = settingsPtr->parm("MultipleInteractions:pT0Ref"); + double ecmRef = settingsPtr->parm("MultipleInteractions:ecmRef"); + double ecmPow = settingsPtr->parm("MultipleInteractions:ecmPow"); + double pT0 = pT0timesMI * pT0Ref * pow(eCM / ecmRef, ecmPow); + pT20 = pT0 * pT0; + + // Initialize alpha_strong object as for multiple interactions, + // alternatively as for hard processes. + double alphaSvalue; + int alphaSorder; + if (useSameAlphaSasMI) { + alphaSvalue = settingsPtr->parm("MultipleInteractions:alphaSvalue"); + alphaSorder = settingsPtr->mode("MultipleInteractions:alphaSorder"); + } else { + alphaSvalue = settingsPtr->parm("SigmaProcess:alphaSvalue"); + alphaSorder = settingsPtr->mode("SigmaProcess:alphaSorder"); + } + alphaS.init( alphaSvalue, alphaSorder); + + // Initialization finished. + isInit = true; + } + + // Only modify 2 -> 2 processes. + int nFinal = sigmaProcessPtr->nFinal(); + if (nFinal != 2) return 1.; + + // pT scale of process. Weight pT^4 / (pT^2 + pT0^2)^2 + double pTHat = phaseSpacePtr->pTHat(); + double pT2 = pTHat * pTHat; + double wt = pow2( pT2 / (pT20 + pT2) ); + + if (numberAlphaS > 0) { + // Renormalization scale and assumed alpha_strong. + double Q2RenOld = sigmaProcessPtr->Q2Ren(); + double alphaSOld = sigmaProcessPtr->alphaSRen(); + + // Reweight to new alpha_strong at new scale. + double Q2RenNew = pT20 + Q2RenOld; + double alphaSNew = alphaS.alphaS(Q2RenNew); + wt *= pow( alphaSNew / alphaSOld, numberAlphaS); + } + + // End weight calculation. + return wt; + +} + + +//========================================================================== + +} // end namespace Pythia8 diff --git a/PYTHIA8/pythia8140/xmldoc/ASecondHardProcess.xml b/PYTHIA8/pythia8140/xmldoc/ASecondHardProcess.xml new file mode 100644 index 00000000000..4d94c8b28a7 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ASecondHardProcess.xml @@ -0,0 +1,398 @@ + + +

A Second Hard Process

+ +When you have selected a set of hard processes for hadron beams, the +multiple interactions +framework can add further interactions to build up a realistic +underlying event. These further interactions can come from a wide +variety of processes, and will occasionally be quite hard. They +do represent a realistic random mix, however, which means one cannot +predetermine what will happen. Occasionally there may be cases +where one wants to specify also the second hard interaction rather +precisely. The options on this page allow you to do precisely that. + + +Generate two hard scatterings in a collision between hadron beams. +The hardest process can be any combination of internal processes, +available in the normal process +selection machinery, or external input. Here you must further +specify which set of processes to allow for the second hard one, see +the following. + + +

Process Selection

+ +In principle the whole process +selection allowed for the first process could be repeated +for the second one. However, this would probably be overkill. +Therefore here a more limited set of prepackaged process collections +are made available, that can then be further combined at will. +Since the description is almost completely symmetric between the +first and the second process, you always have the possibility +to pick one of the two processes according to the complete list +of possibilities. + +

+Here comes the list of allowed sets of processes, to combine at will: + + +Standard QCD 2 -> 2 processes involving gluons and +d, u, s, c, b quarks. + + + +A prompt photon recoiling against a quark or gluon jet. + + +Two prompt photons recoiling against each other. + + +Production of charmonium via colour singlet and colour octet channels. + + +Production of bottomonium via colour singlet and colour octet channels. + + +Scattering q qbar -> gamma^*/Z^0, with full interference +between the gamma^* and Z^0. + + + +Scattering q qbar' -> W^+-. + + + +Scattering q qbar -> gamma^*/Z^0 g and +q g -> gamma^*/Z^0 q. + + + +Scattering q qbar' -> W^+- g and +q g -> W^+- q'. + + + +Production of a top pair, either via QCD processes or via an +intermediate gamma^*/Z^0 resonance. + + + +Production of a single top, either via a t- or +an s-channel W^+- resonance. + + +

+A further process collection comes with a warning flag: + + +The q qbar -> b bbar and g g -> b bbar processes. +These are already included in the TwoJets sample above, +so it would be doublecounting to include both, but we assume there +may be cases where the b subsample will be of special interest. +This subsample does not include flavour-excitation or gluon-splitting +contributions to the b rate, however, so, depending +on the topology if interest, it may or may not be a good approximation. + + +

Cuts and scales

+ +The second hard process obeys exactly the same selection rules for +phase space cuts and +couplings and scales +as the first one does. Specifically, a pTmin cut for +2 -> 2 processes would apply to the first and the second hard +process alike, and ballpark half of the time the second could be +generated with a larger pT than the first. (Exact numbers +depending on the relative shape of the two cross sections.) That is, +first and second is only used as an administrative distinction between +the two, not as a physics ordering one. + +

+Optionally it is possible to pick the mass and pT +phase space cuts separately for +the second hard interaction. The main application presumably would +be to allow a second process that is softer than the first, but still +hard. But one is also free to make the second process harder than the +first, if desired. So long as the two pT (or mass) ranges +overlap the ordering will not be the same in all events, however. + +

Cross-section calculation

+ +As an introduction, a brief reminder of Poissonian statistics. +Assume a stochastic process in time, for now not necessarily a +high-energy physics one, where the probability for an event to occur +at any given time is independent of what happens at other times. +Then the probability for n events to occur in a finite +time interval is + +P_n = <n>^n exp(-<n>) / n! + +where <n> is the average number of events. If this +number is small we can approximate exp(-<n>) = 1 , +so that P_1 = <n> and +P_2 = <n>^2 / 2 = P_1^2 / 2. + +

+Now further assume that the events actually are of two different +kinds a and b, occuring independently of each +other, such that <n> = <n_a> + <n_b>. +It then follows that the probability of having one event of type +a (or b) and nothing else is +P_1a = <n_a> (or P_1b = <n_b>). +From + +P_2 = (<n_a> + <n_b>)^2 / 2 = (P_1a + P_1b)^2 / 2 = +(P_1a^2 + 2 P_1a P_1b + P_1b^2) / 2 + +it is easy to read off that the probability to have exactly two +events of kind a and none of b is +P_2aa = P_1a^2 / 2 whereas that of having one a +and one b is P_2ab = P_1a P_1b. Note that the +former, with two identical events, contains a factor 1/2 +while the latter, with two different ones, does not. If viewed +in a time-ordered sense, the difference is that the latter can be +obtained two ways, either first an a and then a b +or else first a b and then an a. + +

+To translate this language into cross-sections for high-energy +events, we assume that interactions can occur at different pT +values independently of each other inside inelastic nondiffractive +(= "minbias") events. Then the above probabilities translate into +P_n = sigma_n / sigma_ND where sigma_ND is the +total nondiffractive cross section. Again we want to assume that +exp(-<n>) is close to unity, i.e. that the total +hard cross section above pTmin is much smaller than +sigma_ND. The hard cross section is dominated by QCD +jet production, and a reasonable precaution is to require a +pTmin of at least 20 GeV at LHC energies. +(For 2 -> 1 processes such as +q qbar -> gamma^*/Z^0 (-> f fbar) one can instead make a +similar cut on mass.) Then the generic equation +P_2 = P_1^2 / 2 translates into +sigma_2/sigma_ND = (sigma_1 / sigma_ND)^2 / 2 or +sigma_2 = sigma_1^2 / (2 sigma_ND). + +

+Again different processes a, b, c, ... contribute, +and by the same reasoning we obtain +sigma_2aa = sigma_1a^2 / (2 sigma_ND), +sigma_2ab = sigma_1a sigma_1b / sigma_ND, +and so on. + +

+There is one important correction to this picture: all collisions +do no occur under equal conditions. Some are more central in impact +parameter, others more peripheral. This leads to a further element of +variability: central collisions are likely to have more activity +than the average, peripheral less. Integrated over impact +parameter standard cross sections are recovered, but correlations +are affected by a "trigger bias" effect: if you select for events +with a hard process you favour events at small impact parameter +which have above-average activity, and therefore also increased +chance for further interactions. (In PYTHIA this is the origin +of the "pedestal effect", i.e. that events with a hard interaction +have more underlying activity than the level found in minimum-bias +events.) When you specify a matter overlap profile in the +multiple-interactions scenario, such an enhancement/depletion factor +f_impact is chosen event-by-event and can be averaged +during the course of the run. As an example, the double Gaussian +form used in Tune A gives approximately +<f_impact> = 2.5. The above equations therefore +have to be modified to +sigma_2aa = <f_impact> sigma_1a^2 / (2 sigma_ND), +sigma_2ab = <f_impact> sigma_1a sigma_1b / sigma_ND. +Experimentalists often instead use the notation +sigma_2ab = sigma_1a sigma_1b / sigma_eff, +from which we see that PYTHIA "predicts" +sigma_eff = sigma_ND / <f_impact>. +When the generation of multiple interactions is switched off it is +not possible to calculate <f_impact> and therefore +it is set to unity. + +

+When this recipe is to be applied to calculate +actual cross sections, it is useful to distinguish three cases, +depending on which set of processes are selected to study for +the first and second interaction. + +

+(1) The processes a for the first interaction and +b for the second one have no overlap at all. +For instance, the first could be TwoJets and the +second TwoPhotons. In that case, the two interactions +can be selected independently, and cross sections tabulated +for each separate subprocess in the two above classes. At the +end of the run, the cross sections in a should be multiplied +by <f_impact> sigma_1b / sigma_ND to bring them to +the correct overall level, and those in b by +<f_impact> sigma_1a / sigma_ND. + +

+(2) Exactly the same processes a are selected for the +first and second interaction. In that case it works as above, +with a = b, and it is only necessary to multiply by an +additional factor 1/2. A compensating factor of 2 +is automatically obtained for picking two different subprocesses, +e.g. if TwoJets is selected for both interactions, +then the combination of the two subprocesses q qbar -> g g +and g g -> g g can trivially be obtained two ways. + +

+(3) The list of subprocesses partly but not completely overlap. +For instance, the first process is allowed to contain a +or c and the second b or c, where +there is no overlap between a and b. Then, +when an independent selection for the first and second interaction +both pick one of the subprocesses in c, half of those +events have to be thrown, and the stored cross section reduced +accordingly. Considering the four possible combinations of first +and second process, this gives a + +sigma'_1 = sigma_1a + sigma_1c * (sigma_2b + sigma_2c/2) / +(sigma_2b + sigma_2c) + +with the factor 1/2 for the sigma_1c sigma_2c term. +At the end of the day, this sigma'_1 should be multiplied +by the normalization factor + +f_1norm = <f_impact> (sigma_2b + sigma_2c) / sigma_ND + +here without a factor 1/2 (or else it would have been +doublecounted). This gives the correct + +(sigma_2b + sigma_2c) * sigma'_1 = sigma_1a * sigma_2b ++ sigma_1a * sigma_2c + sigma_1c * sigma_2b + sigma_1c * sigma_2c/2 + +The second interaction can be handled in exact analogy. + +

+For the considerations above it is assumed that the phase space cuts +are the same for the two processes. It is possible to set the mass and +transverse momentum cuts differently, however. This changes nothing +for processes that already are different. For two collisions of the +same type it is partly a matter of interpretation what is intended. +If we consider the case of the same process in two non-overlapping +phase space regions, most likely we want to consider them as +separate processes, in the sense that we expect a factor 2 relative +to Poissonian statistics from either of the two hardest processes +populating either of the two phase space regions. In total we are +therefore lead to adopt the same strategy as in case (3) above: +only in the overlapping part of the two allowed phase space regions +could two processes be identical and thus appear with a 1/2 factor, +elsewhere the two processes are never identical and do not +include the 1/2 factor. We reiterate, however, that the case of +partly but not completely overlapping phase space regions for one and +the same process is tricky, and not to be used without prior +deliberation. + +

+The listing obtained with the pythia.statistics() +already contain these corrections factors, i.e. cross sections +are for the occurence of two interactions of the specified kinds. +There is not a full tabulation of the matrix of all the possible +combinations of a specific first process together with a specific +second one (but the information is there for the user to do that, +if desired). Instead pythia.statistics() shows this +matrix projected onto the set of processes and associated cross +sections for the first and the second interaction, respectively. +Up to statistical fluctuations, these two sections of the +pythia.statistics() listing both add up to the same +total cross section for the event sample. + +

+There is a further special feature to be noted for this listing, +and that is the difference between the number of "selected" events +and the number of "accepted" ones. Here is how that comes about. +Originally the first and second process are selected completely +independently. The generation (in)efficiency is reflected in the +different number of intially tried events for the first and second +process, leading to the same number of selected events. While +acceptable on their own, the combination of the two processes may +be unacceptable, however. It may be that the two processes added +together use more energy-momentum than kinematically allowed, or, +even if not, are disfavoured when the PYTHIA approach to provide +correlated parton densities is applied. Alternatively, referring +to case (3) above, it may be because half of the events should +be thrown for identical processes. Taken together, it is these +effects that reduced the event number from "selected" to "accepted". +(A further reduction may occur if a +user hook rejects some events.) + +

+It is allowed to use external Les Houches Accord input for the +hardest process, and then pick an internal one for the second hardest. +In this case PYTHIA does not have access to your thinking concerning +the external process, and cannot know whether it overlaps with the +internal or not. (External events q qbar' -> e+ nu_e could +agree with the internal W ones, or be a W' resonance +in a BSM scenario, to give one example.) Therefore the combined cross +section is always based on the scenario (1) above. Corrections for +correlated parton densities are included also in this case, however. +That is, an external event that takes a large fraction of the incoming +beam momenta stands a fair chance of being rejected when it has to be +combined with another hard process. For this reason the "selected" and +"accepted" event numbers are likely to disagree. + +

+In the cross section calculation above, the sigma'_1 +cross sections are based on the number of accepted events, while +the f_1norm factor is evaluated based on the cross sections +for selected events. That way the suppression by correlations +between the two processes does not get to be doublecounted. + +

+The pythia.statistics() listing contains two final +lines, indicating the summed cross sections sigma_1sum and +sigma_2sum for the first and second set of processes, at +the "selected" stage above, plus information on the sigma_ND +and <f_impact> used. The total cross section +generated is related to this by + +<f_impact> * (sigma_1sum * sigma_2sum / sigma_ND) * +(n_accepted / n_selected) + + with an additional factor of 1/2 for case 2 above. + +

+The error quoted for the cross section of a process is a combination +in quadrature of the error on this process alone with the error on +the normalization factor, including the error on +<f_impact>. As always it is a purely statistical one +and of course hides considerably bigger systematic uncertainties. + +

Event information

+ +Normally the process event record only contains the +hardest interaction, but in this case also the second hardest +is stored there. If both of them are 2 -> 2 ones, the +first would be stored in lines 3 - 6 and the second in 7 - 10. +For both, status codes 21 - 29 would be used, as for a hardest +process. Any resonance decay chains would occur after the two +main processes, to allow normal parsing. The beams in 1 and 2 +only appear in one copy. This structure is echoed in the +full event event record. + +

+Most of the properties accessible by the +pythia.info +methods refer to the first process, whether that happens to be the +hardest or not. The code and pT scale of the second process +are accessible by the info.codeMI(1) and +info.pTMI(1), however. + +

+The sigmaGen() and sigmaErr() methods provide +the cross section and its error for the event sample as a whole, +combining the information from the two hard processes as described +above. In particular, the former should be used to give the +weight of the generated event sample. The statitical error estimate +is somewhat cruder and gives a larger value than the +subprocess-by-subprocess one employed in +pythia.statistics(), but this number is +anyway less relevant, since systematical errors are likely to dominate. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/AccessPYTHIA6Processes.xml b/PYTHIA8/pythia8140/xmldoc/AccessPYTHIA6Processes.xml new file mode 100644 index 00000000000..4bec8d0e3d8 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/AccessPYTHIA6Processes.xml @@ -0,0 +1,110 @@ + + +

Access PYTHIA 6 Processes

+ +Gradually all relevant processes from PYTHIA 6 are being +re-implemented in PYTHIA 8, but this transition is not finished. +For a while longer it may therefore at times be convenient to +access the Fortran PYTHIA 6 process library. In order to give +this access at runtime, and not only by writing/reading event files, +an interface is provided to C++. This interface is residing in +Pythia6Interface.h, and in addition the PYTHIA 6 library +must be linked. The latter should normally be the most recent +Fortran PYTHIA version, but must be at least 6.314, since this is +the first version that allows processes to be output in the Les +Houches format (and not only input). + +

+The routines interfaced are +

    +
  • pygive(command) to give in a command to change a +setting, e.g. to decide which processes should be generated, +
  • pyinit( frame, beam, target, wIn) to initialize +the event generation chain,
    • +
  • pyupin() to fill this initialization information +in the HEPRUP commonblock,
    • +
  • pyupev() to generate the next hard process and +fill the event information in the HEPEUP commonblock,
    • +
  • pylist( mode) to list the event at the process +level,
    • +
  • pystat( mode) to print statistics on the event +generation process.
    • +
+Details on allowed arguments are given in the PYTHIA 6.4 manual. + +

+These methods can be used in context of the +LHAupFortran class. +The existing code there takes care of converting HEPRUP +and HEPEUP commonblock information from Fortran to C++, +and of making it available to the PYTHIA 8 methods. What needs to be +supplied are the two LHAupFortran::fillHepRup() and +LHAupFortran::fillHepEup() methods. The first can +contain an arbitrary number of pygive(...), followed +by pyinit(...) and pyupin() in that order. +The second only needs to contain pyupev(). Finally, +the use of pylist(...) and pystat(...) +is entirely optional, and calls are best put directly in the +main program. + +

+This means that all other Fortran routines have not been interfaced +and cannot be accessed directly from the C++ code; there is no need +for them in the current setup. + +

+PYTHIA 6.4 does its own rejection of events internally, according to +the strategy option 3. However, the current runtime interface does not +take cross-section information from PYTHIA 6.4. This means that both +the initial maxima and the final cross sections printed by the PYTHIA 8 +routines are irrelevant in this case. Instead you have to study the +standard PYTHIA 6.4 initialization printout and call on +pystat(...) at the end of the run to obtain this information. +It also means that you cannot mix with internally generated events, +unlike what could have been allowed for strategy 3. Should a strong need +arise, PYTHIA 6.4 could be modified to work with strategy option 1 and +thus allow a mixing with internal processes, but we do not expect this +to happen. + +

+An example of a fillHepRup() method to set up +Z^0 production at LHC, with masses above 50 GeV, would be +

+bool LHAinitFortran::fillHepRup() { 
+  Pythia6Interface::pygive("msel = 11"); 
+  Pythia6Interface::pygive("ckin(1) = 50."); 
+  Pythia6Interface::pyinit("cms","p","p",14000.);   
+  Pythia6Interface::pyupin();
+  return true;
+}
+
+and the process-generic fillHepEup() method would be +
+bool LHAupFortran::fillHepEup() { 
+  Pythia6Interface::pyupev();
+  return true;
+}
+
+Note that, of all parameters that could be set with the +PYGIVE, only those that influence the generation of the +hard processes have any impact, since this is the only part of the +Fortran code that is used. Also, if you want to set many parameters, +you can easily collect them in one file (separate from PYTHIA 8 +input) and parse that file. + +

+All hard PYTHIA 6 processes should be available for full generation +in PYTHIA 8, at least to the extent that they are defined for beams +of protons and antiprotons, which is the key application for PYTHIA 8 +so far. Soft processes, i.e. elastic and diffractive scattering, as well +as minimum-bias events, require a different kinematics machinery, and +can only be generated with the internal PYTHIA 8 processes. + +

+A simple example is found in main51.cc, another with parsed +input in main52.cc and a third with HepMC output in +main54.cc. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/AdvancedUsage.xml b/PYTHIA8/pythia8140/xmldoc/AdvancedUsage.xml new file mode 100644 index 00000000000..1c32fc08ef1 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/AdvancedUsage.xml @@ -0,0 +1,209 @@ + + +

Advanced Usage

+ +On this page we collect information on a number of classes that +the normal user would not encounter. There are cases where the +information is essential, however, for instance to +implement your own showers. + +

The subsystems

+ +One aspect that complicates administration is that an event +can contain several subsystems, each consisting of one MI and its +associated ISR and FSR. To first approximation these systems are +assumed to evolve independently, but to second they are connected by +the interleaved evolution, and potentially by rescattering effects. +The partons of a given subsystem therefore do not have to be stored +consecutively. + +

+The PartonSystems class is primarily used to keep track +of the current positions of all partons belonging to each system, +represented by the index iPos for a parton stored in the +event-record slot event[iPos]. With "all" we mean the +currently defined two incoming partons, or none for a resonance decay, +and the current set of outgoing partons, but with all ISR and FSR +intermediate-state partons omitted. That is, it stores all partons +that could be subject to some action in the next step of the +combined MI/ISR/FSR/BR description. As a special case, an outgoing +parton is stored even if it undergoes a rescattering, and thus no +longer belongs to the final state proper. + +

+The partonSystems instance of PartonSystems +class is a public member of the Pythia top-level class, +but is also available as a pointer partonSystemsPtr in +various PartonLevel classes, e.g. inside the current +instances of the TimeShower and SpaceShower +classes. + +

+A number of PartonSystems methods can be used to set or +get information on the subsystems: +

    +
  • clear() resets all the contents in preparation for the +next event. +
  • addSys() add a new (initially empty) subsystem to the +current list and return its index iSys in the list, +where index 0 is the hardest subcollision and so on. +
  • sizeSys() the number of separate subsystems.
    • +
  • setInA(iSys, iPos), setInB(iSys, iPos) store position +iPos of the incoming parton from beam A or beam B to the +iSys'th subcollision. These values are 0 initially, and +should so remain if there are no beams, such as in resonance decays. +
    • +
  • addOut(iSys, iPos) store position iPos +of a new outgoing parton in the iSys'th subcollision, +by appending it at the end of the current vector, with beginning in +slot 0.
    • +
  • setOut(iSys, iMem, iPos) store position iPos +in the iMem'th slot in the vector of outgoing partons in the +iSys'th subcollision. Here iMem must be in +the range already constructed by addOut calls.
    • +
  • replace(iSys, iPosOld, iPosNew) replace the existing +incoming or outgoing parton position iPosOld by +iPosNew in the iSys'th subcollision.
    • +
  • setSHat(iSys, sHat) set the invariant squared mass +sHat of the iSys'th subcollision.
    • +
  • hasInAB(iSys) true if an incoming parton has been set +for beam A or beam B (and hence should have been set for both) in the +iSys'th subcollision, else false.
    • +
  • getInA(iSys), getInB(iSys) the position iPos +of the incoming parton from beam A or beam B to the iSys'th +subcollision.
    • +
  • sizeOut(iSys) the number of outgoing partons +in the iSys'th subcollision.
    • +
  • getOut(iSys, iMem) the position iPos +of an outgoing parton in the iSys'th subcollision, +with the iMem range limited by sizeOut(iSys). +These partons are not guaranteed to appear in any particular order.
    • +
  • sizeAll(iSys) the total number of incoming and outgoing +partons in the iSys'th subcollision.
    • +
  • getAll(iSys, iMem) the position iPos +of an incoming or outgoing parton in the iSys'th subcollision. +In case there are beams it gives same as getInA(iSys) and + getInB(iSys) for indices 0 and 1, and thereafter agrees with +getOut(iSys, iMem) offset two positions. If there are no +beams it is identical with getOut(iSys, iMem).
    • +
  • getSHat(iSys) the invariant squared mass +sHat of the iSys'th subcollision.
    • +
  • list() print a listing of all the system information, +except for the sHat values.
    • +
+ +

+New systems are created from the hard process and by the MI, not from +any of the other components. Both FSR and ISR modify the position +of partons, however. Since an FSR or ISR branching typically implies +a new state with one more parton than before, an outgoing parton must +be added to the system. Furthermore, in a branching, several existing +partons may also be moved to new slots, including the incoming beam ones. +In a FSR 1 -> 2 branching it is irrelevant which parton position +you let overwrite the existing slot and which is added to the end of +the system. + +

+The system information must be kept up-to-date. Both the MI ISR, FSR and +BR descriptions make extensive use of the existing information. As an +example, the introduction of primordial kT in the beam remnants +will fail if the information on which final-state partons belong to which +system is out-of-date. The introduction of rescattering as part of the +MI framework adds further complications, where an outgoing parton of one +subsystem may be the incoming one of another system. This part of the code +is still under development. + +

+Currently the system information is kept throughout the continued +history of the event. Specifically, resonance decays create new systems, +appended to the existing ones. This could be useful during the +hadronization stage, to collect the partons that belong to a resonace +with preserved mass when a small string collapses to one particle, +but is not yet used for that. + +

The beams

+ +The different subsystems are tied together by them sharing the same +initial beam particles, and thereby being restricted by energy-momentum +and flavour conservation issues. The information stored in the two +beam particles, here called beamA and beamB, +is therefore as crucial to keep correct as the above subsystem list. + +

+Both beam objects are of the BeamParticle class. +Each such object contains a vector with the partons extracted from it. +The number of such partons, beamX.size() (X = A or B), +of course is the same as the above number of subsystems in the event +record. (The two diverge at the BR step, where further beam remnants +are added to the beams without corresponding to new subsystems.) +The individual partons are accessed by an overloaded indexing +operator to a vector of ResolvedParton objects. The +iPos() property corresponds to the iPos +one above, i.e. providing the position in the main event record of +a parton. In particular, +beamA[iSys].iPos() = partonSystemsPtr->getInA(iSys) and +beamB[iSys].iPos() = partonSystemsPtr->getInB(iSys). +Whereas thus the indices of the two incoming partons to a subsystem +are stored in two places, the ones of the outgoing partons only +appear in the system part of the PartonSystems class. + +

+Just as the subsystems in PartonSystems must be updated, +so must the information in the two BeamParticle's, e.g. +with methodsbeamX[iSys].iPos( iPosIn) when an incoming +parton is replaced by a new one in line iPosIn. Furthermore +the new parton identity should be set by beamX[iSys].id( idIn) +and the new x energy-momentum fraction by +beamX[iSys].x( xIn). The three can be combined in one go +by beamX[iSys].update( iPosIn, idIn, xIn). + +

+To be specific, it is assumed that, at each step, the two incoming +partons are moving along the +-z axis and are massless. +Since the event is constructed in the c.m. frame of the incoming +beams this implies that x = 2 E / E_cm. +If the x values are not defined accordingly or not kept +up-to-date the BR treatment will not conserve energy-momentum. + +

+In return, the BeamParticle objects give access to some +useful methods. The beamX.xf( id, x, Q2) returns the +standard PDF weight x f_id(x, Q^2). More intererstingly, +beamX.xfISR( iSys, id, x, Q2) returns the modified weight +required when several subsystems have to share the energy and flavours. +Thus iSys is added as an extra argument, and the momentum +already assigned to the other subsystems is not available for evolution, +i.e. the maximal x is correspondingly smaller than unity. +Also flavour issues are handled in a similar spirit. + +

+An additional complication is that a parton can be either valence or +sea, and in the latter case the BR treatment also distinguishes +companion quarks, i.e. quark-antiquark pairs that are assumed to +come from the same original g -> q qbar branching, whether +perturbative or not. This can be queried either with the +beamX[iSys].companion() method, for detailed information, +or with the beamX[iSys].isValence(), +beamX[iSys].isUnmatched() and +beamX[iSys].isCompanion() metods for yes/no answers +whether a parton is valence, unmatched sea or matched sea. +This choice should affect the ISR evolution; e.g., a valence quark +cannot be constructed back to come from a gluon. + +

+To keep this info up-to-date, the beamX.pickValSeaComp() +method should be called whenever a parton of a new flavour has been +picked in the ISR backwards evolution, but not if the flavour has not +been changed, since then one should not be allowed to switch back and +forth between the same quark being considered as valence or as sea. +Since the pickValSeaComp() method makes use of the +current parton-density values, it should be preceded by a call +to beamX.xfISR( iSys, id, x, Q2), where the values in +the call are the now finally accepted ones for the newly-found mother. +(Such a call is likely to have been made before, during the evolution, +but is not likely to be the most recent one, i.e. still in memory, and +therefore had better be redone.) + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/BeamParameters.xml b/PYTHIA8/pythia8140/xmldoc/BeamParameters.xml new file mode 100644 index 00000000000..62c6352c285 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/BeamParameters.xml @@ -0,0 +1,270 @@ + + +

Beam Parameters

+ +The settings on this page relate to the beam identities and energies, +to a beam momentum spread and to a beam interaction spot. +As always, momenta and energies are to be given in units of GeV, +and of space and time in mm. + +

Incoming beams

+ +There are two ways to set the identities and energies of the two incoming +beam particles. One is to use the init() method with no +arguments. Then the settings variables below will be read and used. The +alternative is to call init(...) +with arguments that provide this information. Then you need not use the +variables below (although it would still be possible). Note that, if nothing +is done, you will default to LHC at 14 TeV. + +

+Currently the beam particles must be either a hadron pair or a lepton +pair. In the former category p p and pbar p +combinations dominate, but it is also possible to combine with +pi^+, pi^- and pi^0. In the latter +e^+ e^- and mu^+ mu^- would be the most useful +combinations, but also others should work if combined with an +appropriate hard process. + + +The PDG id code for the first incoming particle. +Allowed codes include +
2212 = p, -2212 = pbar, +
211 = pi^+, -211 = pi^-, 111 = pi^0, +
990 = Pomeron (used in diffractive machinery; +here mainly for debug purposes), +
11 = e^-, -11 = e^+, +
13 = mu^-, -13 = mu^+, +
and a few more leptons/neutrinos in a few combinations. + + + +The PDG id code for the second incoming particle. + + + +Choice of frame for the two colliding particles. + + + + + + + +Collision CM energy, to be set if Beams:frameType = 1. + + + +The energy of the first incoming particle, moving in the ++z direction, to be set if Beams:frameType = 2. +If the particle energy is smaller than its mass +it is assumed to be at rest. + + + +The energy of the second incoming particle, moving in the +-z direction, to be set if Beams:frameType = 2. +If the particle energy is smaller than its mass +it is assumed to be at rest. + + + +The p_x component of the first incoming particle, +to be set if Beams:frameType = 3. + + + +The p_y component of the first incoming particle, +to be set if Beams:frameType = 3. + + + +The p_z component of the first incoming particle, +to be set if Beams:frameType = 3. + + + +The p_x component of the second incoming particle, +to be set if Beams:frameType = 3. + + + +The p_y component of the second incoming particle, +to be set if Beams:frameType = 3. + + + +The p_z component of the second incoming particle, +to be set if Beams:frameType = 3. + + + +The name of a Les Houches Event File, +to be set if Beams:frameType = 4. + + +

Beam momentum spread

+ +This framework currently is intended for a modest beam spread, such as +experienced at hadron colliders. Thus it can be safely assumed that the +physics does not change over the CM energy range probed, so that the +parameters of the physics initialization at the nominal energy can be +used as is. Currently it can not be used for the more extensive +energy spread expected at linear e^+ e^- colliders. Also, +any attempt to combine it with external Les Houches input of +parton-level events is at own risk. + +

+On this page you can set the momentum spread according to a simple +Gaussian distribution. If you instead want a more sophisticated +parametrization, you can write and link your own +BeamShape class. + + +Allow the beam momenta to be smeared around their initialization +nominal values. + + + +The width of a Gaussian distribution of the p_x spread of the +first incoming particle. + + + +The width of a Gaussian distribution of the p_y spread of the +first incoming particle. + + + +The width of a Gaussian distribution of the p_z spread of the +first incoming particle. + + + +The triply Gaussian distribution (p_x, p_y, p_z) is restricted to +a maximal total deviation from the nominal values (p_x0, p_y0, p_z0) +for the first incoming particle, like + +(p_x - p_x0)^2/sigma_px^2 + (p_y - p_y0)^2/sigma_py^2 + +(p_z - p_z0)^2/sigma_pz^2 < maxDev^2 + +(Note the absence of a factor 2 in the denominator, unlike the Gaussians +used to pick (p_x, p_y, p_z).) + + + +The width of a Gaussian distribution of the p_x spread of the +second incoming particle. + + + +The width of a Gaussian distribution of the p_y spread of the +second incoming particle. + + + +The width of a Gaussian distribution of the p_z spread of the +second incoming particle. + + + +The triply Gaussian distribution (p_x, p_y, p_z) is restricted to +a maximal total deviation from the nominal values (p_x0, p_y0, p_z0), +for the second incoming particle, like + +(p_x - p_x0)^2/sigma_px^2 + (p_y - p_y0)^2/sigma_py^2 + +(p_z - p_z0)^2/sigma_pz^2 < maxDev^2 + +(Note the absence of a factor 2 in the denominator, unlike the Gaussians +used to pick (p_x, p_y, p_z).) + + +

Beam interaction vertex

+ +On this page you can set the spread of the interaction vertex according to +a simple Gaussian distribution. If you instead want a more sophisticated +parametrization, you can write and link your own +BeamShape class. + + +Allow the interaction vertex of the two colliding beams to be smeared. +If off, then the vertex is set to be the origin. + + + +The width of a Gaussian distribution of the x location of the +interaction vertex. + + + +The width of a Gaussian distribution of the y location of the +interaction vertex. + + + +The width of a Gaussian distribution of the z location of the +interaction vertex. + + + +The triply Gaussian distribution of interaction vertex position +(x, y, z) is restricted to a maximal total deviation from the +origin, like + +x^2/sigma_x^2 + y^2/sigma_y^2 + z^2/sigma_z^2 < maxDevVertex^2 + +(Note the absence of a factor 2 in the denominator, unlike the Gaussians +used to pick (x, y, z).) + + + +The width of a Gaussian distribution of the collision time (in units of +mm/c). Note that, if the above space parametrization is viewed as the +effect of two incoming beams along the +-z axis, with each beam +having a Gaussian spread, then the spread of the time would also become +a Gaussian with the same width as the z one (times the +velocity of the beams, which we expect is close to unity). For flexibility +we have not enforced any such relation, however. + + + +The collision time is restricted to be in the range +|t| < sigma_t * maxDevTime. + + +

+The distributions above are all centered at the origin. It is also +possible to shift the above distributions to be centered around another +nominal position. You must have Beams:allowVertexSpread = on +to use this possibility. + + +The x location of the interaction vertex is centered at this value. + + + +The y location of the interaction vertex is centered at this value. + + + +The z location of the interaction vertex is centered at this value. + + + +The time t of the interaction vertex is centered at this value. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/BeamRemnants.xml b/PYTHIA8/pythia8140/xmldoc/BeamRemnants.xml new file mode 100644 index 00000000000..47399a8b966 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/BeamRemnants.xml @@ -0,0 +1,303 @@ + + +

Beam Remnants

+ +

Introduction

+ +The BeamParticle class contains information on all partons +extracted from a beam (so far). As each consecutive multiple interaction +defines its respective incoming parton to the hard scattering a +new slot is added to the list. This information is modified when +the backwards evolution of the spacelike shower defines a new +initiator parton. It is used, both for the multiple interactions +and the spacelike showers, to define rescaled parton densities based +on the x and flavours already extracted, and to distinguish +between valence, sea and companion quarks. Once the perturbative +evolution is finished, further beam remnants are added to obtain a +consistent set of flavours. The current physics framework is further +described in Sjo04. + +

+The introduction of rescattering +in the multiple interactions framework further complicates the +processing of events. Specifically, when combined with showers, +the momentum of an individual parton is no longer uniquely associated +with one single subcollision. Nevertheless the parton is classified +with one system, owing to the technical and administrative complications +of more complete classifications. Therefore the addition of primordial +kT to the subsystem initiator partons does not automatically +guarantee overall pT conservation. Various tricks are used to +minimize the mismatch, with a brute force shift of all parton +pT's as a final step. + +

+Much of the above information is stored in a vector of +ResolvedParton objects, which each contains flavour and +momentum information, as well as valence/companion information and more. +The BeamParticle method list() shows the +contents of this vector, mainly for debug purposes. + +

+The BeamRemnants class takes over for the final step +of adding primordial kT to the initiators and remnants, +assigning the relative longitudinal momentum sharing among the +remnants, and constructing the overall kinematics and colour flow. +This step couples the two sides of an event, and could therefore +not be covered in the BeamParticle class, which only +considers one beam at a time. + +

+The methods of these classes are not intended for general use, +and so are not described here. + +

+In addition to the parameters described on this page, note that the +choice of parton densities is made +in the Pythia class. Then pointers to the pdf's are handed +on to BeamParticle at initialization, for all subsequent +usage. + +

Primordial kT

+ +The primordial kT of initiators of hard-scattering subsystems +are selected according to Gaussian distributions in p_x and +p_y separately. The widths of these distributions are chosen +to be dependent on the hard scale of the central process and on the mass +of the whole subsystem defined by the two initiators: + +sigma = (sigma_soft * Q_half + sigma_hard * Q) / (Q_half + Q) + * m / (m_half + m) + +Here Q is the hard-process renormalization scale for the +hardest process and the pT scale for subsequent multiple +interactions, m the mass of the system, and +sigma_soft, sigma_hard, Q_half and +m_half parameters defined below. Furthermore each separately +defined beam remnant has a distribution of width sigma_remn, +independently of kinematical variables. + + +Allow or not selection of primordial kT according to the +parameter values below. + + + +The width sigma_soft in the above equation, assigned as a +primordial kT to initiators in the soft-interaction limit. + + + +The width sigma_hard in the above equation, assigned as a +primordial kT to initiators in the hard-interaction limit. + + + +The scale Q_half in the equation above, defining the +half-way point between hard and soft interactions. + + + +The scale m_half in the equation above, defining the +half-way point between low-mass and high-mass subsystems. +(Kinematics construction can easily fail if a system is assigned +a primordial kT value higher than its mass, so the +mass-dampening is intended to reduce some troubles later on.) + + + +The width sigma_remn, assigned as a primordial kT +to beam-remnant partons. + + +

+A net kT imbalance is obtained from the vector sum of the +primordial kT values of all initiators and all beam remnants. +This quantity is compensated by a shift shared equally between +all partons, except that the dampening factor m / (m_half + m) +is again used to suppress the role of small-mass systems. + +

+Note that the current sigma definition implies that +<pT^2> = <p_x^2>+ <p_y^2> = 2 sigma^2. +It thus cannot be compared directly with the sigma +of nonperturbative hadronization, where each quark-antiquark +breakup corresponds to <pT^2> = sigma^2 and only +for hadrons it holds that <pT^2> = 2 sigma^2. +The comparison is further complicated by the reduction of +primordial kT values by the overall compensation mechanism. + + +Is only relevant when rescattering +is switched on in the multiple interactions scenario. For a normal +interaction the rapidity and mass of a system is preserved when +primordial kT is introduced, by appropriate modification of the +incoming parton momenta. Kinematics construction is more complicated for +a rescattering, and two options are offered. Differences between these +can be used to explore systematic uncertainties in the rescattering +framework.
+The default behaviour is to keep the incoming rescattered parton as is, +but to modify the unrescattered incoming parton so as to preserve the +invariant mass of the system. Thereby the rapidity of the rescattering +is modified.
+The alternative is to retain the rapidity (and mass) of the rescattered +system when primordial kT is introduced. This is made at the +expense of a modified longitudinal momentum of the incoming rescattered +parton, so that it does not agree with the momentum it ought to have had +by the kinematics of the previous interaction.
+For a double rescattering, when both incoming partons have already scattered, +there is no obvious way to retain the invariant mass of the system in the +first approach, so the second is always used. + + +

Colour flow

+ +The colour flows in the separate subprocesses defined in the +multiple-interactions scenario are tied together via the assignment +of colour flow in the beam remnant. This is not an unambiguous +procedure, but currently no parameters are directly associated with it. +However, a simple "minimal" procedure of colour flow only via the beam +remnants does not result in a scenario in +agreement with data, notably not a sufficiently steep rise of +<pT>(n_ch). The true origin of this behaviour and the +correct mechanism to reproduce it remains one of the big unsolved issues +at the borderline between perturbative and nonperturbative QCD. +As a simple attempt, an additional step is introduced, wherein the gluons +of a lower-pT system are merged with the ones in a higher-pT one. + + +Allow or not a system to be merged with another one. + + + +A system with a hard scale pT can be merged with one of a +harder scale with a probability that is +pT0_Rec^2 / (pT0_Rec^2 + pT^2), where +pT0_Rec is reconnectRange times pT0, +the latter being the same energy-dependent dampening parameter as +used for multiple interactions. +Thus it is easy to merge a low-pT system with any other, +but difficult to merge two high-pT ones with each other. + + +

+The procedure is used iteratively. Thus first the reconnection probability +P = pT0_Rec^2 / (pT0_Rec^2 + pT^2) of the lowest-pT +system is found, and gives the probability for merger with the +second-lowest one. If not merged, it is tested with the third-lowest one, +and so on. For the m'th higher system the reconnection +probability thus becomes (1 - P)^(m-1) P. That is, there is +no explicit dependence on the higher pT scale, but implicitly +there is via the survival probability of not already having been merged +with a lower-pT system. Also note that the total reconnection +probability for the lowest-pT system in an event with n +systems becomes 1 - (1 - P)^(n-1). Once the fate of the +lowest-pT system has been decided, the second-lowest is considered +with respect to the ones above it, then the third-lowest, and so on. + +

+Once it has been decided which systems should be joined, the actual merging +is carried out in the opposite direction. That is, first the hardest +system is studied, and all colour dipoles in it are found (including to +the beam remnants, as defined by the holes of the incoming partons). +Next each softer system to be merged is studied in turn. Its gluons are, +in decreasing pT order, inserted on the colour dipole i,j +that gives the smallest (p_g p_i)(p_g p_j)/(p_i p_j), i.e. +minimizes the "disturbance" on the existing dipole, in terms of +pT^2 or Lambda measure (string length). The insertion +of the gluon means that the old dipole is replaced by two new ones. +Also the (rather few) quark-antiquark pairs that can be traced back to +a gluon splitting are treated in close analogy with the gluon case. +Quark lines that attach directly to the beam remnants cannot be merged +but are left behind. + +

+The joining procedure can be viewed as a more sophisticated variant of +the one introduced already in Sjo87. Clearly it is ad hoc. +It hopefully captures some elements of truth. The lower pT scale +a system has the larger its spatial extent and therefore the larger its +overlap with other systems. It could be argued that one should classify +individual initial-state partons by pT rather than the system +as a whole. However, for final-state radiation, a soft gluon radiated off +a hard parton is actually produced at late times and therefore probably +less likely to reconnect. In the balance, a classification by system +pT scale appears sensible as a first try. + +

+Note that the reconnection is carried out before resonance decays are +considered. Colour inside a resonance therefore is not reconnected. +This is a deliberate choice, but certainly open to discussion and +extensions at a later stage, as is the rest of this procedure. + +

Further variables

+ + +The maximum valence quark kind allowed in acceptable incoming beams, +for which multiple interactions are simulated. Default is that hadrons +may contain u, d and s quarks, +but not c and b ones, since sensible +kinematics has not really been worked out for the latter. + + + +When a sea quark has been found, a companion antisea quark ought to be +nearby in x. The shape of this distribution can be derived +from the gluon mother distribution convoluted with the +g -> q qbar splitting kernel. In practice, simple solutions +are only feasible if the gluon shape is assumed to be of the form +g(x) ~ (1 - x)^p / x, where p is an integer power, +the parameter above. Allowed values correspond to the cases programmed. +
+Since the whole framework is approximate anyway, this should be good +enough. Note that companions typically are found at small Q^2, +if at all, so the form is supposed to represent g(x) at small +Q^2 scales, close to the lower cutoff for multiple interactions. + + +

+When assigning relative momentum fractions to beam-remnant partons, +valence quarks are chosen according to a distribution like +(1 - x)^power / sqrt(x). This power is given below +for quarks in mesons, and separately for u and d +quarks in the proton, based on the approximate shape of low-Q^2 +parton densities. The power for other baryons is derived from the +proton ones, by an appropriate mixing. The x of a diquark +is chosen as the sum of its two constituent x values, and can +thus be above unity. (A common rescaling of all remnant partons and +particles will fix that.) An additional enhancement of the diquark +momentum is obtained by its x value being rescaled by the +valenceDiqEnhance factor. + + +The abovementioned power for valence quarks in mesons. + + + +The abovementioned power for valence u quarks in protons. + + + +The abovementioned power for valence d quarks in protons. + + + +Enhancement factor for valence diqaurks in baryons, relative to the +simple sum of the two constituent quarks. + + + +The off option is intended for debug purposes only, as +follows. When more than one valence quark is kicked out of a baryon +beam, as part of the multiple interactions scenario, the subsequent +hadronization is described in terms of a junction string topology. +This description involves a number of technical complications that +may make the program more unstable. As an alternative, by switching +this option off, junction configurations are rejected (which gives +an error message that the remnant flavour setup failed), and the +multiple interactions and showers are redone until a +junction-free topology is found. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/BeamShape.xml b/PYTHIA8/pythia8140/xmldoc/BeamShape.xml new file mode 100644 index 00000000000..7c97f4fe69d --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/BeamShape.xml @@ -0,0 +1,79 @@ + + +

Beam Shape

+ +The Beam Parameters +page explains how you can set a momentum spread of the two incoming +beams, and a spread and offset for the location of the interaction +vertex. The spread is based on a simple parametrization in terms of +independent Gaussians, however, which is likely to be too primitive +for realistic applications. + +

+It is therefore possible to define your own class, derived from the +BeamShape base class, and hand it in to Pythia with the + +pythia.setBeamShapePtr( BeamShape*) method. +Below we describe what such a class has to do. An explicit toy example +is shown in main27.cc. + +

+The BeamShape base class has a very simple structure. +It only has two main virtual methods. The first, init(), is +used for initialization. The second, pick(), selects +beam momentum and production vertex in the current event. + + + + +the constructor and destructor do not need to do anything. + + + +the base-class method simply reads in the relevant values stored +in the Settings data base, and saves a pointer to the +random-number generator. You are free to write your own +derived initialization routine, or use the existing one. In the +latter case you can then give your own modified interpretation +to the beam spread parameters defined there. +
The two flags Beams:allowMomentumSpread and +Beams:allowVertexSpread should not be tampered with, +however. These are checked elsewhere to determine whether the beam +shape should be set or not, whereas the other momentum-spread +and vertex-spread parameters are local to this class. + + + +this method is the key one to supply in the derived class. Here you +are free to pick whatever parametrization you desire for beam momenta +and vertex position, including correlations between the two. +At the end of the day, you should set a few protected +double numbers: +
deltaPxA, deltaPyA, deltaPzA for the three-momentum +shift of the first incoming beam, relative to the nominal values; +
deltaPxB, deltaPyB, deltaPzB for the three-momentum +shift of the second incoming beam, relative to the nominal values; +
vertexX, vertexY, vertexZ, vertexT for the +production-vertex position and time. +
As usual, momentum is given in GeV, and space and time in mm, +with c = 1. + + + + + +read out the three-momentum shifts for beams A and B that were set by +pick(). The energy components are put to zero at this stage, +since they are most conveniently calculated after the original and the +shift three-momenta have been added. + + + +read out the production-vertex position and time that were set by +pick(). + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Bibliography.xml b/PYTHIA8/pythia8140/xmldoc/Bibliography.xml new file mode 100644 index 00000000000..d180dea1562 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Bibliography.xml @@ -0,0 +1,275 @@ + + +

Bibliography

+ +
+ +
All08
+
B. Allanach et al., Comput. Phys.Commun. 180 (2009) 8 +[arXiv:0801.0045 [hep-ph]]
+ +
Alt89
+
G. Altarelli, B. Mele and M. Ruiz-Altaba, +Z. Phys. C45 (1989) 109
+ +
Alw06
+
J. Alwall et al., Comput. Phys. Commun. 176 (2007) 300 +[hep-ph/0609017]
+ +
Alw07
+
J. Alwall et al., arXiv:0712.3311 [hep-ph]
+ +
And83
+
B. Andersson, G. Gustafson, G. Ingelman and T. Sjöstrand, +Phys. Rep. 97 (1983) 31
+ +
Ask09
+
S. Ask, Eur. Phys. J. C60 (2009) 509
+ +
Ask10
+
S. Ask et al., arXiv:0912.4233v1 [hep-ph], to appear in +Comput. Phys. Commun.
+ +
Azu05
+
G. Azuelos, P.-H. Beauchemin and C.P. Burgess, J. Phys. G31 (2005) 1
+ +
Bar06
+
M. Bargiotti, talk at the HERA4LHC workshop, +http://mbargiot.web.cern.ch/mbargiot/talks/ + +
Bau90
+
U. Baur, M. Spira and P. M. Zerwas, Phys. Rev. D42 (1990) 815
+ +
Bel10
+
G. Bella et al., arXiv:1004.1649 [hep-ex], +
G. Bella et al., arXiv:1004.2432 [hep-ex]
+ +
Ben85
+
H.-U. Bengtsson, W.-S. Hou, A. Soni and D.H. Stork, +Phys. Rev. Lett. 55 (1985) 2762
+ +
Ben87
+
M. Bengtsson and T. Sjöstrand, Nucl. Phys. B289 (1987) 810
+ +
Ber81
+
F.A. Berends, R. Kleiss, P. De Causmaecker, R. Gastmans and T.T. Wu, +Phys. Lett. 103B (1981) 124
+ +
Ber87
+
UA4 Collaboration, D. Bernard et al., Phys. Lett. B198 (1987) 583
+ +
Ber87a
+
E. Berger, J. Collins, D. Soper and G. Sterman, Nucl. Phys. B286 +(1987) 704; +
K. Streng, CERN-TH.4949 (1988)
+ +
Bij01
+
J. Bijnens et al., Phys. Lett. B503 (2001) 341
+ +
Boo01
+
E. Boos et al., in the Proceedings of the Workshop on Physics +at TeV Colliders, Les Houches, France, 21 May - 1 Jun 2001 +[hep-ph/0109068]
+ +
Bow81
+
M.G. Bowler, Z. Phys. C11 (1981) 169
+ +
Boz07
+
G. Bozzi, B. Fuks, B. Herrmann, M. Klasen, Nucl. Phys. B787 (2007) 1 +[arXiv:0704.1826 [hep-ph]]
+ +
Bru93
+
P. Bruni and G. Ingelman, Phys. Lett. B311 (1993) 317
+ +
Cac06
+
M. Cacciari and G.P. Salam, Phys. Lett. B641 (2006) 57 +[hep-ph/0512210]
+ +
Cac08
+
M. Cacciari, G.P. Salam and G. Soyez, JHEP 04 (2008) 063 +[arXiv:0802.1189 [hep-ph]]
+ +
Cah82
+
R. Cahn, Z. Physik C15 (1982) 253
+ +
Car10
+
L. Carloni and T. Sjöstrand, LU TP 10-17, MCnet/10/11, +arXiv:1006.2911 [hep-ph] +
+ +
Che07
+
K. Cheung, W.-Y. Keung and T.-C. Yuan, +Phys. Rev. D76 (2007) 055003
+ +
Cor09
+
R. Corke and T. Sjöstrand, JHEP 01 (2010) 035 +[arXiv:0911.1909 [hep-ph]]
+ +
Cor10
+
R. Corke and T. Sjöstrand, LU TP 10-07, MCnet/10/04, +[arXiv:1003.2384 [hep-ph]]
+ +
Dav01
+
H. Davoudiasl, J.L. Hewett, T.G. Rizzo, Phys. Rev. D63 (2001) 075004
+ +
Dob01
+
M. Dobbs and J.B. Hansen, Comput. Phys. Commun. 134 (2001) 41
+ +
Don84
+
A. Donnachie and P.V. Landshoff, Nucl. Phys. B244 (1984) 322
+ +
Don92
+
A. Donnachie and P.V. Landshoff, Phys. Lett. B296 (1992) 227
+ +
Ede97
+
P. Eden and G. Gustafson, Z. Phys. C75 (1997) 41
+ +
Eic83
+
E. Eichten, K. D. Lane and M. E. Peskin, Phys. Rev. Lett. 50 (1983) 811; +
P. Chiappetta and M. Perrottet, CERN Yellow Report 90-10, Vol. II, +p. 806
+ +
Glu95
+
M. Glück, E. Reya and A. Vogt, Z. Phys. C67 (1995) 433
+ +
Giu99
+
G.F. Giudice, R. Rattazzi and J.D. Wells, Nucl. Phys. B544 (1999) 3
+ +
Giu04
+
G.F. Giudice, T. Plehn and A. Strumia, Nucl. Phys. B706 (2005) 455
+ +
Gus86
+
G. Gustafson, Phys. Lett. B175 (1986) 453; +
G. Gustafson and U. Pettersson, Nucl. Phys. B306 (1988) 746; +
L. Lönnblad, Comput. Phys. Commun. 71 (1992) 15
+ +
H1P06
+
H1 Collaboration, A. Aktas et al., Eur. Phys. J. C48 (2006) 715 +[hep-ex/0606004]
+ +
H1P07
+
H1 Collaboration, A. Aktas et al., JHEP 0710 (2007) 042 +[arXiv:0708.3217 [hep-ex]]
+ +
Hew88
+
J.L. Hewett and S. Pakvasa, Phys. Rev. D37 (1988) 3165
+ +
Hew07
+
J. L. Hewett and T. G. Rizzo, JHEP 0712 (2007) 009
+ +
Hui97
+
K. Huitu, J. Maalampi, A. Pietilä and M. Raidal, +Nucl. Phys. B487 (1997) 27 and private communication; +
G. Barenboim, K. Huitu, J. Maalampi and M. Raidal, +Phys. Lett. B394 (1997) 132
+ +
Ing97
+
P.Bruni, A. Edin and G.Ingelman, +see PomPyt homepage http://www.isv.uu.se/thep/MC/pompyt/ +
+ +
Jun95
+
H. Jung, Comput. Phys.Commun. 86 (1995) 147
+ +
Kas10
+
T. Kasemets, LU TP 10-03, arXiv:1002.4376 [hep-ph] +
T. Kasemets and T. Sjöstrand, LU TP 10-19, +arXiv:1007.0897v1 [hep-ph]
+ +
Kle89
+
R. Kleiss et al., in `Z physics at LEP 1', +eds. G. Altarelli, R. Kleiss and C. Verzegnassi, +CERN 89-08 (Geneva, 1989), Vol. 3, p. 143
+ +
Kum08
+
M.C. Kumar, P. Mathews, V. Ravindran and A. Tripathi, +Phys. Rev. D77 (2008) 055013
+ +
Lai00
+
CTEQ Collaboration, H.L. Lai et al., +Eur. Phys. J. C12 (2000) 375
+ +
Lon95
+
L. Lönnblad and T. Sjöstrand, Phys. Lett. B351 (1995) 293, +Eur. Phys. J. C2 (1998) 165
+ +
Mar90
+
G. Marsaglia, A. Zaman and W.-W. Tsang, +Stat. Prob. Lett. 9 (1990) 35
+ +
Mar05
+
A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, +Eur. Phys. J. C39 (2005) 155
+ +
Miu99
+
G. Miu and T. Sjöstrand, Phys. Lett. B449 (1999) 313
+ +
Nas00
+
P. Nason et al., in "Standard model physics (and more) at the LHC", +eds. G. Altarelli and M.L. Mangano, CERN 2000-004, p. 231 +[hep-ph/0003142]
+ +
Nor00
+
E. Norrbin and T. Sjöstrand, Eur. Phys. J. C17 (2000) 137
+ +
Nor01
+
E. Norrbin and T. Sjöstrand, Nucl. Phys. B603 (2001) 297
+ +
Pet83
+
C. Peterson, D. Schlatter, I. Schmitt and P. Zerwas, +Phys. Rev. D27 (1983) 105
+ +
Riz08
+
T. G. Rizzo, Phys. Lett. B665 (2008) 361
+ +
Sch94
+
G.A. Schuler and T. Sjöstrand, Phys. Rev. D49 (1994) 2257
+ +
Sch97
+
G.A. Schuler and T. Sjöstrand, Z. Phys. C73 (1997) 677
+ +
Sjo84
+
T. Sjöstrand, Nucl. Phys. B248 (1984) 469
+ +
Sey95
+
M. Seymour, Phys. Lett. B354 (1995) 409
+ +
Sjo85
+
T. Sjöstrand, Phys. Lett. 157B (1985) 321; +
M. Bengtsson, T. Sjöstrand and M. van Zijl, Z. Phys. C32 (1986) 67 +
+ +
Sjo87
+
T. Sjöstrand and M. van Zijl, Phys. Rev. D36 (1987) 2019
+ +
Sjo03
+
T. Sjöstrand and P.Z. Skands, Nucl. Phys. B659 (2003) 243
+ +
Sjo04
+
T. Sjöstrand and P.Z. Skands, JHEP 03 (2004) 053
+ +
Sjo05
+
T. Sjöstrand and P.Z. Skands, Eur. Phys. J. C39 (2005) 129
+ +
Sjo06
+
T. Sjöstrand, S. Mrenna and P.Z. Skands, +JHEP 05 (2006) 026 [hep-ph/0603175]
+ +
Ska04
+
P. Skands et al., JHEP 07 (2004) 036 [hep-ph/0311123]
+ +
Wha05
+
M.R. Whalley, D. Bourilkov and R.C. Group, +in `HERA and the LHC', eds. A. De Roeck and H. Jung, +CERN-2005-014, p. 575 [hep-ph/0508110]
+ +
Yao06
+
Particle Data Group, W.-M. Yao et al., +J. Phys. G33 (2006) 1
+ +
+ + + + diff --git a/PYTHIA8/pythia8140/xmldoc/BoseEinsteinEffects.xml b/PYTHIA8/pythia8140/xmldoc/BoseEinsteinEffects.xml new file mode 100644 index 00000000000..5d8a0026c70 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/BoseEinsteinEffects.xml @@ -0,0 +1,116 @@ + + +

Bose-Einstein Effects

+ +The BoseEinstein class performs shifts of momenta +of identical particles to provide a crude estimate of +Bose-Einstein effects. The algorithm is the BE_32 one described in +Lon95, with a Gaussian parametrization of the enhancement. +We emphasize that this approach is not based on any first-principles +quantum mechanical description of interference phenomena; such +approaches anyway have many problems to contend with. Instead a cruder +but more robust approach is adopted, wherein BE effects are introduced +after the event has already been generated, with the exception of the +decays of long-lived particles. The trick is that momenta of identical +particles are shifted relative to each other so as to provide an +enhancement of pairs closely separated, which is compensated by a +depletion of pairs in an intermediate region of separation. + +

+More precisely, the intended target form of the BE corrrelations in +BE_32 is + +f_2(Q) = (1 + lambda * exp(-Q^2 R^2)) + * (1 + alpha * lambda * exp(-Q^2 R^2/9) * (1 - exp(-Q^2 R^2/4))) + +where Q^2 = (p_1 + p_2)^2 - (m_1 + m_2)^2. +Here the strength lambda and effective radius R +are the two main parameters. The first factor of the +equation is implemented by pulling pairs of identical hadrons closer +to each other. This is done in such a way that three-monentum is +conserved, but at the price of a small but non-negligible negative +shift in the energy of the event. The second factor compensates this +by pushing particles apart. The negative alpha parameter is +determined iteratively, separately for each event, so as to restore +energy conservation. The effective radius parameter is here R/3, +i.e. effects extend further out in Q. Without the dampening +(1 - exp(-Q^2 R^2/4)) in the second factor the value at the +origin would become f_2(0) = (1 + lambda) * (1 + alpha * lambda), +with it the desired value f_2(0) = (1 + lambda) is restored. +The end result can be viewed as a poor man's rendering of a rapidly +dampened oscillatory behaviour in Q. + +

+Further details can be found in Lon95. For instance, the +target is implemented under the assumption that the initial distribution +in Q can be well approximated by pure phase space at small +values, and implicitly generates higher-order effects by the way +the algorithm is implemented. The algorithm is applied after the decay +of short-lived resonances such as the rho, but before the decay +of longer-lived particles. + +

+This algorithm is known to do a reasonable job of describing BE +phenomena at LEP. It has not been tested against data for hadron +colliders, to the best of our knowledge, so one should exercise some +judgement before using it. Therefore by default the master switch +HadronLevel:BoseEinstein is off. +Furthermore, the implementation found here is not (yet) as +sophisticated as the one used at LEP2, in that no provision is made +for particles from separate colour singlet systems, such as +W's and Z's, interfering only at a reduced rate. + +

+Warning: The algorithm will create a new copy of each particle +with shifted momentum by BE effects, with status code 99, while the +original particle with the original momentum at the same time will be +marked as decayed. This means that if you e.g. search for all +pi+- in an event you will often obtain the same particle twice. +One way to protect yourself from unwanted doublecounting is to +use only particles with a positive status code, i.e. ones for which +event[i].isFinal() is true. + + +

Main parameters

+ + +Include effects or not for identical pi^+, pi^- +and pi^0. + + + +Include effects or not for identical K^+, K^-, +K_S^0 and K_L^0. + + + +Include effects or not for identical eta and eta'. + + + +The strength parameter for Bose-Einstein effects. On physical grounds +it should not be above unity, but imperfections in the formalism +used may require that nevertheless. + + + +The size parameter of the region in Q space over which +Bose-Einstein effects are significant. Can be thought of as +the inverse of an effective distance in normal space, +R = hbar / QRef, with R as used in the above equation. +That is, f_2(Q) = (1 + lambda * exp(-(Q/QRef)^2)) * (...). + + + +Particle species with a width above this value (in GeV) are assumed +to be so short-lived that they decay before Bose-Einstein effects +are considered, while otherwise they do not. In the former case the +decay products thus can obtain shifted momenta, in the latter not. +The default has been picked such that both rho and +K^* decay products would be modified. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/CompositenessProcesses.xml b/PYTHIA8/pythia8140/xmldoc/CompositenessProcesses.xml new file mode 100644 index 00000000000..122f97cd8dd --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/CompositenessProcesses.xml @@ -0,0 +1,207 @@ + + +

Compositeness Processes

+ +Compositeness scenarios may give rise to sharp resonances of excited +quarks and leptons. An excited copy of the first generation is +implemented, consisting of spin 1/2 particles. The possibility of +contact interactions between quarks is also implemented in the context +of 2 -> 2 quark scattering. + +

+Related to excited fermions, the current implementation contains gauge +interaction production by quark-gluon fusion or lepton-photon fusion +and contact interaction production by quark-quark or quark-antiquark +scattering. In additions to the compositness scale and couplings listed +below, you are expected to change the excited-fermion masses in accordance +with what is desired. See Bau90 for conventions. + +

+A non-trivial angular dependence is included in the decay for the +2 -> 1 processes, but has not been included for the +2 -> 2 ones. + +

+The quark contact interactions are implemented according to +Eic83. The processes include the QCD contributions +as well as interference. For this reason the two processes +below converge toward, HardQCD:qq2qq and +HardQCD:qqbar2qqbarNew, when the contact interaction +contributions are close to zero. + +

Excited fermions, production processes

+ +A few different production processes have been implemented, which normally +would not overlap and therefore could be run together. + + +Common switch for the group of implemented processes that produce an +excited fermion. + + + +Scatterings d g -> d^*. +Code 4001. + + + +Scatterings u g -> u^*. +Code 4002. + + + +Scatterings s g -> s^*. +Code 4003. + + + +Scatterings c g -> c^*. +Code 4004. + + + +Scatterings b g -> b^*. +Code 4005. + + + +Scatterings e gamma -> e^*. +Code 4011. + + + +Scatterings mu gamma -> mu^*. +Code 4013. + + + +Scatterings tau gamma -> tau^*. +Code 4015. + + + +Scatterings q q(bar) -> d^* q(bar). +Code 4021. + + + +Scatterings q q(bar) -> u^* q(bar). +Code 4022. + + + +Scatterings q q(bar) -> s^* q(bar). +Code 4023. + + + +Scatterings q q(bar) -> c^* q(bar). +Code 4024. + + + +Scatterings q q(bar) -> b^* q(bar). +Code 4025. + + + +Scatterings q qbar -> e^*+- e^-+. +Code 4031. + + + +Scatterings q qbar -> nu_e^* nu_ebar. +Code 4032. + + + +Scatterings q qbar -> mu^*+- mu^-+. +Code 4033. + + + +Scatterings q qbar -> nu_mu^* nu_mubar. +Code 4034. + + + +Scatterings q qbar -> tau^*+- tau^-+. +Code 4035. + + + +Scatterings q qbar -> nu_tau^* nu_taubar. +Code 4036. + + +

Excited fermions, parameters

+ +The basic couplings of the model are + + +Compositeness scale Lambda in GeV. + + + +Strength f of the SU(2) coupling. + + + +Strength f' of the U(1) coupling. + + + +Strength f_c of the SU(3) coupling. + + +

Contact interactions, production processes

+ +The processes including quark contact interactions are + + +Scatterings q q -> q q including contact interactions. +Code 4201. + + + +Scatterings q qbar -> q' qbar' including contact interactions. +Code 4202. + + +

Contact interactions, parameters

+ + +Number of allowed outgoing new quark flavours in the above +q qbar -> q' qbar' process. Similar to HardQCD:nQuarkNew +for the QCD processes. + + + +Compositeness scale Lambda in GeV. + + + +Helicity parameter. + + + + + + +Helicity parameter. + + + + + + +Helicity parameter. + + + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/CouplingsAndScales.xml b/PYTHIA8/pythia8140/xmldoc/CouplingsAndScales.xml new file mode 100644 index 00000000000..f979d7c1e45 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/CouplingsAndScales.xml @@ -0,0 +1,287 @@ + + +

Couplings and Scales

+ +Here is collected some possibilities to modify the scale choices +of couplings and parton densities for all internally implemented +hard processes. This is based on them all being derived from the +SigmaProcess base class. The matrix-element coding is +also used by the multiple-interactions machinery, but there with a +separate choice of alpha_strong(M_Z^2) value and running, +and separate PDF scale choices. Also, in 2 -> 2 and +2 -> 3 processes where resonances are produced, their +couplings and thereby their Breit-Wigner shapes are always evaluated +with the resonance mass as scale, irrespective of the choices below. + +

Couplings and K factor

+ +The size of QCD cross sections is mainly determined by + +The alpha_strong value at scale M_Z^2. + + +

+The actual value is then regulated by the running to the Q^2 +renormalization scale, at which alpha_strong is evaluated + +Order at which alpha_strong runs, + + + + + +

+QED interactions are regulated by the alpha_electromagnetic +value at the Q^2 renormalization scale of an interaction. + +The running of alpha_em used in hard processes. + + + + + +

+In addition there is the possibility of a global rescaling of +cross sections (which could not easily be accommodated by a +changed alpha_strong, since alpha_strong runs) + +Multiply almost all cross sections by this common fix factor. Excluded +are only unresolved processes, where cross sections are better +set directly, and +multiple interactions, which have a separate K factor +of their own. +This degree of freedom is primarily intended for hadron colliders, and +should not normally be used for e^+e^- annihilation processes. + + +

Renormalization scales

+ +The Q^2 renormalization scale can be chosen among a few different +alternatives, separately for 2 -> 1, 2 -> 2 and two +different kinds of 2 -> 3 processes. In addition a common +multiplicative factor may be imposed. + + +The Q^2 renormalization scale for 2 -> 1 processes. +The same options also apply for those 2 -> 2 and 2 -> 3 +processes that have been specially marked as proceeding only through +an s-channel resonance, by the isSChannel() virtual +method of SigmaProcess. + + + + + +The Q^2 renormalization scale for 2 -> 2 processes. + + + + + + + + +The Q^2 renormalization scale for "normal" 2 -> 3 +processes, i.e excepting the vector-boson-fusion processes below. +Here it is assumed that particle masses in the final state either match +or are heavier than that of any t-channel propagator particle. +(Currently only g g / q qbar -> H^0 Q Qbar processes are +implemented, where the "match" criterion holds.) + + + + + + + + + +The Q^2 renormalization scale for 2 -> 3 +vector-boson-fusion processes, i.e. f_1 f_2 -> H^0 f_3 f_4 +with Z^0 or W^+- t-channel propagators. +Here the transverse masses of the outgoing fermions do not reflect the +virtualities of the exchanged bosons. A better estimate is obtained +by replacing the final-state fermion masses by the vector-boson ones +in the definition of transverse masses. We denote these combinations +mT_Vi^2 = m_V^2 + pT_i^2. + + + + + + + + + +The Q^2 renormalization scale for 2 -> 1, +2 -> 2 and 2 -> 3 processes is multiplied by +this factor relative to the scale described above (except for the options +with a fix scale). Should be use sparingly for 2 -> 1 processes. + + + +A fix Q^2 value used as renormalization scale for 2 -> 1, +2 -> 2 and 2 -> 3 processes in some of the options above. + + +

Factorization scales

+ +Corresponding options exist for the Q^2 factorization scale +used as argument in PDF's. Again there is a choice of form for +2 -> 1, 2 -> 2 and 2 -> 3 processes separately. +For simplicity we have let the numbering of options agree, for each event +class separately, between normalization and factorization scales, and the +description has therefore been slightly shortened. The default values are +not necessarily the same, however. + + +The Q^2 factorization scale for 2 -> 1 processes. +The same options also apply for those 2 -> 2 and 2 -> 3 +processes that have been specially marked as proceeding only through +an s-channel resonance. + + + + + +The Q^2 factorization scale for 2 -> 2 processes. + + + + + + + + +The Q^2 factorization scale for "normal" 2 -> 3 +processes, i.e excepting the vector-boson-fusion processes below. + + + + + + + + + +The Q^2 factorization scale for 2 -> 3 +vector-boson-fusion processes, i.e. f_1 f_2 -> H^0 f_3 f_4 +with Z^0 or W^+- t-channel propagators. +Here we again introduce the combinations mT_Vi^2 = m_V^2 + pT_i^2 +as replacements for the normal squared transverse masses of the two +outgoing quarks. + + + + + + + + + +The Q^2 factorization scale for 2 -> 1, +2 -> 2 and 2 -> 3 processes is multiplied by +this factor relative to the scale described above (except for the options +with a fix scale). Should be use sparingly for 2 -> 1 processes. + + + +A fix Q^2 value used as factorization scale for 2 -> 1, +2 -> 2 and 2 -> 3 processes in some of the options above. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Diffraction.xml b/PYTHIA8/pythia8140/xmldoc/Diffraction.xml new file mode 100644 index 00000000000..0d33bf51189 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Diffraction.xml @@ -0,0 +1,234 @@ + + +

Diffraction

+ +

Introduction

+ +Diffraction is not well understood, and several alternative approaches +have been proposed. Here we follw a fairly conventional Pomeron-based +one, but integrated to make full use of the standard PYTHIA machinery +for multiple interactions, parton showers and hadronization. This +is the approach pioneered in the PomPyt program by +Ingelman and collaborators Ing97. + +

+For ease of use (and of modelling), the Pomeron-specific parts of the +generation are subdivided into three sets of parameters that are rather +independent of each other: +
(i) the total, elastic and diffractive cross sections are +parametrized as functions of the CM energy, or can be set by the user +to the desired values, see the +Total Cross Sections page; +
(ii) once it has been decided to have a diffractive process, +a Pomeron flux parametrization is used to pick the mass of the +diffractive system(s) and the t of the exchanged Pomeron, +see below; +
(iii) a diffractive system of a given mass is classified either +as low-mass unresolved, which gives a simple low-pT string +topology, or as high-mass resolved, for which the full machinery of +multiple interactions and parton showers are applied, making use of +Pomeron PDFs. +
The parameters related to multiple interactions, parton showers +and hadronization are kept the same as for normal nondiffractive events, +with only one exception. This may be questioned, especially for the +multiple interactions, but we do not believe that there are currently +enough good diffractive data that would allow detailed separate tunes. + +

+The above subdivision may not represent the way "physics comes about". +For instance, the total diffractive cross section can be viewed as a +convolution of a Pomeron flux with a Pomeron-proton total cross section. +Since neither of the two is known from first principles there will be +a significant amount of ambiguity in the flux factor. The picture is +further complicated by the fact that the possibility of simultaneous +further multiple interactions ("cut Pomerons") will screen the rate of +diffractive systems. In the end, our set of parameters refers to the +effective description that emerges out of these effects, rather than +to the underlying "bare" parameters. + +

Pomeron flux

+ +As already mentioned above, the total diffractive cross section is fixed +by a default energy-dependent parametrization or by the user, see the +Total Cross Sections page. +Therefore we do not attribute any significance to the absolute +normalization of the Pomeron flux. The choice of Pomeron flux model +still will decide on the mass spectrum of diffractive states and the +t spectrum of the Pomeron exchange. + + +Parametrization of the Pomeron flux f_Pom/p( x_Pom, t). + + + + + + +

+In the last two options above, the Pomeron Regge trajectory is +parametrized as + +alpha(t) = 1 + epsilon + alpha' t + +The epsilon and alpha' parameters can be set +separately: + + +The Pomeron trajectory intercept epsilon above. For technical +reasons epsilon > 0 is necessary in the current implementation. + + +The Pomeron trajectory slope alpha' above. + + +

Separation into low and high masses

+ +Preferably one would want to have a perturbative picture of the +dynamics of Pomeron-proton collisions, like multiple interactions +provide for proton-proton ones. However, while PYTHIA by default +will only allow collisions with a CM energy above 10 GeV, the +mass spectrum of diffractive systems will stretch to down to +the order of 1.2 GeV. It would not be feasible to attempt a +perturbative description there. Therefore we do offer a simpler +low-mass description, with only longitudinally stretched strings, +with a gradual switch-over to the perturbative picture for higher +masses. The probability for the latter picture is parametrized as + +P_pert = 1 - exp( (m_diffr - m_min) / m_width ) + +which vanishes for the diffractive system mass +m_diffr < m_min, and is 1 - 1/e = 0.632 for +m_diffr = m_min + m_width. + + +The abovementioned threshold mass m_min for phasing in a +perturbative treatment. If you put this parameter to be bigger than +the CM energy then there will be no perturbative description at all, +but only the older low-pt description. + + + +The abovementioned threshold width m_width. + + +

Low-mass diffraction

+ +When an incoming hadron beam is diffractively excited, it is modeled +as if either a valence quark or a gluon is kicked out from the hadron. +In the former case this produces a simple string to the leftover +remnant, in the latter it gives a hairpin arrangement where a string +is stretched from one quark in the remnant, via the gluon, back to the +rest of the remnant. The latter ought to dominate at higher mass of +the diffractive system. Therefore an approximate behaviour like + +P_q / P_g = N / m^p + +is assumed. + + +The abovementioned normalization N for the relative quark +rate in diffractive systems. + + + +The abovementioned mass-dependence power p for the relative +quark rate in diffractive systems. + + +

+When a gluon is kicked out from the hadron, the longitudinal momentum +sharing between the the two remnant partons is determined by the +same parameters as above. It is plausible that the primordial +kT may be lower than in perturbative processes, however: + + +The width of Gaussian distributions in p_x and p_y +separately that is assigned as a primordial kT to the two +beam remnants when a gluon is kicked out of a diffractive system. + + + +The choice of longitudinal and transverse structure of a diffractive +beam remnant for a kicked-out gluon implies a remnant mass +m_rem distribution (i.e. quark plus diquark invariant mass +for a baryon beam) that knows no bounds. A suppression like +(1 - m_rem^2 / m_diff^2)^p is therefore introduced, where +p is the diffLargeMassSuppress parameter. + + +

High-mass diffraction

+ +The perturbative description need to use parton densities of the +Pomeron. The options are described in the page on +PDF Selection. The standard +perturbative multiple interactions framework then provides +cross sections for parton-parton interactions. In order to +turn these cross section into probabilities one also needs an +ansatz for the Pomeron-proton total cross section. In the literature +one often finds low numbers for this, of the order of 2 mb. +These, if taken at face value, would give way too much activity +per event. There are ways to tame this, e.g. by a larger pT0 +than in the normal pp framework. Actually, there are many reasons +to use a completely different set of parameters for MI in +diffraction than in pp collisions, e.g. with respect to the +impact-parameter picture. A lower number in some frameworks could +alternatively be regarded as a consequence of screening, with +a larger "bare" number. + +

+For now, however, an attempt at the most general solution would +carry too far, and instead we patch up the problem by using a +larger Pomeron-proton total cross section, such that average +activity makes more sense. This should be viewed as the main +tunable parameter in the description of high-mass diffraction. +It is to be fitted to diffractive event-shape data such as the average +charged multiplicity. It would be very closely tied to the choice of +Pomeron PDF; we remind that some of these add up to less than unit +momentum sum in the Pomeron, a choice that also affect the value +one ends up with. + + +The assumed Pomeron-proton effective cross section, as used for +multiple interactions in diffractive systems. A larger value gives +less MI activity per event. + + +There is no point in making the cross section too big, however, since +then pT0 will be adjusted downwards to ensure that the +integrated perturbative cross section stays above this assumed +total cross section. (The requirement of at least one perturbative +interaction per event.) + +

+Also note that, even for a fixed CM energy of events, the diffractive +subsystem will range from the abovementioned threshold mass +m_min to the full CM energy, with a variation of parameters +such as pT0 along this mass range. Therefore multiple +interactions are initialized for a few different diffractive masses, +currently five, and all relevant parameters are interpolated between +them to obtain the behaviour at a specific diffractive mass. +Furthermore, A B ->X B and A B ->A X are +initialized separately, to allow for different beams or PDF's on the +two sides. These two aspects mean that initialization of MI is +appreciably slower when perturbative high-mass diffraction is allowed. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ElectroweakProcesses.xml b/PYTHIA8/pythia8140/xmldoc/ElectroweakProcesses.xml new file mode 100644 index 00000000000..929b3771153 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ElectroweakProcesses.xml @@ -0,0 +1,267 @@ + + +

Electroweak Processes

+ +This page contains processes involving Prompt-photon, gamma^*/Z^0 +and W^+- production, plus a few with t-channel boson +exchange. + +

Prompt photon processes

+ +This group collects the processes where one or two photons are +produced by the hard process. Additional sources of photons +include parton showers and hadron decays. A pT cut +is required to stay away from the unphysical low-pT region. +An eikonalized description, intended to be valid at all pT, +is included as part of the multiple-interactions framework. + + +Common switch for the group of all prompt photon processes, +as listed separately in the following. + + + +Scattering q g -> q gamma. +Code 201. + + + +Scattering q qbar -> g gamma. +Code 202. + + + +Scattering g g -> g gamma. +Note: This is a box graph. The full quark-mass dependence +in the loop leads to very complicated expressions. The current +implementation is based on assuming five massless quarks (see below), +and thus is questionable at small (pT < m_b) or large +(pT > m_t) transverse momenta. +Code 203. + + + +Scattering q qbar -> gamma gamma. +Code 204. + + + +Scattering g g -> gamma gamma. +Note: This is a box graph. The full quark-mass dependence +in the loop leads to very complicated expressions. The current +implementation is based on assuming five massless quarks (see below), +and thus is questionable at small (pT < m_b) or large +(pT > m_t) transverse momenta. +Code 205. + + + +Number of quark flavours included in the box graphs resposible for +g g -> g gamma and g g-> gamma gamma processes. +Owing to the complexity if the massive expressions, quarks are treated +as massless. The default value should be applicable in the range of +transverse momenta above the b mass but below the t one. + + +

Weak boson processes

+ +Under this heading we group processes involving the production +of a single electroweak gauge boson, i.e. a gamma^*/Z^0 +or a W^+-, or a pair of them, or one of them in +combination with a parton. Since the three sets are partly +conflicting, each is associated with its own group flag. +In addition, t-channel exchange of such a boson +between two fermions form a separate group. + +

+There is one flag that can be used to influence the gamma^*/Z^0 +structure in all the processes below where it is produced, unless +otherwise stated. + +Choice of full gamma^*/Z^0 structure or not in relevant +processes. + + + +Note: irrespective of the option used, the particle produced +will always be assigned code 23 for Z^0, and open decay channels +is purely dictated by what is set for the Z^0. + + +

Boson exchange

+ +The two processes in this subgroup is included as part of the +multiple-interactions framework. + + +Common switch for the group of gamma^*/Z^0 +or W^+- exchange between two fermions. + + + +Scattering f f' -> f f' via gamma^*/Z^0 +t-channel exchange, with full interference +between the gamma^* and Z^0. +Code 211. + + + +Scattering f_1 f_2 -> f_3 f_4 via W^+- +t-channel exchange. +Code 212. + + +

Single boson

+ + +Common switch for the group of a single gamma^*/Z^0 +or W^+- production. + + + +Scattering f fbar -> gamma^*/Z^0, with full interference +between the gamma^* and Z^0. +Code 221. + + + +Scattering f fbar' -> W^+-. +Code 222. + + + +Scattering f fbar -> gamma^* -> f' fbar'. Subset of +process 221, but written as a 2 -> 2 process, so that +pT can be used as ordering variable, e.g. in multiple +interactions. Hardcoded for the final state being either of the +five quark flavours or three lepton ones. Not included in the +WeakSingleBoson:all set, but included in the +multiple-interactions framework. +Code 223. + + +

Boson pair

+ + +Common switch for the group of pair production of gamma^*/Z^0 +and W^+-. + + + +Scattering f fbar' -> gamma^*/Z^0 gamma^*/Z^0. +Code 231. + + + +Scattering f fbar' -> Z^0 W^+-. Note that here the +gamma^* contribution is not (currently) included. +Code 232. + + + +Scattering f fbar -> W^+ W^-. +Code 233. + + +

Boson and parton

+ + +Common switch for the group of production of a single electroweak +gauge boson, i.e. a gamma^*/Z^0 or a W^+-, in +association with a parton, i.e. a quark, gluon, photon or lepton. +These processes give first-order corrections to the ones in the +WeakSingleBoson class, and both sets cannot be used +simultaneously without unphysical doublecounting. The current class +should only be used to study the high-pT tail of the +gauge-boson production processes (for LHC applications at least +pT > 20 GeV), while the ones in WeakSingleBoson +should be used for inclusive production. + + + +Scattering q qbar -> gamma^*/Z^0 g. +Code 241. + + + +Scattering q g -> gamma^*/Z^0 q . +Code 242. + + + +Scattering f fbar -> gamma^*/Z^0 gamma. +Code 243. + + + +Scattering f gamma -> gamma^*/Z^0 f. +Code 244. + + + +Scattering q qbar -> W^+- g. +Code 251. + + + +Scattering q g -> W^+- q. +Code 252. + + + +Scattering f fbar -> W^+- gamma. +Code 253. + + + +Scattering f gamma -> W^+- f. +Code 254. + + +

Photon Collision Processes

+ +A few electroweak two-photon production processes are available. +To use them, photon PDFs have to be defined for the incoming +beam particles. For proton beams an appropriate set would be +MRST QED 2004 Mar05, available in the LHAPDF library. + + +Common switch for the group of six processes presented below. + + + +Scatterings gamma gamma -> q qbar, where q +is a light quark (u, d, s) . +Code 261. + + + +Scattering gamma gamma -> c cbar. +Code 262. + + + +Scattering gamma gamma -> b bbar. +Code 263. + + + +Scattering gamma gamma -> e+ e-. +Code 264. + + + +Scattering gamma gamma -> mu+ mu-. +Code 265. + + + +Scattering gamma gamma -> tau+ tau-. +Code 266. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ErrorChecks.xml b/PYTHIA8/pythia8140/xmldoc/ErrorChecks.xml new file mode 100644 index 00000000000..97617d7db1d --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ErrorChecks.xml @@ -0,0 +1,71 @@ + + +

Error Checks

+ +There is a few settings related to error checking during program +execution. Many other checks are performed as well, but do not +have any specific setting related to themselves. + + +Check the particle data tables for potential problems during +initialization. This includes inconsistent use of charge in particle +names, inconsistent setup of mass, mass range, width and lifetime, +sum of branching ratios not unity (allowed but discouraged) or charge +not conserved in a decay channel. Warnings should be viewed as reasons +to check further, but need not indicate a true problem, and also not all +problems may be caught. +The pythia.particleData.checkTable(level) method, +used for these checks, may also be called directly. + + + +The level of verbosity and checks of particle data, if switched on. + + + + + + + + +When an event has been successfully generated, check that the +final event record in event does not contain any +unphysical particles, or nonconserved charge or energy-momentum. +If this check fails, then pythia.next() obtains the +value false, i.e. the event is counted as aborted. + + + +The number of erroneous events, in the above check, for which +event listing and other detailed information will be printed. +After that, only the normal error messages will be issued. +Error counters are always updated, and accumulated numbers can be +shown with pythia.statistics() at the end of the run. + + + +Maximum allowed summed deviation of E, p_x, +p_y and p_z between the incoming beams and the +final state, as a fraction of the initial energy, above which the +event is counted as aborted. +(Unfortunetely roundoff errors do not scale linearly with the energy, +and also have a very long tail. So while most events at lower energies +may be correct to better than 1e-10, at LHC it does not have to signal +any fundamental bug if also the default tolerance above is violated +occasionally.) + + + +A check on the same summed deviation as above, but counted as a +warning rather than an error, and not leading to the event being +classified as aborted. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/EventAnalysis.xml b/PYTHIA8/pythia8140/xmldoc/EventAnalysis.xml new file mode 100644 index 00000000000..ae040050966 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/EventAnalysis.xml @@ -0,0 +1,512 @@ + + +

Event Analysis

+ +

Introduction

+ +The routines in this section are intended to be used to analyze +event properties. As such they are not part of the main event +generation chain, but can be used in comparisons between Monte +Carlo events and real data. They are rather free-standing, but +assume that input is provided in the PYTHIA 8 +Event format, and use a few basic facilities such +as four-vectors. + +

+In addition to the methods presented here, there is also the +possibility to make use of external +jet finders . + +

Sphericity

+ +The standard sphericity tensor is + + S^{ab} = (sum_i p_i^a p_i^b) / (sum_i p_i^2) + +where the sum i runs over the particles in the event, +a, b = x, y, z, and p without such an index is +the absolute size of the three-momentum . This tensor can be +diagonalized to find eigenvalues and eigenvectors. + +

+The above tensor can be generalized by introducing a power +r, such that + + S^{ab} = (sum_i p_i^a p_i^b p_i^{r-2}) / (sum_i p_i^r) + +In particular, r = 1 gives a linear dependence on momenta +and thus a collinear safe definition, unlike sphericity. + +

+To do sphericity analyses you have to set up a Sphericity +instance, and then feed in events to it, one at a time. The results +for the latest event are available as output from a few methods. + + +create a sphericity analysis object, where + +is the power r defined above, i.e. +gives Spericity, and +gives the linear form. + + +tells which particles are analyzed, +all final-state particles, +all observable final-state particles, +i.e. excluding neutrinos and other particles without strong or +electromagnetic interactions (the isVisible() +particle method), and + +only charged final-state particles. + + + + +perform a sphericity analysis, where +is an object of the Event class, +most likely the pythia.event one. + + is the output stream for +error messages. (The method does not rely on the Info +mchinery for error messages.) + +
If the routine returns false the +analysis failed, e.g. if too few particles are present to analyze. + + +

+After the analysis has been performed, a few methods are available +to return the result of the analysis of the latest event: + + +gives the sphericity (or equivalent if r is not 2), + + + +gives the aplanarity (with the same comment), + + + +gives one of the three eigenvalues for i = 1, 2 or 3, in +descending order, + + + +gives the matching normalized eigenvector, as a Vec4 +with vanishing time/energy component. + + + +provides a listing of the above information. + + +

+There is also one method that returns information accumulated for all +the events analyzed so far. + + +tells the number of times analyze(...) failed to analyze +events, i.e. returned false. + + +

Thrust

+ +Thrust is obtained by varying the thrust axis so that the longitudinal +momentum component projected onto it is maximized, and thrust itself is +then defined as the sum of absolute longitudinal momenta divided by +the sum of absolute momenta. The major axis is found correspondingly +in the plane transverse to thrust, and the minor one is then defined +to be transverse to both. Oblateness is the difference between the major +and the minor values. + +

+The calculation of thrust is more computer-time-intensive than e.g. +linear sphericity, introduced above, and has no specific advantages except +historical precedent. In the PYTHIA 6 implementation the search was +speeded up at the price of then not being guaranteed to hit the absolute +maximum. The current implementation studies all possibilities, but at +the price of being slower, with time consumption for an event with +n particles growing like n^3. + +

+To do thrust analyses you have to set up a Thrust +instance, and then feed in events to it, one at a time. The results +for the latest event are available as output from a few methods. + + +create a thrust analysis object, where + +tells which particles are analyzed, +all final-state particles, +all observable final-state particles, +i.e. excluding neutrinos and other particles without strong or +electromagnetic interactions (the isVisible() +particle method), and + +only charged final-state particles. + + + + +perform a thrust analysis, where +is an object of the Event class, +most likely the pythia.event one. + + is the output stream for +error messages. (The method does not rely on the Info +mchinery for error messages.) + +
If the routine returns false the +analysis failed, e.g. if too few particles are present to analyze. + + +

+After the analysis has been performed, a few methods are available +to return the result of the analysis of the latest event: + + + + + + + + +gives the thrust, major, minor and oblateness values, respectively, + + + +gives the matching normalized event-axis vectors, for i = 1, 2 or 3 +corresponding to thrust, major or minor, as a Vec4 with +vanishing time/energy component. + + + +provides a listing of the above information. + + +

+There is also one method that returns information accumulated for all +the events analyzed so far. + + +tells the number of times analyze(...) failed to analyze +events, i.e. returned false. + + +

ClusterJet

+ +ClusterJet (a.k.a. LUCLUS and +PYCLUS) is a clustering algorithm of the type used for +analyses of e^+e^- events, see the PYTHIA 6 manual. All +visible particles in the events are clustered into jets. A few options +are available for some well-known distance measures. Cutoff +distances can either be given in terms of a scaled quadratic quantity +like y = pT^2/E^2 or an unscaled linear one like pT. + +

+To do jet finding analyses you have to set up a ClusterJet +instance, and then feed in events to it, one at a time. The results +for the latest event are available as output from a few methods. + + +create a ClusterJet instance, where +distance measure, +to be provided as a character string (actually, only the first character +is necessary) +the Lund pT distance, + +the JADE mass distance, and + +the Durham kT measure. + + + +tells which particles are analyzed, +all final-state particles, +all observable final-state particles, +i.e. excluding neutrinos and other particles without strong or +electromagnetic interactions (the isVisible() particle +method), and + +only charged final-state particles. + +masses assumed for the particles +used in the analysis +all massless, +photons are massless while all others are +assigned the pi+- mass, and + +all given their correct masses. + + +perform or not a early preclustering step, where nearby particles +are lumped together so as to speed up the subsequent normal clustering. + + +reassign all particles to the nearest jet each time after two jets +have been joined. + + + + +performs a jet finding analysis, where +is an object of the Event class, +most likely the pythia.event one. + + +is the cutoff joining scale, below which jets are joined. Is given +in quadratic dimensionless quantities. Either yScale +or pTscale must be set nonvanishing, and the larger of +the two dictates the actual value. + + +is the cutoff joining scale, below which jets are joined. Is given +in linear quantities, such as pT or m depending on +the measure used, but always in units of GeV. Either yScale +or pTscale must be set nonvanishing, and the larger of +the two dictates the actual value. + + +the minimum number of jets to be reconstructed. If used, it can override +the yScale and pTscale values. + + +the maximum number of jets to be reconstructed. Is not used if below +nJetMin. If used, it can override the yScale +and pTscale values. Thus e.g. +nJetMin = nJetMax = 3 can be used to reconstruct exactly +3 jets. + + is the output stream for +error messages. (The method does not rely on the Info +mchinery for error messages.) + +
If the routine returns false the analysis failed, +e.g. because the number of particles was smaller than the minimum number +of jets requested. + + +

+After the analysis has been performed, a few ClusterJet +class methods are available to return the result of the analysis: + + +gives the number of jets found, with jets numbered 0 through +size() - 1, + + + +gives a Vec4 corresponding to the four-momentum defined by +the sum of all the contributing particles to the i'th jet, + + + +gives the index of the jet that the particle i of the event +record belongs to, + + + +provides a listing of the reconstructed jets. + + + +the number of most recent clustering scales that have been stored +for readout with the next method. Normally this would be five, +but less if fewer clustering steps occured. + + + +clustering scales, with distance(0) being the most +recent one, i.e. normally the highest, up to distance(4) +being the fifth most recent. That is, with n being the final +number of jets, ClusterJet::size(), the scales at which +n+1 jets become n, n+2 become n+1, +and so on till n+5 become n+4. Nonexisting clustering +scales are returned as zero. The physical interpretation of a scale is +as provided by the respective distance measure (Lund, JADE, Durham). + + +

+There is also one method that returns information accumulated for all +the events analyzed so far. + + +tells the number of times analyze(...) failed to analyze +events, i.e. returned false. + + +

CellJet

+ +CellJet (a.k.a. PYCELL) is a simple cone jet +finder in the UA1 spirit, see the PYTHIA 6 manual. It works in an +(eta, phi, eT) space, where eta is pseudorapidity, +phi azimuthal angle and eT transverse energy. +It will draw cones in R = sqrt(Delta-eta^2 + Delta-phi^2) +around seed cells. If the total eT inside the cone exceeds +the threshold, a jet is formed, and the cells are removed from further +analysis. There are no split or merge procedures, so later-found jets +may be missing some of the edge regions already used up by previous +ones. Not all particles in the event are assigned to jets; leftovers +may be viewed as belonging to beam remnants or the underlying event. +It is not used by any experimental collaboration, but is closely +related to the more recent and better theoretically motivated +anti-kT algorithm Cac08. + +

+To do jet finding analyses you have to set up a CellJet +instance, and then feed in events to it, one at a time. Especially note +that, if you want to use the options where energies are smeared in +order so emulate detector imperfections, you must hand in an external +random number generator, preferably the one residing in the +Pythia class. The results for the latest event are +available as output from a few methods. + + +create a CellJet instance, where + +the maximum +-pseudorapidity that the detector is assumed to cover. + + +the number of equal-sized bins that the +-etaMax range +is assumed to be divided into. + + +the number of equal-sized bins that the phi range ++-pi is assumed to be divided into. + + +tells which particles are analyzed, +all final-state particles, +all observable final-state particles, +i.e. excluding neutrinos and other particles without strong or +electromagnetic interactions (the isVisible() particle +method), +and +only charged final-state particles. + + +strategy to smear the actual eT bin by bin, +no smearing, +smear the eT according to a Gaussian +with width resolution * sqrt(eT), with the Gaussian truncated +at 0 and upperCut * eT, +smear the e = eT * cosh(eta) according +to a Gaussian with width resolution * sqrt(e), with the +Gaussian truncated at 0 and upperCut * e. + + +see above. + + +see above. + + +completely neglect all bins with an eT < threshold. + + +the random-number generator used to select the smearing described +above. Must be handed in for smearing to be possible. If your +Pythia class instance is named pythia, +then &pythia.rndm would be the logical choice. + + + + +performs a jet finding analysis, where +is an object of the Event class, +most likely the pythia.event one. + + +is the minimum transverse energy inside a cone for this to be +accepted as a jet. + + + is the size of the cone in (eta, phi) space drawn around +the geometric center of the jet. + + +the mimimum eT in a cell for this to be acceptable as +the trial center of a jet. + + is the output stream for +error messages. (The method does not rely on the Info +mchinery for error messages.) + +
If the routine returns false the analysis failed, +but currently this is not foreseen ever to happen. + + +

+After the analysis has been performed, a few CellJet +class methods are available to return the result of the analysis: + + +gives the number of jets found, with jets numbered 0 through +size() - 1, + + + +gives the eT of the i'th jet, where jets have been +ordered with decreasing eT values, + + + + + +gives the eta and phi coordinates of the geometrical +center of the i'th jet, + + + + + +gives the eta and phi coordinates of the +eT-weighted center of the i'th jet, + + + +gives the number of particles clustered into the i'th jet, + + + +gives a Vec4 corresponding to the four-momentum defined +by the eT and the weighted center of the i'th jet, + + + +gives a Vec4 corresponding to the four-momentum defined by +the sum of all the contributing cells to the i'th jet, where +each cell contributes a four-momentum as if all the eT is +deposited in the center of the cell, + + + +gives the invariant mass of the i'th jet, defined by the +pMassive above, + + + +provides a listing of the above information (except pMassless, +for reasons of space). + + +

+There is also one method that returns information accumulated for all +the events analyzed so far. + +tells the number of times analyze(...) failed to analyze +events, i.e. returned false. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/EventInformation.xml b/PYTHIA8/pythia8140/xmldoc/EventInformation.xml new file mode 100644 index 00000000000..c17a85eea03 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/EventInformation.xml @@ -0,0 +1,465 @@ + + +

Event Information

+ +The Info class collects various one-of-a-kind information, +some relevant for all events and others for the current event. +An object info is a public member of the Pythia +class, so if you e.g. have declared Pythia pythia, the +Info methods can be accessed by +pythia.info.method(). Most of this is information that +could also be obtained e.g. from the event record, but is here more +directly available. It is primarily intended for processes generated +internally in PYTHIA, but many of the methods would work also for +events fed in via the Les Houches Accord. + +

List information

+ + +a listing of most of the information set for the current event. + + +

The beams

+ + + + +the identities of the two beam particles. + + + + + +the longitudinal momenta of the two beam particles. + + + + + +the energies of the two beam particles. + + + + + +the masses of the two beam particles. + + + + + +the CM energy and its square for the two beams. + + +

Initialization

+ + +normally false, but true if the proposed pTmin scale was too low +in timelike or spacelike showers, or in multiple interactions. In the former +case the pTmin is raised to some minimal value, in the latter the +initialization fails (it is impossible to obtain a minijet cross section +bigger than the nondiffractive one by reducing pTmin). + + +

The event type

+ + + + +the name and code of the process that occured. + + + +the number of final-state partons in the hard process. + + + +are beam particles resolved, i.e. were PDF's used for the process? + + + + + +is either beam diffractively excited? + + + +is the process a minimum-bias one? + + + +has the process been generated from external Les Houches Accord +information? + + + +true if a linked Les Houches class refuses to return any further +events, presumably because it has reached the end of the file from +which events have been read in. + + + +does the process have a subprocess classification? +Currently only true for minbias and Les Houches events, where it allows +the hardest collision to be identified. + + + + + + + +the name, code and number of final-state partons in the subprocess +that occured when hasSub() is true. For a minimum-bias event +the code would always be 101, while codeSub() +would vary depending on the actual hardest interaction, e.g. 111 for +g g -> g g. For a Les Houches event the code would +always be 9999, while codeSub() would be the external +user-defined classification code. The methods below would also provide +information for such particular subcollisions. + + +

Hard process parton densities and scales

+ + + + +the identities of the two partons coming in to the hard process. + + + + + +x fractions of the two partons coming in to the hard process. + + + + + +rapidity and scaled mass-squared of the hard-process subsystem, as +defined by the above x values. + + + + + +parton densities x*f(x,Q^2 )evaluated for the two incoming +partons; could be used e.g. for reweighting purposes. + + + + + +the Q or Q^2 factorization scale at which the +densities were evaluated. + + + + + +true if the two hard incoming partons have been picked +to belong to the valence piece of the parton-density distribution, +else false. Should be interpreted with caution. +Information is not set if you switch off parton-level processing. + + + + + +the alpha_strong and alpha_electromagnetic values used +for the hard process. + + + + + +the Q or Q^2 renormalization scale at which +alpha_strong and alpha_electromagnetic were evaluated. + + +

Hard process kinematics

+ + + + +the invariant mass and its square for the hard process. + + + + + +the remaining two Mandelstam variables; only defined for 2 -> 2 +processes. + + + + + +transverse momentum and its square in the rest frame of a 2 -> 2 +processes. + + + + + +the masses of the two outgoing particles in a 2 -> 2 processes. + + + + + +the polar and azimuthal scattering angles in the rest frame of +a 2 -> 2 process. + + +

Event weight and activity

+ + +weight assigned to the current event. Is normally 1 and thus uninteresting. +However, in case of the +PhaseSpace:increaseMaximum = off default strategy, +an event with a differential cross-section above the assumed one +(in a given phase-space point) is assigned a weight correspondingly +above unity. This should happen only very rarely, if at all, and so +could normally be disregarded. For Les Houches events some strategies +allow negative weights, which then after unweighting lead to events +with weight -1. There are also Les Houches strategies where no unweighting +is done, and therefore a nontrivial event weight must be used e.g. +when filling histograms. + + + + + + + +the number of emissions in the initial-state showering, in the final-state +showering excluding resonance decys, and in the final-state showering +inside resonance decays, respectively. + + + + + + + +Maximum pT scales set for MI, ISR and FSR, given the +process type and scale choice for the hard interactions. The actual +evolution will run down from these scales. + + + +The current pT scale in the combined MI, ISR and FSR evolution. +Useful for classification in user hooks, +but not once the event has been evolved. + + +

Multiple interactions

+ + +the impact parameter b assumed for the current collision when +multiple interactions are simulated. Is not expressed in any physical +size (like fm), but only rescaled so that the average should be unity +for minimum-bias events (meaning less than that for events with hard +processes). + + + +The choice of impact parameter implies an enhancement or depletion of +the rate of subsequent interactions, as given by this number. Again +the average is normalized be unity for minimum-bias events (meaning +more than that for events with hard processes). + + + +the number of hard interactions in the current event. Is 0 for elastic +and diffractive events, and else at least 1, with more possible from +multiple interactions. + + + + + +the process code and transverse momentum of the i'th +subprocess, with i in the range from 0 to +nMI() - 1. The values for subprocess 0 is redundant with +information already provided above. + + + + + +are normally zero. However, if the i'th subprocess is +a rescattering, i.e. either or both incoming partons come from the +outgoing state of previous scatterings, they give the position in the +event record of the outgoing-state parton that rescatters. +iAMI and iBMI then denote partons coming from +the first or second beam, respectively. + + +

Cross sections

+ +Here are the currently available methods related to the event sample +as a whole. While continuously updated during the run, it is recommended +only to study these properties at the end of the event generation, +when the full statistics is available. + + + + + + +the total number of tried phase-space points, selected hard processes +and finally accepted events, summed over all allowed subprocesses. +The first number is only intended for a study of the phase-space selection +efficiency. The last two numbers usually only disagree if the user introduces +some veto during the event-generation process; then the former is the number +of acceptable events found by PYTHIA and the latter the number that also +were approved by the user. If you set a +second hard process there may also be a mismatch. + + + + + +the estimated cross section and its estimated error, +summed over all allowed subprocesses, in units of mb. The numbers refer to +the accepted event sample above, i.e. after any user veto. + + +

Loop counters

+ +Mainly for internal/debug purposes, a number of loop counters from +various parts of the program are stored in the Info class, +so that one can keep track of how the event generation is progressing. +This may be especially useful in the context of the +User Hooks facility. + + +the method that gives you access to the value of the various loop +counters. + the counter number you want to access: + counters that refer to the run as a whole, +i.e. are set 0 at the beginning of the run and then only can increase. + + the number of successful constructor calls for the +Pythia class (can only be 0 or 1). + + the number of times a Pythia::init(...) +call has been begun. + + the number of times a Pythia::init(...) +call has been completed successfully. + + the number of times a Pythia::next() +call has been begun. + + the number of times a Pythia::next() +call has been completed successfully. + + counters that refer to each individual event, +and are reset and updated in the top-level Pythia::next() +method. + + the number of times the selection of a new hard +process has been begun. Normally this should only happen once, unless a +user veto is set to abort the current process and try a new one. + + the number of times the selection of a new hard +process has been completed successfully. + + as 11, but additionally the process should +survive any user veto and go on to the parton- and hadron-level stages. + + as 11, but additionally the process should +survive the parton- and hadron-level stage and any user cuts. + + the number of times the loop over parton- and +hadron-level processing has begun for a hard process. Is reset each +time counter 12 above is reached. + + the number of times the above loop has successfully +completed the parton-level step. + + the number of times the above loop has successfully +completed the checks and user vetoes after the parton-level step. + + the number of times the above loop has successfully +completed the hadron-level step. + + the number of times the above loop has successfully +completed the checks and user vetoes after the hadron-level step. + + counters that refer to a local part of the +individual event, and are reset at the beginning of this part. + + the current system being processed in +PartonLevel::next(). Is almost always 1, but for double +diffraction the two diffractive systems are 1 and 2, respectively. + + the number of times the processing of the +current system (see above) has begun. + + the number of times a step has begun in the +combined MI/ISR/FSR evolution downwards in pT +for the current system. + + the number of time MI has been selected for the +downwards step above. + + the number of time ISR has been selected for the +downwards step above. + + the number of time FSR has been selected for the +downwards step above. + + the number of time MI has been accepted as the +downwards step above, after the vetoes. + + the number of time ISR has been accepted as the +downwards step above, after the vetoes. + + the number of time FSR has been accepted as the +downwards step above, after the vetoes. + + the number of times a step has begun in the +separate (optional) FSR evolution downwards in pT +for the current system. + + the number of time FSR has been selected for the +downwards step above. + + the number of time FSR has been accepted as the +downwards step above, after the vetoes. + + counters that are unused (currently), and +that therefore are free to use, with the help of the two methods below. + + + + + +set the above counters to a given value. Only to be used by you +for the unassigned counters 40 - 49. + the counter number, see above. + + set the counter to this number; +normally the default value is what you want. + + + +increase the above counters by a given amount. Only to be used by you +for the unassigned counters 40 - 49. + the counter number, see above. + + increase the counter by this amount; +normally the default value is what you want. + + + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/EventRecord.xml b/PYTHIA8/pythia8140/xmldoc/EventRecord.xml new file mode 100644 index 00000000000..6f88b31db2f --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/EventRecord.xml @@ -0,0 +1,500 @@ + + +

The Event Record

+ +A Pythia instance contains two members of the +Event class. The one called process provides +a brief summary of the main steps of the hard process, while the +one called event contains the full history. The +user would normally interact mainly with the second one, so +we will examplify primarily with that one. + +

+The Event class to first approximation is a vector of +Particles, so that it can expand to fit the current +event size. The index operator is overloaded, so that e.g. +event[i] corresponds to the i'th particle +of the object event. Thus event[i].id() +returns the identity of the i'th particle, and so on. +Therefore the methods of the +Particle class +are at least as essential as those of the Event class +itself. + +

+As used inside PYTHIA, some conventions are imposed on the structure +of the event record. Entry 0 of the vector<Particle> +is used to represent the event as a whole, with its total four-momentum +and invariant mass, but does not form part of the event history. +Lines 1 and 2 contains the two incoming beams, and only from here on +history tracing works as could be expected. That way unassigned mother +and daughter indices can be put 0 without ambiguity. Depending on the +task at hand, a loop may therefore start at index 1 rather than 0 +without any loss. Specifically, for translation to other event record +formats such as HepMC Dob01, where the first index is 1, the +Pythia entry 0 definitely ought to be skipped in order to minimize the +danger of indexing errors. + +

+In the following we will list the methods available. +Only a few of them have a function to fill in normal user code. + +

Basic output methods

+ +Some methods are available to read out information on the +current event record: + + + + +returns a (const) reference to the i'th particle +in the event record, which can be used to get (or set) all the +properties of this particle. + + + +The event size, i.e. the sie of the vector<Particle>. +Thus valid particles, to be accessed by the above indexing operator, +are stored in the range 0 <= i < size(). See comment +above about the (ir)relevance of entry 0. + + + + + + + + + +Provide a listing of the whole event, i.e. of the +vector<Particle>. The methods with fewer arguments +call the final one with the respective default values, and are +non-inlined so they can be used in a debugger. The basic identity +code, status, mother, daughter, colour, four-momentum and mass data +are always given, but the methods can also be called with a few +optional arguments for further information: + optionally give a +second line for each particle, with the production scale (in GeV), the +production vertex (in mm or mm/c) and the invariant lifetime +(also in mm/c). + + +gives a list of all daughters and mothers of a particle, as defined by +the motherList(i) and daughterList(i) methods +described below. It is mainly intended for debug purposes. + + a reference to the ostream +object to which the event listing will be directed. + + + + +

+Each Particle has two mother and two daughter indices. +These may be used to encode zero, one, two or more mothers/daughters, +depending on the combination of values and status code, according to +well-defined rules. The +two methods below can do this job easier for you. + + +returns a vector of all the mother indices of the particle at index +i. This list is empty for entries 0, 1 and 2, +i.e. the "system" in line 0 is not counted as part of the history. +Normally the list contains one or two mothers, but it can also be more, +e.g. in string fragmentation the whole fragmenting system is counted +as mothers to the primary hadrons. Many particles may have the same +motherList. Mothers are listed in ascending order. + + + +returns a vector of all the daughter indices of the particle at index +i. This list is empty for a particle that did +not decay (or, if the evolution is stopped early enough, a parton +that did not branch), while otherwise it can contain a list of +varying length, from one to many. For the two incoming beam particles, +all shower initiators and beam remnants are counted as daughters, +with the one in slot 0 being the one leading up to the hardest +interaction. The "system" in line 0 does not have any daughters, +i.e. is not counted as part of the history. Many partons may have the +same daughterList. Daughters are listed in ascending order. + + + +returns the status code according to the HepMC conventions agreed in +February 2009. This convention does not preserve the full information +provided by the internal PYTHIA status code, as obtained by +Particle::status(), but comes reasonably close. +The allowed output values are: +

    +
  • 0 : an empty entry, with no meaningful information and therefore +to be skipped unconditionally (should not occur in PYTHIA);
    • +
  • 1 : a final-state particle, i.e. a particle that is not decayed +further by the generator (may also include unstable particles that +are to be decayed later, as part of the detector simulation);
    • +
  • 2 : a decayed Standard Model hadron or tau or mu lepton, excepting +virtual intermediate states thereof (i.e. the particle must undergo +a normal decay, not e.g. a shower branching);
    • +
  • 3 : a documentation entry (not used in PYTHIA);
    • +
  • 4 : an incoming beam particle;
    • +
  • 11 - 200 : an intermediate (decayed/branched/...) particle that does +not fulfill the criteria of status code 2, with a generator-dependent +classification of its nature; in PYTHIA the absolute value of the normal +status code is used.
    • +
+ + + +

Further output methods

+ +The above methods are the main ones that a normal user would make +frequent use of. There are some further methods that also could come +in handy, in the exploration of the history of an event, but where +the outcome is not always obvious if one is not familiar with the +detailed structure of an event record. + + + + +are used to trace carbon copies of the particle at index i up +to its top mother or down to its bottom daughter. If there are no such +carbon copies, i itself will be returned. A carbon copy is +when the "same" particle appears several times in the event record, but +with changed momentum owing to recoil effects. + + + + + +also trace top mother and bottom daughter, but do not require carbon +copies, only that one can find an unbroken chain, of mothers or daughters, +with the same flavour id code. When it encounters ambiguities, +say a g -> g g branching or a u u -> u u hard scattering, +it will stop the tracing and return the current position. It can be confused +by nontrivial flavour changes, e.g. a hard process u d -> d u +by W^+- exchange will give the wrong answer. These methods +therefore are of limited use for common particles, in particular for the +gluon, but should work well for "rare" particles. + + + +returns a vector of all the sister indices of the particle at index +i, i.e. all the daughters of the first mother, except the +particle itself. + + + +returns a vector of all the sister indices of the particle at index +i, tracking up and back down through carbon copies +if required. That is, the particle is first traced up with +iTopCopy() before its mother is found, and then all +the particles in the daughterList() of this mother are +traced down with iBotCopy(), omitting the original +particle itself. Any non-final particles are removed from the list. +Should this make the list empty the search criterion is widened so that +all final daughters are allowed, not only carbon-copy ones. A second +argument false inhibits the second step, and increases +the risk that an empty list is returned. A typical example of this +is for ISR cascades, e.g. e -> e gamma where the photon +may not have any obvious sister in the final state if the bottom copy +of the photon is an electron that annihilates and thus is not part of +the final state. + + + +traces the particle i upwards through mother, grandmother, +and so on, until either iAncestor is found or the top of +the record is reached. Normally one unique mother is required, +as is the case e.g. in decay chains or in parton showers, so that +e.g. the tracing through a hard scattering would not work. For +hadronization, first-rank hadrons are identified with the respective +string endpoint quark, which may be useful e.g. for b physics, +while higher-rank hadrons give false. Currently also +ministrings that collapsed to one single hadron and junction topologies +give false. + + +

+One data member in an Event object is used to keep track +of the largest col() or acol() colour tag set +so far, so that new ones do not clash. + + +This sets the initial colour tag value used, so that the first one +assigned is startColTag + 1, etc. The Les Houches accord +Boo01 suggests this number to be 500, but 100 works equally +well. + + + +forces the current colour tag value to be the larger of the input +colTag and the above Event:startColTag +values. + + + +returns the current maximum colour tag. + + + +increases the current maximum colour tag by one and returns this +new value. This method is used whenever a new colour tag is needed. + + +

+Many event properties are accessible via the Info class, +see here. Since they are used +directly in the event generation, a few are stored directly in the +Event class, however. + + + + +set or get the scale (in GeV) of the hardest process in the event. +Matches the function of the scale variable in the +Les Houches Accord. + + + + + +set or get the scale (in GeV) of a second hard process in the event, +in those cases where such a one +has been requested. + + +

Constructors and modifications of the event record

+ +Although you would not normally need to create your own +Event instance, there may be times where that +could be convenient. The typical exampel would be if you want to +create a new event record that is the sum of a few different ones, +e.g. if you want to simulate pileup events. There may also be cases +where you want to add one or a few particles to an existing event +record. + + +creates an empty event record, but with a reserved size +capacity for the Particle vector. + + + +copies the input event record. + + + +appends an event to an existing one. For the appended particles +mother, daughter and colour tags are shifted to make a consistent +record. The zeroth particle of the appended event is not copied, +but the zeroth particle of the combined event is updated to the +full energy-momentum content. + + + +initializes colour, the pointer to the particle database, and the +header specification used for the event listing. We remind that a +Pythia object contains two event records +process and event. Thus one may e.g. +call either pythia.process.list() or +pythia.event.list(). To distinguish those two rapidly +at visual inspection, the "Pythia Event Listing" header +is printed out differently, in one case adding +"(hard process)" and in the other +"(complete event)". When += is used to +append an event, the modified event is printed with +"(combination of several events)" as a reminder. + + + +empties event record. Specifically the Particle vector +size is reset to zero. + + + +empties the event record, as clear() above, but then +fills the zero entry of the Particle vector with the +pseudoparticle used to represent the event as a whole. At this point +the pseudoparticle is not assigned any momentum or mass. + + + +removes the last n particle entries; must be a positive +number. + + + +appends a particle to the bottom of the event record and +returns the index of this position. + + + +appends a particle to the bottom of the event record and +returns the index of this position; +see here for the meaning +of the various particle properties. + + + +appends a particle to the bottom of the event record and +returns the index of this position, as above but with four-momentum +as a Vec4. + + + + + +appends a particle to the bottom of the event record and +returns the index of this position, as above but with vanishing +(i.e. zero) mother and daughter indices. + + + +send in a pointer to the ParticleData database for +particle iSet, by default the most recently appended +particle. Also generates a pointer to the +ParticleDataEntry object of the identity code +of the particle. + + + +copies the existing particle in entry iCopy to the +bottom of the event record and returns the index of this position. +By default, i.e. with newStatus = 0, everything is +copied precisely as it is, which means that history information +has to be modified further by hand to make sense. With a positive +newStatus, the new copy is set up to be the daughter of +the old, with status code newStatus, while the status +code of iCopy is negated. With a negative +newStatus, the new copy is instead set up to be the +mother of iCopy. + + + +returns a reference to the last particle in the event record. + + + +each particle in the event record has a pointer to the whole database +and another to the particle species itself, used to find some particle +properties. The latter pointer is automatically set/changed whenever +the particle identity is set/changed by one of the normal methods. +(It is the "changed" part that prompts the inclusion of a pointer +to the whole database.) Of course the pointer values are specific to +the memory locations of the current run, and so it has no sense to +save them if events are written to file. Should you use some +persistency scheme that bypasses the normal methods when the event is +read back in, you can use restorePtrs() afterwards to set +these pointers appropriately. + + +

+A few methods exist to rotate and boost events. These derive from the +Vec4 methods, and affect both the +momentum and the vertex (position) components of all particles. + + +rotate all particles in the event by this polar and azimuthal angle +(expressed in radians). + + + + + + + +boost all particles in the event by this three-vector. +Optionally you may provide the gamma value as a fourth argument, +which may help avoid roundoff errors for big boosts. You may alternatively +supply a Vec4 four-vector, in which case the boost vector +becomes beta = p/E. + + + +rotate and boost by the combined action encoded in the +RotBstMatrix M. + + +

The Junction Class

+ +The event record also contains a vector of junctions, which often +is empty or else contains only a very few per event. Methods are +available to add further junctions or query the current junction list. +This is only for the expert user, however, and is not discussed +further here, but only the main points. + +

+A junction stores the properites associated with a baryon number that +is fully resolved, i.e. where three different colour indices are +involved. There are two main applications, +

    +
  1. baryon beams, where at least two valence quarks are kicked out, +and so the motion of the baryon number is notrivial;
    2. +
  2. baryon-number violating processes, e.g. in SUSY with broken +R-parity.
    3. +
+Information on junctions is set, partly in the process generation, +partly in the beam remnants machinery, and used by the fragmentation +routines, but the normal user does not have to know the details. + +

+For each junction, information is stored on the kind of junction, and +on the three (anti)colour indices that are involved in the junction. +The possibilities foreseen are: +

    +
  • kind = 1 : incoming colourless particle to three +outgoing colours (e.g. baryon beam remnant or +neutralino -> q q q);
    • +
  • kind = 2 : incoming colourless particle to three +outgoing anticolours;
    • +
  • kind = 3 : one incoming anticolor (stored first) +and two outgoing colours (e.g. antisquark decaying to quark);
    • +
  • kind = 4 : one incoming color (stored first) and two +outgoing anticolours;
    • +
  • kind = 5 : incoming colour octet to three colours, +where the incoming colour passes through unchanged and so need not +be bokkept here, while the incoming anticolor (stored first) and the +two outgoing colours are (e.g. gluino decay to three quarks);
    • +
  • kind = 6 : incoming colour octet to three anticolours, +where the incoming anticolour passes through unchanged and so need not +be bookkept here, while the incoming color (stored first) and the two +outgoing colours are.
    • +
+The odd (even) kind codes corresponds to a +1 (-1) change in +baryon number across the junction. +Warning: Currently only kind = 1, 2 are +implemented. + +

+The kind and colour information in the list of junctions can be set +or read with methods of the Event class, but are not of +common interest and so not described here. + +

+A listing of current junctions can be obtained with the +listJunctions() method. + +

Subsystems

+ +Separate from the event record as such, but closely tied to it is the +PartonSystems class, +which mainly stores the parton indices of incoming and outgoing partons, +classified by collision subsystem. Such information is needed to +interleave multiple interactions, initial-state showers and final-state +showers, and append beam remnants. It could also be used in other places. +It is intended to be accessed only by experts, such as implementors of +new showering models. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/EventStatistics.xml b/PYTHIA8/pythia8140/xmldoc/EventStatistics.xml new file mode 100644 index 00000000000..702218fb1aa --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/EventStatistics.xml @@ -0,0 +1,118 @@ + + +

Event Statistics

+ +At the end of the run you will want to write out the final statistics +on number of events generated, the corresponding cross sections and +the number of errors encountered. This is done with the +pythia.statistics() method, assuming pythia is +an instance of the Pythia class: + + +write out statistics on cross sections and errors. This is based on +calls to the methods below, for the two kinds of information. + +if true it allows a more extensive listing than the default +one, see multiple-interactions statistics below. + + if true it implies that all counters, +e.g on events generated and errors experienced, are reset to zero whenever +the routine is called. The default instead is that all stored +statistics information is unaffected by the call. +Counters are automatically reset in each new Pythia::init() +call, however, so the only time the reset option makes a +difference is if statistics is called several times in a +(sub)run. + + + +

Cross-section statistics

+ +The ProcessLevel::statistics() method cannot be accessed +directly, but only via the Pythia::statistics() call above. +When called it will loop over the list of existing processes, and for +each write out name, code, the number of tried, selected and accepted +events, the cross section and the estimated error on the latter. +The three different event numbers are related to the Monte Carlo method +used, whereby an initial upper estimate of the cross section is used to +select a large number of trial phase-space points, whereof then not all +survive. Rejections are normally done by the internal machinery, but can +also be obtained by user hooks. +Therefore: +
    +
  • tried events reflect the original number of +phase-space points probed, as part of the upper estimate;
    • +
  • selected events correspond to those that survive +the internal Monte-Carlo selection procedure;
    • +
  • accepted events are those that also survive +the additional user cuts.
    • +
+In most runs there would be no user hooks implemented, and then the +numbers of selected and of accepted events will agree. Aborted events +(see below) usually appear in the selected statistics but not in the +accepted one. + +

+For Les Houches events the total cross section will be correctly +displayed; however the (optional) error value will not be used, so that +the reported error will be smaller than the correct statistical ones, +and often vanish completely. Furthermore, while the number of events +is shown for each user process, the cross section is only for the sum +of them. + +

Error messages

+ +When Pythia is run, errors may occur, and give rise to warning messages. +These may be of varying severity, as follows: +
    +
  • Abort means things went seriously wrong, and the +initialization or event generation failed. In the former case it is +not possible to generate events at all, in the latter the current +event is flawed and should be skipped. In either case the respective +method, Pythia::init(...) or Pythia::next(), +then also returns the value false. There are occasions +where an abort may be deliberate, such as when a file of Les Houches +Events is read and the end of the file is reached.
    • +
  • Error normally is less severe. Typically the program will +back up one step and try again. There are cases where this is not possible, +in particular during the initialization and the generation of a hard +process, and then the error may be followed by an abort as a direct +consequence (with two separate messages).
    • +
  • Warning is even less severe. In some cases the program will +try again, with good chances of success, in others no measure at all +need to be taken.
    • +
+ +

+The error messages is handled by a small part of the Info +class. It is handed any abort, error or warning messages during the event +generation phase, and will store each distinct message, with a counter +for how many times it is issued. Thus it is possible to limit the number +of identical messages issued, currently hardcoded so that each kind of +error message is only printed once +(static const int TIMESTOPRINT = 1). +This can be overridden by the calling routine, so that all messages of +this kind are shown, which is particularly relevant for the +initialization stage. +The summary table printed by Pythia::statistics() +provides a table with all the different messages issued, in +alphabetical order, with the total number of times each was generated. + +

Multiple-interactions statistics

+ +If you call Pythia::statistics(true), i.e. with the first +optional argument true, also statistics on multiple +interactions is printed, comprising a list of all allowed subprocesses +with how many times each of them has been generated. For the minimum-bias +process this also includes the hardest interaction, while else the +hardest process is excluded from the statistics. (This is because +the hardest process is of the same character and generated by the same +machinery in the former case but not in the latter. Also, for the +former case only, the standard statistics listing only lists +minimum bias as one single process, i.e. does not further specify +the character of the hardest subprocess, so there is not any overlap +between the two.) + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ExternalDecays.xml b/PYTHIA8/pythia8140/xmldoc/ExternalDecays.xml new file mode 100644 index 00000000000..de1331f111c --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ExternalDecays.xml @@ -0,0 +1,72 @@ + + +

External Decays

+ +DecayHandler is a base class for the external handling of +decays. It is intended for normal particle decays, primarily +B mesons and tau, and cannot be used to redirect +decays of heavy resonances like t or Z^0. +The user-written derived class is called if a pointer to it has +been given with the +pythia.decayPtr() +method, where it also is specified which particles it will be called for. +This particle information is accessible with the +doExternalDecay() +method. + +

+There is only one pure virtual method in DecayHandler, +to do the decay: + +where + is a list of particle PDG identity codes, + + is a list of their respective masses (in GeV), and + + is a list of their respective four-momenta. + + + +

+At input, these vectors each have size one, so that idProd[0], +mProd[0] and pProd[0] contain information on the +particle that is to be decayed. At output, the vectors should have +increased by the addition of all the decay products. Even if initially +defined in the rest frame of the mother, the products should have been +boosted so that their four-momenta add up to the pProd[0] of +the decaying particle. + +

+Should it be of interest to know the prehistory of the decaying +particle, e.g. to set some helicity information affecting the +decay angular distribution, the full event record is available +read-only, with info in which slot iDec the decaying particle +is stored. + +

+The routine should return true if it managed the decay and +false otherwise, in which case Pythia will try +to do the decay itself. This e.g. means you can choose to do some decay +channels yourself, and leave others to Pythia. To avoid +doublecounting, the channels you want to handle should be switched off +in the Pythia particle database. In the beginning of the +external decay method you should then return +false with a probability given by the sum of the branching +ratios for those channels you do not want to handle yourself. + +

+Note that the decay vertex is always set by Pythia, and that +B-Bbar oscillations have already been taken into account, +if they were switched on. Thus idProd[0] may be the opposite +of event[iDec].id(), where the latter provides the code at +production. + +

+A sample test program is available in main23.cc, providing +a simple example of how to use this facility. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ExtraDimensionalProcesses.xml b/PYTHIA8/pythia8140/xmldoc/ExtraDimensionalProcesses.xml new file mode 100644 index 00000000000..7de41912afd --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ExtraDimensionalProcesses.xml @@ -0,0 +1,445 @@ + + +

Extra-Dimensional Processes

+ +Scenarios with extra dimensions (ED) allow a multitude of processes. +Currently three different categories of processes are implemented. +The first involves the production of excited Kaluza Klein states +within so-called Randall-Sundrum (RS) scenarios, the second is +related to resonance production in TeV-1 sized extra dimensions +and the third relates to phenomena from large extra dimensions (LED). +Due to the close relation between the LED model and a so-called +unparticle model, similar unparticle processes are also kept in this +section. + +

Randall-Sundrum Resonances, production processes

+ +The graviton (G*) and gluon (KKgluon*) resonance states are assigned +PDG code 5100039 and 5100021 respectively. Decays into fermion, gluon +and photon pairs are handled with the correct angular distributions, +while other decay channels currently are handled isotropically. + +

+Warning: The possible decays of a graviton into scalars +(i.e. Higgs and longitudinal Z/W) is currently not implemented and +in some scenarios, where for example the SM is allowed to propagate +in the ED bulk, these decay modes can be significant. + +

+There are two lowest-order processes that together normally +should be sufficient for a simulation of G^* production. + + +Common switch for the group of lowest-order G^* production +processes, i.e. the two ones below. + + + +Scatterings g g -> G^*. +Code 5001. + + + +Scatterings f fbar -> G^*. +Code 5002. + + +

+In addition there are three first-order processes included. These +are of less interest, but can be used for dedicated studies of the +high-pT tail of G^* production. As usual, it would +be double counting to include the lowest-order and first-order +processes simultaneously. Therefore the latter ones are not included +with the ExtraDimensionsG*:all = on option. In this set +of processes all decay angles are assumed isotropic. + + +Scatterings g g -> G^* g. +Code 5003. + + + +Scatterings q g -> G^* q. +Code 5004. + + + +Scatterings q qbar -> G^* g. +Code 5005. + + +

+Currently there is one process for the production of a gluon resonance. + + +Scatterings q qbar -> KKgluon^*. +Code 5006. + + +

Randall-Sundrum Resonances, parameters

+ +In the above scenario the main free parameters are the masses, which +are set as usual. In addition there are the following coupling parameters. +The coupling kappaMG follows the conventions in Bij01, +where as the flavour dependent couplings follow the conventions used in +Dav01. + + +Parameter to choose between the two scenarios: +off, SM on the TeV brane (common kappaMG coupling); +on, SM in the ED bulk (flavour dependent couplings). +At the moment this parameter is only relevant for the lowest-order +graviton (G*) resonance. + + + +dimensionless coupling, which enters quadratically in all partial +widths of the G^*. Is +kappa m_G* = sqrt(2) x_1 k / Mbar_Pl, +where x_1 = 3.83 is the first zero of the J_1 Bessel +function and Mbar_Pl is the modified Planck mass. + + + +Coupling between graviton and leptons. + + + +Coupling between graviton and light quarks. + + + +Coupling between graviton and bottom quark. + + + +Coupling between graviton and top quark. + + + +Coupling between graviton and vector bosons. + + + +Coupling between KK gluon and light quarks. + + + +Coupling between KK gluon and bottom quarks. + + + +Coupling between KK gluon and top quarks. + + +

TeV^-1 Sized Extra Dimension, production processes

+ +This section contains a processes involving the production +of electroweak KK gauge bosons, i.e. gamma_{KK}/Z_{KK}, +in one TeV^-1 sized extra dimension. This scenario is described +in Bel10. + + +Scatterings f fbar -> (gamma_{KK}/Z_{KK}) -> f fbar , +Code 5011. + + +

TeV^-1 Sized Extra Dimension, parameters

+ +Irrespective of the parameter options used, the particle produced, +gamma_{KK}/Z_{KK}, will always be assigned code 5000023 +and open decay channels is purely dictated by what is set for the +Z^0. + + +Choice of full gamma_{KK}/Z_{KK} structure or not in relevant +processes. + + + + + + + + + +The number of included KK excitations. + + + +The KK mass m^*, given by the inverse of the single extra +dimension radius. + + +

Large Extra Dimensions, production processes

+ +The LED graviton, where the KK-modes normally are summed and do not +give rise to phenomena individually, is assigned PDG code 5000039. +The graviton emission and virtual graviton exchange processes uses +the same implementation as the corresponding unparticle processes, +which are all described in Ask10. It is also possible to +generate monojet events from scalar graviton emission as described +in Azu05, by turning on the option GravScalar. + +

+Note: As discussed in Ask09, for the graviton or +unparticle emission processes the underlying Breit-Wigner mass +distribution should be matched to the graviton mass spectrum in order +to achieve an optimal MC efficiency. + +

+The following lowest order graviton emission processes are available. + + +Common switch for the group of lowest-order G jet emission +processes, i.e. the three ones below. + + + +Scatterings g g -> G g. +Code 5021. + + + +Scatterings q g -> G q. +Code 5022. + + + +Scatterings q qbar -> G g. +Code 5023. + + + +Scatterings f fbar -> G Z. +Code 5024. + + + +Scatterings f fbar -> G gamma. This process corresponds +to the photon limit of the G Z process, as described in +Ask09. +Code 5025. + + +

+The following LED processes with virtual graviton exchange are +available. + + +Scatterings f fbar -> (LED G*) -> gamma gamma. If the +graviton contribution is zero, the results corresponds to the +SM contribution, i.e. equivalent to +PromptPhoton:ffbar2gammagamma. +Code 5026. + + + +Scatterings g g -> (LED G*) -> gamma gamma. +Code 5027. + + + +Scatterings f fbar -> (LED G*) -> l l , where +l is a charged lepton. If the graviton contribution +is zero, the results corresponds to the SM contribution, i.e. +similar to WeakSingleBoson:ffbar2gmZ. Does not +include t-channel amplitude relevant for e^+e^- to e^+e^- +and no K-factor is used. +Code 5028. + + + +Scatterings g g -> (LED G*) -> l l. +Code 5029. + + +

Large Extra Dimensions, parameters

+ + +Allow the monojet processes to produce scalar graviton emission +instead of the default tensor one. The scalar option is according +to the processes described in Azu05 and includes two +coupling constants below. + + + +Number of extra dimensions. + + + +Fundamental scale of gravity in D = 4 + n dimensions. + + + +Ultraviolet cutoff parameter for the virtual graviton exchange processes. + + + +Options for when the hard scale of the process (e.g. sHat) +approaches or exceed the scale of validity of the low energy effective +theory (e.g. M_D). Note: Option 1 only concerns the +graviton emission processes and the form factor is currently not available +for the scalar graviton processes. + + + + + + + +Form factor parameter. + + + +Coupling related to scalar graviton emission. + + + +Coupling related to scalar graviton emission. + + +

Unparticles, production processes

+ +As mentioned above, the similar unparticle and graviton processes +share the same implementations. The unparticle processes, however, +only uses the dedicated unparticle parameters below. The unparticle +is also assigned the PDG code 5000039 and is therefore called +Graviton in the event record. The graviton and unparticle +emission as well as virtual graviton and unparticle exchange processes +are described in Ask10. + +

+Note: As discussed in Ask09, for the graviton or +unparticle emission processes the underlying Breit-Wigner mass +distribution should be matched to the graviton mass spectrum in order +to achieve an optimal MC efficiency. + +

+The following unparticle emission processes are available. + + +Common switch for the group of lowest-order U jet emission +processes, i.e. the three ones below. + + + +Scatterings g g -> U g. +Code 5045. + + + +Scatterings q g -> U q. +Code 5046. + + + +Scatterings q qbar -> U g. +Code 5047. + + + +Scatterings f fbar -> U Z. +Code 5041. + + + +Scatterings f fbar -> U gamma. This process corresponds +to the photon limit of the U Z process, as described in +Ask09. +Code 5042. + + +

+The following processes with virtual unparticle exchange are available. + + +Scatterings f fbar -> (U*) -> gamma gamma. If the unparticle +contribution is zero in the spin-2 case, the results corresponds to +the SM contribution, i.e. equivalent to +PromptPhoton:ffbar2gammagamma. +Code 5043. + + + +Scatterings g g -> (U*) -> gamma gamma. +Code 5044. + + + +Scatterings f fbar -> (U*) -> l lbar , where +l is a charged lepton. If the unparticle contribution +is zero, the results corresponds to the SM contribution, i.e. +similar to WeakSingleBoson:ffbar2gmZ. Does not +include t-channel amplitude relevant for e^+e^- to e^+e^- +and no K-factor is used. +Code 5048. + + + +Scatterings g g -> (U*) -> l lbar. +Code 5049. + + +

Unparticles, parameters

+ + +Unparticle spin. + + + +Scale dimension parameter. + + + +Unparticle renormalization scale. + + + +Unparticle coupling to the SM fields. + + + +Ratio, lambda'/lambda, between the two possible coupling constants +of the spin-2 ME. Warning: A ratio value different from one +give rise to an IR divergence which makes the event generation very slow, so +this values is fixed to ratio = 1 for the moment. + + + +Options for when the hard scale of the process (e.g. sHat) +approaches or exceed the scale of validity of the low energy effective +theory (Lambda_U). This mode only concerns the unparticle +emission processes. + + + + + +Chiral unparticle couplings, gXX = gLL = gRR. Only relevant +for lepton production from spin-1 unparticle exchange. + + + + + + +Chiral unparticle couplings, gXY = gLR = gRL. Only relevant +for lepton production from spin-1 unparticle exchange. + + + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/FlavourSelection.xml b/PYTHIA8/pythia8140/xmldoc/FlavourSelection.xml new file mode 100644 index 00000000000..7b7c3e3d107 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/FlavourSelection.xml @@ -0,0 +1,356 @@ + + +

Flavour Selection

+ +The StringFlav class handles the choice of a new flavour +in the fragmentation process, and the production of a new hadron +from a set of input flavours. It is mainly used by the string +fragmentation machinery (including ministrings), but also e.g. +in some particle decays and for some beam-remnant cases. The basic +concepts are in agreement with And83. The baryon-sector +implementation is based on the MSTJ(12)=3 option of +PYTHIA 6, i.e. new SU(6) weights scheme with at most one popcorn meson. + +

+The relative production rates of different particle species is +influenced by the parameters below. Some have only an impact on +one specific quantity, but most directly or indirectly have +consequences for many observables. Therefore the values to use have +to be viewed in the context of a complete tune. + +

New flavours

+ +The main parameters of the selection of a new flavour are + + +the suppression of s quark production relative to ordinary +u or d one. + + + +the suppression of diquark production relative to quark production, +i.e. of baryon relative to meson production. + + + +the suppression of strange diquark production relative to light +diquark production, over and above the one already given by +probStoU. + + + +the suppression of spin 1 diquark production relative to spin 0 one, +apart from the factor of 3 enhancement of spin 0 from counting the +number of states. + + +

Standard-meson production

+ +The bulk of the particle production corresponds to the lowest-lying +pseudoscalar and vector multiplets. Their production rates are +determined by the parameters in this section. + +

+For a given set of flavours, produced according to the probabilities +outlined above, the ratio of vector-to-pseudocalar meson production +is described by the parameters below. +The maximum allowed rate for each case has been set according to +spin-counting rules, but we expect the real rates to be lower, +especially for lighter mesons, owing to the vector-pseudoscalar +mass splitting. + + +the relative production ratio vector/pseudoscalar for light +(u, d) mesons. + + +the relative production ratio vector/pseudoscalar for strange mesons. + + +the relative production ratio vector/pseudoscalar for charm mesons. + + +the relative production ratio vector/pseudoscalar for bottom mesons. + + +

+Inside each light-quark meson nonet, an octet-singlet mixing angle +describes the mixing of the two flavour-diagonal isoscalar = 0 states. +(For terminology and details see Yao06, chapter 14 on the +quark model.) +This angle is needed to specify the probability for such a q qbar +state to project onto a specific meson. More transparent formuale are +obtained by introducing the angle alpha = theta + 54.7 degrees: + + f = (uubar + ddbar)/sqrt(2) * sin(alpha) + ssbar * cos(alpha)
+ f' = (uubar + ddbar)/sqrt(2) * cos(alpha) - ssbar * sin(alpha) + + + +gives the mixing angle theta_PS in the pseudoscalar meson sector +(which is rather poorly determined), expressed in degrees. +Here f is associated with eta' and f' with +eta. (This standard but counterintuitive choice is fixed up +in the code by replacing alpha -> 90^0 - alpha so that +eta <-> eta'; relative signs do not matter since we are +interested in probabilities only.) + + + +gives the mixing angle theta_V in the vector meson sector +(which is somewhat better determined), expressed in degrees. +Here f is associated with omega and f' +with phi. + + +

+Further, the simple model overestimates the production of eta +and, in particular, eta' mesons, which can be rectified by + + +the additional suppression of eta production, multiplying the +normal production probability. Thus 0 means no eta at all +are produced, while 1 means full rate. + + + +the additional suppression of eta' production, multiplying the +normal production probability. Thus 0 means no eta' at all +are produced, while 1 means full rate. + + +

Excited-meson production

+ +Several excited mesons, ie. with radial or orbital excitations, have been +observed at non-negligible production rates. Extrapolated to all states +a fair fraction of all particle production might proceed through such +states. There are big uncertainties, however, since these excited +mesons in many cases are extremely poorly known. This also means that +the modelling of their production and decay is very primitive, and +even that the inclusion of the production of such states may lead to a +degraded agreement with data. Currently the default is that all such +production is switched off. + +

+Parameters are provided to switch them on. By demand, this machinery +has been made more flexible than in the past. Therefore one parameter is +provided for each combination of heaviest flavour +(u/d, s, c or b) and +multiplet produced. In each case the production rate is normalized to +that of the lowest-lying pseudoscalar of the same flavour content, as for +the vector-meson rates introduced above. The multiplets available are the +four obtained for one unit of orbital angular momentum, in the +nonrelativistic classification. Using J to denote the sum of +quark spin S and orbital angular momentum L, i.e. what +would normally be called the spin of the meson, one has: +

    +
  • a pseudovector multiplet with L=1, S=0, J=1;
    • +
  • a scalar multiplet with L=1, S=1, J=0;
    • +
  • a pseudovector multiplet with L=1, S=1, J=1;
    • +
  • a tensor multiplet with L=1, S=1, J=2.
    • +
+ +The maximum allowed rate for each case has been set according to +spin-counting rules, but we expect the real rates to be significantly +lower, owing to mass suppression. + + +the relative pseudovector production ratio +(L=1,S=0,J=1)/pseudoscalar +for light (u, d) mesons. + + + +the relative scalar production ratio +(L=1,S=1,J=0)/pseudoscalar +for light (u, d) mesons. + + + +the relative pseudovector production ratio +(L=1,S=1,J=1)/pseudoscalar +for light (u, d) mesons. + + + +the relative tensor production ratio +(L=1,S=1,J=2)/pseudoscalar +for light (u, d) mesons. + + + +the relative pseudovector production ratio +(L=1,S=0,J=1)/pseudoscalar +for strange mesons. + + + +the relative scalar production ratio +(L=1,S=1,J=0)/pseudoscalar +for strange mesons. + + + +the relative pseudovector production ratio +(L=1,S=1,J=1)/pseudoscalar +for strange mesons. + + + +the relative tensor production ratio +(L=1,S=1,J=2)/pseudoscalar +for strange mesons. + + + +the relative pseudovector production ratio +(L=1,S=0,J=1)/pseudoscalar +for charm mesons. + + + +the relative scalar production ratio +(L=1,S=1,J=0)/pseudoscalar +for charm mesons. + + + +the relative pseudovector production ratio +(L=1,S=1,J=1)/pseudoscalar +for charm mesons. + + + +the relative tensor production ratio +(L=1,S=1,J=2)/pseudoscalar +for charm mesons. + + + +the relative pseudovector production ratio +(L=1,S=0,J=1)/pseudoscalar +for bottom mesons. + + + +the relative scalar production ratio +(L=1,S=1,J=0)/pseudoscalar +for bottom mesons. + + + +the relative pseudovector production ratio +(L=1,S=1,J=1)/pseudoscalar +for bottom mesons. + + + +the relative tensor production ratio +(L=1,S=1,J=2)/pseudoscalar +for bottom mesons. + + +

+In addition, an octet-singlet mixing angle is needed for each multiplet, +as for the pseudoscalar and vector multiplets above. Only for the +tensor multiplet does any determination exist; for the other multiplets +default has been chose so that ssbar does not mix with the light +quarks, and so that the ssbar state is the heavier of the two. + + +gives the mixing angle theta in the (L=1,S=0,J=1) +pseudovector meson sector, expressed in degrees. + + + +gives the mixing angle theta in the (L=1,S=1,J=0) +scalar meson sector, expressed in degrees. + + + +gives the mixing angle theta in the (L=1,S=1,J=1) +pseudovector meson sector, expressed in degrees. + + + +gives the mixing angle theta in the (L=1,S=1,J=2) +tensor meson sector, expressed in degrees. + + +

Baryon production

+ +The relative rate of baryon production is mainly given by the quark +and diquark production parameters above, plus SU(6) Clebsch-Gordans. +The one modifiable parameter related to these coefficients is + + +the suppression, relative to default SU(6) factors, of decuplet +baryon production. Default corresponds to no suppression, while 0 +corresponds to no decuplet production at all. + + +

+In addition, if popcorn production is allowed, wherein a set of mesons +(M) may be producted in between the baryon (B) and +the antibaryon (Bbar), a set of further parameters is introduced. +Currently only the simplest scenario is implemented, wherein at most +one intermediate meson may be produced. + + +gives the relative rates of B Bbar and B M Bbar +production, roughly as + +Prob(B M Bbar) / (Prob(B Bbar) + Prob(B M Bbar)) = +popcornRate / (0.5 + popcornRate) + +(the complete expression depends on all the quark and diquark production +parameters and is therefore not so useful). + + + +extra suppression for having an s sbar pair shared between +the B and Bbar in a B M Bbar configuration. + + + +extra suppression for having a strange meson M in a +B M Bbar configuration. + + +

+Finally, there are some indications that leading-baryon production +may be further suppressed. A proper description should probably be +based on a suppression of early production times Ede97, +but we here only implement a simpler version where production near +the end of a string, as defined by rank, is suppressed. The more +detailed studies suggest that leading c and b baryon +production will be less suppressed, so we leave it open to set +light- and heavy-baryon suppression separately. + + +Suppress leading-baryon production. + + + + + +extra suppression of leading-baryon production for a light-quark +jet, i.e. d, u or s, when +suppressLeadingB = on. Thus 0 means no leading-baryon +production at all, while 1 means full rate. + + + +extra suppression of leading-baryon production for a heavy-quark +jet, i.e. c or b, when +suppressLeadingB = on. Thus 0 means no leading-baryon +production at all, while 1 means full rate. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/FourVectors.xml b/PYTHIA8/pythia8140/xmldoc/FourVectors.xml new file mode 100644 index 00000000000..6ddc6e185e6 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/FourVectors.xml @@ -0,0 +1,418 @@ + + +

Four-Vectors

+ +The Vec4 class gives a simple implementation of four-vectors. +The member function names are based on the assumption that these +represent four-momentum vectors. Thus one can get or set +p_x, p_y, p_z and e, but not x, y, z +or t. This is only a matter of naming, however; a +Vec4 can equally well be used to store a space-time +four-vector. + +

+The Particle object contains a Vec4 p that +stores the particle four-momentum, and another Vec4 vProd +for the production vertex. For the latter the input/output method +names are adapted to the space-time character rather than the normal +energy-momentum one. Thus a user would not normally access the +Vec4 classes directly, but only via the methods of the +Particle class, +see Particle Properties. + +

+Nevertheless you are free to use the PYTHIA four-vectors, e.g. as +part of some simple analysis code based directly on the PYTHIA output, +say to define the four-vector sum of a set of particles. But note that +this class was never set up to allow complete generality, only to +provide the operations that are of use inside PYTHIA. There is no +separate class for three-vectors, since such can easily be represented +by four-vectors where the fourth component is not used. + +

+Four-vectors have the expected functionality: they can be created, +copied, added, multiplied, rotated, boosted, and manipulated in other +ways. Operator overloading is implemented where reasonable. Properties +can be read out, not only the components themselves but also for derived +quantities such as absolute momentum and direction angles. + +

Constructors and basic operators

+ +A few methods are available to create or copy a four-vector: + + +creates a four-vector with all components set to 0. + + + +creates a four-vector copy of the input four-vector. + + + +copies the input four-vector. + + + +gives a four-vector with all components set to value. + + +

Member methods for input

+ +The values stored in a four-vector can be modified in a few different +ways: + + +sets all components to 0. + + + +sets all components to their input values. + + + +sets all components equal to those of the input four-vector. + + + + + + + + + +sets the respective component to the input value. + + +

Member methods for output

+ +A number of methods provides output of basic or derived quantities: + + + + + + + + +gets the respective component. + + + + + +the (squared) mass, calculated from the four-vectors. +If m^2 < 0 the mass is given with a minus sign, +-sqrt(-m^2). Note the possible loss of precision +in the calculation of E^2 - p^2; for particles the +correct mass is stored separately to avoid such problems. + + + + + +the (squared) transverse momentum. + + + + + +the (squared) absolute momentum. + + + + + +the (squared) transverse energy, +eT = e * sin(theta) = e * pT / pAbs. + + + +the polar angle, in the range 0 through +pi. + + + +the azimuthal angle, in the range -pi through pi. + + + +the angle in the xz plane, in the range -pi through +pi, with 0 along the +z axis. + + + + + +the combinations E+-p_z. + +

Friend methods for output

+ +There are also some friend methods that take one, two +or three four-vectors as argument. Several of them only use the +three-vector part of the four-vector. + + +writes out the values of the four components of a Vec4 and, +within brackets, a fifth component being the invariant length of the +four-vector, as provided by mCalc() above, and it all +ended with a newline. + + + + + +the (squared) invariant mass. + + + +the three-product. + + + +the cross-product. + + + + + +the (cosine) of the opening angle between the vectors, +in the range 0 through pi. + + + + + +the (cosine) of the azimuthal angle between the vectors around the +z axis, in the range 0 through pi. + + + + + +the (cosine) of the azimuthal angle between the first two vectors +around the direction of the third, in the range 0 through pi. + + +

Operations with four-vectors

+ +Of course one should be able to add, subtract and scale four-vectors, +and more: + + +return a vector with flipped sign for all components, while leaving +the original vector unchanged. + + + +add a four-vector to an existing one. + + + +subtract a four-vector from an existing one. + + + +multiply all four-vector components by a real number. + + + +divide all four-vector components by a real number. + + + +add two four-vectors. + + + +subtract two four-vectors. + + + + + +multiply a four-vector by a real number. + + + +divide a four-vector by a real number. + + + +four-vector product. + + +

+There are also a few related operations that are normal member methods: + + +multiply the three-vector components by f, but keep the +fourth component unchanged. + + + +multiply all four-vector components by f. + + + +flip the sign of the three-vector components, but keep the +fourth component unchanged. + + + +flip the sign of all four-vector components. + + +

Rotations and boosts

+ +A common task is to rotate or boost four-vectors. In case only one +four-vector is affected the operation may be performed directly on it. +However, in case many particles are affected, the helper class +RotBstMatrix can be used to speed up operations. + + +rotate the three-momentum with the polar angle theta +and the azimuthal angle phi. + + + +rotate the three-momentum with the azimuthal angle phi +around the direction defined by the (n_x, n_y, n_z) +three-vector. + + + +rotate the three-momentum with the azimuthal angle phi +around the direction defined by the three-vector part of n. + + + +boost the four-momentum by beta = (beta_x, beta_y, beta_z). + + + +boost the four-momentum by beta = (beta_x, beta_y, beta_z), +where the gamma = 1/sqrt(1 - beta^2) is also input to allow +better precision when beta is close to unity. + + + +boost the four-momentum by beta = (p_x/E, p_y/E, p_z/E). + + + +boost the four-momentum by beta = (p_x/E, p_y/E, p_z/E), +where the gamma = E/m is also calculated from input to allow +better precision when beta is close to unity. + + + +boost the four-momentum by beta = (-p_x/E, -p_y/E, -p_z/E). + + + +boost the four-momentum by beta = (-p_x/E, -p_y/E, -p_z/E), +where the gamma = E/m is also calculated from input to allow +better precision when beta is close to unity. + + + +perform a combined rotation and boost; see below for a description +of the RotBstMatrix. + + +

+For a longer sequence of rotations and boosts, and where several +Vec4 are to be rotated and boosted in the same way, +a more efficient approach is to define a RotBstMatrix, +which forms a separate auxiliary class. You can build up this +4-by-4 matrix by successive calls to the methods of the class, +such that the matrix encodes the full sequence of operations. +The order in which you do these calls must agree with the imagined +order in which the rotations/boosts should be applied to a +four-momentum, since in general the operations do not commute. + + +creates a diagonal unit matrix, i.e. one that leaves a four-vector +unchanged. + + + +creates a copy of the input matrix. + + + +copies the input matrix. + + + +rotate by this polar and azimuthal angle. + + + +rotate so that a vector originally along the +z axis becomes +parallel with p. More specifically, rotate by -phi, +theta and phi, with angles defined by p. + + + +boost by this beta vector. + + + + + +boost with a beta = p/E or beta = -p/E, respectively. + + + +boost so that p_1 is transformed to p_2. It is assumed +that the two vectors obey p_1^2 = p_2^2. + + + +boost and rotate to the rest frame of p_1 and p_2, +with p_1 along the +z axis. + + + +rotate and boost from the rest frame of p_1 and p_2, +with p_1 along the +z axis, to the actual frame of +p_1 and p_2, i.e. the inverse of the above. + + + +combine the current matrix with another one. + + + +invert the matrix, which corresponds to an opposite sequence and sign +of rotations and boosts. + + + +reset to no rotation/boost; i.e. the default at creation. + + + +crude estimate how much a matrix deviates from the unit matrix: +the sum of the absolute values of all non-diagonal matrix elements +plus the sum of the absolute deviation of the diagonal matrix +elements from unity. + + + +writes out the values of the sixteen components of a +RotBstMatrix, on four consecutive lines and +ended with a newline. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/FourthGenerationProcesses.xml b/PYTHIA8/pythia8140/xmldoc/FourthGenerationProcesses.xml new file mode 100644 index 00000000000..5f4bcee67d0 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/FourthGenerationProcesses.xml @@ -0,0 +1,175 @@ + + +

Fourth-Generation Processes

+ +A fourth generation can be accommodated within the Standard Model, +without the introduction of any new concepts. Many experimental +constraints exist, but it has not been fully excluded. Therefore +we offer a simple implementation, along the lines of the top. +It could also be useful as a template for studies of other +new particles with similar characteristics. + +

+The fourth generation are given names as in the third, but with a prime, +i.e. b' with PDG code 7, t' with code 8, +tau' with code 17, and nu'_tau with code 18. +Most important for you is to assign a mass hierarchy, to decide which +fermions can decay into which. The current implementation assumes that +mass splittings are big enough that fourth-generation fermions can +decay to third-generation ones by the emission of an on-shell W. +To this end, the standard three-generation CKM mixing matrix has been +extended to include a fourth generation, see below. Since no mixing has +been implemented in the neutrino sector it would be assumed that the +lighter of tau' and nu'_tau is stable. No decay modes +have been implemented that go beyond the Standard Model, so +modifications would be needed if e.g. also SUSY is included in the game. + +

Production processes

+ +

1) b' processes

+ +Different ways to produce b' quarks, singly or in pairs. +For a b' t' pair see section 3 below. + + +Common switch for the group of b' production. +Also includes the process f fbar' -> t' b'bar in section 3 below. + + + +Scatterings g g -> b' b'bar. +Code 801. + + + +Scatterings q qbar -> b' b'bar by gluon exchange. +Code 802. + + + +Scatterings q q' -> b' q'' by t-channel exchange +of a W^+- boson. +Code 803. + + + +Scatterings f fbar -> b' b'bar by s-channel exchange +of a gamma^*/Z^0 boson. +Code 804. + + + +Scatterings f fbar' -> b' qbar'' by s-channel exchange +of a W^+- boson. Here q'' is either u or +c. +Code 805. + + + +Scatterings f fbar' -> b' tbar by s-channel exchange +of a W^+- boson. +Code 806. + + +

2) t' processes

+ +Different ways to produce t' quarks, singly or in pairs. +For a b' t' pair see section 3 below. + + +Common switch for the group of t' production. +Also includes the process f fbar' -> t' b'bar in section 3 below. + + + +Scatterings g g -> t' t'bar. +Code 821. + + + +Scatterings q qbar -> t' t'bar by gluon exchange. +Code 822. + + + +Scatterings q q' -> t' q'' by t-channel exchange +of a W^+- boson. +Code 823. + + + +Scatterings f fbar -> t' t'bar by s-channel exchange +of a gamma^*/Z^0 boson. +Code 824. + + + +Scatterings f fbar' -> t' qbar'' by s-channel exchange +of a W^+- boson. +Code 825. + + +

3) Pair-processes with different flavours

+ +Different ways to produce two different fourth-generation fermions. + + +Scatterings f fbar' -> t' b'bar by s-channel exchange +of a W^+- boson. +Code 841. + + + +Scatterings f fbar' -> tau' nu'_taubar by s-channel +exchange of a W^+- boson. +Code 842. + + +

+Missing in this list is scatterings q q' -> t' b' by +t-channel exchange of a W^+- boson, since currently +the matrix element for such processes have not been implemented for +two massive particles in the final state. Since this process would +involve two CKM-suppressed vertices it ought to be small. + +

Parameters

+ +The Cabibbo-Kobayashi-Maskawa matrix is extended by seven further values. +So as not to mess up the Standard Model, the normal 3 * 3 matrix is +kept unitary, and so the new off-diagonal elements lead to a slight +breaking of this. For exploratory studies this should be good enough; +more detailed 4 * 4 tunes to data would only make sense the day there +are evidence for the existence of a fourth generation. + + +The V_ub' matrix element in the 4 * 4 CKM matrix. + + + +The V_cb' matrix element in the 4 * 4 CKM matrix. + + + +The V_tb' matrix element in the 4 * 4 CKM matrix. + + + +The V_t'd matrix element in the 4 * 4 CKM matrix. + + + +The V_t's matrix element in the 4 * 4 CKM matrix. + + + +The V_t'b matrix element in the 4 * 4 CKM matrix. + + + +The V_t'b' matrix element in the 4 * 4 CKM matrix. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Fragmentation.xml b/PYTHIA8/pythia8140/xmldoc/Fragmentation.xml new file mode 100644 index 00000000000..1df79077a5f --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Fragmentation.xml @@ -0,0 +1,310 @@ + + +

Fragmentation

+ +Fragmentation in PYTHIA is based on the Lund string model +And83, Sjo84. Several different aspects are involved in +the physics description, which here therefore is split accordingly. +This also, at least partly, reflect the set of classes involved in +the fragmentation machinery. + +

+The variables collected here have a very wide span of usefulness. +Some would be central in any hadronization tuning exercise, others +should not be touched except by experts. + +

+The fragmentation flavour-choice machinery is also used in a few +other places of the program, notably particle decays, and is thus +described on the separate Flavour +Selection page. + +

Fragmentation functions

+ +The StringZ class handles the choice of longitudinal +lightcone fraction z according to one of two possible +shape sets. + +

+The Lund symmetric fragmentation function And83 is the +only alternative for light quarks. It is of the form + + f(z) = (1/z) * (1-z)^a * exp(-b m_T^2 / z) + +with the two main free parameters a and b to be +tuned to data. They are stored in + + +The a parameter of the Lund symmetric fragmentation function. + + + +The b parameter of the Lund symmetric fragmentation function. + + +

+In principle, each flavour can have a different a. Then, +for going from an old flavour i to a new j one +the shape is + + f(z) = (1/z) * z^{a_i} * ((1-z)/z)^{a_j} * exp(-b * m_T^2 / z) + +This is only implemented for diquarks relative to normal quarks: + + +allows a larger a for diquarks, with total +a = aLund + aExtraDiquark. + + +

+Finally, the Bowler modification Bow81 introduces an extra +factor + + 1/z^{r_Q * b * m_Q^2} + +for heavy quarks. To keep some flexibility, a multiplicative factor +r_Q is introduced, which ought to be unity (provided that +quark masses were uniquely defined) but can be set in + + +r_c, i.e. the above parameter for c quarks. + + + +r_b, i.e. the above parameter for b quarks. + + + +r_h, i.e. the above parameter for heavier hypothetical quarks, +or in general any new coloured particle long-lived enough to hadronize. + + +

+As an alternative, it is possible to switch over to the +Peterson/SLAC formula Pet83 + + f(z) = 1 / ( z * (1 - 1/z - epsilon/(1-z))^2 ) + +for charm, bottom and heavier (defined as above) by the three flags + + +use Peterson for c quarks. + + + +use Peterson for b quarks. + + + +use Peterson for hypothetical heavier quarks. + + +

+When switched on, the corresponding epsilon values are chosen to be + + +epsilon_c, i.e. the above parameter for c quarks. + + + +epsilon_b, i.e. the above parameter for b quarks. + + + +epsilon_h, i.e. the above parameter for hypothetical heavier +quarks, normalized to the case where m_h = m_b. The actually +used parameter is then epsilon = epsilon_h * (m_b^2 / m_h^2). +This allows a sensible scaling to a particle with an unknown higher +mass without the need for a user intervention. + + +

Fragmentation pT

+ +The StringPT class handles the choice of fragmentation +pT. At each string breaking the quark and antiquark of the pair are +supposed to receive opposite and compensating pT kicks according +to a Gaussian distribution in p_x and p_y separately. +Call sigma_q the width of the p_x and p_y +distributions separately, i.e. + + d(Prob) = exp( -(p_x^2 + p_y^2) / 2 sigma_q^2). + +Then the total squared width is + + <pT^2> = <p_x^2> + <p_y^2> = 2 sigma_q^2 = sigma^2. + +It is this latter number that is stored in + + +the width sigma in the fragmentation process. + + +

+Since a normal hadron receives pT contributions for two string +breakings, it has a <p_x^2>_had = <p_y^2>_had = sigma^2, +and thus <pT^2>_had = 2 sigma^2. + +

+Some studies on isolated particles at LEP has indicated the need for +a slightly enhanced rate in the high-pT tail of the above +distribution. This would have to be reviewed in the context of a +complete retune of parton showers and hadronization, but for the +moment we stay with the current recipe, to boost the above pT +by a factor enhancedWidth for a small fraction +enhancedFraction of the breakups, where + + +enhancedFraction,the fraction of string breaks with enhanced +width. + + + +enhancedWidth,the enhancement of the width in this fraction. + + +

Jet joining procedure

+ +String fragmentation is carried out iteratively from both string ends +inwards, which means that the two chains of hadrons have to be joined up +somewhere in the middle of the event. This joining is described by +parameters that in principle follows from the standard fragmentation +parameters, but in a way too complicated to parametrize. The dependence +is rather mild, however, so for a sensible range of variation the +parameters in this section should not be touched. + + +Is used to define a W_min = m_q1 + m_q2 + stopMass, +where m_q1 and m_q2 are the masses of the two +current endpoint quarks or diquarks. + + + +Add to W_min an amount stopNewFlav * m_q_last, +where q_last is the last q qbar pair produced +between the final two hadrons. + + + +The W_min above is then smeared uniformly in the range +W_min_smeared = W_min * [ 1 - stopSmear, 1 + stopSmear ]. + + +

+This W_min_smeared is then compared with the current remaining +W_transverse to determine if there is energy left for further +particle production. If not, i.e. if +W_transverse < W_min_smeared, the final two particles are +produced from what is currently left, if possible. (If not, the +fragmentation process is started over.) + +

Simplifying systems

+ +There are a few situations when it is meaningful to simplify the +original task, one way or another. + + +Decides whether a partonic system should be considered as a normal +string or a ministring, the latter only producing one or two primary +hadrons. The system mass should be above mStringMin plus the +sum of quark/diquark constituent masses for a normal string description, +else the ministring scenario is used. + + + +When two colour-connected partons are very nearby, with at least +one being a gluon, they can be joined into one, to avoid technical +problems of very small string regions. The requirement for joining is +that the invariant mass of the pair is below mJoin, where a +gluon only counts with half its momentum, i.e. with its contribution +to the string region under consideration. (Note that, for technical +reasons, the 0.2 GeV lower limit is de facto hardcoded.) + + + +When the invariant mass of two of the quarks in a three-quark junction +string system becomes too small, the system is simplified to a +quark-diquark simple string. The requirement for this simplification +is that the diquark mass, minus the two quark masses, falls below +mJoinJunction. Gluons on the string between the junction and +the respective quark, if any, are counted as part of the quark +four-momentum. Those on the two combined legs are clustered with the +diquark when it is formed. + + +

Ministrings

+ +The MiniStringFragmentation machinery is only used when a +string system has so small invariant mass that normal string fragmentation +is difficult/impossible. Instead one or two particles are produced, +in the former case shuffling energy-momentum relative to another +colour singlet system in the event, while preserving the invariant +mass of that system. With one exception parameters are the same as +defined for normal string fragmentation, to the extent that they are +at all applicable in this case. + +A discussion of the relevant physics is found in Nor00. +The current implementation does not completely abide to the scheme +presented there, however, but has in part been simplified. (In part +for greater clarity, in part since the class is not quite finished yet.) + + +Whenever the machinery is called, first this many attempts are made +to pick two hadrons that the system fragments to. If the hadrons are +too massive the attempt will fail, but a new subsequent try could +involve other flavour and hadrons and thus still succeed. +After nTry attempts, instead an attempt is made to produce a +single hadron from the system. Should also this fail, some further +attempts at obtaining two hadrons will be made before eventually +giving up. + + +

Junction treatment

+ +A junction topology corresponds to an Y arrangement of strings +i.e. where three string pieces have to be joined up in a junction. +Such topologies can arise if several valence quarks are kicked out +from a proton beam, or in baryon-number-violating SUSY decays. +Special attention is necessary to handle the region just around +the junction, where the baryon number topologically is located. +The junction fragmentation scheme is described in Sjo03. +The parameters in this section should not be touched except by experts. + + +Used to find the effective rest frame of the junction, which is +complicated when the three string legs may contain additional +gluons between the junction and the endpoint. To this end, +a pull is defined as a weighed sum of the momenta on each leg, +where the weight is exp(- eSum / eNormJunction), with +eSum the summed energy of all partons closer to the junction +than the currently considered one (in the junction rest frame). +Should in principle be (close to) sqrt((1 + a) / b), with +a and b the parameters of the Lund symmetric +fragmentation function. + + + +Retry (up to 10 times) when the first two considered strings in to a +junction both have a remaining energy (in the junction rest frame) +above this number. + + + +Retry (up to 10 times) when the first two considered strings in to a +junction has a highest remaining energy (in the junction rest frame) +above a random energy evenly distributed between +eBothLeftJunction and +eBothLeftJunction + eMaxLeftJunction +(drawn anew for each test). + + + +Retry (up to 10 times) when the invariant mass-squared of the final leg +and the leftover momentum of the first two treated legs falls below +eMinLeftJunction times the energy of the final leg (in the +junction rest frame). + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Frontpage.xml b/PYTHIA8/pythia8140/xmldoc/Frontpage.xml new file mode 100644 index 00000000000..a4e79e2475b --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Frontpage.xml @@ -0,0 +1,142 @@ + + +

PYTHIA 8

+ +

Welcome to PYTHIA - The Lund Monte Carlo!

+ +

+PYTHIA 8 is the successor to PYTHIA 6, rewritten from scratch in C++. +With the release of PYTHIA 8.1 it now becomes the official "current" +PYTHIA version, although PYTHIA 6.4 will be supported in parallel +with it for some time to come. Specifically, the new version has not +yet been enough tested and tuned for it to have reached the same level +of reliability as the older one. This testing will only happen if +people begin to work with the program, however, which is why we +encourage a gradual transition to the new version, starting now. +There are some new physics features in PYTHIA 8.1, that would make +use of it more attractive, but also some topics still missing, where +6.4 would have to be used. Further, many obsolete features will not +be carried over, so for some backwards compatibility studies again +6.4 would be the choice. + +

Documentation

+ +On these webpages you will find the up-to-date manual for PYTHIA 8.1. +Use the left-hand index to navigate this documentation of program +elements, especially of all possible program settings. All parameters +are provided with sensible default values, however, so you need only +change those of relevance to your particular study, such as choice of +beams, processes and phase space cuts. The pages also contain a fairly +extensive survey of all methods available to the user, e.g. to study +the produced events. What is lacking on these webpages is an overview, +on the one hand, and an in-depth physics description, on the other. + +

+The overview can be found in the attached PDF file +
A Brief Introduction +to PYTHIA 8.1 +
T. Sjöstrand, S. Mrenna and P. Skands, +Comput. Phys. Comm. 178 (2008) 852 [arXiv:0710.3820]. +
You are strongly recommended to read this summary when you +start out to learn how to use PYTHIA 8.1. Note that some details +have changed since the 8.100 version described there. + +

+For the physics description we refer to the complete +
PYTHIA 6.4 Physics and Manual +
T. Sjöstrand, S. Mrenna and P. Skands, JHEP05 (2006) 026, +
which in detail describes the physics (largely) implemented also in +PYTHIA 8, and also provides a more extensive bibliography than found +here. + +

+When you use PYTHIA 8.1, you should therefore cite both, e.g. like +
T. Sjöstrand, S. Mrenna and P. Skands, JHEP05 (2006) 026, +Comput. Phys. Comm. 178 (2008) 852. + +

+Furthermore, a separate +
+PYTHIA 8 Worksheet, +
also an attached PDF file, offers a practical introduction to +using the generator. It has been developed for and used at a few +summer schools, with minor variations, but is also suited for +self-study. + +

Authors

+ +

+Torbjörn Sjöstrand
+Department of Theoretical Physics, Lund University, +Sölvegatan 14A, SE-223 62 Lund, Sweden
+phone: + 46 - 46 - 222 48 16, e-mail: torbjorn@thep.lu.se + +

+Stefan Ask
+School of Physics and Astronomy, University of Manchester, +Oxford Road, Manchester M13 9PL, United Kingdom
+phone: +41 - 22 - 767 5670, e-mail: Stefan.Ask@cern.ch + +

+Richard Corke
+Department of Theoretical Physics, Lund University, +Sölvegatan 14A, SE-223 62 Lund, Sweden
+phone: + 46 - 46 - 222 31 92, e-mail: richard.corke@thep.lu.se + +

+Stephen Mrenna
+Computing Division, Simulations Group, +Fermi National Accelerator Laboratory, +MS 234, Batavia, IL 60510, USA
+phone: + 1 - 630 - 840 - 2556, e-mail: mrenna@fnal.gov + +

+Peter Skands
+Theoretical Physics, CERN, CH-1211 Geneva 23, Switerland
+phone: + 41 - 22 - 767 2447, e-mail: peter.skands@cern.ch + +

Further contributions

+ +Makefiles, configure scripts and HepMC interface by Mikhail Kirsanov. +
Conversion of XML files to PHP ones by Ben Lloyd. +
Simple Makefile for Win32/NMAKE by Bertrand Bellenot. +
Extended Higgs sector partly implemented by Marc Montull. +
Parts of charm and bottom decay tables courtesy DELPHI and +LHCb collaborations. +
Tunes and comparisons with data, based on Rivet and Professor, +by Hendrik Hoeth. +
Text and code on the use of ROOT in conjunction with PYTHIA +by Rene Brun and Andreas Morsch. +
Code and data for MRST/MSTW PDFs by Robert Thorne and +Graeme Watt. +
Code and data for the CTEQ/CT PDFs by Joey Huston +and colleagues. +
Help with implementing new proton PDFs by Tomas Kasemets. +
Code and data for Pomeron PDFs by H1 collaboration. +
Help with implementing new Pomeron fluxes and PDFs by Sparsh Navin. +
The new Hidden Valley code developed together with Lisa Carloni. +
Code for a Kaluza-Klein electroweak gauge boson provided by +Noam Hod and Mark Sutton. +
Code for equivalent photon flux around an unresolved proton by +Oystein Alvestad. +
Note: in several cases modifications have been made to +the original code, in order to integrate it with PYTHIA. In these cases +the blame for any mistakes has to rest with the regular authors. + +

Licence

+ +PYTHIA 8 is licensed under the +GNU General Public Licence +version 2. +
Please respect the +MCnet Guidelines +for Event Generator Authors and Users. + +

+The program and the documentation is +Copyright © 2010 Torbjörn Sjöstrand + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Glossary.xml b/PYTHIA8/pythia8140/xmldoc/Glossary.xml new file mode 100644 index 00000000000..54aa1f72401 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Glossary.xml @@ -0,0 +1,92 @@ + + +

Glossary

+ +
+ +
BR
+
Beam Remnants; not much used since it may be confused with +Branching Ratio
+ +
BSM
+
Beyond-the-Standard-Model physics, as a generic term for anything +not contained within the SM
+ +
FSR
+
Final-State Radiation, implemented in terms of timelike showers
+ +
LHA
+
Les Houches Accord for user processes, describing which process-level +information should be stored to allow further showering and hadronization +of "skeleton" hard processes
+ +
LHAPDF
+
Les Houches Accord Parton Distribution Functions, originally a standard +format for defining PDF's and later a library with such PDF's
+ +
LHEF
+
Les Houches Event File(s), a file format for storing LHA process and +event information
+ +
ISR
+
Initial-State Radiation, implemented in terms of spacelike showers
+ +
MI
+
Multiple Interactions, i.e. several (more or less) independent +parton-parton subcollisions as part of a hadron-hadron event (sometimes +also called MPI, with P for parton or parton-parton)
+ +
MSSM
+
Minimal Supersymmetric extension of the Standard Model
+ +
PDF
+
Parton Distribution Function (alternatively Parton Density +Function)
+ +
PDG code
+
a scheme for assigning unique integers, particle identity codes, +to known and hypothetical particles; code rules and tables are published +in the RPP (see below).
+ +
pileup
+
several hadron-hadron collisions in a bunch crossing; not to +be confused with MI
+ +
RPP
+
Review of Particle Physics, the biannual review by the ParticleData Group +(PDG) from which many Standard-Model parameter values and much particle data +has been taken (but, given the poor data on many hadron resonances, a lot of +extra (guess)work is needed)
+ +
setting
+
collectively used to denote all the boolean flag, +integer mode, double-precision parm +and string word variables that can be set by the user +to steer the behaviour of a run; normally particle data are considered +separately but clearly are closely related
+ +
SLHA
+
SUSY Les Houchs Accord for interchange of mass and coupling information +in SUSY scenarios, via a well-defined file format
+ +
SM
+
the Standard Model of particle physics
+ +
SUSY
+
SUperSYmmetry
+ +
units
+
Normal PYTHIA input, internal operations and output is based on a set of +standard units, such as: +
GeV for all energies, momenta and masses, always with c = 1; +
mm for all distances and mm/c for all times, +so that again they match for c = 1; +
mb for all cross sections (but input or output via the Les Houches +Accord takes into account that the unit there is pb) +
+ +
+ + + + diff --git a/PYTHIA8/pythia8140/xmldoc/HadronLevelStandalone.xml b/PYTHIA8/pythia8140/xmldoc/HadronLevelStandalone.xml new file mode 100644 index 00000000000..c4d4e7d835a --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/HadronLevelStandalone.xml @@ -0,0 +1,165 @@ + + +

Hadron-Level Standalone

+ +The Les Houches Accord allows external process-level configurations +to be fed in, for subsequent parton-level and hadron-level generation +to be handled internally by PYTHIA. There is no correspondingly +standardized interface if you have external events that have also +been generated through the parton-level stage, so that only the +hadron-level remains to be handled. A non-standard way to achieve this +exists, however, and can be useful both for real applications and +for various tests of the hadronization model on its own. + +

+The key trick is to set the flag ProcessLevel:all = off. +When pythia.next() is called it then does not try to +generate a hard process, and therefore also cannot do anything on the +parton level. Instead only the HadronLevel methods are +called, to take the current content of the event record stored in +pythia.event as a starting point for any hadronization +and decays that are allowed by the normal parameters of this step. +Often the input would consist solely of partons grouped into colour +singlets, but also (colour-singlet) particles are allowed. + +

+To set up all the parameters, a pythia.init() call has +to be used, without any arguments. In brief, the structure of the +main program therefore should be something like +

+  Pythia pythia;                               // Declare generator.
+  Event& event = pythia.event                  // Convenient shorthand.
+  pythia.readString("ProcessLevel:all = off"); // The trick!
+  pythia.init();                               // Initialization.
+  for (int iEvent = 0; iEvent < nEvent; ++iEvent) {
+    // Insert filling of event here!
+    pythia.next();                             // Do the hadron level.
+  }
+
+Of course this should be supplemented by analysis of events, error checks, +and so on, as for a normal PYTHIA run. The unique aspect is how to fill +the event inside the loop, before pythia.next() +is called. + +

Input configuration

+ +To set up a new configuration the first step is to throw away the current +one, with event.reset(). This routine will also reserve +the zeroth entry in the even record to represent the event as a whole. + +

+With the event.append(...) methods a new entry is added at the +bottom of the current record, i.e. the first time it is called entry +number 1 is filled, and so on. The append method basically +exists in four variants, either without or with history information, +and with four-momentum provided either as a Vec4 four-vector +or as four individual components: +

+  append( id, status, col, acol, p, m)
+  append( id, status, col, acol, px, py, pz, e, m)
+  append( id, status, mother1, mother2, daughter1, daughter2, col, acol, p, m)
+  append( id, status, mother1, mother2, daughter1, daughter2, col, acol, px, py, pz, e, m)
+
+The methods return the index at which the entry has been stored, +but normally you would not use this feature. + +

+You can find descriptions of the input variables +here. +The PDG particle code id and the Les Houches Accord colour +col and anticolour acol tags must be set +correctly. The four-momentum and mass have to be provided in units of GeV; +if you omit the mass it defaults to 0. + +

+Outgoing particles that should hadronize should be given status code 23. +Often this is the only status code you need. You could e.g. also fill in +incoming partons with -21 and intermediate ones with -22, if you so wish. +Usually the choice of status codes is not crucial, so long as you recall +that positive numbers correspond to particles that are still around, while +negative numbers denote ones that already hadronized or decayed. However, +so as not to run into contradictions with the internal PYTHIA checks +(when Check:event = on), or with external formats such as +HepMC, we do recommend the above codes. When pythia.next() +is called the positive-status particles that hadronize/decay get the sign +of the status code flipped to negative but the absolute value is retained. +The new particles are added with normal PYTHIA status codes. + +

+For normal hadronization/decays in pythia.next() the +history encoded in the mother and daughter indices is not used. +Therefore the first two append methods, which set all these +indices vanishing, should suffice. The subsequent hadronization/decays +will still be properly documented. + +

+The exception is when you want to include junctions in your string +topology, i.e. have three string pieces meet. Then you must insert in +your event record the (decayed) particle that is the reason for the +presence of a junction, e.g. a baryon beam remnant from which several +valence quarks have been kicked out, or a neutralino that underwent a +baryon-number-violating decay. This particle must have as daughters +the three partons that together carry the baryon number. + +

+The sample program in main21.cc illustrates how you can work +with this facility, both for simple parton configurations and for more +complicated ones with junctions. + +

Repeated hadronization or decay

+ +An alternative approach is possible with the +pythia.forceHadronLevel() routine. This method does +a call to the HadronLevel methods, irrespective of the +value of the HadronLevel:all flag. If you hadronize +externally generated events it is equivalent to a +pythia.next() call with +ProcessLevel:all = off. + +

+The real application instead is for repeated hadronization of the same +PYTHIA process- and parton-level event. This may for some studies +help to save time, given that these two first step are more +time-consuming than the hadronization one. + +

+For repeated hadronization you should first generate an event as usual, +but with HadronLevel:all = off. This event you can save +in a temporary copy, e.g. Event savedEvent = pythia.event. +Inside a loop you copy back with pythia.event = savedEvent, +and call pythia.forceHadronLevel() to obtain a new +hadronization history. + +

+A more limited form of repetition is if you want to decay a given kind +of particle repeatedly, without having to generate the rest of the event +anew. This could be the case e.g. in B physics applications. +Then you can use the pythia.moreDecays() method, which +decays all particles in the event record that have not been decayed +but should have been done so. The +pythia.particleData.mayDecay( id, false/true) method +may be used to switch off/on the decays of a particle species +id, so that it is not decayed in the +pythia.next() call but only inside a loop over a number of +tries. + +

+Between each loop the newly produced decay products must be +removed and the decayed particle status restored to undecayed. +The former is simple, since the new products are appended to the +end of the event record: event.saveSize() saves the +initial size of the event record, and event.restoreSize() +can later be used repeatedly to restore this original size, which means +that the new particles at the end are thrown away. The latter is more +complicated, and requires the user to identify the positions of all +particles of the species and restore a positive status code with +event[i].statusPos(). + +

+The main15.cc program illustrates both these methods, +i.e. either repeated hadronization or repeated decay of PYTHIA +events. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/HepMCInterface.xml b/PYTHIA8/pythia8140/xmldoc/HepMCInterface.xml new file mode 100644 index 00000000000..f87b2921dd0 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/HepMCInterface.xml @@ -0,0 +1,176 @@ + + +

HepMC Interface

+ +An interface to the HepMC Dob01 standard event record +format has been provided by M. Kirsanov. To use it, the relevant +libraires need to be linked, as explained in the README +file. Only version 2 of HepMC is supported. (Version 1 requires +a different interface structure, which was only supported up until +Pythia 8.107.) + +

+The (simple) procedure to translate PYTHIA 8 events into HepMC ones +is illustrated in the main31.cc, main32.cc +and main54.cc main programs. At the core is a call to +the +

+HepMC::I_Pythia8::fill_next_event( pythia, hepmcevt, ievnum = -1, convertGluonTo0 = false ) 
+
+which takes a reference of the generator object and uses it, on the one +hand, to read out and covert the event record in pythia.event +and, on the other hand, to extract and store parton-density (PDF) +information for the hard subprocess from pythia.info. +The optional last argument, if true, allows you to store +gluons as "PDG" code 0 rather than the normal 21; this only applies to +the PDF information, not the event record. + +

+The earlier version of this routine, +

+HepMC::I_Pythia8::fill_next_event( pythia.event, hepmcevt, ievnum = -1 ) 
+
+is retained (for now) for backwards compatibility. It takes a PYTHIA event +as input and returns a HepMC one, but without storing the PDF information. +The latter could then instead be stored by a separate call +
+HepMC::I_Pythia8::pdf_put_info( hepmcevt, pythia, convertGluonTo0 = false ) 
+
+or not, as wished. + +

+The translation routine stores momenta, energies and masses in units +of GeV, and distances and times in units of mm, with c = 1. +This is exactly the units used in PYTHIA. Starting with HepMC 2.04 +the units can be specified; this will be implemented once this or +a later version becomes used by the experimental community. + +

+The status code is now based on the proposed standard for HepMC 2.05, +see the Event::statusHepMC(...) +conversion routine for details. The earlier behaviour, where all +final particles had status 1 and all initial or intermediate ones +status 2, is available as a commented-out line in the +I_Pythia8::fill_next_event(...) method, and so is simple +to recover. + +

+In HepMC 2.05 it also becomes possible to store the generated cross +section and its error. The environment variable +HEPMC_HAS_CROSS_SECTION is used to check whether this +possibility exists and, if it does the current values from +pythia.info.sigmaGen() and +pythia.info.sigmaErr() are stored for each event, +multiplied by 10^9 to convert from mb to pb. Note that +PYTHIA improves it accuracy by Monte Carlo integration in the course +of the run, so the values associated with the last generated event +should be the most accurate ones. + +

The public methods

+ +Here comes a complete list of all public methods of the +I_Pythia8 class in the HepMC +(not Pythia8!) namespace. + + + + +the constructor and destructor take no arguments. + + + +convert a Pythia event to a HepMC one. +Will return true if succeeded. + +the input Pythia generator object, from which both the +event and the parton density information can be obtained. + + +the output GenEvt event, in its standard form. + + +set the event number of the current event. If negative then the +internal event number is used, which is incremented by one for +each new event. + + +the normal gluon identity code 21 is used also when parton density +information is stored, unless this optional argument is set true to +have gluons represented by a 0. This choice does not affect the +normal event record, where a gluon is always 21. + + + + +convert a Pythia event to a HepMC one. +Will return true if succeeded. Do not store parton-density information. + +the input Pythia event, in its standard form. + + +the output GenEvt event, in its standard form. + + +set the event number of the current event. If negative then the +internal event number is used, which is incremented by one for +each new event. + + + + +append parton-density information to an event already stored +by the previous method. + +the output GenEvt event record, in its standard form. + + +the input Pythia generator object, from which both the +event and the parton density information can be obtained. + + +the normal gluon identity code 21 is used also when parton density +information is stored, unless this optional argument is set true to +have gluons represented by a 0. + + + + + + +if there is a conflict in the history information, then trust the +information on mothers above that on daughters. Currently this is +the only option implemented. + + + + + +currently dummy methods intended to resolve conflicts in the event +history. + + + + + +print a warning line, on cerr, when inconsistent mother +and daughter information is encountered. + + + +if problems are encountered then the run is interrupted by an +exit(1) command. Default is not to crash. + + + +connvert the normal GeV energies, momenta and masses to MeV. +Currently not implemented, so everything always is stored as GeV. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/HiddenValleyProcesses.xml b/PYTHIA8/pythia8140/xmldoc/HiddenValleyProcesses.xml new file mode 100644 index 00000000000..a1c9aa66439 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/HiddenValleyProcesses.xml @@ -0,0 +1,318 @@ + + +

Hidden Valley Processes

+ +This Hidden Valley (HV) scenario has been developed specifically +to allow the study of visible consequences of radiation in a +hidden sector, by recoil effect. A key aspect is therefore that +the normal timelike showering machinery has been expanded with a +third kind of radiation, in addition to the QCD and QED ones. +These three kinds of radiation are fully interleaved, i.e. +evolution occurs in a common pT-ordered sequence. +The scenario is described in Car10. + +

Particle content and properties

+ +For simplicity we assume that the HV contains an unbroken SU(N) +gauge symmetry. This is used in the calculation of production cross +sections. These could be rescaled by hand for other gauge groups. + + +is U(1) for Ngauge = 1, is SU(N) if +Ngauge > 1. Note that pair production cross sections +contains a factor of Ngauge for new particles +in the fundamental representation of this group. + + +

+A minimal HV particle content has been introduced. Firstly, there is +a set of 12 particles that mirrors the Standard Model flavour +structure, and is charged under both the SM and the HV symmetry groups. +Each new particle couples flavour-diagonally to a corresponding SM +state, and has the same SM charge and colour, but in addition is in +the fundamental representation of the HV colour, as follows: +
Dv, identity 4900001, partner to the normal +d quark; +
Uv, identity 4900002, partner to the normal +u quark; +
Sv, identity 4900003, partner to the normal +s quark; +
Cv, identity 4900004, partner to the normal +c quark; +
Bv, identity 4900005, partner to the normal +b quark; +
Tv, identity 4900006, partner to the normal +t quark; +
Ev, identity 4900011, partner to the normal +e lepton; +
nuEv, identity 4900012, partner to the normal +nue neutrino; +
MUv, identity 4900013, partner to the normal +mu lepton; +
nuMUv, identity 4900014, partner to the normal +numu neutrino; +
TAUv, identity 4900015, partner to the normal +tau lepton; +
nuTAUv, identity 4900016, partner to the normal +nutau neutrino. +
Collectively we will refer to these states as Fv; +note, however, that they need not be fermions themselves. + +

+In addition the model contains the HV gauge particle, either +a HV gluon or a HV photon, but not both; see Ngauge +above: +
gv, identity 4900021, is the massless +gauge boson of the HV SU(N) group; +
gammav, identity 4900022, is the massless +gauge boson of the HV U(1) group. + +

+Finally, there is a new massive particle with only HV charge sitting +in the fundamental representation of the HV gauge group: +
qv, identity 4900101. + +

The typical scenario would be for pair production of one of the +states presented first above, e.g. g g -> Dv Dvbar. +Such a Dv can radiate gluons and photons like an SM quark, +but in addition HV gluons or HV photons in a similar fashion. +Eventually the Dv will decay like Dv -> d + qv. +The strength of this decay is not set as such, but is implicit in +your choice of width for the Dv state. +Thereafter the d and qv can radiate +further within their respective sectors. The fate of the +qv, gv or gammav, once formed, +is not considered further: they remain invisible. + +

+Only the spin of the HV gluon or HV photon is determined unambiguously +to be unity; for the others you can make your choice. + + +The spin of the HV partners of the SM fermions, e.g. +Dv, Uv, Ev and nuEv. + + + + + + +The spin of qv when the Fv (the HV partners of +the SM fermions) have spin 1/2. (While, if they have spin 0 or 1, +the qv spin is fixed at 1/2.) + + + + + +If the Fv have spin 1 then their production +cross section depends on the presence of ananomalous magnetic dipole +moment, i.e. of a kappa different from unity. For other spins +this parameter is not used. + + +

+You should set the Fv and qv masses appropriately, +with the latter smaller than the former two to allow decays. + +

Production processes

+ + +Common switch for the group of all hard Hidden Valley processes, +as listed separately in the following. + + + +Pair production g g -> Dv Dvbar. +Code 4901. + + + +Pair production g g -> Uv Uvbar. +Code 4902. + + + +Pair production g g -> Sv Svbar. +Code 4903. + + + +Pair production g g -> Cv Cvbar. +Code 4904. + + + +Pair production g g -> Bv Bvbar. +Code 4905. + + + +Pair production g g -> Tv Tvbar. +Code 4906. + + + +Pair production q qbar -> Dv Dvbar +via intermediate gluon. +Code 4911. + + + +Pair production q qbar -> Uv Uvbar +via intermediate gluon. +Code 4912. + + + +Pair production q qbar -> Sv Svbar +via intermediate gluon. +Code 4913. + + + +Pair production q qbar -> Cv Cvbar +via intermediate gluon. +Code 4914. + + + +Pair production q qbar -> Bv Bvbar +via intermediate gluon. +Code 4915. + + + +Pair production q qbar -> Tv Tvbar +via intermediate gluon. +Code 4916. + + + +Pair production f fbar -> Dv Dvbar +via intermediate gamma*/Z^*. +Code 4921. + + + +Pair production f fbar -> Uv Uvbar +via intermediate gamma*/Z^*. +Code 4922. + + + +Pair production f fbar -> Sv Svbar +via intermediate gamma*/Z^*. +Code 4923. + + + +Pair production f fbar -> Cv Cvbar +via intermediate gamma*/Z^*. +Code 4924. + + + +Pair production f fbar -> Bv Bvbar +via intermediate gamma*/Z^*. +Code 4925. + + + +Pair production f fbar -> Tv Tvbar +via intermediate gamma*/Z^*. +Code 4926. + + + +Pair production f fbar -> Ev Evbar +via intermediate gamma*/Z^*. +Code 4931. + + + +Pair production f fbar -> nuEv nuEvbar +via intermediate gamma*/Z^*. +Code 4932. + + + +Pair production f fbar -> MUv MUvbar +via intermediate gamma*/Z^*. +Code 4933. + + + +Pair production f fbar -> nuMUv nuMUvbar +via intermediate gamma*/Z^*. +Code 4934. + + + +Pair production f fbar -> TAUv TAUvbar +via intermediate gamma*/Z^*. +Code 4935. + + + +Pair production f fbar -> nuTAUv nuTAUvbar +via intermediate gamma*/Z^*. +Code 4936. + + +

Timelike showers

+ +One key point of this HV scenario is that radiation off the +HV-charged particles is allowed. This is done by the standard +final-state showering machinery. (HV particles are not produced +in initial-state radiation.) All the (anti)particles Fv +and qv have one (negative) unit of HV charge. That is, +radiation closely mimics the one in QCD. Both QCD, QED and HV +radiation are interleaved in one common sequence of decreasing +emission pT scales. Each radiation kind defines a set of +dipoles, usually spanned between a radiating parton and its recoil +partner, such that the invariant mass of the pair is not changed +when a radiation occurs. This need not follow from trivial colour +assignments, but is often obvious. For instance, in a decay +Qv -> q + qv the QCD dipole is between the q and +the hole after Qv, but qv becomes the recoiler +should a radiation occur, while the role of q and qv +is reversed for HV radiation. + +

This also includes matrix-element corrections for a number +of decay processes, with colour, spin and mass effects included +Nor01. They were calculated within the context of the +particle content of the MSSM, however, which does not include spin 1 +particles with unit colour charge. In such cases spin 0 is assumed +instead. By experience, the main effects come from mass and colour +flow anyway, so this is not a bad approximation. (Furthermore the +MSSM formulae allow for gamma_5 factors from wave +functions or vertices; these are even less important.) + +

An emitted gv can branch in its turn, +gv -> gv + gv. This radiation may affect momenta +in the visible sector by recoil effect, but this is a minor +effect relative to the primary emission of the gv. + + +switch on final-state shower of gv or gammav +in a HV production process. + + + +fixed alpha scale of gv/gammav emission; corresponds to +alpha_strong of QCD or alpha_em of QED. For +shower branchings such as Dv -> Dv + gv the coupling is +multiplied by C_F = (N^2 - 1) / (2 * N) for an +SU(N) group and for gv -> gv + gv by N. + + + +lowest allowed pT of emission. Chosen with same default +as in normal QCD showers. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/HiggsProcesses.xml b/PYTHIA8/pythia8140/xmldoc/HiggsProcesses.xml new file mode 100644 index 00000000000..8ec5fbfae28 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/HiggsProcesses.xml @@ -0,0 +1,910 @@ + + +

Higgs Processes

+ +This page documents Higgs production within and beyond the Standard Model +(SM and BSM for short). This includes several different processes and, +for the BSM scenarios, a large set of parameters that would only be fixed +within a more specific framework such as MSSM. Two choices can be made +irrespective of the particular model: + + +The partial width of a Higgs particle to a pair of gauge bosons, +W^+ W^- or Z^0 Z^0, depends cubically on the +Higgs mass. When selecting the Higgs according to a Breit-Wigner, +so that the actual mass mHat does not agree with the +nominal m_Higgs one, an ambiguity arises which of the +two to use Sey95. The default is to use a linear +dependence on mHat, i.e. a width proportional to +m_Higgs^2 * mHat, while on gives a +mHat^3 dependence. This does not affect the widths to +fermions, which only depend linearly on mHat. +This flag is used both for SM and BSM Higgses. + + + +The partial width of a Higgs particle to a pair of gluons or photons, +or a gamma Z^0 pair, proceeds in part through quark loops, +mainly b and t. There is some ambiguity what kind +of masses to use. Default is running MSbar ones, but alternatively +fixed pole masses are allowed (as was standard in PYTHIA 6), which +typically gives a noticeably higher cross section for these channels. +(For a decay to a pair of fermions, such as top, the running mass is +used for couplings and the fixed one for phase space.) + + +

Standard-Model Higgs, basic processes

+ +This section provides the standard set of processes that can be +run together to provide a reasonably complete overview of possible +production channels for a single SM Higgs. +The main parameter is the choice of Higgs mass, which can be set in the +normal ParticleData database; thereafter the properties +within the SM are essentially fixed. + + +Common switch for the group of Higgs production within the Standard Model. + + + +Scattering f fbar -> H^0, where f sums over available +flavours except top. Related to the mass-dependent Higgs point coupling +to fermions, so at hadron colliders the bottom contribution will +dominate. +Code 901. + + + +Scattering g g -> H^0 via loop contributions primarily from +top. +Code 902. + + + +Scattering gamma gamma -> H^0 via loop contributions primarily +from top and W. +Code 903. + + + +Scattering f fbar -> H^0 Z^0 via s-channel Z^0 +exchange. +Code 904. + + + +Scattering f fbar -> H^0 W^+- via s-channel W^+- +exchange. +Code 905. + + + +Scattering f f' -> H^0 f f' via Z^0 Z^0 fusion. +Code 906. + + + +Scattering f_1 f_2 -> H^0 f_3 f_4 via W^+ W^- fusion. +Code 907. + + + +Scattering g g -> H^0 t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 908. + + + +Scattering q qbar -> H^0 t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 909. + + +

Standard-Model Higgs, further processes

+ +A number of further production processes has been implemented, that +are specializations of some of the above ones to the high-pT +region. The sets therefore could not be used simultaneously +without unphysical doublecounting, as further explained below. +They are not switched on by the HiggsSM:all flag, but +have to be switched on for each separate process after due consideration. + +

+The first three processes in this section are related to the Higgs +point coupling to fermions, and so primarily are of interest for +b quarks. It is here useful to begin by reminding that +a process like b bbar -> H^0 implies that a b/bbar +is taken from each incoming hadron, leaving behind its respective +antiparticle. The initial-state showers will then add one +g -> b bbar branching on either side, so that effectively +the process becomes g g -> H0 b bbar. This would be the +same basic process as the g g -> H^0 t tbar one used for top. +The difference is that (a) no PDF's are defined for top and +(b) the shower approach would not be good enough to provide sensible +kinematics for the H^0 t tbar subsystem. By contrast, owing +to the b being much lighter than the Higgs, multiple +gluon emissions must be resummed for b, as is done by PDF's +and showers, in order to obtain a sensible description of the total +production rate, when the b quarks predominantly are produced +at small pT values. + + +Scattering q g -> H^0 q. This process gives first-order +corrections to the f fbar -> H^0 one above, and should only be +used to study the high-pT tail, while f fbar -> H^0 +should be used for inclusive production. Only the dominant c +and b contributions are included, and generated separately +for technical reasons. Note that another first-order process would be +q qbar -> H^0 g, which is not explicitly implemented here, +but is obtained from showering off the lowest-order process. It does not +contain any b at large pT, however, so is less +interesting for many applications. +Code 911. + + + +Scattering g g -> H^0 b bbar. This process is yet one order +higher of the b bbar -> H^0 and b g -> H^0 b chain, +where now two quarks should be required above some large pT +threshold. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 912. + + + +Scattering q qbar -> H^0 b bbar via an s-channel +gluon, so closely related to the previous one, but typically less +important owing to the smaller rate of (anti)quarks relative to +gluons. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 913. + + +

+The second set of processes are predominantly first-order corrections +to the g g -> H^0 process, again dominated by the top loop. +We here only provide the kinematical expressions obtained in the +limit that the top quark goes to infinity, but scaled to the +finite-top-mass coupling in g g -> H^0. (Complete loop +expressions are available e.g. in PYTHIA 6.4 but are very lengthy.) +This provides a reasonably accurate description for "intermediate" +pT values, but fails when the pT scale approaches +the top mass. + + +Scattering g g -> H^0 g via loop contributions primarily +from top. +Code 914. + + + +Scattering q g -> H^0 q via loop contributions primarily +from top. Not to be confused with the HiggsSM:qg2Hq +process above, with its direct fermion-to-Higgs coupling. +Code 915. + + + +Scattering q qbar -> H^0 g via an s-channel gluon +and loop contributions primarily from top. Is strictly speaking a +"new" process, not directly derived from g g -> H^0, and +could therefore be included in the standard mix without doublecounting, +but is numerically negligible. +Code 916. + + +

Beyond-the-Standard-Model Higgs, introduction

+ +Further Higgs multiplets arise in a number of scenarios. We here +concentrate on the MSSM scenario with two Higgs doublets, but with +flexibility enough that also other two-Higgs-doublet scenarios could +be represented by a suitable choice of parameters. Conventionally the +Higgs states are labelled h^0, H^0, A^0 and H^+-. +If the scalar and pseudocalar states mix the resulting states are +labelled H_1^0, H_2^0, H_3^0. In process names and parameter +explanations both notations will be used, but for settings labels +we have adapted the shorthand hybrid notation H1 for +h^0(H_1^0), H2 for H^0(H_2^0) and +A3 for A^0(H_3^0). (Recall that the +Settings database does not distinguish upper- and lowercase +characters, so that the user has one thing less to worry about, but here +it causes probles with h^0 vs. H^0.) We leave the issue +of mass ordering between H^0 and A^0 open, and thereby +also that of H_2^0 and H_3^0. + + +Master switch to initialize and use the two-Higgs-doublet states. +If off, only the above SM Higgs processes can be used, with couplings +as predicted in the SM. If on, only the below BSM Higgs processes can +be used, with couplings that can be set freely, also found further down +on this page. + + +

Beyond-the-Standard-Model Higgs, basic processes

+ +This section provides the standard set of processes that can be +run together to provide a reasonably complete overview of possible +production channels for a single neutral Higgs state in a two-doublet +scenarios such as MSSM. The list of processes for neutral states closely +mimics the one found for the SM Higgs. Some of the processes +vanish for a pure pseudoscalar A^0, but are kept for flexiblity +in cases of mixing with the scalar h^0 and H^0 states, +or for use in the context of non-MSSM models. This should work well to +represent e.g. that a small admixture of the "wrong" parity would allow +a process such as q qbar -> A^0 Z^0, which otherwise is forbidden. +However, note that the loop integrals e.g. for g g -> h^0/H^0/A^0 +are hardcoded to be for scalars for the former two particles and for a +pseudoscalar for the latter one, so absolute rates would not be +correctly represented in the case of large scalar/pseudoscalar mixing. + + +Common switch for the group of Higgs production beyond the Standard Model, +as listed below. + + +

1) h^0(H_1^0) processes

+ + +Common switch for the group of h^0(H_1^0) production processes. + + + +Scattering f fbar -> h^0(H_1^0), where f sums over available +flavours except top. +Code 1001. + + + +Scattering g g -> h^0(H_1^0) via loop contributions primarily from +top. +Code 1002. + + + +Scattering gamma gamma -> h^0(H_1^0) via loop contributions primarily +from top and W. +Code 1003. + + + +Scattering f fbar -> h^0(H_1^0) Z^0 via s-channel Z^0 +exchange. +Code 1004. + + + +Scattering f fbar -> h^0(H_1^0) W^+- via s-channel W^+- +exchange. +Code 1005. + + + +Scattering f f' -> h^0(H_1^0) f f' via Z^0 Z^0 fusion. +Code 1006. + + + +Scattering f_1 f_2 -> h^0(H_1^0) f_3 f_4 via W^+ W^- fusion. +Code 1007. + + + +Scattering g g -> h^0(H_1^0) t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1008. + + + +Scattering q qbar -> h^0(H_1^0) t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1009. + + +

2) H^0(H_2^0) processes

+ + +Common switch for the group of H^0(H_2^0) production processes. + + + +Scattering f fbar -> H^0(H_2^0), where f sums over available +flavours except top. +Code 1021. + + + +Scattering g g -> H^0(H_2^0) via loop contributions primarily from +top. +Code 1022. + + + +Scattering gamma gamma -> H^0(H_2^0) via loop contributions primarily +from top and W. +Code 1023. + + + +Scattering f fbar -> H^0(H_2^0) Z^0 via s-channel Z^0 +exchange. +Code 1024. + + + +Scattering f fbar -> H^0(H_2^0) W^+- via s-channel W^+- +exchange. +Code 1025. + + + +Scattering f f' -> H^0(H_2^0) f f' via Z^0 Z^0 fusion. +Code 1026. + + + +Scattering f_1 f_2 -> H^0(H_2^0) f_3 f_4 via W^+ W^- fusion. +Code 1027. + + + +Scattering g g -> H^0(H_2^0) t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1028. + + + +Scattering q qbar -> H^0(H_2^0) t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1029. + +

3) A^0(H_3^0) processes

+ + +Common switch for the group of A^0(H_3^0) production processes. + + + +Scattering f fbar -> A^0(H_3^0), where f sums over available +flavours except top. +Code 1041. + + + +Scattering g g -> A^0(A_3^0) via loop contributions primarily from +top. +Code 1042. + + + +Scattering gamma gamma -> A^0(A_3^0) via loop contributions primarily +from top and W. +Code 1043. + + + +Scattering f fbar -> A^0(A_3^0) Z^0 via s-channel Z^0 +exchange. +Code 1044. + + + +Scattering f fbar -> A^0(A_3^0) W^+- via s-channel W^+- +exchange. +Code 1045. + + + +Scattering f f' -> A^0(A_3^0) f f' via Z^0 Z^0 fusion. +Code 1046. + + + +Scattering f_1 f_2 -> A^0(A_3^0) f_3 f_4 via W^+ W^- fusion. +Code 1047. + + + +Scattering g g -> A^0(A_3^0) t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1048. + + + +Scattering q qbar -> A^0(A_3^0) t tbar via t tbar fusion +(or, alternatively put, Higgs radiation off a top line). +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1049. + +

4) H+- processes

+ + +Common switch for the group of H^+- production processes. + + + +Scattering f fbar' -> H^+-, where f, fbar' sums over +available incoming flavours. Since couplings are assumed +generation-diagonal, in practice this means c sbar -> H^+ +and s cbar -> H^-. +Code 1061. + + + +Scattering b g -> H^+ tbar. At hadron colliders this is the +dominant process for single-charged-Higgs production. +Code 1062. + + +

5) Higgs-pair processes

+ + +Common switch for the group of Higgs pair-production processes. + + + +Scattering f fbar -> A^0(H_3) h^0(H_1). +Code 1081. + + + +Scattering f fbar -> A^0(H_3) H^0(H_2). +Code 1082. + + + +Scattering f fbar -> H^+- h^0(H_1). +Code 1083. + + + +Scattering f fbar -> H^+- H^0(H_2). +Code 1084. + + + +Scattering f fbar -> H+ H-. +Code 1085. + + +

Beyond-the-Standard-Model Higgs, further processes

+ +This section mimics the above section on "Standard-Model Higgs, +further processes", i.e. it contains higher-order corrections +to the processes already listed. The two sets therefore could not +be used simultaneously without unphysical doublecounting. +They are not controlled by any group flag, but have to be switched +on for each separate process after due consideration. We refer to +the standard-model description for a set of further comments on +the processes. + +

1) h^0(H_1^0) processes

+ + +Scattering q g -> h^0 q. This process gives first-order +corrections to the f fbar -> h^0 one above, and should only be +used to study the high-pT tail, while f fbar -> h^0 +should be used for inclusive production. Only the dominant c +and b contributions are included, and generated separately +for technical reasons. Note that another first-order process would be +q qbar -> h^0 g, which is not explicitly implemented here, +but is obtained from showering off the lowest-order process. It does not +contain any b at large pT, however, so is less +interesting for many applications. +Code 1011. + + + +Scattering g g -> h^0 b bbar. This process is yet one order +higher of the b bbar -> h^0 and b g -> h^0 b chain, +where now two quarks should be required above some large pT +threshold. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1012. + + + +Scattering q qbar -> h^0 b bbar via an s-channel +gluon, so closely related to the previous one, but typically less +important owing to the smaller rate of (anti)quarks relative to +gluons. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1013. + + + +Scattering g g -> h^0 g via loop contributions primarily +from top. +Code 1014. + + + +Scattering q g -> h^0 q via loop contributions primarily +from top. Not to be confused with the HiggsBSM:qg2H1q +process above, with its direct fermion-to-Higgs coupling. +Code 1015. + + + +Scattering q qbar -> h^0 g via an s-channel gluon +and loop contributions primarily from top. Is strictly speaking a +"new" process, not directly derived from g g -> h^0, and +could therefore be included in the standard mix without doublecounting, +but is numerically negligible. +Code 1016. + + +

2) H^0(H_2^0) processes

+ + +Scattering q g -> H^0 q. This process gives first-order +corrections to the f fbar -> H^0 one above, and should only be +used to study the high-pT tail, while f fbar -> H^0 +should be used for inclusive production. Only the dominant c +and b contributions are included, and generated separately +for technical reasons. Note that another first-order process would be +q qbar -> H^0 g, which is not explicitly implemented here, +but is obtained from showering off the lowest-order process. It does not +contain any b at large pT, however, so is less +interesting for many applications. +Code 1031. + + + +Scattering g g -> H^0 b bbar. This process is yet one order +higher of the b bbar -> H^0 and b g -> H^0 b chain, +where now two quarks should be required above some large pT +threshold. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1032. + + + +Scattering q qbar -> H^0 b bbar via an s-channel +gluon, so closely related to the previous one, but typically less +important owing to the smaller rate of (anti)quarks relative to +gluons. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1033. + + + +Scattering g g -> H^0 g via loop contributions primarily +from top. +Code 1034. + + + +Scattering q g -> H^0 q via loop contributions primarily +from top. Not to be confused with the HiggsBSM:qg2H1q +process above, with its direct fermion-to-Higgs coupling. +Code 1035. + + + +Scattering q qbar -> H^0 g via an s-channel gluon +and loop contributions primarily from top. Is strictly speaking a +"new" process, not directly derived from g g -> H^0, and +could therefore be included in the standard mix without doublecounting, +but is numerically negligible. +Code 1036. + + +

3) A^0(H_3^0) processes

+ + +Scattering q g -> A^0 q. This process gives first-order +corrections to the f fbar -> A^0 one above, and should only be +used to study the high-pT tail, while f fbar -> A^0 +should be used for inclusive production. Only the dominant c +and b contributions are included, and generated separately +for technical reasons. Note that another first-order process would be +q qbar -> A^0 g, which is not explicitly implemented here, +but is obtained from showering off the lowest-order process. It does not +contain any b at large pT, however, so is less +interesting for many applications. +Code 1051. + + + +Scattering g g -> A^0 b bbar. This process is yet one order +higher of the b bbar -> A^0 and b g -> A^0 b chain, +where now two quarks should be required above some large pT +threshold. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1052. + + + +Scattering q qbar -> A^0 b bbar via an s-channel +gluon, so closely related to the previous one, but typically less +important owing to the smaller rate of (anti)quarks relative to +gluons. +Warning: unfortunately this process is rather slow, owing to a +lengthy cross-section expression and inefficient phase-space selection. +Code 1053. + + + +Scattering g g -> A^0 g via loop contributions primarily +from top. +Code 1054. + + + +Scattering q g -> A^0 q via loop contributions primarily +from top. Not to be confused with the HiggsBSM:qg2H1q +process above, with its direct fermion-to-Higgs coupling. +Code 1055. + + + +Scattering q qbar -> A^0 g via an s-channel gluon +and loop contributions primarily from top. Is strictly speaking a +"new" process, not directly derived from g g -> A^0, and +could therefore be included in the standard mix without doublecounting, +but is numerically negligible. +Code 1056. + + +

Parameters for Beyond-the-Standard-Model Higgs production and decay

+ +This section offers a big flexibility to set couplings of the various +Higgs states to fermions and gauge bosons, and also to each other. +The intention is that, for scenarios like MSSM, you should use standard +input from the SUSY Les Houches +Accord, rather than having to set it all yourself. In other cases, +however, the freedom is there for you to use. Kindly note that some +of the internal calculations of partial widths from the parameters provided +do not include mixing between the scalar and pseudoscalar states. + +

+Masses would be set in the ParticleData database, +while couplings are set below. When possible, the couplings of the Higgs +states are normalized to the corresponding coupling within the SM. +When not, their values within the MSSM are indicated, from which +it should be straightforward to understand what to use instead. +The exception is some couplings that vanish also in the MSSM, where the +normalization has been defined in close analogy with nonvanishing ones. +Some parameter names are asymmetric but crossing can always be used, +i.e. the coupling for A^0 -> H^0 Z^0 obviously is also valid +for H^0 -> A^0 Z^0 and Z^0 -> H^0 A^0. +Note that couplings usually appear quadratically in matrix elements. + + +The h^0(H_1^0) coupling to down-type quarks. + + + +The h^0(H_1^0) coupling to up-type quarks. + + + +The h^0(H_1^0) coupling to (charged) leptons. + + + +The h^0(H_1^0) coupling to Z^0. + + + +The h^0(H_1^0) coupling to W^+-. + + + +The h^0(H_1^0) coupling to H^+- (in loops). +Is sin(beta - alpha) + cos(2 beta) sin(beta + alpha) / +(2 cos^2theta_W) in the MSSM. + + + +The H^0(H_2^0) coupling to down-type quarks. + + + +The H^0(H_2^0) coupling to up-type quarks. + + + +The H^0(H_2^0) coupling to (charged) leptons. + + + +The H^0(H_2^0) coupling to Z^0. + + + +The H^0(H_2^0) coupling to W^+-. + + + +The H^0(H_2^0) coupling to H^+- (in loops). +Is cos(beta - alpha) + cos(2 beta) cos(beta + alpha) / +(2 cos^2theta_W) in the MSSM. + + + +The H^0(H_2^0) coupling to a h^0(H_1^0) pair. +Is cos(2 alpha) cos(beta + alpha) - 2 sin(2 alpha) +sin(beta + alpha) in the MSSM. + + + +The H^0(H_2^0) coupling to an A^0(H_3^0) pair. +Is cos(2 beta) cos(beta + alpha) in the MSSM. + + + +The H^0(H_2^0) coupling to a h^0(H_1^0) Z^0 pair. +Vanishes in the MSSM. + + + +The H^0(H_2^0) coupling to an A^0(H_3^0) h^0(H_1^0) pair. +Vanishes in the MSSM. + + + +The H^0(H_2^0) coupling to a H^+- W-+ pair. +Is sin(beta - alpha) in the MSSM. + + + +The A^0(H_3^0) coupling to down-type quarks. + + + +The A^0(H_3^0) coupling to up-type quarks. + + + +The A^0(H_3^0) coupling to (charged) leptons. + + + +The A^0(H_3^0) coupling to a h^0(H_1^0) Z^0 pair. +Is cos(beta - alpha) in the MSSM. + + + +The A^0(H_3^0) coupling to a H^0(H_2^0) Z^0 pair. +Is sin(beta - alpha) in the MSSM. + + + +The A^0(H_3^0) coupling to Z^0. +Vanishes in the MSSM. + + + +The A^0(H_3^0) coupling to W^+-. +Vanishes in the MSSM. + + + +The A^0(H_3^0) coupling to a h^0(H_1^0) pair. +Vanishes in the MSSM. + + + +The A^0(H_3^0) coupling to H^+-. +Vanishes in the MSSM. + + + +The A^0(H_3^0) coupling to a H^+- W-+ pair. +Is 1 in the MSSM. + + + +The tan(beta) value, which leads to an enhancement of the +H^+- coupling to down-type fermions and suppression to +up-type ones. The same angle also appears in many other places, +but this particular parameter is only used for the charged-Higgs case. + + + +The H^+- coupling to a h^0(H_1^0) W^+- pair. +Is cos(beta - alpha) in the MSSM. + + + +The H^+- coupling to a H^0(H_2^0) W^+- pair. +Is sin(beta - alpha) in the MSSM. + + +

+Another set of parameters are not used in the production stage but +exclusively for the description of angular distributions in decays. + + +possibility to modify angular decay correlations in the decay of a +h^0(H_1) decay Z^0 Z^0 or W^+ W^- to four +fermions. Currently it does not affect the partial width of the +channels, which is only based on the above parameters. + + + + + + + +The eta value of CP-violation in the +HiggsSM:parity = 3 option. + + + +possibility to modify angular decay correlations in the decay of a +H^0(H_2) decay Z^0 Z^0 or W^+ W^- to four +fermions. Currently it does not affect the partial width of the +channels, which is only based on the above parameters. + + + + + + + +The eta value of CP-violation in the +HiggsSM:parity = 3 option. + + + +possibility to modify angular decay correlations in the decay of a +A^0(H_3) decay Z^0 Z^0 or W^+ W^- to four +fermions. Currently it does not affect the partial width of the +channels, which is only based on the above parameters. + + + + + + + +The eta value of CP-violation in the +HiggsSM:parity = 3 option. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Histograms.xml b/PYTHIA8/pythia8140/xmldoc/Histograms.xml new file mode 100644 index 00000000000..9e81db3cb11 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Histograms.xml @@ -0,0 +1,304 @@ + + +

Histograms

+ +The Hist class gives a simple implementation of +one-dimensional histograms, useful for quick-and-dirty testing, +without the need to link to more sophisticated packages. +For this reson it is used in many of the +sample main programs +found in the examples subdirectory. + +

Basic principles

+ +We here provide a simple overview of what is involved. +As a first step you need to declare a histogram, with name, +title, number of bins and x range (from, to). +
+   Hist ZpT( "Z0 pT spectrum", 100, 0., 100.);
+
+Alternatively you can first declare it and later define it: +
+   Hist ZpT;
+   ZpT.book( "Z0 pT spectrum", 100, 0., 100.);
+
+ +Once declared, its contents can be added by repeated calls to +fill, +
+   ZpT.fill( 22.7, 1.); 
+
+where the first argument is the x value and the second the +weight. Since the weight defaults to 1 the last argument could have +been omitted in this case. + +

+A set of overloaded operators have been defined, so that histograms +can be added, subtracted, divided or multiplied by each other. Then the +contents are modified accordingly bin by bin. Thus the relative +deviation between two histograms data and +theory can be found as +

+  diff = (data - theory) / (data + theory);
+
+assuming that diff, data and theory +have been booked with the same number of bins and x range. That +responsibility rests on the user; some checks are made for compatibility, +but not enough to catch all possible mistakes. + +

+Also overloaded operations with double real numbers are available. +Again these four operations are defined bin by bin, i.e. the +corresponding amount is added to, subtracted from, multiplied by or +divided by each bin. The double number can come before or after the +histograms, with obvious results. Thus the inverse of a histogram +result is given by 1. / result. +The two kind of operations can be combined, e.g. +

+  allpT = ZpT + 2. * WpT
+
+Finally, also the +=, -+, *=, /= are overloaded, with +the right-hand side being either a histogram or a real number. + +

Output format

+ +

+A histogram can be printed by making use of the overloaded << +operator, e.g.: +

+   cout << ZpT;
+
+The printout format is inspired by the old HBOOK one. To understand +how to read this format, consider the simplified example +
+                                    
+        3.50*10^ 2  9                     
+        3.00*10^ 2  X   7               
+        2.50*10^ 2  X  1X               
+        2.00*10^ 2  X6 XX                
+        1.50*10^ 2  XX5XX                 
+        1.00*10^ 2  XXXXX                
+        0.50*10^ 2  XXXXX        
+
+          Contents 
+            *10^ 2  31122
+            *10^ 1  47208
+            *10^ 0  79373
+
+          Low edge  -- 
+            *10^ 1  10001 
+            *10^ 0  05050
+
+The key feature is that the Contents and +Low edge have to be read vertically. For instance, +the first bin has the contents +3 * 10^2 + 4 * 10^1 + 7 * 10^0 = 347. Correspondingly, +the other bins have contents 179, 123, 207 and 283. The first bin +stretches from -(1 * 10^1 + 0 * 10^0) = -10 to the +beginning of the second bin, at -(0 * 10^1 + 5 * 10^0) = -5. + +

+The visual representation above the contents give a simple impression +of the shape. An X means that the contents are filled up +to this level, a digit in the topmost row the fraction to which the +last level is filled. So the 9 of the first column indicates this bin +is filled 9/10 of the way from 3.00*10^2 = 300 to +3.50*10^2 = 350, i.e. somewhere close to 345, +or more precisely in the range 342.5 to 347.5. + +

+The printout also provides some other information, such as the +number of entries, i.e. how many times the histogram has been filled, +the total weight inside the histogram, the total weight in underflow +and overflow, and the mean value and root-mean-square width (disregarding +underflow and overflow). The mean and width assumes that all the +contents is in the middle of the respective bin. This is especially +relevant when you plot a integer quantity, such as a multiplicity. +Then it makes sense to book with limits that are half-integers, e.g. +

+   Hist multMI( "number of multiple interactions", 20, -0.5, 19.5);
+
+so that the bins are centered at 0, 1, 2, ..., respectively. This also +avoids ambiguities which bin gets to be filled if entries are +exactly at the border between two bins. Also note that the +fill( xValue) method automatically performs a cast +to double precision where necessary, i.e. xValue +can be an integer. + +

The methods

+ +We here collect a more complete and formal overview of the methods. + + +declare a histogram, but does not define it. + + + +declare and define a histogram, where + +is a string with the title of the histogram at output, + + +is the number of bin the x range will be subdivided into, +limited to be at most 1000, + + +is the lower edge of the histogram, + + +is the upper edge of the histogram. + + + + +creates an identical copy of the histogram in the argument, +including bin contents. + + + +creates an identical copy of the histogram in the argument, +including bin contents, except that a new title is provided +as first argument. + + + +copies all properties of the histogram in the argument, +except that the original histogram title is retained. + + + +define a histogram that previously was only declared; +see above for the meaning of the arguments. + + + +change the title of a histogram, but keep other properties unchanged. + + + +reset bin contents, but keep other histogram properties unchanged. + + + +fill the histogram, where + +is the x position where the filling should occur, and + + +is the amount of weight to be added at this x value. + + + + +appends a simple histogram printout (see above for format) to the +ostream, while leaving the histogram object itself +unchanged. At most 100 columns are allowed to be displayed. +If the number of bins is larger than 100 then the contents of +adjacent bins are added to give the value in each column. (Two by two +up to 200 bins, three by three up to 300, and so on, with the very +last column possibly summing fewer rows than the others.) + + + + + +print a two-column table, where the first column gives the center of +each bin and the second one the corresponding bin contents. The desired +output stream or file name can be provided as argument. The former +is more flexible (e.g., it allows easy append to an existing file), +whereas the latter is simpler for the case that each histogram should +be a file of its own. The table may be useful for plotting e.g. with +Gnuplot. + + + +return the value in bin iBin, ranging from 1 through +numberOfBins, with 0 for underflow and +numberOfBins + 1 for overflow. + + + +return the number of entries, i.e. the number of time that +fill(...) has been called. + + + +checks that the number of bins and upper and lower limits are the +same as in the histogram in the argument. + + + +by default take 10-logarithm of current contents bin by bin. With +optional argument false instead take e-logarithm +of contents bin by bin. If to be used, then right before the +histogram is output. + + + + + +adds or subtracts the current histogram by the contents of the +histogram in the argument if sameSize(...) is true, +else does nothing. + + + + + +multiplies or divides the current histogram by the contents of the +histogram in the argument if sameSize(...) is true, +else does nothing. + + + + + +adds or subtracts each bin content by the common offset f. + + + + + +multiplies or divides each bin content by the common factor f. + + + + + + + +add a constant to a histogram or two histograms to each other, bin by bin. + + + + + + + +subtract a histogram from a constant, a constant from a histogram, +or two histograms from each other, bin by bin. + + + + + + + +multiply a constant by a histogram or two histograms by each other, +bin by bin. + + + + + + + +divide a constant by a histogram, a histogram by a constant, +or two histograms by each other, bin by bin. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ImplementNewShowers.xml b/PYTHIA8/pythia8140/xmldoc/ImplementNewShowers.xml new file mode 100644 index 00000000000..9609e4cd2ce --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ImplementNewShowers.xml @@ -0,0 +1,471 @@ + + +

Implement New Showers

+ +In case you want to replace the PYTHIA initial- and final-state +showers by your own, it is possible but not trivial. The point is +that multiple interactions (MI), initial-state radiation (ISR) and +final-state radiation (FSR) in general appear in one single +interleaved sequence of decreasing pT values. Therefore +shower replacements would have to be able to play the game by such +rules, as we will outline further below. Of course, this still +leaves the field open exactly how to define what to mean by +pT, how to handle recoil effects, how the colour flow is +affected, and so on, so there is certainly room for alternative +showers. A first example of a shower implemented within the PYTHIA +context is VINCIA, +which however so far only handles FSR. + +

+For the moment we assume you want to keep the MI part of the story +unchanged, and make use of the existing beam-remnants (BR) machinery. +If you want to replace both MI, ISR, FSR and BR then you had better +replace the whole PartonLevel module of the code. +If, in addition, you want to produce your own hard processes, +then you only need the +hadron-level standalone +part of the machinery. + +

+In order to write replacement codes for ISR and/or FSR it is useful +to be aware of which information has to be shared between the +different components, and which input/output structure is required +of the relevant methods. For details, nothing beats studying the +existing code. However, here we provide an overview, that should +serve as a useful introduction. + +

+It should be noted that we here primarily address the problem in +its full generality, with interleaved MI, ISR and FSR. There exists +an option TimeShower:interleave = off where only +MI and ISR would be interleaved and FSR be considered after these +two, but still before BR. Most of the aspects described here would +apply also for that case. By contrast, resonance decays are only +considered after all the four above components, and timelike +showers in those decays would never be interleaved with anything +else, so are much simpler to administrate. + +

+Therefore the +pythia.setShowerPtr( timesDecPtr, timesPtr, spacePtr) +method allows two separate pointers to be set to instances of +derived TimeShower classes. The first is only required +to handle decays, say of Z^0 or Upsilon, with no +dependence on beam remnants or ISR. The second, as well as +spacePtr, has to handle the interleaved evolution of MI, +ISR and FSR. Therefore you are free to implement only the first, and +let the PYTHIA default showers take care of the latter two. But, if +you wanted to, you could also set timesDecPtr = 0 and +only provide a timesPtr, or only a spacePtr. +If your timelike shower does both cases, the first two pointers +can agree. The only tiny point to take into account then is that +init( beamAPtr, beamBPtr) is called twice, a first time +to timesDecPtr with beam pointers 0, and a second time +to timesPtr with nonvanishing beam pointers. + +

The event record and associated information

+ +Obviously the main place for sharing information is the event +record, specifically the Event event member of +Pythia, passed around as a reference. It is +assumed you already studied how it works, so here we only draw +attention to a few aspects of special relevance. + +

+One basic principle is that existing partons should not be +overwritten. Instead new partons should be created, even when a +parton only receives a slightly shifted momentum and for the rest +stays the same. Such "carbon copies" by final-state branchings +should be denoted by both daughter indices of the original parton +pointing to the copy, and both mother indices of the copy to the +original. If the copy instead is intended to represent an earlier +step, e.g. in ISR backwards evolution, the role of mothers and +daughters is interchanged. The +event.copy( iCopy, newStatus) +routine can take care of this tedious task; the sign of +newStatus tells the program which case to assume. + +

+To make the event record legible it is essential that the +status codes +are selected appropriately to represent the reason why each new +parton is added to the record. Also remember to change the +status of a parton to be negative whenever an existing parton +is replaced by a set of new daughter partons. + +

+Another important parton property is scale(), +which does not appear in the normal event listing, but only +if you use the extended +Event:listScaleAndVertex = on option. +This property is supposed to represent the production scale +(in GeV) of a parton. In the current FSR and ISR algorithms +it is used to restrict from above the allowed pT +values for branchings of this particular parton. +Beam remnants and other partons that should not radiate are +assigned scale 0. + +

+Auxiliary to the event record proper is the +PartonSystems +class, that keep track of which partons belong together in the +same scattering subsystem. This information must be kept up-to-date +during the shower evolution. + +

+For initial-state showers it is also necessary to keep track of +the partonic content extracted from the beams. This information +is stored in the +BeamParticle +class. + +

The TimeShower interface

+ +If you want to replace the TimeShower class this would +involve replacing the virtual methods among the following ones. + + +The constructor does not need to do anything. + + + +The destructor does not need to do anything. + + + +This method only imports pointers to standard facilities, +and is not virtual. + + + +You have to store your local copy of the pointers to these objects, +since they have to be used during the generation, as explained above. +The pointers could be zero; e.g. a local copy of TimeShower +is created to handle showers in decays such as Upsilon -> q qbar +from inside the ParticleDecays class. This is also the +place to do initialization of whatever parameters you plan to use, +e.g. by reading in them from a user-accessible database like the +Settings one. + + + +The question is whether the FSR should be allowed to occur at larger +scales than the hard process it surrounds. This is process-dependent, +as illustrated below for the the analogous +SpaeShower::limitPTmax(...) method, although the two +kinds of radiation need not have to be modelled identically. +The TimeShower:pTmaxMatch switch allows you to force the +behaviour among three options, but you may replace by your own logic. +
The internal PYTHIA implementation also allows intermediate options, +where emissions can go up to the kinematical limit but be dampened above +the factorization or renormalization scale. Therefore the (square of the) +latter two are provided as optional input parameters. + + + +Relative to the default pT_max evolution scale of the process, +it may still be convenient to vary the matching slightly for the hardest +interaction in an event, to probe the sensitivity to such details. The +base-class implementation returns the value of the +TimeShower:pTmaxFudge parameter. + + + +This is an all-in-one call for shower evolution, and as such cannot be +used for the normal interleaved evolution, where only the routines below +are used. It also cannot be used in resonance decays that form part of +the hard process, since there the +user hooks insert a potential +veto step. Currently this routine is therefore only used in the +hadron-level decays, e.g. Upsilon -> g g g. +
iBeg and iEnd is the position of the +first and last parton of a separate system, typically produced by a +resonance decay. Such a system only evolves in isolation, and in +particular does not relate to the beams. +
The pTmax value sets the maximum scale for evolution, +but normally you would restrict that further for each individual +parton based on its respective scale value. +
The nBranchMax value, if positive, gives the maximum +number of allowed branchings in the call, as useful for matching studies. +
The routine is expected to return the number of FSR branchings that +were generated, but only for non-critical statistics purposes. +
Since the real action typically is delegated to the routines +below, it may well be that the existing code need not be replaced. + + + +Can be used to return the pT evolution scale of the last +branching in the cascade generated with the above +shower(...) method. Is to be set in the internal +pTLastInShower variable, and should be 0 if there +were no branchings. Can be useful for matching studies. + + + +This method is called immediately after a new interaction (or the +products of a resonance decay) has been added, and should then be used +to prepare the subsystem of partons for subsequent evolution. In +the current code this involves identifying all colour and charge +dipole ends: the position of radiating and recoiling partons, maximum +pT scales, possible higher-order matrix elements matchings +to apply, and so on. +
The iSys parameter specifies which parton system +is to be prepared. It is used to extract the set of partons to be +treated, with rules as described in the above section on subsystems. +Specifically, the first two partons represent the incoming state, +or are 0 for resonance decays unrelated to the beams, while the +rest are not required to be in any particular order. + + + +This method is called immediately after rescattering in the description +of multiple interactions. Thus the information on one or several +systems is out-of-date, while that of the others is unchanged. +We do not provide the details here, since we presume few implementors +of new showers will want to touch the technicalities involved +in obtaining a description of rescattering. + + + +This method is called immediately after a spacelike branching in the +iSys'th subsystem. Thus the information for that system is +out-of-date, while that of the others is unchanged. If you want, you are +free to throw away all information for the affected subsystem and call +prepare( iSys, event) to create new one. Alternatively +you may choose only to update the information that has changed. + + + +This is the main driver routine for the downwards evolution. A new +pT is to be selected based on the current information set up +by the routines above, and along with that a branching parton or dipole. +The pTbegAll scale is the maximum scale allowed, from which +the downwards evolution should be begun (usually respecting the maximum +scale of each individual parton). If no emission is found above +pTendAll (and above the respective shower cutoff scales) +then 0. should be returned and no emissions will be allowed. +Both scales can vary from one event to the next: if a scale has +already been selected for MI or ISR it makes no sense to look for +a scale smaller than that from FSR, since it would not be able to +compete, so pTendAll is set correspondingly. As it happens, +FSR is tried before ISR and MI in the interleaved evolution, +but this is an implementational detail that could well change. +
Typically the implementation of this routine would be to set +up a loop over all possible radiating objects (dipoles, dipole ends, ...), +for each pick its possible branching scale and then pick the one +with largest scale as possible winner. At this stage no branching should +actually be carried out, since MI, ISR and FSR still have to be compared +to assign the winner. + + + +This method will be called once FSR has won the competition with +MI and ISR to do the next branching. The candidate branching found +in the previous step should here be carried out in full. The +pre-branching partons should get a negative status code and new +replacement ones added to the end of the event record. Also the +subsystem information should be updated, and possibly also the +beams. +
Should some problem be encountered in this procedure, e.g. if +some not-previously-considered kinematics requirement fails, it is +allowed to return false to indicate that no branching +could be carried out. +
Normally the optional isInterleaved argument would +not be of interest. It can be used to separate resonance decays, false, +from the interleaved evolution together with MI and ISR, true. +More precisely, it separates calls to the timesDecPtr +and the timesPtr instances. + + + +This method is only called if rescattering is switched on in the +description of multiple interactions. It then propagates a recoil +from a timelike branching to internal lines that connect systems. +As for rescatterUpdate above, this is not likely to be +of interest to most implementors of new showers. + + + +This method is not virtual. If a branching is constructed by the +previous routine this tiny method should be able to return the number +of the selected subsystem iSysSel where it occured, +so that the spacelike shower can be told which system to update, +if necessary. Therefore iSysSel must be set in +branch (or already in pTnext). + + + +This method is not at all required. In the current implementation it +outputs a list of all the dipole ends, with information on the +respective dipole. The routine is not called anywhere in the public +code, but has been inserted at various places during the +development/debug phase. + + +

The SpaceShower interface

+ +If you want to replace the SpaceShower class this would +involve replacing the virtual methods in the following. You will find +that much of the story reminds of TimeShower above, and +actually some cut-and-paste of text is involved. In some respects the +description is simpler, since there are no special cases for resonance +decays and non-interleaved evolution. Thus there is no correspondence +to the TimeShower::shower(...) routine. + + +The constructor does not need to do anything. + + + +Also the destructor does not need to do anything. + + + +This method only imports pointers to standard facilities, +and is not virtual. + + + +You have to store your local copy of the pointers to these objects, +since they have to be used during the generation, as explained above. +This is also the place to do initialization of whatever parameters +you plan to use, e.g. by reading in them from a user-accessible +database like the Settings one. + + + +The question is whether the ISR should be allowed to occur at larger +scales than the hard process it surrounds. This is process-dependent. +For instance, if the hard process is Z^0 production we know +that ISR should be allowed to go right up to the kinematical limit. +If it is a 2 -> 2 QCD process the ISR should not exceed +the scale of the hard process, since if so one would doublecount. +The SpaceShower:pTmaxMatch switch allows you to force the +behaviour, or else to program your own logic. The current default +implementation limits pT whenever the final state contains +a quark (except top), gluon or photon, since then the danger of +doublecounting is there. You may replace by your own logic, or leave as is. +
The internal PYTHIA implementation also allows intermediate options, +where emissions can go up to the kinematical limit but be dampened above +the factorization or renormalization scale. Therefore the (square of the) +latter two are provided as optional input parameters. + + + +When the above method limits pT_max to the scale of the process, +it may still be convenient to vary the matching slightly for the hardest +interaction in an event, to probe the sensitivity to such details. The +base-class implementation returns the value of the +SpaceShower:pTmaxFudge parameter. + + + +This method is called immediately after a new interaction has been +added, and should then be used to prepare the subsystem of partons +for subsequent evolution. In the current code this involves identifying +the colour and charge dipole ends: the position of radiating and recoiling +partons, maximum pT scales, and possible higher-order matrix +elements matchings to apply. Depending on what you have in mind you may +choose to store slightly different quantities. You have to use the +subsystem information described above to find the positions of the two +incoming partons (and the outgoing ones) of the system, and from there +the scales at which they were produced. +
The limitPTmax input agrees with the output of the +previous method for the hardest process, and is always true for +subsequent MI, since there an unlimited pT for sure +would lead to doublecounting. + + + +This method is called immediately after a timelike branching in the +iSys'th subsystem. Thus the information for that system may +be out-of-date, and to be updated. For the standard PYTHIA showers +this routine does not need to do anything, but that may be different +in another implementation. + + + +This is the main driver routine for the downwards evolution. A new +pT is to be selected based on the current information set up +by the routines above, and along with that a branching parton or dipole. +The pTbegAll scale is the maximum scale allowed, from which +the downwards evolution should be begun (usually respecting the maximum +scale of each individual parton). If no emission is found above +pTendAll (and above the respective shower cutoff scales) +then 0. should be returned and no emissions will be allowed. +Both scales can vary from one event to the next: if a scale has +already been selected for MI or ISR it makes no sense to look for +a scale smaller than that from FSR, since it would not be able to +compete, so pTendAll is set correspondingly. As it happens, +FSR is tried before ISR and MI in the interleaved evolution, +but this is an implementational detail that could well change. +
Typically the implementation of this routine would be to set +up a loop over all possible radiating objects (dipoles, dipole ends, ...), +for each pick its possible branching scale and then pick the one +with largest scale as possible winner. At this stage no branching should +actually be carried out, since MI, ISR and FSR still have to be compared +to assign the winner. +
The final input nRadIn provides the total number of +ISR and FSR emissions already generated in the event, and so allows a +special treatment for the very first emission, if desired. + + + +This method will be called once FSR has won the competition with +MI and ISR to do the next branching. The candidate branching found +in the previous step should here be carried out in full. The +pre-branching partons should get a negative status code and new +replacement ones added to the end of the event record. Also the +subsystem information should be updated, and possibly also the +beams. +
Should some problem be encountered in this procedure, e.g. if +some not-previously-considered kinematics requirement fails, it is +allowed to return false to indicate that no branching +could be carried out. Also a complete restart of the parton-level +description may be necessary, see doRestart() below. + + + +This method is not virtual. If a branching is constructed by the +previous routine this tiny method should be able to return the number +of the selected subsystem iSysSel where it occured, +so that the spacelike shower can be told which system to update, +if necessary. Therefore iSysSel must be set in +branch (or already in pTnext). + + + +This method is not virtual. If branch(...) above fails +to construct a branching, and the conditions are such that the whole +parton-level description should be restarted, then it should return +true, else not. Currently only the rescattering description can give +thi kind of failures, and so the internal rescatterFail +boolean must be set true when this should happen, and else false. + + + +This method is not at all required. In the current implementation it +outputs a list of all the dipole ends, with information on the +respective dipole. The routine is not called anywhere in the public +code, but has been inserted at various places during the +development/debug phase. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Index.xml b/PYTHIA8/pythia8140/xmldoc/Index.xml new file mode 100644 index 00000000000..e4af69a3a5c --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Index.xml @@ -0,0 +1,121 @@ + + +Pythia logo + +

PYTHIA 8 Index

+ +

Program Overview

+ +Frontpage
+Program Flow
+Settings Scheme
+Particle Data Scheme
+Program Files
+Program Classes
+Program Methods
+Sample Main Programs
+ +

Setup Run Tasks

+ + +Save Settings
+Main-Program Settings
+Beam Parameters
+Random-Number Seed
+PDF Selection
+Master Switches
+Process Selection
+  --   +QCD
+  --   +Electroweak
+  --   +Onia
+  --   +Top
+  --   +Fourth Generation
+  --   +Higgs
+  --   +SUSY
+  --   +New Gauge Bosons
+  --   +Left-Right Symmetry
+  --   +Leptoquark
+  --   +Compositeness
+  --   +Hidden Valleys
+  --   +Extra Dimensions
+A Second Hard Process
+Phase Space Cuts
+Couplings and Scales
+Standard-Model Parameters
+Total Cross Sections
+Resonance Decays
+Timelike Showers
+Spacelike Showers
+Multiple Interactions
+Beam Remnants
+Diffraction
+Fragmentation
+Flavour Selection
+Particle Decays
+Bose-Einstein Effects
+Particle Data
+Error Checks
+Tunes
+ + +

Study Output

+ + +Four-Vectors
+Particle Properties
+Event Record
+Event Information
+Event Statistics
+Event Analysis
+Histograms
+Advanced Usage
+ + +

Link to Other Programs

+ + +Les Houches Accord
+SUSY Les Houches Accord
+HepMC Interface
+ROOT usage
+Semi-Internal Processes
+Semi-Internal Resonances
+Hadron-Level Standalone
+External Decays
+Beam Shape
+Parton Distributions
+Jet Finders
+Random Numbers
+User Hooks
+Implement New Showers
+ + +

Reference Materiel

+ +PYTHIA 6 Translation Table
+Update History
+Bibliography
+Glossary
+Version + +

Separate documents

+ +Brief Introduction
+Worksheet + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/JetFinders.xml b/PYTHIA8/pythia8140/xmldoc/JetFinders.xml new file mode 100644 index 00000000000..ac39c0b4553 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/JetFinders.xml @@ -0,0 +1,27 @@ + + +

Jet Finders

+ +Pythia comes with two built-in +jet finders, ClusterJet for e^+e^- events +and CellJet for hadron collider ones. Especially the +latter is not so well matched to the standards of its field, however. +(But it is closely related to the anti-kT algorithm, +so is also not completely disconnected Cac08.) + +

FastJet

+ +For realistic jet studies the FastJet package +Cac06 has become a standard. Several different +jet options are available, such as kT, +Cambridge/Aachen, anti-kT and SISCone. + +

+Linking to FastJet is foreseen in the configure +file in the examples subdirectory, and the +main61.cc program contains an example how it can +be used with Pythia events. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/LeftRightSymmetryProcesses.xml b/PYTHIA8/pythia8140/xmldoc/LeftRightSymmetryProcesses.xml new file mode 100644 index 00000000000..c863976400d --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/LeftRightSymmetryProcesses.xml @@ -0,0 +1,183 @@ + + +

Left-Right-Symmetry Processes

+ +At current energies, the world is left-handed, i.e. the Standard Model +contains an SU(2)_L group. Left-right symmetry at some larger +scale implies the need for an SU(2)_R group. Thus the particle +content is expanded by right-handed Z_R^0 and W_R^+- +and right-handed neutrinos. The Higgs fields have to be in a triplet +representation, leading to doubly-charged Higgs particles, one set for +each of the two SU(2) groups. Also the number of neutral and +singly-charged Higgs states is increased relative to the Standard Model, +but a search for the lowest-lying states of this kind is no different +from e.g. the freedom already accorded by the MSSM Higgs scenarios. + +

+PYTHIA implements the scenario of Hui97. + +

+The W_R^+- has been implemented as a simple copy of the +ordinary W^+-, with the exception that it couples to +right-handed neutrinos instead of the ordinary left-handed ones. +Thus the standard CKM matrix is used in the quark sector, and the +same vector and axial coupling strengths, leaving only the mass as +free parameter. The Z_R^0 implementation (without interference +with the photon or the ordinary Z^0) allows decays both to +left- and right-handed neutrinos, as well as other fermions, according +to one specific model ansatz. Obviously both the W_R^+- +and the Z_R^0 descriptions are likely to be simplifications, +but provide a starting point. + +

+For the doubly-charged Higgses, the main decay modes implemented are +H_L^++ -> W_L^+ W_L^+, l_i^+ l_j^+ (i, j generation +indices) and H_R^++ -> W_R^+ W_R^+, l_i^+ l_j^+. + +

+The right-handed neutrinos can be allowed to decay further. Assuming them +to have a mass below that of W_R^+-, they decay to three-body +states via a virtual W_R^+-, nu_Rl -> l+- f fbar', +where both lepton charges are allowed owing to the Majorana character +of the neutrinos. If there is a significant mass splitting, also +sequential decays nu_Rl -> l+- l'-+ nu'_Rl are allowed. +Currently the decays are isotropic in phase space. If the neutrino +masses are close to or above the W_R^ ones, this description +has to be substituted by a sequential decay via a real W_R^ +(not implemented, but actually simpler to do than the one here). + + +

Production processes

+ +A few different production processes have been implemented, which normally +would not overlap and therefore could be run together. + + +Common switch for the group of implemented processes within a +left-right-symmetric scenario. + + + +Scatterings f fbar -> Z_R^0. +Code 3101. + + + +Scatterings W_R^+. +Code 3102. + + + +Scatterings l_i l_j -> H_L^--. +Code 3121. + + + +Scatterings l_i gamma -> H_L^-- e^+. +Code 3122. + + + +Scatterings l_i gamma -> H_L^-- mu^+. +Code 3123. + + + +Scatterings l_i gamma -> H_L^-- tau^+. +Code 3124. + + + +Scatterings f_1 f_2 -> H_L^-- f_3 f_4 via WW fusion. +Code 3125. + + + +Scatterings f fbar -> H_L^++ H_L^--. +Code 3126. + + + +Scatterings l_i l_j -> H_R^--. +Code 3141. + + + +Scatterings l_i gamma -> H_R^-- e^+. +Code 3142. + + + +Scatterings l_i gamma -> H_R^-- mu^+. +Code 3143. + + + +Scatterings l_i gamma -> H_R^-- tau^+. +Code 3144. + + + +Scatterings f_1 f_2 -> H_R^-- f_3 f_4 via WW fusion. +Code 3145. + + + +Scatterings f fbar -> H_R^++ H_L^--. +Code 3146. + + +

Parameters

+ +The basic couplings of the model are + + +lefthanded coupling g_L = e / sin(theta). + + + +righthanded coupling g_R, assumed the same as g_L. + + + +vacuum expectation value v_L (in GeV) for the left-triplet. + + +

+The corresponding vacuum expectation value v_R is assumed +given by v_R = sqrt(2) M_WR / g_R and is not stored explicitly. + +

+The Yukawa couplings of a lepton pair to a H^--, assumed the +same for H_L^-- and H_R^--, is described by a symmetric +3-by-3 matrix. The default matrix is dominated by the diagonal elements +and especially by the tau tau one. + + +Yukawa coupling for H^-- -> e- e-. + + + +Yukawa coupling for H^-- -> mu- e-. + + + +Yukawa coupling for H^-- -> mu- mu-. + + + +Yukawa coupling for H^-- -> tau- e-. + + + +Yukawa coupling for H^-- -> tau- mu-. + + + +Yukawa coupling for H^-- -> tau- tau-. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/LeptoquarkProcesses.xml b/PYTHIA8/pythia8140/xmldoc/LeptoquarkProcesses.xml new file mode 100644 index 00000000000..1f891723adb --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/LeptoquarkProcesses.xml @@ -0,0 +1,84 @@ + + +

Leptoquark Processes

+ +Leptoquarks arise in many scenarios, and can have widely different +characteristics, with respect to spin, isospin amd flavour. +The current implentation in no sense attempts to exhaust these +possibilities, but only to encode one of the simplest possibilities, +with a single scalar leptoquark, denoted LQ and assigned PDG +code 42. The leptoquark is assumed to carry specific quark +and lepton quantum numbers, by default u quark plus electron. +These flavour numbers are conserved, i.e. a process such as +u e^- -> LQ -> d nu_e is not allowed. + +

+Although only one leptoquark is implemented, its flavours may be +changed arbitrarily to study the different possibilities. The +flavours of the leptoquark are defined by the quark and lepton +flavours in the decay mode list. Therefore, to change from the +current u e^- to c mu^+, say, you only need +a line +
pythia.readString("42:0:products = 4 -13"); +
in your main program, or the equivalent in a command file. +The former must always be a quark, while the latter could be a lepton +or an antilepton; a charge-conjugate partner is automatically defined +by the program. At initialization, the charge is recalculated as a +function of the flavours defined; also the leptoquark name is redefined +to be of the type LQ_q,l, where actual quark and lepton +flavours are displayed. + +

+The leptoquark is likely to be fairly long-lived, in which case it +could have time to fragment into a mesonic- or baryonic-type state, which +would decay later on. Currently this posibility is not handled; therefore +the leptoquark is always assumed to decay before fragmentation. +For that reason the leptoquark can also not be put stable. + +

Production processes

+ +Four production processes have been implemented, which normally would +not overlap and therefore could be run together. + + +Common switch for the group of lowest-order LQ production +processes, i.e. the four ones below. + + + +Scatterings q l -> LQ. +Code 3201. + + + +Scatterings q g -> LQ l. +Code 3202. + + + +Scatterings g g -> LQ LQbar. +Code 3203. + + + +Scatterings q qbar -> LQ LQbar. +Code 3204. + + +

Parameters

+ +In the above scenario the main free parameters are the leptoquark flavour +content, set as already described, and the LQ mass, set as usual. +In addition there is one further parameter. + + +multiplicative factor in the LQ -> q l squared Yukawa coupling, +and thereby in the LQ width and the q l -> LQ and +other cross sections. Specifically, lambda^2/(4 pi) = k alpha_em, +i.e. it corresponds to the $k$ factor of Hew88. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/LesHouchesAccord.xml b/PYTHIA8/pythia8140/xmldoc/LesHouchesAccord.xml new file mode 100644 index 00000000000..436fd2d9130 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/LesHouchesAccord.xml @@ -0,0 +1,593 @@ + + +

Les Houches Accord

+ +The Les Houches Accord (LHA) for user processes Boo01 is the +standard way to input parton-level information from a +matrix-elements-based generator into PYTHIA. The conventions for +which information should be stored has been defined in a Fortran context, +as two commonblocks. Here a C++ equivalent is defined, as a single class. + +

+The LHAup class is a base class, containing reading and +printout functions, plus two pure virtual functions, one to set +initialization information and one to set information on each new event. +Derived classes have to provide these two virtual functions to do +the actual work. The existing derived classes are for reading information +from a Les Houches Event File (LHEF), from the respective Fortran +commonblocks, or from PYTHIA 8 itself. + +

+You are free to write your own derived classes, using the rules and +methods to be described below. Normally, pointers to objects of such +derived classes should be handed in with the +Pythia::init( LHAup*) +method. However, with the LHEF format a filename can replace the +pointer, see further below. + +

+Let us now describe the methods at your disposal to do the job. + + +the base class constructor takes the choice of mixing/weighting +strategy as optional input argument, and calls setStrategy, +see below. It also reserves some space for processes and particles. + + + +the destructor does not need to do anything. + + + +this method only sets the pointer that allows some information +to be accessed, and is automatically called by +Pythia::init(...). + + +

Initialization

+ +The LHAup class stores information equivalent to the +/HEPRUP/ commonblock, as required to initialize the event +generation chain. The main difference is that the vector container +now allows a flexible number of subprocesses to be defined. For the +rest, names have been modified, since the 6-character-limit does not +apply, and variables have been regrouped for clarity, but nothing +fundamental is changed. + + +this pure virtual method has to be implemented in the derived class, +to set relevant information when called. It should return false if it +fails to set the info. + + +

+Inside setInit(), such information can be set by the following +methods: + + + +sets the properties of the first and second incoming beam, respectively +(cf. the Fortran IDBMUP(1), EBMUP(i), PDFGUP(i), PDFSUP(i), +with i 1 or 2). The parton distribution information +defaults to zero. These numbers can be used to tell which PDF sets were +used when the hard process was generated, while the normal +PDF Selection is used for the further +event generation in PYTHIA. + + + +sets the event weighting and cross section strategy. The default, +provided in the class constructor, is 3, which is the natural value +e.g. for an LHEF. + +chosen strategy (cf. IDWTUP; see Sjo06 +section 9.9.1 for extensive comments). + events come with non-negative weight, given in units +of pb, with an average that converges towards the cross section of the +process. PYTHIA is in charge of the event mixing, i.e. for each new +try decides which process should be generated, and then decides whether +is should be kept, based on a comparison with xMax. +Accepted events therefore have unit weight. + as option 1, except that cross sections can now be +negative and events after unweighting have weight +-1. You can use +Info::weight() +to find the weight of the current event. A correct event mixing requires +that a process that can take both signs should be split in two, one limited +to positive or zero and the other to negative or zero values, with +xMax chosen appropriately for the two. + events come with non-negative weight, in unspecified +units, but such that xMax can be used to unweight the events +to unit weight. Again PYTHIA is in charge of the event mixing. +The total cross section of a process is stored in +xSec. + as option 2, except that cross sections can now be +negative and events after unweighting have weight +-1. As for option -1 +processes with indeterminate sign should be split in two. + events come with unit weight, and are thus accepted +as is. The total cross section of the process is stored in +xSec. + as option 3, except that events now come with weight ++-1. Unlike options -1 and -2 processes with indeterminate sign need not be +split in two, unless you intend to mix with internal PYTHIA processes +(see below). + events come with non-negative weight, given in units +of pb, with an average that converges towards the cross section of the +process, like for option 1. No attempt is made to unweight the events, +however, but all are generated in full, and retain their original weight. +For consistency with normal PYTHIA units, the weight stored in +Info::weight() has been converted to mb, however. + + as option 4, except that events now can come +either with positive or negative weights. +Note 1: if several processes have already been mixed and +stored in a common event file, either LHEF or some private format, it +would be problematical to read back events in a different order. Since it +is then not feasible to let PYTHIA pick the next process type, strategies ++-1 and +-2 would not work. Instead strategy 3 would be the recommended +choice, or -3 if negative-weight events are required. +Note 2: it is possible to switch on internally implemented +processes and have PYTHIA mix these with LHA ones according to their relative +cross sections for strategies +-1, +-2 and 3. It does not work for strategy +-3 unless the positive and negative sectors of the cross sections are in +separate subprocesses (as must always be the case for -1 and -2), since +otherwise the overall mixture of PYTHIA and LHA processes will be off. +Mixing is not possible for strategies +-4, since the weighting procedure +is not specified by the standard. (For instance, the intention may be to +have events biased towards larger pT values in some particular +functional form.) + + + + +sets info on an allowed process (cf. LPRUP, XSECUP, XERRUP, +XMAXUP). +Each new call will append one more entry to the list of processes. +The choice of strategy determines which quantities are mandatory: +xSec for strategies +-2 and +-3, +xErr never, and +xMax for strategies +-1 and +-2. + + +Note: PYTHIA does not make active use of the (optional) +xErr values, but calculates a statistical cross section +error based on the spread of event-to-event weights. This should work +fine for strategy options +-1, but not for the others. Specifically, +for options +-2 and +-3 the weight spread may well vanish, and anyway +is likely to be an underestimate of the true error. If the author of the +LHA input information does provide error information you may use that - +this information is displayed at initialization. If not, then a relative +error decreasing like 1/sqrt(n_acc), where n_acc +is the number of accepted events, should offer a reasonable estimate. + + +update the xSec value of the i'th process +added with addProcess method (i.e. i runs +from 0 through sizeProc() - 1, see below). + + + +update the xErr value of the i'th process +added with addProcess method. + + + +update the xMax value of the i'th process +added with addProcess method. + + +

+Information is handed back by the following methods +(that normally you would not need to touch): + + + + + + + + + + + + + + + +for the beam properties. + + +for the strategy choice. + + +for the number of subprocesses. + + + + + + + + +for process i in the range 0 <= i < +sizeProc(). + + + +prints the above initialization information. This method is +automatically called from Pythia::init(...), +so would normally not need to be called directly by the user. + + +

Event input

+ +The LHAup class also stores information equivalent to the +/HEPEUP/ commonblock, as required to hand in the next +parton-level configuration for complete event generation. The main +difference is that the vector container now allows a flexible number +of partons to be defined. For the rest, names have been modified, +since the 6-character-limit does not apply, and variables have been +regrouped for clarity, but nothing fundamental is changed. + +

+The LHA standard is based on Fortran arrays beginning with +index 1, and mother information is defined accordingly. In order to +be compatible with this convention, the zeroth line of the C++ particle +array is kept empty, so that index 1 also here corresponds to the first +particle. One small incompatibility is that the sizePart() +method returns the full size of the particle array, including the +empty zeroth line, and thus is one larger than the true number of +particles (NUP). + + +this pure virtual method has to be implemented in the derived class, +to set relevant information when called. For strategy options +-1 +and +-2 the input idProcess value specifies which process +that should be generated, while idProcess is irrelevant +for strategies +-3 and +-4. The method should return false if it fails +to set the info, i.e. normally that the supply of events in a file is +exhausted. If so, no event is generated, and Pythia::next() +returns false. You can then interrogate +Info::atEndOfFile() +to confirm that indeed the failure is caused in this method, and decide +to break out of the event generation loop. + +

+Inside a normal setEvent(...) call, information can be set +by the following methods: + +tells which kind of process occured, with what weight, at what scale, +and which alpha_EM and alpha_strong were used +(cf. IDPRUP, XWTGUP, SCALUP, AQEDUP, AQCDUP). This method +also resets the size of the particle list, and adds the empty zeroth +line, so it has to be called before the addParticle method below. + + +gives the properties of the next particle handed in (cf. IDUP, ISTUP, +MOTHUP(1,..), MOTHUP(2,..), ICOLUP(1,..), ICOLUP(2,..), PUP(J,..), +VTIMUP, SPINUP) . + + +

+Information is handed back by the following methods: + +process number. + + +. +Note that the weight stored in Info::weight() as a rule +is not the same as the above weight(): the method here gives +the value before unweighting while the one in info gives +the one after unweighting and thus normally is 1 or -1. Only with strategy +options +-3 and +-4 would the value in info be the same as +here, except for a conversion from pb to mb for +-4. + + + + + + + +scale and couplings at that scale. + + + +the size of the particle array, which is one larger than the number +of particles in the event, since the zeroth entry is kept empty +(see above). + + + + + + + + + + + + + + + + + + + + + + + + + + + +for particle i in the range +0 <= i < sizePart(). (But again note that +i = 0 is an empty line, so the true range begins at 1.) + + +

+In the LHEF description Alw06 an extension to +include information on the parton densities of the colliding partons +is suggested. This optional further information can be set by + +which gives the flavours , the x and the Q scale +(in GeV) at which the parton densities x*f_i(x, Q) have been +evaluated. + + +

+This information is returned by the methods + + + + + + + + + + + + + + + +where the first one tells whether this optional information has been set +for the current event. (setPdf(...) must be called after the +setProcess(...) call of the event for this to work.) + + +

+ +prints the above information for the current event. In cases where the +LHAup object is not available to the user, the +Pythia::LHAeventList(ostream& os = cout) method can +be used, which is a wrapper for the above. + + + +skip ahead nSkip events in the Les Houches generation +sequence, without doing anything further with them. Mainly +intended for debug purposes, e.g. when an event at a known +location in a Les Houches Event File is causing problems. +Will return false if operation fails, specifically if the +end of an LHEF has been reached. The implementation in the base class +simply executes setEvent() the requested number of times. +The derived LHAupLHEF class (see below) only uses the +setNewEventLHEF(...) part of its setEvent() +method, and other derived classes could choose other shortcuts. + + +

+The LHA expects the decay of resonances to be included as part of the +hard process, i.e. if unstable particles are produced in a process then +their decays are also described. This includes Z^0, W^+-, H^0 +and other short-lived particles in models beyond the Standard Model. +Should this not be the case then PYTHIA will perform the decays of all +resonances it knows how to do, in the same way as for internal processes. +Note that you will be on slippery ground if you then restrict the decay of +these resonances to specific allowed channels since, if this is not what +was intended, you will obtain the wrong cross section and potentially the +wrong mix of different event types. (Since the original intention is +unknown, the cross section will not be corrected for the fraction of +open channels, i.e. the procedure used for internal processes is not +applied in this case.) + +

An interface to Les Houches Event Files

+ +The LHEF standard Alw06 specifies a format where a single file +packs initialization and event information. This has become the most +frequently used procedure to process external parton-level events in +Pythia. Therefore a special +Pythia::init(fileName) +initialization option exists, where the LHEF name is provided as input. +Internally this name is then used to create an instance of the derived +class LHAupLHEF, which can do the job of reading an LHEF. + +

+An example how to generate events from an LHEF is found in +main12.cc. Note the use of +Info::atEndOfFile() to find out when the whole +LHEF has been processed. + +

+To allow the sequential use of several event files the +Pythia::init(...) method has an optional second argument: +Pythia::init(fileName, bool skipInit = false). +If called with this argument true then there will be no +initialization, except that the existing LHAupLHEF class +instance will be deleted and replaced by ones pointing to the new file. +It is assumed (but never checked) that the initialization information is +identical, and that the new file simply contains further events of +exactly the same kind as the previous one. An example of this possibility, +and the option to mix with internal processes, is found in +main13.cc. + +

+The workhorses of the LHAupLHEF class are three methods +found in the base class, so as to allow them to be reused in other +contexts. Specifically, it allows derived classes where one parton-level +configuration can be reused several times, e.g. in the context of +matrix-element-to-parton-shower matching (example in preparation). +To begin with also a small utility routine. + + +always returns true in the base class, but in LHAupLHEF +it returns false if the LHEF provided in the constructor is not +found and opened correctly. + + + +read in and set all required initialization information from the +specified stream. Return false if it fails. + + + +read in event information from the specified stream into a staging area +where it can be reused by setOldEventLHEF. + + + +store the event information from the staging area into the normal +location. Thus a single setNewEventLHEF call can be +followed by several setOldEventLHEF ones, so as to +process the same configuration several times. This method currently +only returns true, i.e. any errors should be caught by the preceding +setNewEventLHEF call. + + + +

A runtime Fortran interface

+ +The runtime Fortran interface requires linking to an external Fortran +code. In order to avoid problems with unresolved external references +when this interface is not used, the code has been put in a separate +LHAFortran.h file, that is not included in any of the +other library files. Instead it should be included in the +user-supplied main program, together with the implementation of two +methods below that call the Fortran program to do its part of the job. + +

+The LHAupFortran class derives from LHAup. +It reads initialization and event information from the LHA standard +Fortran commonblocks, assuming these commonblocks behave like two +extern "C" struct named heprup_ and +hepeup_. (Note the final underscore, to match how the +gcc compiler internally names Fortran files.) + +

+The instantiation does not require any arguments. + +

+The user has to supply implementations of the fillHepRup() +and fillHepEup() methods, that is to do the actual calling +of the external Fortran routines that fill the HEPRUP and +HEPEUP commonblocks. The translation of this information to +the C++ structure is provided by the existing setInit() and +setEvent() code. + +

+Up to and including version 8.125 the LHAupFortran class +was used to construct a runtime interface to PYTHIA 6.4. This was +convenient in the early days of PYTHIA 8 evolution, when this program +did not yet contain hard-process generation, and the LHEF standard +did not yet exist. Nowadays it is more of a bother, since a full +cross-platform support leads to many possible combinations. Therefore +the support has been reduced in the current version. Only the +main51.cc example remains as an illustration, where the +previously separate interface code +(include/Pythia6Interface.h) has been inserted in the +beginning. You also need to modify the examples/Makefile +to link main51.cc properly also to a PYTHIA 6.4 library +version, see commented-out section for ideas how to to this. + +

Methods for LHEF output

+ +The main objective of the LHAup class is to feed information +from an external program into PYTHIA. It can be used to export information +as well, however. Specifically, there are four routines in the base class +that can be called to write a Les Houches Event File. These should be +called in sequence in order to build up the proper file structure. + + +Opens a file with the filename indicated, and writes a header plus a brief +comment with date and time information. + + + +Writes initialization information to the file above. Such information should +already have been set with the methods described in the "Initialization" +section above. + + + +Writes event information to the file above. Such information should +already have been set with the methods described in the "Event input" +section above. This call should be repeated once for each event to be +stored. + + + +Writes the closing tag and closes the file. Optionally, if +updateInit = true, this routine will reopen the file from +the beginning, rewrite the same header as openLHEF() did, +and then call initLHEF() again to overwrite the old +information. This is especially geared towards programs, such as PYTHIA +itself, where the cross section information is not available at the +beginning of the run, but only is obtained by Monte Carlo integration +in parallel with the event generation itself. Then the +setXSec( i, xSec), setXErr( i, xSec) and +setXMax( i, xSec) can be used to update the relevant +information before closeLHEF is called. +Warning: overwriting the beginning of a file without +upsetting anything is a delicate operation. It only works when the new +lines require exactly as much space as the old ones did. Thus, if you add +another process in between, the file will be corrupted. + + +

PYTHIA 8 output to an LHEF

+ +The above methods could be used by any program to write an LHEF. +For PYTHIA 8 to do this, a derived class already exists, +LHAupFromPYTHIA8. In order for it to do its job, +it must gain access to the information produced by PYTHIA, +specifically the process event record and the +generic information stored in info. Therefore, if you +are working with an instance pythia of the +Pythia class, you have to instantiate +LHAupFromPYTHIA8 with pointers to the +process and info objects of +pythia: +
LHAupFromPYTHIA8 myLHA(&pythia.process, &pythia.info); + +

+The method setInit() should be called to store the +pythia initialization information in the LHA object, +and setEvent() to store event information. +Furthermore, updateSigma() can be used at the end +of the run to update cross-section information, cf. +closeLHEF(true) above. An example how the +generation, translation and writing methods should be ordered is +found in main20.cc. + +

+Currently there are some limitations, that could be overcome if +necessary. Firstly, you may mix many processes in the same run, +but the cross-section information stored in info only +refers to the sum of them all, and therefore they are all classified +as a common process 9999. Secondly, you should generate your events +in the CM frame of the collision, since this is the assumed frame of +stored Les Houches events, and no boosts have been implemented +for the case that Pythia::process is not in this frame. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/MainProgramSettings.xml b/PYTHIA8/pythia8140/xmldoc/MainProgramSettings.xml new file mode 100644 index 00000000000..79d5ebd353f --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/MainProgramSettings.xml @@ -0,0 +1,200 @@ + + +

Main-Program Settings

+ +

Introduction

+ +The main program is up to the user to write. However, +sample main programs +are provided. In one such class of programs, key settings of the run +are read in from a "cards file". These commands may be of two types
+(a) instructions directly to Pythia, like which +processes to generate, and
+(b) instructions to the main program for what it should do, +like how many events to generate, i.e. how many times +pythia.next() should be called.
+In principle these two kinds could be kept completely separate. +However, to make life simpler, a number of useful main-program +settings are defined on this page, so that they are recognized by +the Settings machinery. They can thus be put among +the other cards without distinction. It is up to you to decide which +ones, if any, you actually want to use when you write your main program. +For convenience, some in the second section below can also be interpreted +directly by Pythia, while the subsequent ones really have +to be used in your main program. + +

+Once you have used the pythia.readFile(fileName) method to +read in the cards file (alternatively with an istream instead +of a fileName), you can interrogate the Settings +database to make the values available in your main program. A slight +complication is that you need to use a different Settings +method for each of the four possible return types that you want to +extract. To save some typing the same method names are found directly +in the Pythia class, and just send on to the +Settings ones to do the job, e.g. +

+  bool   showCS = pythia.flag("Main:showChangedSettings");
+  int    nEvent = pythia.mode("Main:numberOfEvents");
+  double spare1 = pythia.parm("Main:spareParm1");
+  string file   = pythia.word("Main:allSettingsFile"); 
+
+ +

Run settings

+ +Here settings related to how many events to generate and whether +to print some information on data used in run. These variables +can be set in an input "cards" file, and thereafter read out an used +in the user-written main program. Usage is purely optional, but may help +you reduce the need to recompile your main program. + + +The number of events to be generated. + + + +The number of events to list. + + + +Print the number of events generated so far, this many times, +i.e. once every numberOfEvents/numberToShow events. + + + +Allow this many times that pythia.next() returns false, +i.e. that an event is flawed, before aborting the run. + + + +Print a list of the changed flag/mode/parameter/word settings. + + + +Print a list of all flag/mode/parameter/word settings. +Warning: this will be a long list. + + + +Print particle and decay data for the particle with this particular +identity code. Default means that no particle is printed. + + + +Print a list of particle and decay data for those particles +that were changed (one way or another). + + + +In the previous listing also include the resonances that are +initialized at the beginning of a run and thus get new particle +data, even if these may well agree with the default ones. +Warning: this will be a rather long list. + + + +Print a list of all particle and decay data. +Warning: this will be a long list. + + + +Write a file with the changed flag/mode/parameter/word settings, in +a format appropriate to be read in at the beginning of a new +run, using the pythia.readFile(fileName) method. + + + +The name of the file to which the changed flag/mode/parameter/word +settings are written if Main:writeChangedSettings +is on. + + + +Write a file with all flag/mode/parameter/word settings, in +a format appropriate to be read in at the beginning of a new +run, using the pythia.readFile(fileName) method. + + + +The name of the file to which a flag/mode/parameter/word +settings are written if Main:writeAllSettings +is on. + + + +Print all available statistics or only the minimal set at the end +of the run. + + +

Subruns

+ +You can use subruns to carry out +several tasks in the same run. In that case you will need repeated +instances of the first setting below in your command file, and could +additionally use the second and third as well. + + +The number of the current subrun, a non-negative integer, put as +first line in a section of lines to be read for this particular subrun. + + + +If you read several Les Houches Event Files that you want to see +considered as one single combined event sample you can set this flag +on after the first subrun to skip (most of) the +(re-)initialization step. + + + +The number of subruns you intend to use in your current run. +Unlike the two settings above, Pythia itself will not +intepret this number, but you could e.g. have a loop in your main +program to loop over subruns from 0 through +numberOfSubruns - 1. + + +

Spares

+ +For currently unforeseen purposes, a few dummy settings are made +available here. The user can set the desired value in a "cards file" +and then use that value in the main program as desired. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/MasterSwitches.xml b/PYTHIA8/pythia8140/xmldoc/MasterSwitches.xml new file mode 100644 index 00000000000..bb737bb0b7f --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/MasterSwitches.xml @@ -0,0 +1,172 @@ + + +

Master Switches

+ +Sometimes it may be convenient to omit certain aspects of the event +generation chain. This cannot be motivated in a full-blown production +run, but can often be convenient for own understanding and for +debug purposes. The flags on this page allow just that. + +

+The event generation is subdivided into three levels: the process +level, the parton level and the hadron level, and flags are grouped +accordingly. + +

Process Level

+ +The ProcessLevel class administrates the initial step of +the event generation, wherein the basic process is selected. Currently +this is done either using some of the internal processes, or with +Les Houches Accord input. + +

+There could not be a complete event without an initial process, so +it would not be a normal action to switch off this step. Furthermore, +without a process set, it is also not possible to carry out the tasks +on the parton level. It is still possible, however, to hadronize +a parton-level configuration provided by some external program. + + +If off, do not attempt to carry out any generation at all on the +process or parton level. Do allow parton configurations stored in +the event record to hadronize and hadrons to decay, however, as set +by the HadronLevel switches. Further details are found +here. + + +

+For ProcessLevel:all = on one part of the event generation +on this level may be switched off individually: + + +Master switch to allow resonance decays; on/off = true/false. +Normal hadrons and leptons do not count as resonances, so this is +aimed specifically towards Z^0, W^+-, t, h^0 and similar +objects beyond the Standard Model. Do not use this option if you +may produce coloured resonances and intend to allow hadronization, +since currently the program would not know how to handle this. + + +

+It is possible to stop the generation immediately after the basic +process has been selected, see PartonLevel:all below. + +

PartonLevel

+ +The PartonLevel class administrates the middle step of the +event generation, i.e. the evolution from an input (hard) process from +ProcessLevel, containing a few partons only, to a complete +parton-level configuration to be handed on to HadronLevel. +This step involves the application of initial- and final-state radiation, +multiple interactions and the structure of beam remnants. + + +If off then stop the generation after the hard process has been +generated, but before the parton-level and hadron-level steps. +The process record is filled, but the event +one is then not. + + +

+For PartonLevel:all = on some parts of the event generation +on this level may be switched off individually: + + +Master switch for multiple interactions; on/off = true/false. +Further options are found here. + + + +Master switch for initial-state radiation; on/off = true/false. +Further options are found here. + + + +Master switch for initial-state radiation; on/off = true/false. +Further options are found here. +If you leave this switch on, the following two switches allow +more detailed control to switch off only parts of the showers. + + + +Switch for final-state radiation in association with the hard process +itself; on/off = true/false. In addition PartonLevel:FSR +must be on for these emissions to occur. + + + +Master switch for final-state radiation in any resonance decays +subsequent to the hard process itself; on/off = true/false. In addition +PartonLevel:FSR must be on for these emissions to occur. + + +

+Switching off all the above MI/ISR/FSR switches is not equivalent +to setting PartonLevel:all = off. In the former case a +minimal skeleton of parton-level operations are carried out, such as +tying together the scattered partons with the beam remnants into colour +singlets, and storing this information in the event record. +It is therefore possible to go on and hadronize the event, if desired. +In the latter case no operations at all are carried out on the +parton level, and therefore it is also not possible to go on to the +hadron level. + + +Master switch for addition of beam remnants; on/off = true/false. +Only intended for very special applications, and cannot be used to +generate complete events. Specifically, unlike the other switches above, +the program will complain and possibly crash unlike you also set +HadronLevel:all = off and Check:event = off. + + +

+It is possible to stop the generation immediately after the parton level +has been set up, see HadronLevel:all below. + +

HadronLevel

+ +The HadronLevel class administrates the final step of the +event generation, wherein the partonic configuration from +PartonLevel is hadronized, including string fragmentation +and secondary decays. + +

+Most of the code in this class itself deals with subdividing the partonic +content of the event into separate colour singlets, that can be +treated individually by the string fragmentation machinery. When a +junction and an antijunction are directly connected, it also breaks +the string between the two, so that the topology can be reduced back +to two separate one-junction systems, while still preserving the +expected particle flow in the junction-junction string region(s). + + +If off then stop the generation after the hard process and +parton-level activity has been generated, but before the +hadron-level steps. + + +

+For HadronLevel:all = on some parts of the event generation +on this level may be switched off individually: + + +Master switch for hadronization; on/off = true/false. +Further options are found here. + + + +Master switch for decays; on/off = true/false. +Further options are found here. + + + +Master switch for the simulation of Bose-Einstein effects; +on/off = true/false. Further options are found +here. + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/MultipleInteractions.xml b/PYTHIA8/pythia8140/xmldoc/MultipleInteractions.xml new file mode 100644 index 00000000000..178e1e4e704 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/MultipleInteractions.xml @@ -0,0 +1,507 @@ + + +

Multiple Interactions

+ +The starting point for the multiple interactions physics scenario in +PYTHIA is provided by Sjo87. Recent developments have +included a more careful study of flavour and colour correlations, +junction topologies and the relationship to beam remnants +Sjo04, and interleaving with initial-state radiation +Sjo05, making use of transverse-momentum-ordered +initial- and final-state showers. Currently a framework to handle +rescattering is under development. + +

+A big unsolved issue is how the colour of all these subsystems is +correlated. For sure there is a correlation coming from the colour +singlet nature of the incoming beams, but in addition final-state +colour rearrangements may change the picture. Indeed such extra +effects appear necessary to describe data, e.g. on +<pT>(n_ch). A simple implementation of colour +rearrangement is found as part of the +beam remnants description. + +

Main variables

+ +

Matching to hard process

+ +The maximum pT to be allowed for multiple interactions is +related to the nature of the hard process itself. It involves a +delicate balance between not doublecounting and not leaving any +gaps in the coverage. The best procedure may depend on information +only the user has: how the events were generated and mixed (e.g. with +Les Houches Accord external input), and how they are intended to be +used. Therefore a few options are available, with a sensible default +behaviour. + +Way in which the maximum scale for multiple interactions is set +to match the scale of the hard process itself. + + + + + +

Cross-section parameters

+ +The rate of interactions is determined by + +The value of alpha_strong at m_Z. Default value is +picked equal to the one used in CTEQ 5L. + + +

+The actual value is then regulated by the running to the scale +pT^2, at which it is evaluated + +The order at which alpha_strong runs at scales away from +m_Z. + + + + + +

+QED interactions are regulated by the alpha_electromagnetic +value at the pT^2 scale of an interaction. + + +The running of alpha_em used in hard processes. + + + + + +

+Note that the choices of alpha_strong and alpha_em +made here override the ones implemented in the normal process machinery, +but only for the interactions generated by the +MultipleInteractions class. + +

+In addition there is the possibility of a global rescaling of +cross sections (which could not easily be accommodated by a +changed alpha_strong, since alpha_strong runs) + +Multiply all cross sections by this fix factor. + + +

+The processes used to generate multiple interactions form a subset +of the standard library of hard processes. The input is slightly +different from the standard hard-process machinery, however, +since incoming flavours, the alpha_strong value and most +of the kinematics are aready fixed when the process is called. +It is possible to regulate the set of processes that are included in the +multiple-interactions framework. + + +Set of processes included in the machinery. + + + + + + +

Cross-section regularization

+ +There are two complementary ways of regularizing the small-pT +divergence, a sharp cutoff and a smooth dampening. These can be +combined as desired, but it makes sense to coordinate with how the +same issue is handled in spacelike +showers. Actually, by default, the parameters defined here are +used also for the spacelike showers, but this can be overridden. + +

+Regularization of the divergence of the QCD cross section for +pT -> 0 is obtained by a factor pT^4 / (pT0^2 + pT^2)^2, +and by using an alpha_s(pT0^2 + pT^2). An energy dependence +of the pT0 choice is introduced by two further parameters, +so that pT0Ref is the pT0 value for the reference +CM energy, pT0Ref = pT0(ecmRef). +Warning: if a large pT0 is picked for multiple +interactions, such that the integrated interaction cross section is +below the nondiffractive inelastic one, this pT0 will +automatically be scaled down to cope. + +

+The actual pT0 parameter used at a given CM energy scale, +ecmNow, is obtained as + + pT0 = pT0(ecmNow) = pT0Ref * (ecmNow / ecmRef)^ecmPow + +where pT0Ref, ecmRef and ecmPow are the +three parameters below. + + +The pT0Ref scale in the above formula. +Note: pT0Ref is one of the key parameters in a +complete PYTHIA tune. Its value is intimately tied to a number of other +choices, such as that of colour flow description, so unfortunately it is +difficult to give an independent meaning to pT0Ref. + + + +The ecmRef reference energy scale introduced above. + + + +The ecmPow energy rescaling pace introduced above. + + +

+Alternatively, or in combination, a sharp cut can be used. + +Lower cutoff in pT, below which no further interactions +are allowed. Normally pT0 above would be used to provide +the main regularization of the cross section for pT -> 0, +in which case pTmin is used mainly for technical reasons. +It is possible, however, to set pT0Ref = 0 and use +pTmin to provide a step-function regularization, or to +combine them in intermediate approaches. Currently pTmin +is taken to be energy-independent. + + +

+Gösta Gustafson has proposed (private communication, unpublished) +that the amount of screening, as encapsulated in the pT0 +parameter, fluctuates from one event to the next. Specifically, +high-activity event are more likely to lead to interactions at large +pT scales, but the high activity simultaneously leads to a +larger screening of interactions at smaller pT. Such a scenario +can approximately be simulated by scaling up the pT0 by a +factor sqrt(n), where n is the number of interactions +considered so far, including the current one. That is, for the first +interaction the dampening factor is pT^4 / (pT0^2 + pT^2)^2, +for the second pT^4 / (2 pT0^2 + pT^2)^2, for the third +pT^4 / (3 pT0^2 + pT^2)^2, and so on. Optionally the scheme +may also be applied to ISR emissions. For simplicity the same +alpha_s(pT0^2 + pT^2) is used throughout. Note that, in this +scenario the pT0 scale must be lower than in the normal case +to begin with, since it later is increased back up. Also note that the +idea with this scenario is to propose an alternative to colour +reconnection to understand the rise of <pT>(n_ch), +so that the amount of colour reconnection should be reduced. + +Choice to activate the above screening scenario, i.e. an increasing +effective pT0 for consecutive interactions. + + + + + +

Impact-parameter dependence

+ +The choice of impact-parameter dependence is regulated by several +parameters. + + +Choice of impact parameter profile for the incoming hadron beams. + + + + + + + +When assuming a double Gaussian matter profile, bProfile = 2, +the inner core is assumed to have a radius that is a factor +coreRadius smaller than the rest. + + + +When assuming a double Gaussian matter profile, bProfile = 2, +the inner core is assumed to have a fraction coreFraction +of the matter content of the hadron. + + + +When bProfile = 3 it gives the power of the assumed overlap +shape exp(- b^expPow). Default corresponds to a simple +exponential drop, which is not too dissimilar from the overlap +obtained with the standard double Gaussian parameters. For +expPow = 2 we reduce to the simple Gaussian, bProfile = 1, +and for expPow -> infinity to no impact parameter dependence +at all, bProfile = 0. For small expPow the program +becomes slow and unstable, so the min limit must be respected. + + +

Rescattering

+ +It is possible that a parton may rescatter, i.e. undergo a further +interaction subsequent to the first one. The machinery to model this +kind of physics has only recently become fully operational +Cor09, and is therefore not yet so well explored. + +

+The rescatting framework has ties with other parts of the program, +notably with the beam remnants. + + +Switch to allow rescattering of partons; on/off = true/false.
+Warning: use with caution since machinery is still not +so well tested. + + + +Switch to allow rescattering of partons, where both incoming partons +have already rescattered; on/off = true/false. Is only used if +MultipleInteractions:allowRescatter is switched on.
+Warning: currently there is no complete implementation that +combines it with shower evolution, so you must use +PartonLevel:ISR = off and PartonLevel:FSR = off. +If not, a warning will be issued and double rescattering will not be +simulated. The rate also comes out to be much lower than for single +rescattering, so to first approximation it can be neglected. + + + +Selection of which partons rescatter against unscattered partons +from the incoming beams A and B, based on their rapidity value +y in the collision rest frame. Here ySep is +shorthand for MultipleInteractions:ySepRescatter and +deltaY for MultipleInteractions:deltaYRescatter, +defined below. The description is symmetric between the two beams, +so only one case is described below. + + + + + + + + +used for some of the MultipleInteractions:rescatterMode +options above, as the rapidity for which a scattered parton has a 50% +probability to be considered as a potential rescatterer. +A ySep > 0 generally implies that some central partons cannot +rescatter at all, while a ySep < 0 instead allows central +partons to scatter against either beam. + + + +used for some of the MultipleInteractions:rescatterMode +options above, as the width of the rapidity transition region, where the +probability rises from zero to unity that a scattered parton is considered +as a potential rescatterer. + + + +

Further variables

+ +These should normally not be touched. Their only function is for +cross-checks. + + +Number of allowed incoming quark flavours in the beams; a change +to 4 would thus exclude b and bbar as incoming +partons, etc. + + + +The allowed pT range is split (unevenly) into 100 bins, +and in each of these the interaction cross section is evaluated in +nSample random phase space points. The full integral is used +at initialization, and the differential one during the run as a +"Sudakov form factor" for the choice of the hardest interaction. +A larger number implies increased accuracy of the calculations. + + +

Technical notes

+ +Relative to the articles mentioned above, not much has happened. +The main news is a technical one, that the phase space of the +2 -> 2 (massless) QCD processes is now sampled in +dy_3 dy_4 dpT^2, where y_3 and y_4 are +the rapidities of the two produced partons. One can show that + + (dx_1 / x_1) * (dx_2 / x_2) * d(tHat) = dy_3 * dy_4 * dpT^2 + +Furthermore, since cross sections are dominated by the "Rutherford" +one of t-channel gluon exchange, which is enhanced by a +factor of 9/4 for each incoming gluon, effective structure functions +are defined as + + F(x, pT2) = (9/4) * xg(x, pT2) + sum_i xq_i(x, pT2) + +With this technical shift of factors 9/4 from cross sections to parton +densities, a common upper estimate of + + d(sigmaHat)/d(pT2) < pi * alpha_strong^2 / pT^4 + +is obtained. + +

+In fact this estimate can be reduced by a factor of 1/2 for the +following reason: for any configuration (y_3, y_4, pT2) also +one with (y_4, y_3, pT2) lies in the phase space. Not both +of those can enjoy being enhanced by the tHat -> 0 +singularity of + + d(sigmaHat) propto 1/tHat^2. + +Or if they are, which is possible with identical partons like +q q -> q q and g g -> g g, each singularity comes +with half the strength. So, when integrating/averaging over the two +configurations, the estimated d(sigmaHat)/d(pT2) drops. +Actually, it drops even further, since the naive estimate above is +based on + + (4 /9) * (1 + (uHat/sHat)^2) < 8/9 < 1 + +The 8/9 value would be approached for tHat -> 0, which +implies sHat >> pT2 and thus a heavy parton-distribution +penalty, while parton distributions are largest for +tHat = uHat = -sHat/2, where the above expression +evaluates to 5/9. A fudge factor is therefore introduced to go the +final step, so it can easily be modifed when further non-Rutherford +processes are added, or should parton distributions change significantly. + +

+At initialization, it is assumed that + + d(sigma)/d(pT2) < d(sigmaHat)/d(pT2) * F(x_T, pT2) * F(x_T, pT2) + * (2 y_max(pT))^2 + +where the first factor is the upper estimate as above, the second two +the parton density sum evaluated at y_3 = y_ 4 = 0 so that +x_1 = x_2 = x_T = 2 pT / E_cm, where the product is expected +to be maximal, and the final is the phase space for +-y_max < y_{3,4} < y_max. +The right-hand side expression is scanned logarithmically in y, +and a N is determined such that it always is below +N/pT^4. + +

+To describe the dampening of the cross section at pT -> 0 by +colour screening, the actual cross section is multiplied by a +regularization factor (pT^2 / (pT^2 + pT0^2))^2, and the +alpha_s is evaluated at a scale pT^2 + pT0^2, +where pT0 is a free parameter of the order of 2 - 4 GeV. +Since pT0 can be energy-dependent, an ansatz + + pT0(ecm) = pT0Ref * (ecm/ecmRef)^ecmPow + +is used, where ecm is the current CM frame energy, +ecmRef is an arbitrary reference energy where pT0Ref +is defined, and ecmPow gives the energy rescaling pace. For +technical reasons, also an absolute lower pT scale pTmin, +by default 0.2 GeV, is introduced. In principle, it is possible to +recover older scenarios with a sharp pT cutoff by setting +pT0 = 0 and letting pTmin be a larger number. + +

+The above scanning strategy is then slightly modified: instead of +an upper estimate N/pT^4 one of the form +N/(pT^2 + r * pT0^2)^2 is used. At first glance, r = 1 +would seem to be fixed by the form of the regularization procedure, +but this does not take into account the nontrivial dependence on +alpha_s, parton distributions and phase space. A better +Monte Carlo efficiency is obtained for r somewhat below unity, +and currently r = 0.25 is hardcoded. + +In the generation a trial pT2 is then selected according to + + d(Prob)/d(pT2) = (1/sigma_ND) * N/(pT^2 + r * pT0^2)^2 * ("Sudakov") + +For the trial pT2, a y_3 and a y_4 are then +selected, and incoming flavours according to the respective +F(x_i, pT2), and then the cross section is evaluated for this +flavour combination. The ratio of trial/upper estimate gives the +probability of survival. + +

+Actually, to profit from the factor 1/2 mentioned above, the cross +section for the combination with y_3 and y_4 +interchanged is also tried, which corresponds to exchanging tHat +and uHat, and the average formed, while the final kinematics +is given by the relative importance of the two. + +

+Furthermore, since large y values are disfavoured by dropping +PDF's, a factor + + WT_y = (1 - (y_3/y_max)^2) * (1 - (y_4/y_max)^2) + +is evaluated, and used as a survival probability before the more +time-consuming PDF+ME evaluation, with surviving events given a +compensating weight 1/WT_y. + +

+An impact-parameter dependencs is also allowed. Based on the hard +pT scale of the first interaction, and enhancement/depletion +factor is picked, which multiplies the rate of subsequent interactions. + +

+Parton densities are rescaled and modified to take into account the +energy-momentum and flavours kicked out by already-considered +interactions. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/NewGaugeBosonProcesses.xml b/PYTHIA8/pythia8140/xmldoc/NewGaugeBosonProcesses.xml new file mode 100644 index 00000000000..ff9e7fba956 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/NewGaugeBosonProcesses.xml @@ -0,0 +1,344 @@ + + +

New-Gauge-Boson Processes

+ +This page contains the production of new Z'^0 and +W'^+- gauge bosons, e.g. within the context of a new +U(1) or SU(2) gauge group, and also a +(rather speculative) horizontal gauge boson R^0. +Left-right-symmetry scenarios also contain new gauge bosons, +but are described +separately. + +

Z'^0

+ +This group only contains one subprocess, with the full +gamma^*/Z^0/Z'^0 interference structure for couplings +to fermion pairs. It is possible to pick only a subset, e.g, only +the pure Z'^0 piece. No higher-order processes are +available explicitly, but the ISR showers contain automatic +matching to the Z'^0 + 1 jet matrix elements, as for +the corresponding gamma^*/Z^0 process. + + +Scattering f fbar ->Z'^0. +Code 3001. + + + +Choice of full gamma^*/Z^0/Z'^0 structure or not in +the above process. Note that, with the Z'^0 part switched +off, this process is reduced to what already exists among +electroweak processes, +so those options are here only for crosschecks. + + + + + + + +Note: irrespective of the option used, the particle produced +will always be assigned code 32 for Z'^0, and open decay channels +is purely dictated by what is set for the Z'^0. + + +

+The couplings of the Z'^0 to quarks and leptons can +either be assumed universal, i.e. generation-independent, or not. +In the former case eight numbers parametrize the vector and axial +couplings of down-type quarks, up-type quarks, leptons and neutrinos, +respectively. Depending on your assumed neutrino nature you may +want to restrict your freedom in that sector, but no limitations +are enforced by the program. The default corresponds to the same +couplings as that of the Standard Model Z^0, with axial +couplings a_f = +-1 and vector couplings +v_f = a_f - 4 e_f sin^2(theta_W), with +sin^2(theta_W) = 0.23. Without universality +the same eight numbers have to be set separately also for the +second and the third generation. The choice of fixed axial and +vector couplings implies a resonance width that increases linearly +with the Z'^0 mass. + +

+By a suitable choice of the parameters, it is possible to simulate +just about any imaginable Z'^0 scenario, with full +interference effects in cross sections and decay angular +distributions and generation-dependent couplings; the default values +should mainly be viewed as placeholders. The conversion +from the coupling conventions in a set of different Z'^0 +models in the literature to those used in PYTHIA is described by +C. +Ciobanu et al. + + +If on then you need only set the first-generation couplings +below, and these are automatically also used for the second and +third generation. If off, then couplings can be chosen separately +for each generation. + + +

+Here are the couplings always valid for the first generation, +and normally also for the second and third by trivial analogy: + + +vector coupling of d quarks. + + + +axial coupling of d quarks. + + + +vector coupling of u quarks. + + + +axial coupling of u quarks. + + + +vector coupling of e leptons. + + + +axial coupling of e leptons. + + + +vector coupling of nu_e neutrinos. + + + +axial coupling of nu_e neutrinos. + + +

+Here are the further couplings that are specific for +a scenario with Zprime:universality swiched off: + + +vector coupling of s quarks. + + + +axial coupling of s quarks. + + + +vector coupling of c quarks. + + + +axial coupling of c quarks. + + + +vector coupling of mu leptons. + + + +axial coupling of mu leptons. + + + +vector coupling of nu_mu neutrinos. + + + +axial coupling of nu_mu neutrinos. + + + +vector coupling of b quarks. + + + +axial coupling of b quarks. + + + +vector coupling of t quarks. + + + +axial coupling of t quarks. + + + +vector coupling of tau leptons. + + + +axial coupling of tau leptons. + + + +vector coupling of nu_tau neutrinos. + + + +axial coupling of nu_tau neutrinos. + + +

+The coupling to the decay channel Z'^0 -> W^+ W^- is +more model-dependent. By default it is therefore off, but can be +switched on as follows. Furthermore, we have left some amount of +freedom in the choice of decay angular correlations in this +channel, but obviously alternative shapes could be imagined. + + +the coupling Z'^0 -> W^+ W^- is taken to be this number +times m_W^2 / m_Z'^2 times the Z^0 -> W^+ W^- +coupling. Thus a unit value corresponds to the +Z^0 -> W^+ W^- coupling, scaled down by a factor +m_W^2 / m_Z'^2, and gives a Z'^0 partial +width into this channel that again increases linearly. If you +cancel this behaviour, by letting Zprime:coup2WW be +proportional to m_Z'^2 / m_W^2, you instead obtain a +partial width that goes like the fifth power of the Z'^0 +mass. These two extremes correspond to the "extended gauge model" +and the "reference model", respectively, of Alt89. +Note that this channel only includes the pure Z' part, +while f fbar -> gamma^*/Z^*0 -> W^+ W^- is available +as a separate electroweak process. + + + +in the decay chain Z'^0 -> W^+ W^- ->f_1 fbar_2 f_3 fbar_4 +the decay angular distributions is taken to be a mixture of two +possible shapes. This parameter gives the fraction that is distributed +as in Higgs h^0 -> W^+ W^- (longitudinal bosons), +with the remainder (by default all) is taken to be the same as for +Z^0 -> W^+ W^- (a mixture of transverse and longitudinal +bosons). + + +

+A massive Z'^0 is also likely to decay into Higgses +and potentially into other now unknown particles. Such possibilities +clearly are quite model-dependent, and have not been included +for now. + +

W'^+-

+ +The W'^+- implementation is less ambitious than the +Z'^0. Specifically, while indirect detection of a +Z'^0 through its interference contribution is +a possible discovery channel in lepton colliders, there is no +equally compelling case for W^+-/W'^+- interference +effects being of importance for discovery, and such interference +has therefore not been implemented for now. Related to this, a +Z'^0 could appear on its own in a new U(1) group, +while W'^+- would have to sit in a SU(2) group +and thus have a Z'^0 partner that is likely to be found +first. Only one process is implemented but, like for the +W^+-, the ISR showers contain automatic matching to the +W'^+- + 1 jet matrix elements. + + +Scattering f fbar' -> W'^+-. +Code 3021. + + +

+The couplings of the W'^+- are here assumed universal, +i.e. the same for all generations. One may set vector and axial +couplings freely, separately for the q qbar' and the +l nu_l decay channels. The defaults correspond to the +V - A structure and normalization of the Standard Model +W^+-, but can be changed to simulate a wide selection +of models. One limitation is that, for simplicity, the same +Cabibbo--Kobayashi--Maskawa quark mixing matrix is assumed as for +the standard W^+-. Depending on your assumed neutrino +nature you may want to restrict your freedom in the lepton sector, +but no limitations are enforced by the program. + + +vector coupling of quarks. + + + +axial coupling of quarks. + + + +vector coupling of leptons. + + + +axial coupling of leptons. + + +

+The coupling to the decay channel W'^+- -> W^+- Z^0 is +more model-dependent, like for Z'^0 -> W^+ W^- described +above. By default it is therefore off, but can be +switched on as follows. Furthermore, we have left some amount of +freedom in the choice of decay angular correlations in this +channel, but obviously alternative shapes could be imagined. + + +the coupling W'^0 -> W^+- Z^0 is taken to be this number +times m_W^2 / m_W'^2 times the W^+- -> W^+- Z^0 +coupling. Thus a unit value corresponds to the +W^+- -> W^+- Z^0 coupling, scaled down by a factor +m_W^2 / m_W'^2, and gives a W'^+- partial +width into this channel that increases linearly with the +W'^+- mass. If you cancel this behaviour, by letting +Wprime:coup2WZ be proportional to m_W'^2 / m_W^2, +you instead obtain a partial width that goes like the fifth power +of the W'^+- mass. These two extremes correspond to the +"extended gauge model" and the "reference model", respectively, +of Alt89. + + + +in the decay chain W'^+- -> W^+- Z^0 ->f_1 fbar_2 f_3 fbar_4 +the decay angular distributions is taken to be a mixture of two +possible shapes. This parameter gives the fraction that is distributed +as in Higgs H^+- -> W^+- Z^0 (longitudinal bosons), +with the remainder (by default all) is taken to be the same as for +W^+- -> W^+- Z^0 (a mixture of transverse and longitudinal +bosons). + + +

+A massive W'^+- is also likely to decay into Higgses +and potentially into other now unknown particles. Such possibilities +clearly are quite model-dependent, and have not been included +for now. + +

R^0

+ +The R^0 boson (particle code 41) represents one possible +scenario for a horizontal gauge boson, i.e. a gauge boson +that couples between the generations, inducing processes like +s dbar -> R^0 -> mu^- e^+. Experimental limits on +flavour-changing neutral currents forces such a boson to be fairly +heavy. In spite of being neutral the antiparticle is distinct from +the particle: one carries a net positive generation number and +the other a negative one. This particular model has no new +parameters beyond the R^0 mass. Decays are assumed isotropic. +For further details see Ben85. + + +Scattering f_1 fbar_2 -> R^0 -> f_3 fbar_4, where +f_1 and fbar_2 are separated by +- one +generation and similarly for f_3 and fbar_4. +Thus possible final states are e.g. d sbar, u cbar +s bbar, c tbar, e- mu+ and +mu- tau+. +Code 3041. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/OniaProcesses.xml b/PYTHIA8/pythia8140/xmldoc/OniaProcesses.xml new file mode 100644 index 00000000000..3532afeb850 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/OniaProcesses.xml @@ -0,0 +1,301 @@ + + +

Onia Processes

+ +Production of J/psi or Upsilon, directly and via chi states and the +colour-octet mechanism. +In each process the square-bracketed expression specifies the state +in spectroscopic notation, (2S+1) L J, followed by +(1) for colour-singlet states and (8) for +colour-octet ditto. + +

+The original Fortran code for these processes has been contributed +by Stefan Wolf [unpublished]. For the C++ version only the unpolarized +expressions are retained, since the theoretical predictions of the +colour-octet model anyway do not agree with the experimental +observations. Furthermore, the polarization effects are modest, +so isotropic decay is not a bad starting point. Such an event sample +can afterwards be reweighted at will by the user, to test various +assumptions. + +

+The description of +final-state radiation +is in this case based on some further model assumptions. + +

+Most of the processes below are divergent in the limit +pT -> 0, and therefore a pTmin scale should +be set. Comparisons with data indicate that this divergence +can be tamed the same way as for the normal QCD 2 -> 2 cross +sections, which makes sense, since they are all dominated by the +same kind of t-channel gluon exchange. It is therefore +possible to use the SuppressSmallPT +user hook to impose a reweighting that cancels the low-pT +divergence. + +

+An eikonalized description of these processes is included in the +multiple-interactions framework. Here the low-pT dampening +is automatic, and additionally the framework is more consistent +(e.g. with respect to energy-momentum constraints and the +impact-parameter description) for events where the onium production +is not the hardest subprocess, as would often be the case in the +low-pT limit. + +

Charmonium

+ + +Common switch for the group of charmonium production. + + + +g g -> ccbar[3S1(1)] g. +Code 401. + + + +g g -> ccbar[3P0(1)] g. +Code 402. + + + +g g -> ccbar[3P1(1)] g. +Code 403. + + + +g g -> ccbar[3P2(1)] g. +Code 404. + + + +q g -> ccbar[3P0(1)] q. +Code 405. + + + +q g -> ccbar[3P1(1)] q. +Code 406. + + + +q g -> ccbar[3P2(1)] q. +Code 407. + + + +q qbar -> ccbar[3P0(1)] g. +Code 408. + + + +q qbar -> ccbar[3P1(1)] g. +Code 409. + + + +q qbar -> ccbar[3P2(1)] g. +Code 410. + + + +g g -> ccbar[3S1(8)] g. +Code 411. + + + +g g -> ccbar[3S1(8)] g. +Code 412. + + + +g g -> ccbar[3S1(8)] g. +Code 413. + + + +q g -> ccbar[3S1(8)] q. +Code 414. + + + +q g -> ccbar[3S1(8)] q. +Code 415. + + + +q g -> ccbar[3S1(8)] q. +Code 416. + + + +q qbar -> ccbar[3S1(8)] g. +Code 417. + + + +q qbar -> ccbar[3S1(8)] g. +Code 418. + + + +q qbar -> ccbar[3S1(8)] g. +Code 419. + + +

Bottomonium

+ + +Common switch for the group of charmonium production. + + + +g g -> bbbar[3S1(1)] g. +Code 501. + + + +g g -> bbbar[3P0(1)] g. +Code 502. + + + +g g -> bbbar[3P1(1)] g. +Code 503. + + + +g g -> bbbar[3P2(1)] g. +Code 504. + + + +q g -> bbbar[3P0(1)] q. +Code 505. + + + +q g -> bbbar[3P1(1)] q. +Code 506. + + + +q g -> bbbar[3P2(1)] q. +Code 507. + + + +q qbar -> bbbar[3P0(1)] g. +Code 508. + + + +q qbar -> bbbar[3P1(1)] g. +Code 509. + + + +q qbar -> bbbar[3P2(1)] g. +Code 510. + + + +g g -> bbbar[3S1(8)] g. +Code 511. + + + +g g -> bbbar[3S1(8)] g. +Code 512. + + + +g g -> bbbar[3S1(8)] g. +Code 513. + + + +q g -> bbbar[3S1(8)] q. +Code 514. + + + +q g -> bbbar[3S1(8)] q. +Code 515. + + + +q g -> bbbar[3S1(8)] q. +Code 516. + + + +q qbar -> bbbar[3S1(8)] g. +Code 517. + + + +q qbar -> bbbar[3S1(8)] g. +Code 518. + + + +q qbar -> bbbar[3S1(8)] g. +Code 519. + + +

Onium matrix elements

+ +The implementation of charmonium and bottomonium production, including +the colour-octet production mechanism, requires information on NRQCD +matrix elements for the various wavefunctions involved. Default values +for these are encoded in the following ten variables. They +are taken from Nas00; see also Bar06. + + +<O(J/psi)[3S1(1)]>. + + + +<O(J/psi)[3S1(8)]>. + + + +<O(J/psi)[1S0(8)]>. + + + +<O(J/psi)[3P0(8)]>/m_c^2. + + + +<O(chi_c0)[3P0(8)]>/m_c^2. + + + +<O(Upsilon)[3S1(1)]>. + + + +<O(Upsilon)[3S1(8)]>. + + + +<O(Upsilon)[1S0(8)]>. + + + +<O(Upsilon)[3P0(8)]>/m_b^2. + + + +<O(chi_b0)[3P0(8)]>/m_b^2. + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/PDFSelection.xml b/PYTHIA8/pythia8140/xmldoc/PDFSelection.xml new file mode 100644 index 00000000000..8726d191985 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/PDFSelection.xml @@ -0,0 +1,405 @@ + + +

PDF Selection

+ +This page contains five subsections. The first deals with how to +pick the parton distribution set for protons, including from LHAPDF, +to be used for all proton and antiproton beams. The second is a special +option that allows a separate PDF set to be used for the hard process +only, while the first choice would still apply to everything else. +The third and fourth give access to pion and Pomeron PDF's, respectively, +the latter being used to describe diffractive systems. +The fifth gives the possibility to switch off the lepton +"parton density". + +

Parton densities for protons

+ +The selection of parton densities is made once and then is propagated +through the program. It is essential to make an informed choice, +for several reasons Kas10: +Warning 1: the choice of PDF set affects a number of +properties of events. A change of PDF therefore requires a complete +retuning e.g. of the multiple-interactions model for minimum-bias and +underlying events. +Warning 2: People often underestimate the differences +between different sets on the market. The sets for the same order are +constructed to behave more or less similarly at large x and +Q^2, while the multiple interactions are dominated by the +behaviour in the region of small x and Q^2. A good +PDF parametrization ought to be sensible down to x = 10^-6 +(x = 10^-7) and Q^2 = 1 GeV^2 for Tevatron (LHC) +applications. Unfortunately there are distributions on the market that +completely derail in that region. The main41.cc and +main42.cc programs in the examples +subdirectory provide some examples of absolutely minimal sanity checks +before a new PDF set is put in production. +Warning 3: NLO and LO sets tend to have quite different +behaviours, e.g. NLO ones have less gluons at small x, which then is +compensated by positive corrections in the NLO matrix elements. +Therefore do not blindly assume that an NLO tune has to be better than +an LO one when combined with the LO matrix elements in PYTHIA. There are +explicit examples where such thinking can lead you down the wrong alley, +especially if you study low-pT physics. In the list below you +should therefore be extra cautious when using set 6 or set 9. + +

+The simplest option is to pick one +of the distributions available internally: + + +Parton densities to be used for proton beams (and, by implication, +antiproton ones): + + + + + + + + + + + + + +Note: the alpha_s(M_Z) values and the order of the +running in the description above is purely informative, and does not +affect any other parts of the program. Instead you have the freedom to +set alpha_s(M_Z) value and running separately for +hard processes +(including resonance decays), +multiple interactions, +initial-state radiation, and +final-state radiation. + +

+This is a reasonably complete list of recent LO fits, both +ones within the normal LO context and ones with modifications for better +matching to event generators. In addition two older sets are +included for backwards reference (most studies to date are based on +CTEQ 5L). If you link to the +LHAPDF +library Wha05 you get access to a much wider selection. +Warning 1: owing to previous problems with the behaviour +of PDF's beyond the x and Q^2 boundaries of a set, +you should only use LHAPDF version 5.3.0 or later. +Warning 2: the behaviour of the LHAPDF sets need not be +identical with the implementation found in PYTHIA. Specifically we +are aware of the following points that may influence a comparison. +
(a) CTEQ 5L in PYTHIA is the parametrization, in LHAPDF the grid +interpolation. +
(b) MRST LO* and LO** in PYTHIA is based on an updated edition, +where one makes use of the expanded MSTW grid format, while LHAPDF +is based on the original smaller grid. +
(c) The CTEQ 6 and CT09MC sets in PYTHIA are frozen at the +boundaries of the grid, by recommendation of the authors, while +LHAPDF also offers an option with a smooth extrapolation outside +the grid boundaries. + + +If off then the choice of proton PDF is based on PDF:pSet +above. If on then it is instead based on the choice of +PDF:LHAPDFset and PDF:LHAPDFmember below. +Note: in order for this option to work you must have +compiled PYTHIA appropriately and have set the LHAPATH +environment variable to provide the data-files directory of your local +LHAPDF installation. See the README file in the examples +directory for further instructions. + + + +Name of proton PDF set from LHAPDF to be used. You have to choose +from the + +list of available sets. Examples of some fairly recent ones +(but still less recent than found above) would be +cteq61.LHpdf, cteq61.LHgrid, cteq6l.LHpdf, cteq6ll.LHpdf, +MRST2004nlo.LHpdf, MRST2004nlo.LHgrid, MRST2004nnlo.LHgrid and +MRST2004FF3lo.LHgrid. If you pick a LHpdf set it will require some +calculation the first time it is called. +Technical note: if you provide a name beginning with a +slash (/) it is assumed you want to provide the full file path and then +initPDFsetM(name) is called, else the correct path is assumed +already set and initPDFsetByNameM(name) is called. + + + +Further choice of a specific member from the set picked above. Member 0 +should normally correspond to the central value, with higher values +corresponding to different error PDF's somewhat off in different +directions. You have to check from set to set which options are open. +Note: you can only use one member in a run, so if you +want to sweep over many members you either have to do many separate +runs or, as a simplification, save the +pdf weights at the hard scattering +and do an offline reweighting of events. + + + +Parton densities have a guaranteed range of validity in x +and Q^2, and what should be done beyond that range usually is +not explained by the authors of PDF sets. Nevertheless these boundaries +very often are exceeded, e.g. minimum-bias studies at LHC may sample +x values down to 10^-8, while many PDF sets stop +already at 10^-5. The default behaviour is then that the +PDF's are frozen at the boundary, i.e. xf(x,Q^2) is fixed at +its value at x_min for all values x < x_min, +and so on. This is a conservative approach. Alternatively, if you +switch on extrapolation, then parametrizations will be extended beyond +the boundaries, by some prescription. In some cases this will provide a +more realistic answer, in others complete rubbish. Another problem is +that some of the PDF-set codes will write a warning message anytime the +limits are exceeded, thus swamping your output file. Therefore you should +study a set seriously before you run it with this switch on. + + +

+If you want to use PDF's not found in LHAPDF, or you want to interface +LHAPDF another way, you have full freedom to use the more generic +interface options. + +

Parton densities for protons in the hard process

+ +The above options provides a PDF set that will be used everywhere: +for the hard process, the parton showers and the multiple interactions +alike. As already mentioned, therefore a change of PDF should be +accompanied by a complete retuning of the whole MI framework, +and maybe more. There are cases where one may want to explore +different PDF options for the hard process, but would not want to touch +the rest. If several different sets are to be compared, a simple +reweighting based on the originally +used flavour, x, Q^2 and PDF values may offer the +best route. The options in this section allow a choice of the PDF set +for the hard process alone, while the choice made in the previous section +would still be used for everything else. The hardest interaction +of the minimum-bias process is part of the multiple-interactions +framework and so does not count as a hard process here. + +

+Of course it is inconsistent to use different PDF's in different parts +of an event, but if the x and Q^2 ranges mainly accessed +by the components are rather different then the contradiction would not be +too glaring. Furthermore, since standard PDF's are one-particle-inclusive +we anyway have to 'invent' our own PDF modifications to handle configurations +where more than one parton is kicked out of the proton Sjo04. + +

+The PDF choices that can be made are the same as above, so we do not +repeat the detailed discussion. + + +If on then select a separate PDF set for the hard process, using the +variables below. If off then use the same PDF set for everything, +as already chosen above. + + + +Parton densities to be used for proton beams (and, by implication, +antiproton ones): + + + + + + + + + + + + + + + +If off then the choice of proton PDF is based on hardpPDFset +above. If on then it is instead based on the choice of +hardLHAPDFset and hardLHAPDFmember below. + + + +Name of proton PDF set from LHAPDF to be used. + + + +Further choice of a specific member from the set picked above. + + +

+Note that there is no separate equivalent of the +PDF:extrapolateLHAPDF flag specifically for the hard +PDF. Since LHAPDF only has one global flag for extrapolation or not, +the choice for the normal PDF's also applies to the hard ones. + +

Parton densities for pions

+ +The parton densities of the pion are considerably less well known than +those of the proton. There are only rather few sets on the market, +and none particularly recent. Only one comes built-in, but others can +be accessed from LHAPDF. Input parametrizations are for the pi+. +>From this the pi- is obtained by charge conjugation and the +pi0 from averaging (half the pions have d dbar +valence quark content, half u ubar. + +

+Much of the switches are taken over from the proton case, with obvious +modifications; therefore the description is briefer. Currently we have +not seen the need to allow separate parton densities for hard processes. +When using LHAPDF the PDF:extrapolateLHAPDF switch of the +proton also applies to pions. + + +Internal parton densities that can be used for pion beams, currently with +only one choice. + + + + +If off then the choice of proton PDF is based on PDF:piSet +above. If on then it is instead based on the choice of +PDF:piLHAPDFset and PDF:piLHAPDFmember below. + + + +Name of pion PDF set from LHAPDF to be used. You have to choose from the + +list of available sets. + + + +Further choice of a specific member from the set picked above. + + +

Parton densities for Pomerons

+ +The Pomeron is introduced in the description of diffractive events, +i.e. a diffractive system is viewed as a Pomeron-proton collision at a +reduced CM energy. Here the PDF's are even less well known. +Most experimental parametrizations are NLO, which makes them less +well suited for Monte Carlo applications. Furthemore note that +the momentum sum is arbitrarily normalized to a non-unity value. + + +Parton densities that can be used for Pomeron beams. + + + + + + + + + +the parameter a in the ansatz xg(x) = N_ab x^a (1 - x)^b +for option 1 above. + + + +the parameter b in the ansatz xg(x) = N_ab x^a (1 - x)^b +for option 1 above. + + + +the parameter a in the ansatz xq(x) = N_ab x^a (1 - x)^b +for option 1 above. + + + +the parameter b in the ansatz xq(x) = N_ab x^a (1 - x)^b +for option 1 above. + + + +the fraction of the Pomeron momentum carried by quarks +for option 1 above, with the rest carried by gluons. + + + +the suppression of the s quark density relative to that of the +d and u ones for option 1 above. + + + +Rescale the four H1 fits above by this uniform factor, e.g. to bring +up their momentum sum to around unity. By default all three have +a momentum sum of order 0.5, suggesting that a factor around 2.0 +should be used. You can use examples/main41.cc to get +a more precise value. Note that also other parameters in the +diffraction framework may need to +be retuned when this parameter is changed. + + +

Parton densities for leptons

+ +For electrons/leptons there is no need to choose between different +parametrizations, since only one implementation is available, and +should be rather uncontroversial (apart from some technical details). +However, insofar as e.g. e^+ e^- data often are corrected +back to a world without any initial-state photon radiation, it is +useful to have a corresponding option available here. + + +Use parton densities for lepton beams or not. If off the colliding +leptons carry the full beam energy, if on part of the energy is +radiated away by initial-state photons. In the latter case the +initial-state showers will generate the angles and energies of the +set of photons that go with the collision. In addition one collinear +photon per beam carries any leftover amount of energy not described +by shower emissions. If the initial-state showers are switched off +these collinear photons will carry the full radiated energy. + + +

Incoming parton selection

+ +There is one useful degree of freedom to restrict the set of incoming +quark flavours for hard processes. It does not change the PDF's as such, +only which quarks are allowed to contribute to the hard-process cross +sections. Note that separate but similarly named modes are available +for multiple interactions and spacelike showers. + + +Number of allowed incoming quark flavours in the beams; a change +to 4 would thus exclude b and bbar as incoming +partons, etc. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/PYTHIA6TranslationTable.xml b/PYTHIA8/pythia8140/xmldoc/PYTHIA6TranslationTable.xml new file mode 100644 index 00000000000..f58e4c3e946 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/PYTHIA6TranslationTable.xml @@ -0,0 +1,100 @@ + + +

PYTHIA 6 Translation Table

+ +For those more familiar with PYTHIA 6 than PYTHIA 8, here comes a table +that shows the approximate correspondence between some commonly used +variables in the two programs.The list can be expanded to meet explicit +needs (channel your suggestions via the Monte Carlo responsible of your +collaboration), but there is no question of ever providing anywhere near +a complete coverage. + +

Selecting properties of event generation

+ +For PYTHIA 8 you should use the pythia->readString("command") +to give in the commands listed below, assuming that you have access to a +pointer pythia to an instance of the Pythia class. + + + + + + + + + + + + + + + + + + + + + + + + +
PYTHIA 6 PYTHIA 8 Comment
MSEL = 1 SoftQCD:minBias = on soft and hard QCD events (for pp/pbarp)
MSEL = 2 SoftQCD:all = on as above, plus elastic and diffractive (for pp/pbarp)
MSTP(61) = 0 PartonLevel:ISR = off no initial-state radiation
MSTP(71) = 0 PartonLevel:FSR = off no final-state radiation
MSTP(81) = 0 PartonLevel:MI = off no multiple parton-parton interactions
MSTP(111) = 0 HadronLevel:all = off no hadronization and no decays
+ +

Information about generated event

+ +Several PYTHIA 6 variables are stored in two places, and then both are +given below. For PYTHIA 8 it is assumed that you have access to a pointer +pythia to an instance of the Pythia class. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
PYTHIA 6 PYTHIA 8 Comment
msti(1), mint(1) pythia->info.code() process ID (but changed numbering)
pari(13), vint(43) pythia->info.mHat() invariant mass of the hard subprocess
pari(17), vint(47) pythia->info.pTHat() transverse momentum of the hard subprocess (2 -> 2)
pari(21), vint(51) pythia->info.QRen() renormalization scale Q of the hard subprocess (default definition changed)
vint(57) pythia->info.alphaEM() electromagnetic coupling constant in the hard subprocess
vint(58) pythia->info.alphaS() strong coupling constant in the hard subprocess
msti(15), mint(15) pythia->info.id1() ID of the first incoming parton
msti(16), mint(16) pythia->info.id2() ID of the second incoming parton
pari(33), vint(41) pythia->info.x1() momentum fraction x of the first incoming parton
pari(34), vint(42) pythia->info.x2() momentum fraction x of the second incoming parton
pari(23), vint(53) pythia->info.QFac() factorization scale Q of the hard subprocess (default definition changed)
pari(29), vint(39) pythia->info.pdf1() x1*f(x1) (PDF density 1)
pari(30), vint(40) pythia->info.pdf2() x2*f(x2) (PDF density 2)
pari(7), vint(97) pythia->info.weight() event weight (normally unity)
+ + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ParticleData.xml b/PYTHIA8/pythia8140/xmldoc/ParticleData.xml new file mode 100644 index 00000000000..c5a6028c97a --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ParticleData.xml @@ -0,0 +1,7998 @@ + + +

Particle Data

+ +The structure and operation of the particle data table is described +here. That page +also describes how default data properties can be changed. The +current page provides the actual default values. + +

Main settings

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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ParticleDataScheme.xml b/PYTHIA8/pythia8140/xmldoc/ParticleDataScheme.xml new file mode 100644 index 00000000000..54c393fa3f1 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ParticleDataScheme.xml @@ -0,0 +1,1498 @@ + + +

The Particle Data Scheme

+ +The particle data scheme may take somewhat longer to understand than +the settings one. In particular the set of methods to access information +is rather more varied, to allow better functionality for advanced usage. +However, PYTHIA does come with a sensible default set of particle +properties and decay tables. Thus there is no need to learn any of the +methods on this page to get going. Only when you perceive a specific need +does it make sense to learn the basics. + +

+The central section on this page is the Operation one. The preceding +sections are there mainly to introduce the basic structure and the set +of properties that can be accessed. The subsequent sections provide a +complete listing of the existing public methods, which most users +probably will have little interaction with. + +

Databases

+ +The management of particle data is based on three classes: +
    +
  • ParticleData, which is the top-level class, with +methods that can be used to interrogate all particle data. It contains +a map of PDG particle identity numbers Yao06 onto the relevant +ParticleDataEntry objects,
    • +
  • ParticleDataEntry, which stores the relevant information +on an individual particle species, and
    • +
  • DecayChannel, which stores info on one particular decay +mode of a particle.
    • + +
+The objects of these classes together form a database that is +continuously being used as the program has to assign particle masses, +select decay modes, etc. + +

+Each Pythia object has a public member +particleData of the ParticleData class. +Therefore you access the particle data methods as +pythia.particleData.command(argument), +assuming that pythia is an instance of the +Pythia class. Further, for some of the most frequent user +tasks, Pythia methods have been defined, so that +pythia.command(argument) +would work, see further below. + +

+A fundamental difference between the particle data classes and the +settings ones is that the former are accessed regularly during the +event generation process, as a new particle is produced and its mass +need to be set, e.g., while the latter are mainly/only used +at the initialization stage. Nevertheless, it is not a good idea to +change data in either of them in mid-run, since this may lead to +inconsistencies. + +

Stored properties for particles

+ +The main properties stored for each particle are as follows. +Different ways to set and get these properties will be described +further down. + +
    + +
  • name: a character string with the name of the +particle. Particle and antiparticle names are stored separately, +with void returned when no antiparticle exists.
    • + +
  • spinType: the spin type, of the form 2 s + 1, +with special code 0 for entries of unknown or indeterminate spin.
    • + +
  • chargeType: three times the charge (to make it an +integer).
    • + +
  • colType: the colour type, with 0 uncoloured, 1 triplet, +-1 antitriplet and 2 octet.
    • + +
  • m0: the nominal mass m_0 (in GeV).
    • + +
  • mWidth: the width Gamma of the Breit-Wigner +distribution (in GeV).
    • + +
  • mMin: the lower limit of the allowed mass range +generated by the Breit-Wigner (in GeV). Has no meaning for particles +without width, and would typically be 0 there.
    • + +
  • mMax: the upper limit of the allowed mass range +generated by the Breit-Wigner (in GeV). If mMax < mMin then +no upper limit is imposed. Has no meaning for particles without width, +and would typically be 0 there.
    • + +
  • tau0: the nominal proper lifetime tau_0 +(in mm/c).
    • + +
  • isResonance: a flag telling whether a particle species +is considered as a resonance or not. Here +"resonance" is used as shorthand +for any massive particle where the decay process should be counted as part +of the hard process itself, and thus be performed before showers and other +event aspects are added. Restrictions on allowed decay channels is also +directly reflected in the cross section of simulated processes, while +those of normal hadrons and other light particles are not. +In practice, it is reserved for states above the b bbar +bound systems in mass, i.e. for W, Z, t, Higgs states, +supersymmetric states and (most?) other states in any new theory. +All particles with m0 above 20 GeV are by default +initialized to be considered as resonances.
    • + +
  • mayDecay: a flag telling whether a particle species +may decay or not, offering the main user switch. Whether a given particle +of this kind then actually will decay also depends on it having allowed +decay channels, and on other flags for +particle decays. +All particles with tau0 below 1000 mm are +by default initialized to allow decays.
    • + +
  • doExternalDecays: a flag telling whether a particle +should be handled by an external decay package or not, with the latter +default. Can be manipulated as described on this page, but should +normally not be. Instead the +Pythia::decayPtr(...) +method should be provided with the list of relevant particles.
    • + +
  • isVisible: a flag telling whether a particle species +is to be considered as visible in a detector or not, as used e.g. in +analysis routines. By default this includes neutrinos and a few BSM +particles (gravitino, sneutrinos, neutralinos) that have neither strong +nor electromagnetic charge, and are not made up of constituents that +have it. The value of this flag is only relevant if a particle is +long-lived enough actually to make it to a detector.
    • + +
  • doForceWidth: a flag valid only for resonances where +PYTHIA contains code to calculate the width of the resonance from +encoded matrix-element expressions, i.e. the Z^0, W^+-, +t, h^0, and a few more. The normal behaviour +(false) is then that the width is calculated from the mass, +but it is possible to force the +resonance to retain the nominal width. Branching ratios and the running +of the total width are unaffected.
    • + +
+ +

Stored properties for decays

+ +An unstable particle has a decay table consisting of one or more +decay channel. The following properties are stored for each such channel. +Again different ways to set and get these properties will be described +further down. +
    + +
  • onMode: integer code for use or not of channel,
    +0 if a channel is off,
    +1 if on,
    +2 if on for a particle but off for an antiparticle,
    +3 if on for an antiparticle but off for a particle.
    +If a particle is its own antiparticle then 2 is on and 3 off +but, of course, for such particles it is much simpler and safer +to use only 1 and 0.
    +The 2 and 3 options can be used e.g. to encode CP violation in +B decays, or to let the W's in a q qbar -> W^+ W^- +process decay in different channels.
    • + +
  • bRatio: the branching ratio of the channel.
    • + +
  • meMode: the mode of processing this channel, possibly +with matrix elements; see the +particle decays description
    • +for the list of possibilities. + +
  • multiplicity: the number of decay products of the +channel. Can be at most 8.
    • + +
  • product(i): the identity code of the decay products, +where i runs between 0 and +multiplicity - 1. Trailing positions are filled with 0. +
    • + +
+ +

Operation

+ +The normal flow of the particle data operations is: + +
    + +
  1. +When a Pythia object pythia is created, the +pythia.particleData member is asked to scan the +ParticleData.xml file. + +

    +All lines beginning with <particle are scanned for +information on a particle species, and all lines beginning with +<channel are assumed to contain a decay channel of the +enclosing particle. In both cases XML syntax is used, with attributes +used to identify the stored properties, and with omitted properties +defaulting back to 0 where meaningful. The particle and channel +information may be split over several lines, up to the > endtoken. +The format of a <particle tag is: +

    +    <particle id="..." name="..." antiName="..." spinType="..." chargeType="..." colType="..." 
+       m0="..." mWidth="..." mMin="..." mMax="..." tau0="...">
+    </particle>
+
    +where the fields are the properties already introduced above. +Note that isResonance, mayDecay, +doExternalDecay, isVisible and +doForceWidth are not set here, but are provided with +default values by the rules described above. Once initialized, also +these latter properties can be changed, see below.
    + +The format of a <channel> tag is: +
    +    <channel onMode="..." bRatio="..." meMode="..." products="..." />
+
    +again see properties above. The products are given as a blank-separated +list of id codes. +Important: the values in the .xml file should not +be changed, except by the PYTHIA authors. Any changes should be done +with the help of the methods described below. +
    2. + +

  2. +Between the creation of the Pythia object and the +init call for it, you may use the methods of the +ParticleData class to modify some of the default values. +Several different approaches can be chosen for this. + +

    +a) Inside your main program you can directly set values with +

    +    pythia.readString(string);
+
    +where both the variable name and the value are contained inside +the character string, separated by blanks and/or a =, e.g. +
    +    pythia.readString("111:mayDecay = off"); 
+
    +switches off the decays of the pi^0.
    + +The particle id (> 0) and the property to be changed must be given, +separated by a colon.
    + +The allowed properties are: name, antiName, +spinType, chargeType, colType, +m0, mWidth, mMin, +mMax, tau0, isResonance, +mayDecay, doExternalDecay, +isVisible and doForceWidth. All of these +names are case-insensitive. Names that do not match an existing +variable are ignored.
    + +Strings beginning with a non-alphanumeric character, like # or !, +are assumed to be comments and are not processed at all. For +bool values, the following notation may be used +interchangeably: true = on = yes = ok = 1, while everything +else gives false (including but not limited to +false, off, no and +0). + +

    +Particle data often comes in sets of closely related information. +Therefore some properties expect the value to consist of several +numbers. These can then be separated by blanks (or by commas). +A simple example is names, which expects both the +name and antiname to be given. A more interesting one is the +all property, +

      
+    id:all = name antiName spinType chargeType colType m0 mWidth mMin mMax tau0
+
    +where all the current information on the particle itself is replaced, +but any decay channels are kept unchanged. Using new instead +of all also removes any previous decay channels. +If the string contains fewer fields than expected the trailing +properties are set to vanish ("void", 0 or 0.). Note that such a +truncated string should not be followed by a comment, since this +comment would then be read in as if it contained the missing properties. +The truncation can be done anywhere, specifically a string with only +id:new defines a new "empty" particle. +As before, isResonance, mayDecay, +doExternalDecay, isVisible and +doForceWidth are (re)set to their default values, and +would have to be changed separately if required. + +

    +A further command is rescaleBR, which rescales each of the +existing branching ratios with a common factor, such that their new +sum is the provided value. This may be a first step towards adding +new decay channels, see further below. + +

    +Alternatively the id code may be followed by another integer, +which then gives the decay channel number. This then has to be +followed by the property specific to this channel, either +onMode, bRatio, meMode or +products. In the latter case all the products of +the channel should be given: +

    +    id:channel:products =  product1 product2 ....  
+
    +The line will be scanned until the end of the line, or until a +non-number word is encountered, or until the maximum allowed number +of eight products is encountered, whichever happens first. (Thus the +multiplicity of a decay channel need not be input; it is automatically +calculated from the products list.) It is also possible to replace all +the properties of a channel in a similar way: +
    +    id:channel:all = onMode bRatio meMode product1 product2 ....  
+
    +To add a new channel at the end, use +
    +    id:addChannel = onMode bRatio meMode product1 product2 ....
+
    + +

    +It is currently not possible to remove a channel selectively, but +setting its branching ratio vanishing is as effective. If you want to +remove all existing channels and force decays into one new channel +you can use +

    +    id:oneChannel = onMode bRatio meMode product1 product2 ....
+
    + A first oneChannel command could be followed by +several subsequent addChannel ones, to build +up a completely new decay table for an existing particle. + +

    +When adding new channels or changing branching ratios in general, +note that, once a particle is to be decayed, the sum of branching +ratios is always rescaled to unity. Beforehand, rescaleBR +may be used to rescale an existing branching ratio by the given factor. + +

    +There are a few commands that will study all the decay channels of the +given particle, to switch them on or off as desired. The +

    +    id:onMode = onMode
+
    +will set the onMode property of all channels to the +desired value. The +
     
+    id:offIfAny   = product1 product2 .... 
+    id:onIfAny    = product1 product2 .... 
+    id:onPosIfAny = product1 product2 .... 
+    id:onNegIfAny = product1 product2 .... 
+
    +will set the onMode 0, 1, 2 or 3, respectively, for all +channels which contain any of the enumerated products, where the matching +to these products is done without distinction of particles and +antiparticles. Note that "Pos" and "Neg" +are slightly misleading since it refers to the particle and antiparticle +of the id species rather than charge, but should still be +simpler to remember and understand than alternative notations. +Correspondingly +
     
+    id:offIfAll   = product1 product2 .... 
+    id:onIfAll    = product1 product2 .... 
+    id:onPosIfAll = product1 product2 .... 
+    id:onNegIfAll = product1 product2 .... 
+
    +will set the onMode 0, 1, 2 or 3, respectively, for all +channels which contain all of the enumerated products, again without +distinction of particles and antiparticles. If the same product appears +twice in the list it must also appear twice in the decay channel, and +so on. The decay channel is allowed to contain further particles, +beyond the product list. By contrast, +
     
+    id:offIfMatch   = product1 product2 .... 
+    id:onIfMatch    = product1 product2 .... 
+    id:onPosIfMatch = product1 product2 .... 
+    id:onPosIfMatch = product1 product2 .... 
+
    +requires the decay-channel multiplicity to agree with that of the product +list, but otherwise works as the onIfAll/offIfAll methods. + +

    +Note that the action of several of the commands depends on the order +in which they are executed, as one would logically expect. For instance, +id:oneChannel removes all decay channels of id +and thus all previous changes in this decay table, while subsequent +additions or changes would still take effect. Another example would be that +23:onMode = off followed by 23:onIfAny = 1 2 3 4 5 +would let the Z^0 decay to quarks, while no decays would be +allowed if the order were to be reversed. + +

    +b) The Pythia readString(string) method actually +does not do changes itself, but sends on the string either to the +ParticleData class or to the Settings one, +depending on whether the string begins with a digit or a letter. +If desired, it is possible to communicate directly with the corresponding +ParticleData method: +

    +    pythia.particleData.readString("111:mayDecay = off"); 
+    pythia.particleData.readString("15:2:products = 16 -211"); 
+
    +In this case, changes intended for Settings would not be +understood. + +

    +c) Underlying this are commands for all the individual properties in +the ParticleData class, one for each. These are +further described below. Thus, an example now reads +

    +    pythia.particleData.mayDecay(111, false);
+
    +Boolean values should here be given as true or +false. + +

    +d) A simpler and more useful way is to collect all your changes +in a separate file, with one line per change, e.g. +

    +    111:mayDecay = off
+
    +The file can be read by the +
    +    pythia.readFile(fileName); 
+
    +method, where fileName is a string, e.g. +pythia.readFile("main.cmnd") (or an istream +instead of a fileName). Each line is processed as +described for the string in 2a). This file can freely mix commands to +the Settings and ParticleData classes. +
    3. + +

  3. +A routine reInit(fileName) is provided, and can be used to +zero the particle data table and reinitialize it from scratch. +Such a call might be useful if several subruns are to be made with +widely different particle data - normally the maps are only built +from scratch once, namely when the Pythia() object is +created. Also, there is no other possibility to restore the default +values, unlike for the settings. +

    4. + +

  4. +You may at any time obtain a listing of all the particle data by calling +

    +    pythia.particleData.listAll();
+
    +The listing is by increasing id number. It shows the basic +quantities introduced above. Some are abbreviated in the header to fit on +the lines: spn = spinType, chg = chargeType, +col = colType, res = isResonance, +dec = mayDecay && canDecay (the latter checks that decay +channels have been defined), ext = doExternalDecay, +vis = isVisible and wid = doForceWidth.
    + +To list only those particles that were changed (one way or another, the +listing will not tell what property or decay channel was changed), instead use +
    +    pythia.particleData.listChanged();
+
    +(This info is based on a further hasChanged flag of a particle +or a channel, set true whenever any of the changing methods are +used. It is possible to manipulate this value, but this is not recommended.) +By default the internal initialization of the widths of resonances such as +gamma^*/Z^0, W^+-, t/tbar, H^0 do not count as changes; if you want +to list also those changes instead call listChanged(true). +
    + +To list only one particle, give its id code as argument to +the list(...) function.. To list a restricted set of particles, +give in their id codes to list(...) as a +vector<int>. +
    5. + +

  5. +For wholesale changes of particle properties all available data can be +written out, edited, and then read back in again. These methods are +mainly intended for expert users. You can choose between two alternative +syntaxes. + +

    +a) XML syntax, using the <particle and +<channel lines already described. You use the method +particleData.listXML(fileName) to produce such an XML +file and particleData.readXML(fileName) to read it back +in after editing. + +

    +b) Fixed/free format, using exactly the same information as illustrated +for the <particle and <channel lines +above, but now without any tags. This means that all information fields +must be provided (if there is no antiparticle then write +void), in the correct order (while the order is irrelevant +with XML syntax), and all on one line. Information is written out in +properly lined-up columns, but the reading is done using free format, +so fields need only be separated by at least one blank. Each new particle +is supposed to be separated by (at least) one blank line, whereas no +blank lines are allowed between the particle line and the subsequent +decay channel lines, if any. You use the method +particleData.listFF(fileName) to produce such a fixed/free +file and particleData.readFF(fileName) to read it back +in after editing. + +

    +As an alternative to the readXML and readFF +methods you can also use the +particleData.reInit(fileName, xmlFormat) method, where +xmlFormat = true (default) corresponds to reading an XML +file and xmlFormat = false to a fixed/free format one. + +

    +To check that the new particle and decay tables makes sense, you can use +the particleData.checkTable() method, either directly or by +switching it on among the standard +error checks. +

    6. + +
+ +

The public methods

+ +In the following we present briefly the public methods in the three +classes used to build up the particle database. The order +is top-down, i.e from the full table of all particles to a single +particle to a single channel. +Note that these methods usually are less elegant and safe than the +input methods outlined above. If you use any of these methods, it is +likely to be the ones in the full database, i.e. the first ones to be +covered in the following. + +

+For convenience, we have grouped related input and output methods +together. It should be obvious from the context which is which: +the input is of type void and has an extra last argument, +namely is the input value, while the output method returns a +quantity of the expected type. + +

The ParticleData methods

+ + +the constructor has no arguments and does not do anything. Internal. + + + +initialize pointers to a few other classes. Internal. + + + +read in an XML-style file with particle data and initialize the +particle data tables accordingly. This command is executed +in the Pythia constructor, i.e. is mainly for +internal use. + +the name of the data file to be read. When called from the +Pythia constructor the directory is provided by the +PYTHIA8DATA +environment variable, if set, else by the argument of this constructor, +which has the default value "../xmldoc". + + + + +overwrite the existing database by reading from the specified file. +Unlike init above this method is not called by the +Pythia constructor, but is entirely intended for users +who want to replace the existing particle data with their own. +the path and name of file to be read. + +if true read the same kind of XML-style file +as used by init, if not use an alternative "free format" +file (i.e. without any XML tags, but with well-defined rules +specifying in which order properties are stored). + + + + +initialize Breit-Wigner shape parameters for all particles, +and the detailed handling of resonances, i.e. particles with +perturbatively calculable partial widths, which can be used to +obtain a mass-dependent Breit-Wigner and a dynamic choice of +decay channels. Called from Pythia::init(). + + + + + +read in XML-style data from a file or write it out to a file. For the +former one can also decide whether to reset all particles to scratch, +or only overwrite those particles in the file. The former method is +used by init and reInit above. + + + + + +read in free-format-style data from a file or write it out to a file. +For the former one can also decide whether to reset all particles to +scratch, or only overwrite those particles in the file. The former +method is used by reInit above. + + + +read in a string and interpret is as a new or changed particle data. +The possibilities are extensively described above. It is normally +used indirectly, via Pythia::readString(...) and +Pythia::readFile(...). + +the string to be interpreted as an instruction. + + +write a warning message or not whenever the instruction does not make +sense, e.g. if the particle does not exist in the database. + + +stream for error printout. + +Note: the method returns false if it fails to +make sense out of the input string. + + + + + + + + + +methods intended to present a listing of particle data in a readable +format. The first three are special cases of the fourth. The first +lists all particle data, the second only data for those particles that +were changed after the original creation of the particle data table. +Resonances are a special case since they can get their data changed +by being linked to an object that does the calculation of branching +ratios. The second method does not count such resonances as changed, +whereas the third does and thus lists all resonances. + + + + + +list particle data for one single particle, with the identity code as +input, or for a set of particles, with an input vector of identity codes. + + + + + +check that the particle decay table makes sense, especially for decays. + level of checks. 0 is only mininal, +e.g. if a particle has no open decay channels. 1, which is the level +of the first method, provides warning if any individual channel is +closed, except for resonances. 2 also prints the +branching-ratio-averaged threshold mass. 11 and 12 are like 1 and 2, +but also include resonances in the detailed checks. + + + + + + +add a particle to the decay table; in the first form a partcle which is +its own antiparticle, in the second where a separate antiparticle exists. + + + +change all the properties of the particle associated with a given +identity code. + + + +query whether the particle data table contains the particle of the +identity code. + + + +return the identity code of the sequentially next particle stored in table. + + + +bool whether a distinct antiparticle exists or not. Is true if an +antiparticle name has been set (and is different from +void). + + + + + + + + +< +particle and antiparticle names are stored separately, the sign of +id determines which of the two is returned, with +void used to indicate the absence of an antiparticle. + + + + + +the spin type, of the form 2 s + 1, with special code 0 +for entries of unknown or indeterminate spin. + + + + + +three times the charge (to make it an integer), taking into account +the sign of id. + + + +the electrical charge of a particle, equal to +chargeType(id)/3. + + + + + +the colour type, with 0 uncoloured, 1 triplet, -1 antitriplet and 2 +octet, taking into account the sign of id. + + + + + +the nominal mass m_0 (in GeV). + + + + + +the width Gamma of the Breit-Wigner distribution (in GeV). + + + + + +the lower limit of the allowed mass range generated by the Breit-Wigner +(in GeV). Has no meaning for particles without width, and would +typically be 0 there. + + + + + +the upper limit of the allowed mass range generated by the Breit-Wigner +(in GeV). If mMax < mMin then no upper limit is imposed. +Has no meaning for particles without width, and would typically +be 0 there. + + + +similar to mMin() above, except that for particles with +no width the m0(id) value is returned. + + + +similar to mMax() above, except that for particles with +no width the m0(id) value is returned. + + + + + +the nominal proper lifetime tau_0 (in mm/c). + + + + + +a flag telling whether a particle species are considered as a resonance +or not. Here "resonance" +is used as shorthand for any massive particle +where the decay process should be counted as part of the hard process +itself, and thus be performed before showers and other event aspects +are added. Restrictions on allowed decay channels is also directly +reflected in the cross section of simulated processes, while those of +normal hadrons and other light particles are not. +In practice, it is reserved for states above the b bbar +bound systems in mass, i.e. for W, Z, t, Higgs states, +supersymmetric states and (most?) other states in any new theory. +All particles with m0 above 20 GeV are by default +initialized to be considered as resonances. + + + + + +a flag telling whether a particle species may decay or not, offering +the main user switch. Whether a given particle of this kind then actually +will decay also depends on it having allowed decay channels, and on +other flags for particle decays. +All particles with tau0 below 1000 mm are +by default initialized to allow decays. + + + + + +a flag telling whether a particle should be handled by an external +decay package or not, with the latter default. Can be manipulated as +described on this page, but should normally not be. Instead the +pythia.decayPtr +method should be provided with the list of relevant particles. + + + + + +a flag telling whether a particle species is to be considered as +visible in a detector or not, as used e.g. in analysis routines. +By default this includes neutrinos and a few BSM particles +(gravitino, sneutrinos, neutralinos) that have neither strong nor +electromagnetic charge, and are not made up of constituents that +have it. The value of this flag is only relevant if a particle is +long-lived enough actually to make it to a detector. + + + + + +a flag valid only for resonances where PYTHIA contains code to +calculate the width of the resonance from encoded matrix-element +expressions, i.e. the Z^0, W^+-, t, +h^0, and a few more. The normal behaviour (false) +is then that the width is calculated from the mass, but it is +possible to force the resonance +to retain the nominal width. Branching ratios and the running of the +total width are unaffected. + + + + + +keep track of whether the data for a particle has been changed +in any respect between initialization and the current status. +Is used e.g. by the listChanged method to determine +which particles to list. + + + +tells whether a particle will have a Breit-Wigner mass distribution or +not. Is determined by an internal logic based on the particle width and +on the value of the +ParticleData:modeBreitWigner +switch. + + + +is the constituent mass for a quark, hardcoded as +m_u = m_d = 0.325, m_s = 0.50, m_c = 1.60 +and m_b = 5.0 GeV, for a diquark the sum of quark constituent +masses, and for everything else the same as the ordinary mass. + + + +returns a mass distributed according to a truncated Breit-Wigner, +with parameters as described here. Is equal to m0(id) for +particles without width. + + + +calculate the running mass of species id when probed at a +hard mass scale of mH. Only applied to obtain the +running quark masses; for all other particle the normal fixed mass +is used. + + + +true for a particle with at least one decay channel defined. + + + +true for a lepton or an antilepton (including neutrinos). + + + +true for a quark or an antiquark. + + + +true for a gluon. + + + +true for a diquark or antidiquark. + + + +true for a hadron (made up out of normal quarks and gluons, +i.e. not for R-hadrons and other exotic states). + + + +true for a meson. + + + +true for a baryon or antibaryon. + + + +true for an intermediate hadron-like state with a colour octet charge +as used in the colour octet model for +onia production. + + + +extracts the heaviest quark or antiquark, i.e. one with largest +id number, for a hadron. + + + +is 1 for a quark, 2 for a diquark, 3 for a baryon, the same with a +minus sign for antiparticles, and else zero. + + + +rescales all partial branching ratios by a common factor, such that +the sum afterward becomes newSumBR. + + + +set a pointer for a particle kind to a ResonanceWidths object. +This is done, from inside ParticleData::initWidths, only for +resonances, i.e. for particles such as Z^0, W^+-, top, +Higgs, and new unstable states beyond the Standard Model. The presence +of such an object will allow a more dynamic calculation of partial and +total widths, as illustrated by the following methods. + + + +initialize the treatment of a resonance. + + + +calculate the total with for a resonance of a given current mass, +optionally including coupling to incoming flavour state (consider +the gamma*/Z^0 combination), optionally excluding decay +channels that have been closed by the user, and optionally storing +the results in the normal decay table. + + + +special case of resWidth, where only open channels are +included, but results are not stored in the normal decay table. + + + +special case of resWidth, where only open channels are +included, and results are stored in the normal decay table. + + + +calculate the fraction of the full branching ratio that is left +open by the user choice of allowed decay channels. Can be applied +to a final state with up to three resonances. Since the procedure +is multiplicative, it would be easy to generalize also to more. + + + +the factor used to rescale all partial widths in case the total +width is being forced to a specific value by the user. + + + +special case to calculate one final-state width; currently only used +for Higgs decay to q qbar, g g or +gamma gamma. + + + +returns a pointer to the ParticleDataEntry object. +The methods in the next section can then be used to manipulate +this object. + + +

The ParticleDataEntry methods

+ +Most of the methods that can be applied to a single +ParticleDataEntry object are almost identical with +those used above for the ParticleData, except +that the id argument is no longer needed to find +the right entry in the table. By and large, this makes direct +access to the ParticleDataEntry methods superfluous. +There are a few methods that are unique to each class, however. +Furthermore, to avoid some naming ambiguities, many methods that +set values begin with set. + + + + +there are two alternative constructors, that both expect the +properties of a particle as input. The first assumes that there +is only one particle, thet latter that there is a +particle-antiparticle pair (but if the antiparticle name is +void one reverts back to the particle-only case). + + + +the destructor is needed to delete any ResonanceWidths +objects that have been created and linked to the respective particle. + + + +initialize some particle flags with default values, e.g. whether +a particle is a resonance, may decay, or is visible. Is called from the +constructors and from setAll. + + + +initialize pointer back to the whole database (so that masses of +decay products can be accessed, e.g.). + + + +change all the properties of the particle associated with a given +identity code. + + + +the PDG identity code. + + + +tell whether a separate antiparticle exists. + + + + + + + + + +set or get the particle or antiparticle name. Only the sign of +id is needed to distinguish particle/antiparticle. + + + + + +set or get the particle spin type, i.e. 2 s + 1, or 0 in some +special cases. + + + + + + + +set or get the particle charge type, i.e. three times the charge, +or the charge itself. Only the sign of id is needed +to distinguish particle/antiparticle. + + + + + +set or get the particle colour type, 0 for singlet, 1 for triplet, +-1 for antitriplet, 2 for octet. Only the sign of id +is needed to distinguish particle/antiparticle. + + + + + +the nominal mass m_0 (in GeV). + + + + + +the width Gamma of the Breit-Wigner distribution (in GeV). + + + + + +the lower limit of the allowed mass range generated by the Breit-Wigner +(in GeV). Has no meaning for particles without width, and would +typically be 0 there. + + + + + +the upper limit of the allowed mass range generated by the Breit-Wigner +(in GeV). If mMax < mMin then no upper limit is imposed. +Has no meaning for particles without width, and would typically +be 0 there. + + + +similar to mMin() above, except that for particles with +no width the m0(id) value is returned. + + + +similar to mMax() above, except that for particles with +no width the m0(id) value is returned. + + + + + +the nominal proper lifetime tau_0 (in mm/c). + + + + + +a flag telling whether a particle species are considered as a resonance +or not. Here "resonance" +is used as shorthand for any massive particle +where the decay process should be counted as part of the hard process +itself, and thus be performed before showers and other event aspects +are added. Restrictions on allowed decay channels is also directly +reflected in the cross section of simulated processes, while those of +normal hadrons and other light particles are not. +In practice, it is reserved for states above the b bbar +bound systems in mass, i.e. for W, Z, t, Higgs states, +supersymmetric states and (most?) other states in any new theory. +All particles with m0 above 20 GeV are by default +initialized to be considered as resonances. + + + + + +a flag telling whether a particle species may decay or not, offering +the main user switch. Whether a given particle of this kind then actually +will decay also depends on it having allowed decay channels, and on +other flags for particle decays. +All particles with tau0 below 1000 mm are +by default initialized to allow decays. + + + + + +a flag telling whether a particle should be handled by an external +decay package or not, with the latter default. Can be manipulated as +described on this page, but should normally not be. Instead the +pythia.decayPtr +method should be provided with the list of relevant particles. + + + + + +a flag telling whether a particle species is to be considered as +visible in a detector or not, as used e.g. in analysis routines. +By default this includes neutrinos and a few BSM particles +(gravitino, sneutrinos, neutralinos) that have neither strong nor +electromagnetic charge, and are not made up of constituents that +have it. The value of this flag is only relevant if a particle is +long-lived enough actually to make it to a detector. + + + + + +a flag valid only for resonances where PYTHIA contains code to +calculate the width of the resonance from encoded matrix-element +expressions, i.e. the Z^0, W^+-, t, +h^0, and a few more. The normal behaviour (false) +is then that the width is calculated from the mass, but it is +possible to force the resonance +to retain the nominal width. Branching ratios and the running of the +total width are unaffected. + + + + + +keep track of whether the data for a particle has been changed +in any respect between initialization and the current status. +Is used e.g. by the ParticleData::listChanged method +to determine which particles to list. + + + +Prepare the Breit-Wigner mass selection by precalculating +frequently-used expressions. + + + +is the constituent mass for a quark, hardcoded as +m_u = m_d = 0.325, m_s = 0.50, m_c = 1.60 +and m_b = 5.0 GeV, for a diquark the sum of quark constituent +masses, and for everything else the same as the ordinary mass. + + + +give the mass of a particle, either at the nominal value +or picked according to a (linear or quadratic) Breit-Wigner. + + + +calculate the running quark mass at a hard scale mH. +For other particles the on-shell mass is given. + + + +tells whether a particle will have a Breit-Wigner mass distribution or +not. Is determined by an internal logic based on the particle width and +on the value of the +ParticleData:modeBreitWigner switch. + + + +true for a particle with at least one decay channel defined. + + + +true for a lepton or an antilepton (including neutrinos). + + + +true for a quark or an antiquark. + + + +true for a gluon. + + + +true for a diquark or antidiquark. + + + +true for a hadron (made up out of normal quarks and gluons, +i.e. not for R-hadrons and other exotic states). + + + +true for a meson. + + + +true for a baryon or antibaryon. + + + +true for an intermediate hadron-like state with a colour octet charge +as used in the colour octet model for +onia production. + + + +extracts the heaviest quark or antiquark, i.e. one with largest +id number, for a hadron. Only the sign of the input +argument is relevant. + + + +is 1 for a quark, 2 for a diquark, 3 for a baryon, the same with a +minus sign for antiparticles, and else zero. Only the sign of the +input argument is relevant. + + + +resets to an empty decay table. + + + +adds a decay channel with up to 8 products. + + + +returns the number of decay channels for a particle. + + + + + +gain access to a specified channel in the decay table. + + + +rescales all partial branching ratios by a common factor, such that +the sum afterward becomes newSumBR. + + + +prepare to pick a decay channel. + + + +pick a decay channel according to branching ratios from +preparePick. + + + + + +set or get a pointer to an object that can be used for dynamic calculation +of partial and total resonance widths. Here a resonance is a particle +such as top, Z^0, W^+-, Higgs, and new unstable states +beyond the Standard Model. + + + +initialize the treatment of a resonance. + + + +calculate the total with for a resonance of a given current mass, +optionally including coupling to incoming flavour state (consider +the gamma*/Z^0 combination), optionally excluding decay +channels that have been closed by the user, and optionally storing +the results in the normal decay table. For the first argument only +the sign is relevant. + + + +special case of resWidth, where only open channels are +included, but results are not stored in the normal decay table. + + + +special case of resWidth, where only open channels are +included, and results are stored in the normal decay table. + + + +calculate the fraction of the full branching ratio that is left +open by the user choice of allowed decay channels. + + + +the factor used to rescale all partial widths in case the total +width is being forced to a specific value by the user. + + + +special case to calculate one final-state width; currently only used +for Higgs decay to q qbar, g g or +gamma gamma. + + +

The DecayChannel methods

+ +The properties stored in an individual decay channel can be set or get +by the methods in this section. + + +the constructor for a decay channel. Internal. + + + + + +set or get the onMode of a decay channel,
+0 if a channel is off,
+1 if on,
+2 if on for a particle but off for an antiparticle,
+3 if on for an antiparticle but off for a particle.
+If a particle is its own antiparticle then 2 is on and 3 off +but, of course, for such particles it is much simpler and safer +to use only 1 and 0.
+The 2 and 3 options can be used e.g. to encode CP violation in +B decays, or to let the W's in a q qbar -> W^+ W^- +process decay in different channels. + + + + + +set or get the branching ratio of the channel. Second argument only +for internal use. + + + +multiply the current branching ratio by fac. + + + + + +set or get the mode of processing this channel, possibly with matrix +elements (see the particle decays +description). + + + + + +set or get the number of decay products in a channel, at most 8. +(Is normally not to be set by hand, since it is automatically +updated whenever the products list is changed.) + + + + + +set or get a list of the decay products, 8 products 0 <= i < 8, +with trailing unused ones set to 0. + + + + + +used for internal purposes, to know which decay modes have been changed. + + + + + + + +find if the decay product list contains the one, two or three particle +identities provided. If the same code is repeated then so must it be in +the products list. Matching also requires correct sign. + + + + + +set or get the current branching ratio, taking into account on/off +switches and dynamic width for resonances. For internal use. + + + + + +set or get the current partial width of the channel; intended for +resonances where the widhts are recalculated based on the current +resonance mass. For internal use. + + + +multiply the current partial width by factor. + + + + + +set or get the fraction of secondary open widths, separately for +positive and negative particles. For internal use. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ParticleDecays.xml b/PYTHIA8/pythia8140/xmldoc/ParticleDecays.xml new file mode 100644 index 00000000000..899d4e95929 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ParticleDecays.xml @@ -0,0 +1,255 @@ + + +

Particle Decays

+ +The ParticleDecays class performs the sequential decays of +all unstable hadrons produced in the string fragmentation stage, +i.e. up to and including b hadrons and their decay products, +such as the tau lepton. It is not to be used for the decay of +more massive resonances, such as top, +Z^0 or SUSY, where decays must be performed already at the +ProcessLevel of the event generation. + +

+The decay description essentially copies the one present in +PYTHIA since many years, but with some improvements, e.g. in the decay +tables and the number of decay models available. Some issues may need +further polishing. + +

Variables determining whether a particle decays

+ +Before a particle is actually decayed, a number of checks are made. + +

+(i) Decay modes must have been defined for the particle kind; +tested by the canDecay() method of Event +(and ParticleData). + +

+(ii) The main switch for allowing this particle kind to decay must +be on; tested by the mayDecay() method of Event +(and ParticleData). + +

+(iii) Particles may be requested to have a nominal proper lifetime +tau0 below a threshold. + + +When on, only particles with tau0 < tau0Max are decayed. + + + +The above tau0Max, expressed in mm/c. + + +

+(iv) Particles may be requested to have an actual proper lifetime +tau below a threshold. + + +When on, only particles with tau < tauMax are decayed. + + + +The above tauMax, expressed in mm/c.
+In order for this and the subsequent tests to work, a tau +is selected and stored for each particle, whether in the end it +decays or not. (If each test would use a different temporary +tau it would lead to inconsistencies.) + + +

+(v) Particles may be requested to decay within a given distance +of the origin. + + +When on, only particles with a decay within a radius r < rMax +are decayed. There is assumed to be no magnetic field or other +detector effects. + + + +The above rMax, expressed in mm. + + +

+(vi) Particles may be requested to decay within a given cylidrical +volume around the origin. + + +When on, only particles with a decay within a volume limited by +rho = sqrt(x^2 + y^2) < xyMax and |z| < zMax +are decayed. There is assumed to be no magnetic field or other +detector effects. + + + +The above xyMax, expressed in mm. + + + +The above zMax, expressed in mm. + + +

Mixing

+ + +Allow or not B^0 - B^0bar and B_s^0 - B_s^0bar mixing. + + + +The mixing parameter x_d = Delta(m_B^0)/Gamma_B^0 in the +B^0 - B^0bar system. (Default from RPP2006.) + + + +The mixing parameter x_s = Delta(m_B_s^0)/Gamma_B_s^0 in the +B_s^0 - B_s^0bar system. (Delta-m from CDF hep-ex-0609040, +Gamma from RPP2006.) + + +

Other variables

+ + +Minimum mass difference required between the decaying mother mass +and the sum of the daughter masses, kept as a safety margin to avoid +numerical problems in the decay generation. + + + +In semileptonic decays to more than one hadron, such as +B -> nu l D pi, decay products after the first three are +dampened in momentum by an explicit weight factor +exp(-p^2/sigmaSoft^2), where p is the +three-momentum in the rest frame of the decaying particle. +This takes into account that such further particles come from the +fragmentation of the spectator parton and thus should be soft. + + +

+When a decay mode is defined in terms of a partonic content, a random +multiplicity (and a random flavour set) of hadrons is to be picked, +especially for some charm and bottom decays. This is done according to +a Poissonian distribution, for n_p normal particles and +n_q quarks the average value is chosen as + + n_p/ 2 + n_q/4 + multIncrease * ln ( mDiff / multRefMass) + +with mDiff the difference between the decaying particle mass +and the sum of the normal-particle masses and the constituent quark masses. +For gluonic systems multGoffset offers and optional additional +term to the multiplicity. The lowest possible multiplicity is +n_p + n_q/2 (but at least 2) and the highest possible 10. +If the picked hadrons have a summed mass above that of the mother a +new try is made, including a new multiplicity. These constraints +imply that the actual average multiplicity does not quite agree with +the formula above. + + +The above multIncrease parameter. + + + +The above multRefMass parameter. + + + +The above multGoffset parameter. + + + +When a decay is given as a list of four partons to be turned into +hadrons (primarily for modes 41 - 80) it is assumed that they are +listed in pairs, as a first and a second colour singlet, which could +give rise to separate sets of hadrons. Here colRearrange is +the probability that this original assignment is not respected, and +default corresponds to no memory of this original colour topology. + + + +When a particle decays to q qbar, g g, g g g +or gamma g g, with meMode > 90, allow or not a +shower to develop from it, before the partonic system is hadronized. +(The typical example is Upsilon decay.) + + +In addition, some variables defined for string fragmentation and for +flavour production are used also here. + +

Modes for Matrix Element Processing

+ +Some decays can be treated better than what pure phase space allows, +by reweighting with appropriate matrix elements. In others a partonic +content has to be converted to a set of hadrons. The presence of such +corrections is signalled by a nonvanishing meMode() value +for a decay mode in the particle +data table. The list of allowed possibilities almost agrees with the +PYTHIA 6 ones, but several obsolete choices have been removed, +a few new introduced, and most have been moved for better consistency. +Here is the list of currently allowed meMode() codes: +
    +
  • 0 : pure phase space of produced particles ("default"); +input of partons is allowed and then the partonic content is +converted into the minimal number of hadrons (i.e. one per +parton pair, but at least two particles in total)
    • +
  • 1 : omega and phi -> pi+ pi- pi0
    • +
  • 2 : polarization in V -> PS + PS (V = vector, +PS = pseudoscalar), when V is produced by +PS -> PS + V or PS -> gamma + V
    • +
  • 11 : Dalitz decay into one particle, in addition to the +lepton pair (also allowed to specify a quark-antiquark pair that +should collapse to a single hadron)
    • +
  • 12 : Dalitz decay into two or more particles in addition +to the lepton pair
    • +
  • 13 : double Dalitz decay into two lepton pairs
    • +
  • 21 : decay to phase space, but weight up neutrino_tau spectrum +in tau decay
    • +
  • 22 : weak decay; if there is a quark spectator system it collapses to +one hadron; for leptonic/semileptonic decays the V-A matrix element +is used, for hadronic decays simple phase space
    • +
  • 23 : as 22, but require at least three particles in decay
    • +
  • 31 : decays of type B -> gamma X, very primitive simulation where +X is given in terms of its flavour content, the X multiplicity is picked +according to a geometrical distribution with average number 2, and +the photon energy spectrum is weighted up relative to pure phase space
    • +
  • 42 - 50 : turn partons into a random number of hadrons, picked according +to a Poissonian with average value as described above, but at least +code - 40 and at most 10, and then distribute then in pure +phase space; make a new try with another multiplicity if the sum of daughter +masses exceed the mother one
    • +
  • 52 - 60 : as 42 - 50, with multiplicity between code - 50 +and 10, but avoid already explicitly listed non-partonic channels
    • +
  • 62 - 70 : as 42 - 50, but fixed multiplicity code - 60
    • +
  • 72 - 80 : as 42 - 50, but fixed multiplicity code - 70, +and avoid already explicitly listed non-partonic channels
    • +
  • 91 : decay to q qbar or g g, which should shower +and hadronize
    • +
  • 92 : decay onium to g g g or g g gamma +(with matrix element), which should shower and hadronize
    • +
  • 100 - : reserved for the description of partial widths of +resonances
    • +
+ +Three special decay product identity codes are defined. +
    +
  • 81: remnant flavour. Used for weak decays of c and b hadrons, where the +c or b quark decays and the other quarks are considered as a spectator +remnant in this decay. In practice only used for baryons with multiple +c and b quarks, which presumably would never be used, but have simple +(copied) just-in-case decay tables. Assumed to be last decay product.
    • +
  • 82: random flavour, picked by the standard fragmentation flavour +machinery, used to start a sequence of hadrons, for matrix element +codes in 41 - 80. Assumed to be first decay product, with -82 as second +and last. Where multiplicity is free to be picked it is selected as for +normal quarkonic systems. Currently unused.
    • +
  • 83: as for 82, with matched pair 83, -83 of decay products. The +difference is that here the pair is supposed to come from a closed gluon +loop (e.g. eta_c -> g g) and so have a somewhat higher average +multiplicity than the simple string assumed for 82, see the +ParticleDecays:multGoffset parameter above.
    • +
+ + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ParticleProperties.xml b/PYTHIA8/pythia8140/xmldoc/ParticleProperties.xml new file mode 100644 index 00000000000..4b0138e2e2f --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ParticleProperties.xml @@ -0,0 +1,688 @@ + + +

Particle Properties

+ +A Particle corresponds to one entry/slot in the +event record. Its properties therefore is a mix of ones belonging +to a particle-as-such, like its identity code or four-momentum, +and ones related to the event-as-a-whole, like which mother it has. + +

+What is stored for each particle is +

    +
  • the identity code,
    • +
  • the status code,
    • +
  • two mother indices,
    • +
  • two daughter indices,
    • +
  • a colour and an anticolour index,
    • +
  • the four-momentum and mass,
    • +
  • the scale at which the particle was produced (optional),
    • +
  • the production vertex and proper lifetime (optional),
    • +
  • a pointer to the particle kind in the particle data table, and
    • +
  • a pointer to the whole particle data table.
    • +
+From these, a number of further quantities may be derived. + +

Basic output methods

+ +The following member functions can be used to extract the most important +information: + + +the identity of a particle, according to the PDG particle codes +Yao06. + + + +status code. The status code includes information on how a particle was +produced, i.e. where in the program execution it was inserted into the +event record, and why. It also tells whether the particle is still present +or not. It does not tell how a particle disappeared, whether by a decay, +a shower branching, a hadronization process, or whatever, but this is +implicit in the status code of its daughter(s). The basic scheme is: +
    +
  • status = +- (10 * i + j)
    • +
  • + : still remaining particles
    • +
  • - : decayed/branched/fragmented/... and not remaining
    • +
  • i = 1 - 9 : stage of event generation inside PYTHIA
    • +
  • i = 10 -19 : reserved for future expansion
    • +
  • i >= 20 : free for add-on programs
    • +
  • j = 1 - 9 : further specification
    • +
+In detail, the list of used or foreseen status codes is: +
    +
  • 11 - 19 : beam particles
    • +
      +
    • 11 : the event as a whole
      • +
    • 12 : incoming beam
      • +
    • 13 : incoming beam-inside-beam (e.g. gamma + inside e)
      • +
    • 14 : outgoing elastically scattered
      • +
    • 15 : outgoing diffractively scattered
      • +
    +
  • 21 - 29 : particles of the hardest subprocess
    • +
      +
    • 21 : incoming
      • +
    • 22 : intermediate (intended to have preserved mass)
      • +
    • 23 : outgoing
      • +
    +
  • 31 - 39 : particles of subsequent subprocesses
    • +
      +
    • 31 : incoming
      • +
    • 32 : intermediate (intended to have preserved mass)
      • +
    • 33 : outgoing
      • +
    • 34 : incoming that has already scattered
      • +
    +
  • 41 - 49 : particles produced by initial-state-showers
    • +
      +
    • 41 : incoming on spacelike main branch
      • +
    • 42 : incoming copy of recoiler
      • +
    • 43 : outgoing produced by a branching
      • +
    • 44 : outgoing shifted by a branching
      • +
    • 45 : incoming rescattered parton, with changed kinematics + owing to ISR in the mother system (cf. status 34)
      • +
    • 46 : incoming copy of recoiler when this is a rescattered + parton (cf. status 42)
      • +
    +
  • 51 - 59 : particles produced by final-state-showers
    • +
      +
    • 51 : outgoing produced by parton branching
      • +
    • 52 : outgoing copy of recoiler, with changed momentum
      • +
    • 53 : copy of recoiler when this is incoming parton, + with changed momentum
      • +
    • 54 : copy of a recoiler, when in the initial state of a + different system from the radiator
      • +
    • 55 : copy of a recoiler, when in the final state of a + different system from the radiator
      • +
    +
  • 61 - 69 : particles produced by beam-remnant treatment
    • +
      +
    • 61 : incoming subprocess particle with primordial kT + included
      • +
    • 62 : outgoing subprocess particle with primordial kT + included
      • +
    • 63 : outgoing beam remnant
      • +
    +
  • 71 - 79 : partons in preparation of hadronization process
    • +
      +
    • 71 : copied partons to collect into contiguous colour singlet
      • +
    • 72 : copied recoiling singlet when ministring collapses to + one hadron and momentum has to be reshuffled
      • +
    • 73 : combination of very nearby partons into one
      • +
    • 74 : combination of two junction quarks (+ nearby gluons) + to a diquark
      • +
    • 75 : gluons split to decouple a junction-antijunction pair
      • +
    • 76 : partons with momentum shuffled to decouple a + junction-antijunction pair
      • +
    • 77 : temporary opposing parton when fragmenting first two + strings in to junction (should disappear again)
      • +
    • 78 : temporary combined diquark end when fragmenting last + string in to junction (should disappear again)
      • +
    +
  • 81 - 89 : primary hadrons produced by hadronization process
    • +
      +
    • 81 : from ministring into one hadron
      • +
    • 82 : from ministring into two hadrons
      • +
    • 83, 84 : from normal string (the difference between the two + is technical, whether fragmented off from the top of the + string system or from the bottom, useful for debug only)
      • +
    • 85, 86 : primary produced hadrons in junction frogmentation of + the first two string legs in to the junction, + in order of treatment
      • +
    +
  • 91 - 99 : particles produced in decay process, or by Bose-Einstein + effects
    • +
      +
    • 91 : normal decay products
      • +
    • 92 : decay products after oscillation B0 <-> B0bar or + B_s0 <-> B_s0bar
      • +
    • 93, 94 : decay handled by external program, normally + or with oscillation
      • +
    • 99 : particles with momenta shifted by Bose-Einstein effects + (not a proper decay, but bookkept as an 1 -> 1 such, + happening after decays of short-lived resonances but before + decays of longer-lived particles)
      • +
    +
  • 101 - 199 : reserved for future expansion
    • +
  • 201 - : free to be used by anybody
    • +
+ + + + + +the indices in the event record where the first and last mothers are +stored, if any. There are five allowed combinations of mother1 +and mother2: +
    +
  1. mother1 = mother2 = 0: for lines 0 - 2, where line 0 +represents the event as a whole, and 1 and 2 the two incoming +beam particles;
    2. +
  2. mother1 = mother2 > 0: the particle is a "carbon copy" +of its mother, but with changed momentum as a "recoil" effect, +e.g. in a shower;
    3. +
  3. mother1 > 0, mother2 = 0: the "normal" mother case, where +it is meaningful to speak of one single mother to several products, +in a shower or decay;
    4. +
  4. mother1 < mother2, both > 0, for +abs(status) = 81 - 86: primary hadrons produced from the +fragmentation of a string spanning the range from mother1 +to mother2, so that all partons in this range should be +considered mothers;
    5. +
  5. mother1 < mother2, both > 0, except case 4: particles +with two truly different mothers, in particular the particles emerging +from a hard 2 -> n interaction.
    6. +
+Note 1: in backwards evolution of initial-state showers, +the mother may well appear below the daughter in the event record. +Note 2: the motherList(i) method of the +Event class returns a vector of all the mothers, +providing a uniform representation for all five cases. + + + + + +the indices in the event record where the first and last daughters +are stored, if any. There are five allowed combinations of +daughter1 and daughter2: +
    +
  1. daughter1 = daughter2 = 0: there are no daughters +(so far);
    2. +
  2. daughter1 = daughter2 > 0: the particle has a +"carbon copy" as its sole daughter, but with changed momentum +as a "recoil" effect, e.g. in a shower;
    3. +
  3. daughter1 > 0, daughter2 = 0: each of the incoming beams +has only (at most) one daughter, namely the initiator parton of the +hardest interaction; further, in a 2 -> 1 hard interaction, +like q qbar -> Z^0, or in a clustering of two nearby partons, +the initial partons only have this one daughter;
    4. +
  4. daughter1 < daughter2, both > 0: the particle has +a range of decay products from daughter1 to +daughter2;
  5. daughter2 < daughter1, +both > 0: the particle has two separately stored decay products (e.g. +in backwards evolution of initial-state showers).
    6. +
+Note 1: in backwards evolution of initial-state showers, the +daughters may well appear below the mother in the event record. +Note 2: the mother-daughter relation normally is reciprocal, +but not always. An example is hadron beams (indices 1 and 2), where each +beam remnant and the initiator of each multiple interaction has the +respective beam as mother, but the beam itself only has the initiator +of the hardest interaction as daughter. +Note 3: the daughterList(i) method of the +Event class returns a vector of all the daughters, +providing a uniform representation for all five cases. With this method, +also all the daughters of the beams are caught, with the initiators of +the basic process given first, while the rest are in no guaranteed order +(since they are found by a scanning of the event record for particles +with the beam as mother, with no further information). + + + + + +the colour and anticolour tags, Les Houches Accord Boo01 +style (starting from tag 101 by default, see below). + + + + + + + + + +the particle four-momentum components. + + + +the particle four-momentum vector, with components as above. + + + +the particle mass, stored with a minus sign (times the absolute value) +for spacelike virtual particles. + + + +the scale at which a parton was produced, which can be used to restrict +its radiation to lower scales in subsequent steps of the shower evolution. +Note that scale is linear in momenta, not quadratic (i.e. Q, +not Q^2). + + + + + + + + + +the production vertex coordinates, in mm or mm/c. + + + +The production vertex four-vector. Note that the components of a +Vec4 are named px(), py(), pz() and e() +which of course then should be reinterpreted as above. + + + +the proper lifetime, in mm/c. It is assigned for all hadrons with +positive nominal tau, tau_0 > 0, because it can be used +by PYTHIA to decide whether a particle should or should not be allowed +to decay, e.g. based on the decay vertex distance to the primary interaction +vertex. + + +

Input methods

+ +The same method names as above are also overloaded in versions that +set values. These have an input argument of the same type as the +respective output above, and are of type void. + +

+There are also a few alternative methods for input: + + + + +sets the status sign positive or negative, without changing the absolute value. + + + +changes the absolute value but retains the original sign. + + + +sets both mothers in one go. + + + +sets both daughters in one go. + + + +sets both colour and anticolour in one go. + + + +sets the four-momentum components in one go. + + + +sets the production vertex components in one go. + + +

Further output methods

+ +

+In addition, a number of derived quantities can easily be obtained, +but cannot be set, such as: + + +the absolute value of the particle identity code. + + + +the absolute value of the status code. + + + +true for a remaining particle, i.e. one with positive status code, +else false. Thus, after an event has been fully generated, it +separates the final-state particles from intermediate-stage ones. +(If used earlier in the generation process, a particle then +considered final may well decay later.) + + + +true for particles with a status code -34, -45, -46 or -54, else false. +This singles out partons that have been created in a previous +scattering but here are bookkept as belonging to the incoming state +of another scattering. + + + +production vertex has been set; if false then production at the origin +is assumed. + + + +squared mass, which can be negative for spacelike partons. + + + + + +(squared) mass calculated from the four-momentum; should agree +with m(), m2() up to roundoff. Negative for spacelike +virtualities. + + + +energy calculated from the mass and three-momentum; should agree +with e() up to roundoff. For spacelike partons a +positive-energy solution is picked. This need not be the correct +one, so it is recommended not to use the method in such cases. + + + + + +(squared) transverse momentum. + + + + + +(squared) transverse mass. If m_T^2 is negative, which can happen +for a spacelike parton, then mT() returns +-sqrt(-m_T^2), by analogy with the negative sign used to store +spacelike masses. + + + + + +(squared) three-momentum size. + + + + + +(squared) transverse energy, +eT = e * sin(theta) = e * pT / pAbs. + + + + + +polar and azimuthal angle. + + + +angle in the (p_x, p_z) plane, between -pi and ++pi, with 0 along the +z axis + + + + + +E +- p_z. + + + + + +rapidity and pseudorapidity. + + + + + + + + + +the decay vertex coordinates, in mm or mm/c. This decay vertex is +calculated from the production vertex, the proper lifetime and the +four-momentum assuming no magnetic field or other detector interference. +It can be used to decide whether a decay should be performed or not, +and thus is defined also for particles which PYTHIA did not let decay. + + +

+Each Particle contains a pointer to the respective +ParticleDataEntry object in the +particle data tables. +This gives access to properties of the particle species as such. It is +there mainly for convenience, and should be thrown if an event is +written to disk, to avoid any problems of object persistency. Should +an event later be read back in, the pointer will be recreated from the +id code if the normal input methods are used. (Use the +Event::restorePtrs() method +if your persistency scheme bypasses the normal methods.) This pointer is +used by the following member functions: + + +the name of the particle. + + + +as above, but for negative-status particles the name is given in +brackets to emphasize that they are intermediaries. + + + +2 *spin + 1 when defined, else 0. + + + + + +charge, and three times it to make an integer. + + + + + +charge different from or equal to 0. + + + +0 for colour singlets, 1 for triplets, +-1 for antitriplets and 2 for octets. + + + +the nominal mass of the particle, according to the data tables. + + + + + + + +the width of the particle, and the minimum and maximum allowed mass value +for particles with a width, according to the data tables. + + + +the mass of the particle, picked according to a Breit-Wigner +distribution for particles with width. It is different each time called, +and is therefore only used once per particle to set its mass +m(). + + + +will give the constituent masses for quarks and diquarks, +else the same masses as with m0(). + + + +the nominal lifetime tau_0 > 0, in mm/c, of the particle species. +It is used to assign the actual lifetime tau. + + + +flag whether particle has been declared unstable or not, offering +the main user switch to select which particle species to decay. + + + +flag whether decay modes have been declared for a particle, +so that it could be decayed, should that be requested. + + + +particles that are decayed by an external program. + + + +particles where the decay is to be treated as part of the hard process, +typically with nominal mass above 20 GeV (W^+-, Z^0, t, ...). + + + +particles with strong or electric charge, or composed of ones having it, +which thereby should be considered visible in a normal detector. + + + +true for a lepton or an antilepton (including neutrinos). + + + +true for a quark or an antiquark. + + + +true for a gluon. + + + +true for a hadron (made up out of normal quarks and gluons, +i.e. not for R-hadrons and other exotic states). + + + +a reference to the ParticleDataEntry. + + +

+Not part of the Particle class proper, but obviously tightly +linked, are the two methods + + + + +the (squared) invariant mass of two particles. + + +

Methods that perform operations

+ +There are some further methods, some of them inherited from +Vec4, to modify the properties of a particle. +They are of little interest to the normal user. + + +multiply the three-momentum components by fac. + + + +multiply the four-momentum components by fac. + + + +multiply the four-momentum components and the mass by fac. + + + +rotate three-momentum and production vertex by these polar and azimuthal +angles. + + + +boost four-momentum and production vertex by this three-vector. + + + +as above, but also input the gamma value, to reduce roundoff errors. + + + +boost four-momentum and production vertex by +beta = (px/e, py/e, pz/e). + + + +as above, but also use gamma> = e/m to reduce roundoff errors. + + + + + +as above, but with sign of boost flipped. + + + +combined rotation and boost of the four-momentum and production vertex. + + + +add a positive offset to the mother and daughter indices, i.e. +if mother1 is above minMother then +addMother is added to it, same with mother2, +if daughter1 is above minDaughter then +addDaughter is added to it, same with daughter2. + + + +add a positive offset to colour indices, i.e. if col is +positive then addCol is added to it, same with acol. + + +

Constructors and operators

+ +Normally a user would not need to create new particles. However, if +necessary, the following constructors and methods may be of interest. + + +constructs an empty particle, i.e. where all properties have been set 0 +or equivalent. + + + +constructs a particle with the input properties provided, and non-provided +ones set 0. + + + +constructs a particle with the input properties provided, and non-provided +ones set 0. + + + +constructs an particle that is a copy of the input one. + + + +copies the input particle. + + + +sets the pointer to the ParticleData objects, +i.e. to the full particle data table. Also calls setPDEPtr +below. + + + +sets the pointer to the ParticleDataEntry object of the +particle, based on its current id code. + + +

Final notes

+ +The +Event +class also contains a few methods defined for individual particles, +but these may require some search in the event record and therefore +cannot be defined as Particle methods. + +

+Currently there is no information on polarization states. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/PartonDistributions.xml b/PYTHIA8/pythia8140/xmldoc/PartonDistributions.xml new file mode 100644 index 00000000000..0cf33f07b6c --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/PartonDistributions.xml @@ -0,0 +1,132 @@ + + +

Parton Distributions

+ +The parton distributions file contains the PDF class. +PDF is the base class, from which specific PDF +classes are derived. + +

+The choice of which PDF to use is made by settings in the +Pythia class, see here. +These settings also allow to access all the proton PDF's available in the +LHAPDF library Wha05. Thus there is no need for a normal user +to study the PDF class. The structure must only be understood +when interfacing new PDF's, e.g. ones not yet found in LHAPDF. + +

The PDF base class

+ +PDF defines the interface that all PDF classes should respect. +The constructor requires the incoming beam species to be given: +even if used for a proton PDF, one needs to know whether the beam +is actually an antiproton. This is one of the reasons why Pythia +always defines two PDF objects in an event, one for each beam. + +

+Once a PDF object has been constructed, call it pdf, +the main method is pdf.xf( id, x, Q2), which returns +x*f_id(x, Q2), properly taking into account whether the beam +is an antiparticle or not. + +

+Whenever the xf member is called with a new flavour, x +or Q^2, the xfUpdate member is called to do the actual +updating. This routine may either update that particular flavour or all +flavours at this (x, Q^2) point. (In the latter case the saved +id value idSav should be set to 9.) The choice is +to be made by the producer of a given set, based on what he/she deems most +effective, given that sometimes only one flavour need be evaluated, and +about equally often all flavours are needed at the same x and +Q^2. Anyway, the latest value is always kept in memory. This is +the other reason why Pythia has one separate PDF +object for each beam, so that values at different x can be kept +in memory. + +

+Two further public methods are xfVal( id, x, Q2) and +xfSea( id, x, Q2). These are simple variants whereby +the quark distributions can be subdivided into a valence and a sea part. +If these are not directly accessible in the parametrization, onc can +make the simplified choices u_sea = ubar_sea, u_val = u_tot - u_sea, +and correspondingly for d. (Positivity will always be guaranteed +at output.) The xfUpdate method should also take care of +updating this information. + +

+A method setExtrapolate(bool) allows you to switch between +freezing parametrizations at the x and Q^2 boundaries +(false) or extrapolating them outside the boundaries +(true). This method is only implemented for the LHAPDF class +below. If you implement a new PDF you are free to use this method, but it +would be smarter to hardcode the desired limiting behaviour. + +

Derived classes

+ +There is only one pure virtual method, xfUpdate, that +therefore must be implemented in any derived class. A reasonable +number of such classes come with the program: + +

+For protons: +

    +
  • LHAPDFinterface provides an interface to the +LHAPDF libraryWha05.
    • +
  • GRV94L gives the GRV 94 L parametrization +Glu95.
    • +
  • CTEQ5L gives the CTEQ 5 L parametrization +Lai00.
    • +
  • MSTWpdf gives the four distributions of the +MRST/MSTW group that have been implemented.
    • +
  • CTEQ6pdf gives the six distributions of the +CTEQ/CT group that have been implemented.
    • +
+The current default is CTEQ 5L, which has been used in most studies +to date. + +

+For charged pions: +

    +
  • GRVpiL gives the GRV 1992 pi+ parametrization.
    • +
+ +

+For Pomerons (used to describe diffraction): +

    +
  • PomFix gives a simple but flexible +Q2-independent parametrization.
    • +
  • PomH1FitAB gives the H1 2006 Fit A and Fit B +parametrizations.
    • +
  • PomH1Jets gives the H1 2007 Jets parametrization.
    • +
+ +

+For charged leptons (e, mu, tau): +

    +
  • Lepton gives a QED parametrization Kle89. +In QED there are not so many ambiguities, so here one set should be +enough. On the other hand, there is the problem that the +lepton-inside-lepton pdf is integrably divergent for x -> 1, +which gives numerical problems. Like in PYTHIA 6, the pdf is therefore +made to vanish for x > 1 - 10^{-10}, and scaled up in the range +1 - 10^{-7} < x < 1 - 10^{-10} in such a way that the +total area under the pdf is preserved.
    • +
  • LeptonPoint gives the trivial distribution of a +pointlike (i.e. unresolved) lepton or neutrino.
    • +
+ +There is another method, isSetup(), that returns the +base-class boolean variable isSet. This variable is +initially true, but could be set false if the +setup procedure of a PDF failed, e.g. if the user has chosen an unknown +PDF set. + +

+The MRST/MSTW, CTEQ/CT and H1 PDF routines are based on the interpolation +in (x, Q) grids. The grid files are stored in the +xmldoc subdirectory, like settings and particle data. +Only PDF sets that will be used are read in during the initialization +stage. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/PhaseSpaceCuts.xml b/PYTHIA8/pythia8140/xmldoc/PhaseSpaceCuts.xml new file mode 100644 index 00000000000..b44063e5220 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/PhaseSpaceCuts.xml @@ -0,0 +1,257 @@ + + +

Phase Space Cuts

+ +PhaseSpace is base class for all hard-process phase-space +generators, either generic 2 -> 1 or 2 -> 2 ones, +or specialized ones like for elastic and diffractive scattering. + +

+In it, it is possible to constrain the kinematics of most processes. +(Exceptions are "soft physics", i.e. minimum bias, elastic and +diffractive processes. The Coulomb singularity for elastic scatterings, +if simulated, is handled separately.) +These constraints apply in the rest frame of the hard subprocess, and +topologies normally would be changed e.g. by subsequent showering +activity. The cross section of a process is adjusted to only +correspond to the allowed phase space. + +

+The more particles in the final state, the more cuts could be applied. +Here we have tried to remain with the useful minimum, however. More +generic possibilities could be handled by the +user hooks facility. + +

Cuts in all processes

+ + +The minimum invariant mass. + + + +The maximum invariant mass. +A value below mHatMin means there is no upper limit. + + +

Cuts in 2 -> 1 processes

+ +When a resonance id is produced, the +mMin(id) and +mMax(id) +methods restrict the allowed mass range +of this resonance. Therefore the allowed range is chosen to be the +overlap of this range and the mHatMin to +mHatMax range above. Most resonances by default have no +upper mass limit, so effects mainly concern the lower limit. +Should there be no overlap between the two ranges then the process +will be switched off. + +

Cuts in 2 -> 2 processes

+ + +The minimum invariant pT. + + + +The maximum invariant pT. +A value below pTHatMin means there is no upper limit. + + + +Extra pT cut to avoid the divergences of some processes +in the limit pT -> 0. Specifically, if either or both +produced particles have a mass below pTHatMinDiverge +then pT is limited from below by the larger of +pTHatMin and pTHatMinDiverge. + + + +Allows masses to be selected according to Breit-Wigner shapes in +2 -> 2 processes, whenever particles have been declared +with a nonvanishing width above the threshold below. In those cases +also the limits below will be used for the mass selection. For +2 -> 1 processes the Breit-Wigner shape is part of the +cross section itself, and therefore always included. + + + +The minimum width a resonance must have for the mass to be dynamically +selected according to a Breit-Wigner shape, within the limits set below. +Only applies when useBreitWigners is on; else the nominal +mass value is always used. + + +

+For a particle with a Breit-Wigner shape selected, according to the +rules above and to the rules of the particle species itself, the +mMin(id) and +mMax(id) +methods restrict the allowed mass range of the particle, just like for +the 2 -> 1 processes. + +

Cuts in 2 -> 3 processes

+ +There are two main classes of 2 -> 3 processes. One is the +processes such as WW/ZZ-fusion Higgs production, i.e. +q q -> q q H, where there are no special singularities +associated with two partons in the final state being collinear, +or even for pT -> 0. For this class, no further cuts +have been introduced than those already available for 2 -> 2 +processes. Specifically, for now all three are restricted exactly the +same way by pTHatMin and pTHatMax. As above, +Breit-Wigner mass ranges can be restricted. + +

+The other 2 -> 3 event class is QCD processes, such as +g g -> g g g. Here the soft and collinear singularities +play a major role, and the phase space generation and cuts have +been adapted to this. For this class, an alternative set of cuts +is used, as outlined in the following. First of all the three +outgoing partons are ordered in falling pT, i.e. +pT_3 > pT_4 > pT_5 (where the labelling 3, 4, 5 of the outgoing +partons is random, i.e. unrelated to the order specified in the +process name). The allowed ranges of pT_3 and pT_5 +can be specified, but obviously pT_3max >= pT_5max and +pT_3min >= pT_5min. The pT_4 is not constrained +explicitly, but is constructed from the vector sum of pT_3 +and pT_5, subject to the constraint that it has to lie +between the two in magnitude. While the pT cuts take care +of singularities collinear with the incoming beams, it is also +necessary to handle final-state singularities, when two outgoing +partons become collinear. This is done by requiring a minimal +separation in R, where +R^2 = (Delta eta)^2 + (Delta phi)^2. +Finally, a note about efficiency. The QCD 2 -> 3 phase space +is not set up to explicitly include mHat as one of the basic +variables. Such a cut is only done after a phase space point is already +selected, which means that a narrow mass choice will slow down the +program appreciably. Also narrow pT_3 and pT_5 bins +are likely to give inefficient generation, if it gives rise to +significant indirect restrictions on pT_4. + + +The minimum invariant pT of the highest-pT parton in +QCD 2 -> 3 processes. + + + +The maximum invariant pT of the highest-pT parton in +QCD 2 -> 3 processes +A value below pTHat3Min means there is no upper limit. + + + +The minimum invariant pT of the lowest-pT parton in +QCD 2 -> 3 processes. + + + +The maximum invariant pT of the lowest-pT parton in +QCD 2 -> 3 processes +A value below pTHat5Min means there is no upper limit. + + + +The minimum separation R in (eta, phi) space between +any two outgoing partons in QCD 2 -> 3 processes. + + + +

Cuts for a second hard process

+ +If you use the machinery that allows the generation of a specified +second hard process then, +by default, the same phase space cuts will be used for it as listed +above. Optionally, however, you may use a second set of cuts, as +described here. In this context "first" and "second" is merely a +technical distinction; you are welcome e.g. to pick pT ranges +such that the second interaction always has a larger pT than +the first. + + +By default use the same cuts for a second hard process as for the +first. If off then instead use the mass and pT +cuts below, where relevant. (The other cuts above still remain the same.) + + + +The minimum invariant mass for a second interaction, if separate. + + + +The maximum invariant mass for a second interaction, if separate. +A value below mHatMin means there is no upper limit. + + + +The minimum invariant pT for a second interaction, if separate. + + + +The maximum invariant pT for a second interaction, if separate. +A value below pTHatMin means there is no upper limit. + + +

Generation strategy and documentation

+ +During the initialization stage a simplified function is found, +that is intended to be above the true cross-section behaviour +over the whole of phase space. It is chosen to be easily integrable +and invertible. That way a trial phase space point can be selected +according this simple function, and then be accepted by the ratio of +true to the simple function. For a good efficieny the ratio should be +close to unity, yet never above it. This constrains the absolute +normalization of the simple function. The initial search may fail to +find the phase space point where the true-to-simple ratio is maximal, +however. This then can lead to subsequent maximum violations, where the +ratio is above unity. Two alternative strategies are implemented to +handle such situations, see below. + + +Possibility to print information on the search for phase-space +coefficients that (in a multichannel approach) provides an analytical +upper envelope of the differential cross section, and the +corresponding upper estimate of the cross section. Of interest +for crosschecks by expert users only. + + + +Possibility to print information whenever the assumed maximum +differential cross section of a process is violated, i.e. when +the initial maximization procedure did not find the true maximum. +Also, should negative cross sections occur, print whenever a more +negative value is encountered. + + + +Strategy for handling cases where a larger cross section is +obtained during the event generation than was assumed at initialization, +i.e. when a violation occurs. +
off:each event comes with a weight, which normally is unity +(as a consequence of the acceptance/rejection step), and is found in +Info::weight(). +For events which exceed the maximum instead the true-to-simple ratio +is stored as event weight, which then is above unity. If the user so +wishes this weight can then be carried along when event properties are +histogrammed. Since normally such violations should be rare and not +too much above unity one could expect most users to ignore such issues +be default. Should maximum violations turn out to be frequent (visible +in the Pythia::statistics() +output) the option exists to use the information. +
on:the maximum is increased whenever it is exceeded. Thus +events generated after this point will be "correctly" distributed, +while ones generated previously obviously then have had too high a +relative weight. If violations occur early on and/or are small this +strategy should do a good job of correcting to the desired phase-space +distribution. This strategy may be more convenient for the normal user, +who would not wish to worry about event weights. It does have the +disadvantage that the raised maximum introduces an extra amount of +"history memory" to the generation sequence, so that it becomes less +easy to save-and-restore the random-number +state for debugging purposes. + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ProcessSelection.xml b/PYTHIA8/pythia8140/xmldoc/ProcessSelection.xml new file mode 100644 index 00000000000..2d0725b4743 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ProcessSelection.xml @@ -0,0 +1,140 @@ + + +

Process Selection

+ +There is no way PYTHIA could contain all processes of interest, +neither in terms of potential physics topics nor in terms of +high-multiplicity final states. What exists is a reasonably +complete setup of all 2 -> 1 and 2 -> 2 +processes within the Standard Model, plus some examples of +processes beyond that, again for low multiplicities. Combined with +the PYTHIA parton showers, this should be enough to get a flying +start in the study of many physics scenarios. +Other processes could be fed in via the +Les Houches Accord +or be implemented as a +Semi-Internal Process. +In the latter case the existing processes would act as obvious +templates. + +

+By default all processes are switched off. You should switch on +those you want to simulate. This may be done at two (occasionally +three) levels, either for each individual process or for a group of +processes. That is, a process is going to be generated either if its +own flag or its group flag is on. There is no built-in construction +to switch on a group and then switch off a few of its members. + +

+Each process is assigned an integer code. This code is not used in +the internal administration of events (so having the same code for +two completely different processes would not be a problem), but only +intended to allow a simpler user separation of different processes. +Also the process name is available, as a string. + +

+To ease navigation, the list of processes has been split into several +separate pages, by main topic. The classification is hopefully +intuitive, but by no means unambiguous. For instance, essentially +all processes involve QCD, so the "QCD processes" are the ones that +only involve QCD. (And also that is not completely true, once one +includes all that may happen in multiple interactions.) On these +separate pages also appear the settings that are completely local +to that particular process class, but not the ones that have a +broader usage. + +

QCD Processes

+ +QCD processes fall in two main categories: soft and hard. The soft ones +contain elastic, diffractive and "minimum-bias" events, together +covering the total cross section. Hard processea are the normal +2 -> 2 ones, including charm and bottom production. +
Reserved code range: 101 - 199. + +

Electroweak Processes

+ +Prompt-photon, gamma^*/Z^0 and W^+- production, +plus a few processes with t-channel boson exchange. +
Reserved code range: 201 - 299. + +

Onia Processes

+ +Colour singlet and octet production of charmonium and bottomonium. +
Reserved code range: 401 - 499 for charmonium and +501 - 599 for bottomonium. + +

Top Processes

+ +Top production, singly or doubly. +
Reserved code range: 601 - 699. + +

Fourth-Generation +Processes

+ +Production of hypothetical fourth-generation fermions. +
Reserved code range: 801 - 899. + +

Higgs Processes

+ +Higgs production, within or beyond the Standard Model. +See section on Left-Right-Symmetry processes for doubly charged Higgses. +
Reserved code range: 901 - 999 for a Standard Model Higgs +and 1001 - 1199 for MSSM Higgses. + +

SUSY Processes

+ +Production of supersymmetric particles, currently barely begun. +
Reserved code range: 1001 - 2999. (Whereof 1001 - 1199 +for Higgses; see above.) + +

New-Gauge-Boson +Processes

+ +Production of new gauge bosons such as Z' and W'. +
Reserved code range: 3001 - 3099. + +

Left-Right-Symmetry +Processes

+ +Production of righthanded Z_R and W_R bosons and of +doubly charged Higgses. +
Reserved code range: 3101 - 3199. + +

Leptoquark Processes

+ +Production of a simple scalar leptoquark state. +
Reserved code range: 3201 - 3299. + +

Compositeness Processes

+ +Production of excited fermion states and contact-interaction modification +to interactions between fermions (excluding technicolor; see below). +
Reserved code range: 4001 - 4099. + +

Technicolor Processes

+ +Production of technicolor particles and modifications of QCD processes +by technicolor interactions. Does not exist yet. +
Reserved code range: 4101 - 4199. + +

Hidden Valley Processes

+A scenario for the pair prodiction of new particles with couplings +under a new gauge group, with invisible gauge bosons. Radiation of +these gauge bosons is included in the standard final-state parton +shower. +
Reserved code range: 4901 - 4999. + +

Extra-Dimensional +Processes

+ +A vast area, here represented by the production of a Randall-Sundrum +excited graviton state and a Kaluza-Klein gluon, a Kaluza-Klein tower +of gamma/Z^0 excitations in one TeV^- sized extra dimension, +several Large Extra Dimension processes, and a few related Unparticle +processes. +
Reserved code range: 5001 - 5099. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ProgramClasses.xml b/PYTHIA8/pythia8140/xmldoc/ProgramClasses.xml new file mode 100644 index 00000000000..561f3fbf643 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ProgramClasses.xml @@ -0,0 +1,220 @@ + + +

Program Classes

+ +The complete PYTHIA 8 package contains +a multitude of classes. +There is no reason to describe all of them, with all of their +methods, since most should not be touched by a normal user. +Nevertheless some of the crucial ones are described in detail, +as a help not only to advanced users but also to developers. +We here provide a quick reference (still incomplete) which +classes you can find described where on these pages. Normally +you have to scroll down to find the details, since the top of +the page contains information of more general interest. + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
ClassReferenceComment
BeamShapeBeam Shapevertex amd beam momentum spread
CellJetEvent Analysisjet cone clustering analysis, intended for hadron collider +topologies
ClusterJetEvent Analysisjet clustering analysis, intended for e^+e^- +collider topologies
CoupSMStandard Model Parameterscouplings and mixing matrices
CoupSUSYSUSY Les Houches Accordcompute and store SUSY couplings, using input from SusyLesHouches
DecayChannelParticle Data Schemethe properties of a single decay channel of particle species
EventEvent Recordthe complete event record
HepMC::I_Pythia8HepMC Interfaceconvert a PYTHIA event record to the HepMC format
HistHistogramsa primitive built-in histogramming package
InfoEvent Informationvarious one-of-a-kind information on the current event
LHAPDFInterfaceParton Distributionsuse PDF sets from the LHAPDF library
LHAupLes Houches Accordbase class for Les Houches external hard-event input
ParticleParticle Propertiesthe properties of a particle in the event record
ParticleDataParticle Data Schemethe database of particle species properties
ParticleDataEntryParticle Data Schemethe properties of a particle species
PDFParton Distributionsbase class for all PDFs
PythiaProgram Flowthe top-level class, that drives the generation process
ResonanceWidthsSemi-Internal Resonancesbase class for all resonance-width treatment
RndmRandomNumbersa primitive built-in histogramming package
RotBstMatrixFour-Vectorsrotation and boosts of four-vectors
SettingsSettings Schemethe database that regulates the behaviour of the program
SigmaProcessSemi-Internal Processesbase class for all hard-process cross sections
SpaceShowerImplement New Showersspacelike, i..e. initial-state showers
SphericityEvent Analysissphericity analysis of events
SusyLesHouchesSUSY Les Houches Accordreading in of SLHA information
ThrustEvent Analysisthrust analysis of events
TimeShowerImplement New Showerstimelike, i..e. final-state showers
UserHooksUser Hooksget access to some steps of the generation process
Vec4Four-Vectorsfour-vectors
+ +

+You can also access an extensive list of the public +methods in these classes, +which compensates for the brevity of the current page. + + diff --git a/PYTHIA8/pythia8140/xmldoc/ProgramFiles.xml b/PYTHIA8/pythia8140/xmldoc/ProgramFiles.xml new file mode 100644 index 00000000000..688dc023468 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ProgramFiles.xml @@ -0,0 +1,348 @@ + + +

Program Files

+ +The code is subdivided into a set of files, mainly by physics +task. Each file typically contains one main class, but often +with a few related helper classes that are not used elsewhere in +the program. Normally the files come in pairs. +
    +
  • A header file, .h in the include +subdirectory, where the public interface of the class is declared, +and inline methods are defined.
    • +
  • A source code file, .cc in the src +subdirectory, where most of the methods are implemented.
    • +
+During compilation, related dependency files, .d, and +compiled code, .o are created in the tmp +subdirectory. + +

+In part the .xml documentation files in the +xmldoc subdirectory have matching names, but the match +is broken by the desire to group topics more by user interaction than +internal operation. On these pages the function of the different code +files is summarized. Currently, each .xml file is also +translated into an .html one in the +htmldoc subdirectory, to allow easy viewing of the +contents in a web browser, and an .php one in +phpdoc, for more sophisticated interactivity +if that subdirectory is installed on a web server. + +

+Here is the current list of files, ordered alphabetically, with a brief +description of contents. + + +contains routines to analyze events. Currently it can do sphericity, +thrust, Lund/Jade/Durham jet clustering, and cone-jet finding. + + + +contains some basic facilities of general use: a random number +generator Rndm, a four-vector class Vec4, and a +histogram class Hist. + + + +contains information on all partons extracted from one of the two +beams. Defines modified parton distributions accordingly during the +showering and multiple interactions processing, thereby extending on +the one-particle-inclusive distributions defined by the previous class. +Finds the internal structure for a beam remnant. + + + +adds primordial kT to the set of hard subsystems, +and combines these subsystems with the two beam remnants to provide +the overall energy-momentum picture. Also ties together all the +colour lines into consistent singlets. + + + +generates momentum spread of beams, and spread of collision vertex +position. + + + +provides a simple method to impose Bose-Einstein correlations on +pairs of identical mesons. + + + +contains the event record, which basically is a vector of particles. +This file also contains the Particle class, used by +Event. Pythia uses two Event +objects, one for the process-level record (process) and +one for the complete event (event). + + + +contains the classes for describing the fragmentation steps in +flavour and in longitudinal and transverse momentum. + + + +defines some containers of parton systems, for use in +the fragmentation routines. + + + +turns the parton-level event above into a set of outgoing particles, +by applying string fragmentation (with special treatment for low-mass +systems) and secondary decays, and optionally Bose-Einstein corrections. + + + +contains an interface to convert the PYTHIA 8 event record into the +HepMC format. The HepMCInterface.cc file is located in +the subdirectory hepmcinterface and is used to build a +separate libhepmcinterface library. + + + +is a simple container that gives access to some information on the +nature of the current process, such as Mandelstam variables. +Also contains a small database for errors and warnings encountered +during program execution. + + + +gives the possibility to feed in parton configurations for the +subsequent event generation. One base class is defined, with containers +for initialization and event information, that can be read from +Pythia. Derived classes allow for a few different cases. + + + +is a header file only, for a class derived from the above LesHouches +one, to be used for runtime interfacing to Fortran programs, such as +PYTHIA 6. + + + +is a header file only, with interfaces to the key LHAPDF routines, +as needed for a runtime interface. There is a file +lhapdfdummy/LHAPDFdummy.cc with matching dummy +implementations, however. This file is used to build a separate +liblhapdfdummy library, to be linked when the LHAPDF +library is not used, so as to avoid problems with undefined references. + + + +performs string fragmentation in cases where the colour singlet +subsystem mass is so small that one or at most two primary hadrons +should be produced from it. + + + +performs multiple parton-parton interactions. + + + +contains a database of all necessary particle data (masses, names, ..) +and decay channels. + + + +performs the decays of all normal unstable hadrons and leptons, i.e. +in mass up to and including b bbar systems. It is not +intended for decays of electroweak resonances, like Z^0. + + + +contains parton distribution functions for the proton and electron. +Currently very simple, with only two p parametrizations +and one e ditto available, but it is possible to link in +external sets. + + + +turns the (hard) process above into a complete set of partons, by +adding initial- and final-state radiation, multiple parton--parton +interactions, and beam remnants. + + + +keeps track of which partons belong to which partonic susbsystem, +i.e. one of the multiple (semi)hard interactiosn with associated +showers. + + + +selects a point in phase space for the hard-process generation, +optimized separately for each process to give improved Monte Carlo +efficiency. + + + +packages the information on a given subprocess, combining the +phase-space selection and cross-section evaluation machineries +with some statistics information. Also sets up the list of processes +to be studied in a run. + + + +handles the generation of the (hard) process that sets the character +of the event. This involves either using internally implemented +processes or linking to Les Houches information. The latter can +be by runtime interfaces or by reading in a file. This step also +includes resonance decays. + + + +is the main class, that administrates the whole event generation +process by making use of all the others classes. Objects of most +other classes reside (directly or indirectly) inside Pythia, +so only a Pythia object needs to be explicitly instantiated +and addressed by the user. + + + +is only a .h file, containing a typedef for +double precision complex numbers. + + + +contains most of the Stdlib headers used in PYTHIA 8, +with using directives. It defines M_PI if +this is not already done. Also a few simple inline methods: +pow2(x), pow3(x), pow4(x), +pow5(x) and pow6(x) for small integer +powers, and sqrtpos(x) where a max(0., x) +ensures that one does not take the square root of a negative number. +Also non-inlined GammaReal(x) for the Gamma +function value of a real argument. + + + +decays resonances as part of the hard-process stage, in many cases +(but not all) including angular correlations between the decay products. + + + +encodes some properties of resonances, in particular the dynamic +calculation of widths. + + + +contains a database of all flags, modes, parameters and words that +determine the performance of the generator. Initial values are obtained +from the contents of the .xml files, but these values can +then be changed by the user. + + + +contains the cross sections and matrix elements for production of +some particles in compositeness scenarios, specifically excited +fermions. + + + +contains the cross sections and matrix elements for electroweak +processes involving photons, Z^0's and W^+-'s. + + + +contains the cross sections and matrix elements for processes in +scenarios involving extra dimensions. + + + +contains the cross sections and matrix elements for some generic +processes, to be used as building blocks for a few BSM scenarios. + + + +contains the cross sections and matrix elements for Higgs production. + + + +contains the cross sections and matrix elements for particle production +in left-right-symmetry scenarios, specifically righthanded Z +and W bosons and doubly-charged Higgs bosons. + + + +contains the cross sections and matrix elements for leptoquark production. + + + +contains the cross sections and matrix elements for a Z'^0, +a W^+- and a horizontal gauge boson R^0. + + + +contains the cross sections and matrix elements for charmonium and +bottomonium production. + + + +contains the base class and derived classes for the evaluation of +different matrix elements. Also keeps track of allowed incoming +parton configurations and their cross sections, including parton +densities. In order to keep this file from becoming too big, actual +cross sections are found in several separate files of derived classes: +SigmaQCD, SigmaEW, SigmaOnia, +SigmaHiggs, SigmaSUSY, +SigmaNewGaugeBosons, SigmaLeftRightSym, +SigmaLeptoquark, SigmaCompositeness, +SigmaExtraDim and SigmaGeneric. + + + +contains the cross sections and matrix elements for soft and hard +QCD processes. + + + +contains the cross sections and matrix elements for Supersymmetric +processes. + + + +contains parametrizations of total, elastic and diffractive hadronic +cross sections. + + + +performs spacelike initial-state transverse-momentum-ordered +shower evolution. + + + +contains the running alpha_strong, with Lambda +matching at flavour thresholds, the running alpha_em, +CKM mixing matrices, and a few other parameters such as +sin^2(theta_W). + + + +performs string fragmentation of a given set of partons. + + + +stores the various couplings used for SUSY cross sections and +decays, as calculated from input e.g. based on the SUSY Les Houches +Accord. + + + +contains information on SUSY parameters and particle data as specified +by the SUSY Les Houches Accord. + + + +performs timelike final-state transverse-momentum-ordered +shower evolution. + + + +Provides a way for a user to study the event at a few intermediate +stages of evolution, to reject the event as a whole or to modify +its cross-section weight. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ProgramFlow.xml b/PYTHIA8/pythia8140/xmldoc/ProgramFlow.xml new file mode 100644 index 00000000000..5d92023d1b5 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ProgramFlow.xml @@ -0,0 +1,1073 @@ + + +

Program Flow

+ +Recall that, to first order, the event generation process can be +subdivided into three stages: +
    +
  1. Initializaion.
    2. +
  2. The event loop.
    3. +
  3. Finishing.
    4. +
+This is reflected in how the top-level Pythia class should +be used in the user-supplied main program, further outlined in the +following. Since the nature of the run is defined at the initialization +stage, this is where most of the PYTHIA user code has to be written. +So as not to confuse the reader unduly, the description of initialization +options has been subdivided into what would normally be used and what is +intended for more special applications. + +

+At the bottom of this webpge is a complete survey of all public +Pythia methods and data members, in a more formal style +than the task-oriented descriptions found in the preceding sections. +This offers complementary information. + +

Initialization - normal usage

+ +
    + +
  1. +Already at the top of the main program file, you need to include the proper +header file +
    +    #include "Pythia.h"
+
    +To simplify typing, it also makes sense to declare +
    +    using namespace Pythia8; 
+
    +
    2. + +

    +

  2. +The first step is to create a generator object, +e.g. with +
    +     Pythia pythia;
+
    +It is this object that we will use from now on. Normally a run +will only contain one Pythia object. (But you can +use several Pythia objects, which then will be +independent of each other.)
    +By default all output from Pythia will be on the +cout stream, but the list methods below do +allow output to alternative streams or files. +
    3. + +

    +

  3. +You next want to set up the character of the run. +The pages under the "Setup Run Tasks" heading in the index +describe all the options available (with some very few exceptions, +found on the other pages). +The default values and your modifications are stored in two databases, +one for generic settings +and one for particle data. +Both of these are initialized with their default values by the +Pythia constructor. The default values can then be +changed, primarily by one of the two ways below, or by a combination +of them.
    + +

    +a) You can use the +

    +    pythia.readString(string);
+
    +method repeatedly to do a change of a property at a time. +The information in the string is case-insensitive, but upper- and +lowercase can be combined for clarity. The rules are that
    +(i) if the first nonblank character of the string is a letter +it is assumed to contain a setting, and is sent on to +pythia.settings.readString(string);
    +(ii) if instead the string begins with a digit it is assumed to +contain particle data updates, and so sent on to +pythia.particleData.readString(string);
    +(iii) if none of the above, the string is assumed to be a comment, +i.e. nothing will be done.
    +In the former two cases, a warning is issued whenever a string +cannot be recognized (maybe because of a spelling mistake).
    +Some examples would be +
    +    pythia.readString("TimeShower:pTmin = 1.0");
+    pythia.readString("111:mayDecay = false");
+
    +The readString(string) method is intended primarily for +a few changes. It can also be useful if you want to construct a +parser for input files that contain commands both to PYTHIA and to +other libraries.
    + +

    +b) You can read in a file containing a list of those variables +you want to see changed, with a +

    +    pythia.readFile(fileName);
+
    +Each line in this file with be processes by the +readString(string) method introduced above. You can thus +freely mix comment lines and lines handed on to Settings +or to ParticleData.
    +This approach is better suited for more extensive changes than a direct +usage of readString(string), and can also avoid having to +recompile and relink your main program between runs.
    +It is also possible to read input from an istream, by +default cin, rather than from a file. This may be convenient +if information is generated on-the-fly, within the same run. +
    +
    4. + +

    +

  4. +Next comes the initialization stage, where all +remaining details of the generation are to be specified. The +init(...) method allows a few different input formats, +so you can pick the one convenient for you: + +

    +a) pythia.init( idA, idB, eCM);
    +lets you specify the identities and the CM energy of the two incoming +beam particles, with A (B) assumed moving in the +z (-z) +direction. + +

    +b) pythia.init( idA, idB, eA, eB);
    +is similar, but the two beam energies can be different, so the +collisions do not occur in the CM frame. If one of the beam energies +is below the particle mass you obtain a fixed-target topology. + +

    +c) pythia.init( idA, idB, pxA, pyA, pzA, pxB, pyB, pzB);
    +is similar, but here you provide the three-momenta +(p_x, p_y, p_z) of the two incoming particles, +to allow for arbitrary beam directions. + +

    +d) pythia.init(fileName);
    +assumes a file in the Les Houches +Event File format is provided. + +

    +e) pythia.init();
    +with no arguments will read the beam parameters from the +Main +group of variables, which provides you with the same possibilities as +the above options a, b, c and d. If you don't change any of those you will +default to proton-proton collisions at 14 TeV, i.e. the nominal LHC +values. + +

    +f) pythia.init( LHAup*);
    +assumes Les Houches Accord +initialization and event information is available in an LHAup +class object, and that a pointer to this object is handed in. + +

    +

  5. +If you want to have a list of the generator and particle data used, +either only what has been changed or everything, you can use +
    +    pythia.settings.listChanged();
+    pythia.settings.listAll();
+    pythia.particleData.listChanged(); 
+    pythia.particleData.listAll(); 
+
    +
    6. + +
+ +

The event loop

+ +
    + +
  1. +Inside the event generation loop you generate the +next event using the next() method, +
    +    pythia.next();
+
    +This method takes no arguments; everything has already been specified. +It does return a bool value, however, false when the +generation failed. This can be a "programmed death" when the +supply of input parton-level configurations on file is exhausted. +It can alternatively signal a failure of Pythia to +generate an event, or unphysical features in the event record at the +end of the generation step. It makes sense to allow a few false +values before a run is aborted, so long as the related faulty +events are skipped. +
    2. + +

    +

  2. +The generated event is now stored in the event +object, of type Event, +which is a public member of pythia. You therefore have +access to all the tools described on the pages under the "Study Output" +header in the index. For instance, an event can be listed with +pythia.event.list(), the identity of the i'th +particle is given by +pythia.event[i].id(), and so on.
    +The hard process - roughly the information normally stored in the +Les Houches Accord event record - is available as a second object, +process, also of type Event.
    +A third useful public object is +info, which offers +a set of one-of-a kind pieces of information about the most recent +event. +
    3. + +
+ +

Finishing

+ +
    + +
  1. At the end of the generation process, you can call +
    +    pythia.statistics(); 
+
    +to get some run statistics, on cross sections and the number of errors +and warnings encountered. +
    2. + +
+ +

Advanced usage, mainly for initialization

+ +A) Necessary data are automatically loaded when you use the +default PYTHIA installation directory structure and run the main +programs in the examples subdirectory. However, in the +general case, you must provide the path of the xmldoc +directory, where default settings and particle data are found. +This can be done in two ways. + +
    + +
  1. +You can set the environment variable PYTHIA8DATA to +contain the location of the xmldoc directory. In the +csh and tcsh shells this could e.g. be +
    +     setenv PYTHIA8DATA /home/myname/pythia81xx/xmldoc
+
    +while in other shells it could be +
    +     export PYTHIA8DATA=/home/myname/pythia81xx/xmldoc
+
    +where xx is the subversion number.
    +Recall that environment variables set locally are only defined in the +current instance of the shell. The above lines should go into your +.cshrc and .bashrc files, respectively, +if you want a more permanant assignment. +
    2. + +

    +

  2. +You can provide the path as argument to the Pythia +constructor, e.g. +
    +     Pythia pythia("/home/myname/pythia81xx/xmldoc");
+
    +
    3. +
+where again xx is the subversion number.
+When PYTHIA8DATA is set it takes precedence, else +the path in the constructor is used, else one defaults to the +../xmldoc directory. + +

+B) You can override the default behaviour of PYTHIA not only by the +settings and particle data, but also by replacing some of the +PYTHIA standard routines by ones of your own. Of course, this is only +possible if your routines fit into the general PYTHIA framework. +Therefore they must be coded according to the the rules relevant +in each case, as a derived class of a PYTHIA base class, and a pointer +to such an object must be handed in by one of the methods below. +These calls must be made before the pythia.init(...) call. + +

    + +
  1. +If you are not satisfied with the list of parton density functions that +are implemented internally or available via the LHAPDF interface +(see the PDF Selection page), you +can suppy your own by a call to the setPDFPtr(...) method +
    +      pythia.setPDFptr( pdfAPtr, pdfBPtr); 
+
    +where pdfAPtr and pdfBPtr are pointers to +two Pythia PDF +objects. Note that pdfAPtr and pdfBPtr +cannot point to the same object; even if the PDF set is the same, +two copies are needed to keep track of two separate sets of x +and density values.
    +If you further wish to use separate PDF's for the hard process of an +event than the ones being used for everything else, the extended form +
    +      pythia.setPDFptr( pdfAPtr, pdfBPtr, pdfHardAPtr, pdfHardBPtr); 
+
    +allows you to specify those separately, and then the first two sets +would only be used for the showers and for multiple interactions. +
    2. + +

    +

  2. +If you want to perform some particle decays with an +external generator, you can call the setDecayPtr(...) +method +
    +      pythia.setDecayPtr( decayHandlePtr, particles);
+
    +where the decayHandlePtr derives from the +DecayHandler base +class and particles is a vector of particle codes to be +handled. +
    3. + +

    +

  3. +If you want to use an external random number generator, +you can call the setRndmEnginePtr(...) method +
    +      pythia.setRndmEnginePtr( rndmEnginePtr); 
+
    +where rndmEnginePtr derives from the +RndmEngine base class. +The Pythia default random number generator is perfectly +good, so this is only intended for consistency in bigger frameworks. +
    4. + +

    +

  4. +If you want to interrupt the evolution at various stages, +to interrogate the event and possibly veto it, or you want to +reweight the cross section, you can use +
    +      pythia.setUserHooksPtr( userHooksPtr); 
+
    +where userHooksPtr derives from the +UserHooks base class. +
    5. + +

    +

  5. +If you want to use your own parametrization of beam momentum spread and +interaction vertex, rather than the provided simple Gaussian +parametrization (off by default), you can call +
    +      pythia.setBeamShapePtr( beamShapePtr); 
+
    +where beamShapePtr derives from the +BeamShape base class. +
    6. + +

    +

  6. +If you want to implement a cross section of your own, but still make use +of the built-in phase space selection machinery, you can use +
    +      pythia.setSigmaPtr( sigmaPtr);
+
    +where sigmaPtr of type SigmaProcess* is an +instance of a class derived from one of the Sigma1Process, +Sigma2Process and Sigma3Process base classes +in their turn derived from +SigmaProcess. +This call can be used repeatedly to hand in several different processes. +
    7. + +

    +

  7. +If your cross section contains the production of a new resonance +with known analytical expression for all the relevant partial widths, +you can make this resonance available to the program with +
    +      pythia.setResonancePtr( resonancePtr);
+
    +where resonancePtr of type ResonanceWidths* +is an instance of a class derived from the +ResonanceWidths +base class. In addition you need to add the particle to the normal +particle and decay database. +This procedure can be used repeatedly to hand in several different +resonances. +
    8. + +

    +

  8. +If you are a real expert and want to replace +the PYTHIA initial- and final-state showers, you can use +
    +      pythia.setShowerPtr( timesDecPtr, timesPtr, spacePtr);
+
    +where timesDecPtr and timesPtr +derive from the TimeShower base class, and +spacePtr from SpaceShower. +
    9. + +

    +

  9. +The initTunes(...) method allows you to initialize the settings +of a specific tune at an early stage, so that you can change some of the +tune values between the initTunes(...) and the +init(...) calls. This method should not be used if you want +to use an existing tune as is, or make your own changes altogether. +See the initTunes(...) description below for more details. +
    10. + +
+ +

+C) Some comments on collecting several tasks in the same run. +

    + +
  1. +PYTHIA has not been written for threadsafe execution on multicore +processors. If you want to use all cores, +the most efficient way presumably is to start correspondingly many jobs, +with different random number seeds, and add the statistics at the end. +
    2. + +

    +

  2. +In some cases it is convenient to use more than one Pythia +object. The key example would be the simultaneous generation of signal +and pileup events, see main19.cc. The two objects are then +set up and initialized separately, and generate events completely +independently of each other. It is only afterwards that the event records +are combined into one single super-event per beam crossing. +
    3. + +

    +

  3. +When time is not an issue, it may be that you want to perform several +separate subruns sequentially inside a run, e.g. to combine results for +several kinematical regions or to compare results for some different +tunes of the underlying event. One way to go is to create (and destroy) +one pythia object for each subrun, in which case they are +completely separate. You can also use the same pythia object, +only doing a new init(...) call for each subrun. In that +case, the settings and particle databases remain as they were in the +previous subrun, only affected by the specific changes you introduced in +the meantime. You can put those changes in the main program, with +pythia.readString(string), using your own logic to decide +which ones to execute in which subrun. A corresponding possibility +exists with pythia.readFile(fileName, subrun) (or an +istream instead of a fileName), which as second +argument can take a non-negative subrun number. Then only those +sections of the file before any Main:subrun = ... line +or with matching subrun number will be read. That is, the +file could have a structure like +
    +    ( lines always read, i.e. "default values" always (re)set )
+    Main:subrun = 1
+    ( lines only read with readFile(fileName, 1) )
+    Main:subrun = 2
+    ( lines only read with readFile(fileName, 2) )
+
    +Both of these possibilities are illustrated in main08.cc. +
    4. + +

    +

  4. +When working with Les Houches Event Files, it may well be that your +intended input event sample is spread over several files, that you all +want to turn into complete events in one and the same run. There is no +problem with looping over several subruns, where each new subrun +is initialized with a new file. However, in that case you will do +a complete re-initialization each time around. If you want to avoid +this, note that there is an optional second argument for LHEF +initialization: pythia.init(fileName, skipInit). +Alternatively, the tag Main:LHEFskipInit can be put +in a file of commands to obtain the same effect. +Here skipInit defaults to false, +but if set true then the new file will be simulated +with the same initialization data as already set in a previous +pythia.init(...) call. The burden rests on you to ensure +that this is indeed correct, e.g. that the two event samples have not +been generated for different beam energies. +
    5. + +
+ +

The Pythia Class

+ +Here follows the complete survey of all public Pythia +methods and data members. + +

Constructor and destructor

+ + +creates an instance of the Pythia event generators, +and sets initial default values, notably for all settings and +particle data. You may use several Pythia instances +in the same run; only when you want to access external static +libraries could this cause problems. (This includes in particular +Fortran libraries such as LHAPDF.) +allows you to choose +from which directory the default settings and particle data values +are read in. If the PYTHIA8DATA environment variable +has been set it takes precedence. Else this optional argument allows +you to choose another directory location than the default one. Note +that it is only the directory location you can change, its contents +must be the ones of the xmldoc directory in the +standard distribution. + + + + +the destructor deletes the objects created by the constructor. + +

Set up run

+ + +reads in a single string, that is interpreted as an instruction to +modify the value of a setting or +particle data, as already described +above. + +the string to be interpreted as an instruction. + + +write a warning message or not whenever the instruction does not make +sense, e.g. if the variable does not exist in the databases. + +Note: the method returns false if it fails to +make sense out of the string. + + + + + + + + + +reads in a whole file, where each line is interpreted as an instruction +to modify the value of a setting or +particle data, cf. the above +readString method. All four forms of the +readFile command share code for actually reading a file. + +the file from which instructions are read. + + +an istream from which instructions are read. + + +write a warning message or not whenever the instruction does not make +sense, e.g. if the variable does not exist in the databases. In the +command forms where warn is omitted it is true. + + +allows you have several optional sets of commands within the same file. +Only those sections of the file before any Main:subrun = ... +line or following such a line with matching subrun number will be read. +The subrun number should not be negative; negative codes like +SUBRUNDEFAULT corresponds to no specific subrun. + +Note: the method returns false if it fails to +make sense out of any one line. + + + +offers the possibility to link in external PDF sets for usage inside +the program. The rules for constructing your own class from +the PDF base class are described +here. + +pointers to two PDF-derived objects, one for each of +the incoming beams. The two objects have to be instantiated by you +in your program. Even if the two beam particles are the same +(protons, say) two separate instances are required, since current +information is cached in the objects. If both arguments are zero +then any previous linkage to external PDF's is disconnected, +see further Note 2 below. + + +pointers to two further PDF-derived objects, one for each +of the incoming beams. Normally only the first two arguments above would +be used, and then the same PDF sets would be invoked everywhere. If you +provide these two further pointers then two different sets of PDF's are +used. This second set is then exclusively for the generation of the hard +process from the process matrix elements library. The first set above +is for everything else, notably parton showers and multiple interactions. + +Note 1: The method returns false if the input is obviously +incorrect, e.g. if two (nonzero) pointers agree. +Note 2: If you want to combine several subruns you can +call setPDFPtr with new arguments before each +Pythia::init(...) call. To revert from external PDF's +to the normal internal PDF selection you must call +setPDFPtr(0, 0) before Pythia::init(...). + + + +offers the possibility to link to an external program that can do some +of the particle decays, instad of using the internal decay machinery. +With particles we here mean the normal hadrons and leptons, not +top quarks, electroweak bosons or new particles in BSM scenarios. +The rules for constructing your own class from the +DecayHandler base class are described +here. Note that you can only +provide one external object, but this object in its turn could +very well hand on different particles to separate decay libraries. + +pointer to a DecayHandler-derived object. This object +must be instantiated by you in your program. + + vector with the PDG identity codes +of the particles that should be handled by the external decay package. +You should only give the particle (positive) codes; the respective +antiparticle is always included as well. + +Note: The method currently always returns true. + + + +offers the possibility to link to an external random number generator. +The rules for constructing your own class from the +RndmEngine base class are described +here. + +pointer to a RndmEngine-derived object. This object +must be instantiated by you in your program. + +Note: The method returns true if the pointer is different +from 0. + + + +offers the possibility to interact with the generation process at +a few different specified points, e.g. to reject undesirable events +at an early stage to save computer time. The rules for constructing +your own class from the UserHooks base class are described +here. You can only hand in one such +pointer, but this may be to a class that implements several of the +different allowed possibilities. + +pointer to a userHooks-derived object. This object +must be instantiated by you in your program. + +Note: The method currently always returns true. + + + +offers the possibility to provide your own shape of the momentum and +space-time spread of the incoming beams. The rules for constructing +your own class from the BeamShape base class are described +here. + +pointer to a BeamShape-derived object. This object +must be instantiated by you in your program. + +Note: The method currently always returns true. + + + +offers the possibility to link your own implementation of a process +and its cross section, to make it a part of the normal process +generation machinery, without having to recompile the +Pythia library itself. The rules for constructing your +own class from the SigmaProcess base class are described +here. You may call this +routine repeatedly, to add as many new processes as you wish. + +pointer to a SigmaProcess-derived object. This object +must be instantiated by you in your program. + +Note: The method currently always returns true. + + + +offers the possibility to link your own implementation of the +calculation of partial resonance widths, to make it a part of the +normal process generation machinery, without having to recompile the +Pythia library itself. This allows the decay of new +resonances to be handled internally, when combined with new particle +data. Note that the decay of normal hadrons cannot be modelled here; +this is for New Physics resonances. The rules for constructing your +own class from the ResonanceWidths base class are described +here. You may call this +routine repeatedly, to add as many new resonances as you wish. + +pointer to a ResonanceWidths-derived object. This object +must be instantiated by you in your program. + +Note: The method currently always returns true. + + + +offers the possibility to link your own parton shower routines as +replacements for the default ones. This is much more complicated +since the showers are so central and are so interlinked with other +parts of the program. Therefore it is also possible to do the +replacement in stages, from the more independent to the more +intertwined. The rules for constructing your own classes from the +TimeShower and SpaceShowerbase classes +are described here. These +objects must be instantiated by you in your program. + +pointer to a TimeShower-derived object for doing +timelike shower evolution in resonance decays, e.g. of a +Z^0. This is decoupled from beam remnants and parton +distributions, and is therefore the simplest kind of shower +to write. If you provide a value 0 then the internal shower +routine will be used. + + +pointer to a TimeShower-derived object for doing +all other timelike shower evolution, which is normally interleaved +with multiple interactions and spacelike showers, introducing +both further physics and further technical issues. If you retain +the default value 0 then the internal shower routine will be used. +You are allowed to use the same pointer as above for the +timesDecPtr if the same shower can fulfill both tasks. + + +pointer to a SpaceShower-derived object for doing +all spacelike shower evolution, which is normally interleaved +with multiple interactions and timelike showers. If you retain +the default value 0 then the internal shower routine will be used. + +Note: The method currently always returns true. + + + +prepackages the parameter settings of some PYTHIA tunes. While +the readString(...) and readFile(...) +methods can be used to set the parameters of some already +existing tune, one by one, this is time-consuming and error-prone. +Therefore the initTunes(...) method provides a set of +tunes, hopefully growing with time, that can be selected by the +two switches Tune:ee and +Tune:pp. Default is 0, +meaning no changes. Nornally initTunes(...) is +automatically called from inside the init(...) method, +so you would not call it yourself. This can be constraining if you +want to use almost, but not quite, an existing tune. Specifically, +any attempts to set one or a few of the parameters differently by +readString(...) or readFile(...) calls +before initialization would not work, since they would be overwritten +during init(...). This is where the possibility to call +initTunes(...) directly comes to the rescue. You could +then by hand pick the desired tune, afterwards change whatever settings +you wish, and retain these changes during initialization by having +Tune:ee = Tune:pp = 0. + the settings obtained from +e^+e^- data, see Tune:ee +for a list of valid values. If you call initTunes(...) +with this option nonzero you would want to keep Tune:ee +equal to zero, or else the whole point is lost. + + the additional settings that +can only be extracted from pp/ppbar data see +Tune:pp for a list of valid +values. Comment as above. + + +

Initialize

+ +At the initialization stage all the information provided above is +processed, and the stage is set up for the subsequent generation +of events. Several alterative forms of the init method +are available for this stage; pick the one most convenient. + + +initialize for collisions in the center-of-mass frame, with the +beams moving in the +-z directions. + +particle identity code for the two incoming beams. + + +the CM energy of the collisions. + +Note: The method returns false if the +initialization fails. It is then not possible to generate any +events. + + + +initialize for collisions with back-to-back beams, +moving in the +-z directions, but with different energies. + +particle identity code for the two incoming beams. + + +the energies of the two beams. If an energy is set to be below +the mass of the respective beam particle that particle is taken to +be at rest. This offers a simple possibility to simulate +fixed-target collisions. + +Note: The method returns false if the +initialization fails. It is then not possible to generate any +events. + + + +initialize for collisions with arbitrary beam directions. + +particle identity code for the two incoming beams. + + +the three-momntum vector (p_x, p_y, p_z) of the first +incoming beam. + + +the three-momntum vector (p_x, p_y, p_z) of the second +incoming beam. + +Note: The method returns false if the +initialization fails. It is then not possible to generate any +events. + + + +initialize for hard-process collisions fed in from an external file +with events, written according to the +Les Houches Event File +standard. + +the file name (including path, where required) where the +events are stored, including relevant information on beam +identities and energies. + + +By default this method does a complete reinitialization of the +generation process. If you set this argument to true then +no reinitialization will occur, only the pointer to the event +file is updated. This may come in handy if the full event sample +is split across several files generated under the same conditions +(except random numbers, of course). You then do the first +initialization with the default, and all subsequent ones with +true. Note that things may go wrong if the files are not created +under the same conditions. + +Note: The method returns false if the +initialization fails. It is then not possible to generate any +events. + + + +initialize for collisions, in any of the four above possibilities. +In this option the beams are not specified by input arguments, +but instead by the settings in the +Beam Parameters section. +This allows the beams to be specified in the same file as other +run instructions. The default settings give pp collisions at 14 TeV. +Note: The method returns false if the +initialization fails. It is then not possible to generate any +events. + + + +initialize for hard-process collisions fed in from an external +source of events, consistent with the Les Houches Accord standard. +The rules for constructing your own class from the LHAup +base class are described here. +This class is also required to provide the beam parameters. + +pointer to a LHAup-derived object. This object +must be instantiated by you in your program. + +Note: The method returns false if the +initialization fails. It is then not possible to generate any +events. + + +

Generate events

+ +The next() method is the main one to generate events. +In this section we also put a few other specialized methods that +may be useful in some circumstances. + + +generate the next event. No input parameters are required; all +instructions have already been set up in the initialization stage. +Note: The method returns false if the event generation +fails. The event record is then not consistent and should not be +studied. When reading in hard collisions from a Les Houches Event File +the problem may be that the end of the file has been reached. This +can be checked with the +Info::atEndOfFile() +method. + + + +hadronize the existing event record, i.e. perform string fragmentation +and particle decays. There are two main applications. Firstly, +you can use the same parton-level content as a basis for repeated +hadronization attempts, in schemes intended to save computer time. +Secondly, you may have an external program that can simulate the full +partonic level of the event - hard process, parton showers, multiple +interactions, beam remnants, colour flow, and so on - but not +hadronization. Further details are found +here. +Note: The method returns false if the hadronization +fails. The event record is then not consistent and should not be +studied. + + + +perform decays of all particles in the event record that have not been +decayed but should have been done so. This can be used e.g. for +repeated decay attempts, in schemes intended to save computer time. +Further details are found here. +Note: The method returns false if the decays fail. The +event record is then not consistent and should not be studied. + + + +list the Les Houches Accord information on the current event, see +LHAup::listEvent(...). +(Other listings are available via the class members below, so this +listing is a special case that would not fit elsewhere.) + +output stream where the listing occurs. + + + + +skip ahead a number of events in the Les Houches generation +sequence, without doing anything further with them, see +LHAup::skipEvent(nSkip). +Mainly intended for debug purposes, e.g. when an event at a known +location in a Les Houches Event File is causing problems. + +number of events to skip. + +Note: The method returns false if the operation fails, +specifically if the end of a LHEF has been reached, cf. +next() above. + + +

Finalize

+ +There is no required finalization step; you can stop generating events +when and how you want. It is still recommended that you make it a +routine to call the following method at the end. + + +list statistics on the event generation, specifically total and partial +cross sections and the number of different errors. For more details see +here. + +if true also statistics on multiple interactions is shown, by default not. + + if true then all counters, +e.g on events generated and errors experienced, are reset to zero + whenever the routine is called. The default instead is that +all stored statistics information is unaffected by the call. Counters +are automatically reset in each new Pythia::init(...) +call, however, so the only time the reset option makes a +difference is if statistics(...) is called several times +in a (sub)run. + + + +

Interrogate settings

+ +Normally settings are used in the setup and initialization stages +to determine the character of a run, e.g. read from a file with the +above-described Pythia::readFile(...) method. +There is no strict need for a user to interact with the +Settings database in any other way. However, as an option, +some settings variables have been left free for the user to set in +such a file, and then use in the main program to directly affect the +performance of that program, see +here. A typical example would +be the number of events to generate. For such applications the +following shortcuts to some Settings methods may be +convenient. + + +read in a boolean variable from the Settings database. + +the name of the variable to be read. + + + + +read in an integer variable from the Settings database. + +the name of the variable to be read. + + + + +read in a double-precision variable from the Settings +database. + +the name of the variable to be read. + + + + +read in a string variable from the Settings database. + +the name of the variable to be read. + + + +

Data members

+ +The Pythia class contains a few public data members, +several of which play a central role. We list them here, with +links to the places where they are further described. + + +the hard-process event record, see here +for further details. + + + +the complete event record, see here +for further details. + + + +further information on the event-generation process, see +here for further details. + + + +the settings database, see here +for further details. + + + +the particle properties and decay tables database, see +here for further details. + + + +the random number generator, see here +and here for further details. + + + +Standard Model couplings and mixing matrices, see +here for further details. + + + +parameters and particle data in the context of supersymmetric models, +see here for further details. + + + +a grouping of the partons in the event record by subsystem, +see here for further details. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ProgramMethods.xml b/PYTHIA8/pythia8140/xmldoc/ProgramMethods.xml new file mode 100644 index 00000000000..06bc7adc5ee --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ProgramMethods.xml @@ -0,0 +1,17 @@ + + +

Program Methods

+ +This is an alphabetical index of all methods that are documented +elsewhere on these pages, beginning with the few methods that +do not belong to a class. Many of them are only intended for experts, +while undocumented ones are only for code authors. + +

+The index is constructed dynamically from the methods described +on the other webpages, as part of the conversion from xml to +html and php. Therefore this xml page is only a dummy one. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/QCDProcesses.xml b/PYTHIA8/pythia8140/xmldoc/QCDProcesses.xml new file mode 100644 index 00000000000..6916ca45229 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/QCDProcesses.xml @@ -0,0 +1,261 @@ + + +

QCD Processes

+ +This section is subdivided into soft and hard QCD processes, with +open charm and bottom production set aside as a special part of the +latter, and three-jet topologies as a special subset. Kindly note +that there is a considerable amount of overlap between the soft and +hard process classes, so that you are likely to doublecount +if you include both in a run. + +

Soft QCD processes

+ +As a rule, the processes in this class should not be mixed with +the simulation of other processes. All by themselves, they are +intended to represent the total cross section of hadron collisions, +with the exception of the "rare processes" that one wishes to study +separately. In particular, jet physics at all scales occurs as part +of the minimum-bias description. + +

+We here use the "minimum bias" expression as a shorthand for +inelastic, nondiffractive events. Strictly speaking, "minimum bias" +represents an experimental procedure of accepting "everything", with +some non-universal cuts to exclude elastic and diffractive topologies. +In practice, the experimental mimimum-bias sample may then contain +some contamination of what is in PYTHIA classified as diffractive, +especially (high-mass) double diffractive. + +

+Some options to modify these cross sections are found on the +Total Cross Sections page. + + +Common switch for the group of all soft QCD processes, +as listed separately in the following. + + + +Minimum-bias events, based on an +eikonalized description of all the hard QCD processes, so +includes them in combinationation with low-pT events. +Code 101.
+Since the current description is handled by the multiple-interactions +machinery as part of the parton-level processing, no hard process at +all is defined at the process-level part of the event generation. +Fortunately, in this case a special +codeSub() +method provides information on the first, i.e. hardest, subprocess +selected by the multiple-interactions machinery. + + + + +Elastic scattering A B -> A B. +Code 102. It is possible to include +Coulomb corrections, but by default this is off. + + + +Single diffractive scattering A B -> X B and +A B -> A X. See page on +Diffraction for details. Codes 103 and 104. + + + +Double diffractive scattering A B -> X_1 X_2. +See page on Diffraction +for details. Code 105. + + +

Hard QCD processes

+ +This group contains the processes for QCD jet production above +some minimum pT threshold. The pT_min cut cannot be put +too low, or else unreasonably large jet cross sections will be obtained. +This is because the divergent perturbative QCD cross section is used +in this process group, without any regularization modifications. +An eikonalized description, intended to be valid at all pT, +is instead included as part of the multiple-interactions framework, +specifically in SoftQCD:minBias above. +Warning 1: you must remember to set the +PhaseSpace:pTHatMin value if you use any of these +processes; there is no sensible default. +Warning 2: you must not mix processes from the +SoftQCD and HardQCD process groups, since +this is likely to lead to doublecounting. + + +Common switch for the group of all hard QCD processes, +as listed separately in the following. + + + +Scatterings g g -> g g. +Code 111. + + + +Scatterings g g -> q qbar, where q by default +is a light quark (u, d, s) (see below). +Code 112. + + + +Scatterings q g -> q g and qbar g -> qbar g. +Code 113. + + + +Scatterings q q' -> q q', q qbar' -> q qbar', +qbar qbar' -> qbar qbar', where q' and q +may agree, but the outgoing flavours equals the incoming ones +Code 114. + + + +Scatterings q qbar -> g g. +Code 115. + + + +Scatterings q qbar -> q' qbar', where q' +by default is a light quark (u, d, s) (see below). +Code 116. + + + +Number of allowed outgoing new quark flavours in the above +g g -> q qbar and q qbar -> q' qbar' processes, +where quarks are treated as massless in the matrix-element expressions +(but correctly in the phase space). It is thus assumed that c cbar +and b bbar are added separately with masses taken into account, +using the processes below. A change to 4 would also include c cbar +in the massless approximation, etc. In order to avoid doublecounting +the processes below should then not be used simultaneously. + + +

Hard QCD processes: heavy-flavour subset

+ +These processes form a natural part of the above class, but can +also be generated separately. Formally the heavy-quark mass makes +these matrix elements finite in the pT -> 0 limit, but at +high energies one may still question the validity of the expressions +at low pT values, like for the other hard-QCD processes. +Also as above, an eikonalized description, intended to be valid at all +pT, is included as part of the multiple-interactions framework. +
Note that the processes below only represent the "tip of the iceberg" +of charm and bottom production at high energies, where flavour excitation +and shower branchings provide major additional sources. All these sources +come together in the descriptions offered by SoftQCD:minBias +and HardQCD:all. + + +Scatterings g g -> c cbar. +Code 121. + + + +Scatterings q qbar -> c cbar. +Code 122. + + + +Scatterings g g -> b bbar. +Code 123. + + + +Scatterings q qbar -> b bbar. +Code 124. + + +

Hard QCD three-parton processes

+ +Three-parton final states are generated by showers off two-parton +processes. Topologies then cannot be specified beforehand, beyond +what is provided by the two-parton hard process. For some checks +it may be convenient to have access to the dedicated three-parton +final states, which is what this set of processes allows. +Cross sections have been taken from Ber81. +
Note that the processes in this section are not +affected by the HardQCD:all switch. In fact, it would +be doublecounting to include both the HardQCD:all and +the HardQCD:3parton processes in a run or study. +
Warning: this section is still incomplete, e.g. the +selection of colour flow is very simple, and so it should only +be used with caution. + + +Common switch for the group of all hard QCD processes with three +partons in the final state, as listed separately in the following. + + + +Scatterings g g -> g g g. +Code 131. + + + +Scatterings q qbar -> g g g. +Code 132. + + + +Scatterings q g -> q g g and qbar g -> qbar g g. +Code 133. + + + +Scatterings q q' -> q q' g, q qbar' -> q qbar' g, +and qbar qbar' -> qbar qbar' g. +Code 134. + + + +Scatterings q q -> q q g and +qbar qbar -> qbar qbar g +(q qbar -> q qbar g scatterings are considered separately +below, see HardQCD:qqbar2qqbargSame). +Code 135. + + + +Scatterings q qbar -> q' qbar' g, where q' +by default is a light quark (u, d, s) +(see HardQCD:nQuarkNew above). +Code 136. + + + +Scatterings q qbar -> q qbar g. +Code 137. + + + +Scatterings g g -> q qbar g, where q by +default is a light quark (u, d, s) +(see HardQCD:nQuarkNew above). +Code 138. + + + +Scatterings q g -> q q' qbar' and +qbar g -> qbar qbar' q', where q' +by default is a light quark (u, d, s) +(see HardQCD:nQuarkNew above). +Code 139. + + + +Scatterings q g -> q q qbar and +qbar g -> qbar qbar q. +Code 140. + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ROOTusage.xml b/PYTHIA8/pythia8140/xmldoc/ROOTusage.xml new file mode 100644 index 00000000000..581dc950a8f --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ROOTusage.xml @@ -0,0 +1,162 @@ + + +

ROOT usage

+ +Many PYTHIA users wish to use ROOT to produce histograms, or even to +run PYTHIA as a plugin to ROOT. This is possible. It is not a task +supported by the PYTHIA team, however. All issues involving ROOT usage +should be directed to the ROOT team, or to the local support team of +your collaboration. Below some helpful hints have been collected. +The text is based on a contribution by Andreas Morsch, +and the second example is provided by Rene Brun. Another example may +be found in the VINCIA +add-on program for parton showers, but this should also work for +a PYTHIA standalone run. + +

Interfaces

+ +ROOT provides two simple interfaces +(wrappers) for PYTHIA 8. Both are located in the +
+    yourROOTinstallationPath/montecarlo/pythia8
+
+directory. (Type which root if you want to find out where +ROOT has been installed. It will print +yourROOTinstallationPath/bin/root). + +
    +
  • +TPythia8 is an implementation of the + +TGenerator interface for PYTHIA 8. +
    It allows you to use PYTHIA within a ROOT macro or as a plug-in +for a general-purpose particle generator based on this interface. The +main methods of the interface are +
    * TPythia8::GenerateEvent() which triggers the generation +of the next event, and +
    * TPythia8::ImportParticles(TClonesArray* particles) +which copies the native PYTHIA stack into a + +TClonesArray of + +TParticles. +
    In addition, we implemented some methods that are directly related +to corresponding PYTHIA methods: +
    +* ReadString(const char* string) -> readString(...)
+* ReadConfigFile(const char* string) -> readFile(...)
+* Initialize(int idAin, int idBin, double ecms) -> init(...)
+* EventListing() -> event.list()
+* PrintStatistic() -> statistics()
+
    + These methods provide already the basic PYTHIA functionality +interactively from the ROOT command line. However, this does not mean +that the usage of PYTHIA from within ROOT is restricted to these methods. +In compiled code, one can always obtain a pointer to the +Pythia instance via +
    +    Pythia8::Pythia* pythia8 = TPythia8::Pythia8();
+
    +giving access to the full PYTHIA functionality. +
    • +
  • +TPythia8Decayer is an implementation of the + +TVirtualMCDecayer interface. +
    It allows you to use PYTHIA as a plug-in decayer for simulation +frameworks based on the Virtual Monte Carlo +(VMC) interface +classes. The main methods of the interface are +
    * TPythia8Decayer::Init() for initialisation, +
    * TPythia8Decayer::Decay(Int_t pdg, TLorentzVector*< p) +to decay a particle with PDG code pdg and + +4-momentum p, and +
    * ImportParticles(TClonesArray* particles) +to retrieve the decay products as + +TParticles in the + +TClonesArray particles. +
    • +
+ +

Installation of ROOT with PYTHIA 8 support

+ +In order to use PYTHIA 8 with ROOT you need a ROOT version that has been + +installed from source. The reason is that the interfaces depend on +PYTHIA header files that are not distributed with ROOT. Installing ROOT +is not more difficult than the PYTHIA installation. + +

+Define an environment variable for the path to your pythia8 +installation directory +

+    export PYTHIA8=YourPathToPythia8
+
+Before compiling ROOT + +configure ROOT running the +yourROOTinstallationPath/configure command +including the following options: +
+    --enable-pythia8 
+    --with-pythia8-incdir=$PYTHIA8/include 
+    --with-pythia8-libdir=$PYTHIA8/lib
+
+In case ROOT has already been compiled before, it will only recompile +the pythia8 module and build the library +libEGPythia8. + +

An example

+ +A +basic example for generating minimum-bias events with PYTHIA 8 inside +a ROOT macro, and filling some histograms with the kinematics of the +final-state particles is provided in +
+    yourROOTinstallationDirectory/tutorials/pythia/pythia8.C
+
+Note that before executing this script +
    +
  • the environment variable PYTHIA8 must point to the +pythia8100 (or newer) installation directory, and
    • +
  • the environment variable PYTHIA8DATA must be defined +and it must point to $PYTHIA8/xmldoc.
    • +
+ +

+Looking at the example code you will see that it is necessary to +load three libraries before running the actual code: +

+    gSystem->Load("$PYTHIA8/lib/libpythia8"); // Pythia 8
+    gSystem->Load("libEG"); // The library with the TGenerator interface
+    gSystem->Load("libEGPythia8"); // The TPythia8 implementation
+
+ +

A second example

+ +It is not necessary to run PYTHIA as a ROOT plug-in. One can also perform +the generation and analysis of events in a completely standalone fashion, +and only use ROOT for the histogramming step. One example, with a +lightly modified version of main01.cc, is available in +the rootexample subdirectory. + +

+Here +

    +
  • ex1.C is the small main program writing the Tree.
    • +
  • goex1 is a small script that +
    a) generates the dictionary for all PYTHIA classes involved in the IO +(first line; note that you only need to execute it once); and +
    b) links the ex1 executable with the relevant libs.
    • +
  • pythiaLinkdef.h is the input file indicating to rootcint +which PYTHIA classes to process.
    • +
  • pythiaROOT.h is a small include declaring Pythia8 +namespace as default.
    • +
+ + + + diff --git a/PYTHIA8/pythia8140/xmldoc/RandomNumberSeed.xml b/PYTHIA8/pythia8140/xmldoc/RandomNumberSeed.xml new file mode 100644 index 00000000000..e8d7cf572f9 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/RandomNumberSeed.xml @@ -0,0 +1,32 @@ + + +

Random-Number Seed

+ +The seed of the random number generator can be set as follows: + + +Indicates whether a user-set seed should be used every time the +Pythia::init routine is called. If off, the random number +generator is initialized with its default seed at the beginning +of the run, and never again. If on, each new Pythia::init +call (should several be made in the same run) results in the random +number being re-initialized, thereby possibly starting over with the +same sequence, if you do not watch out. + + + +The seed to be used, if setSeed is on.
+A negative value gives the default seed,
+a value 0 gives a random seed based on the time, and
+a value between 1 and 900,000,000 a unique different random number +sequence. + + +

+For more on random numbers see here. +This includes methods to save and restore the state of the generator, +and some preprogrammed methods to generate non-uniform random numbers. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/RandomNumbers.xml b/PYTHIA8/pythia8140/xmldoc/RandomNumbers.xml new file mode 100644 index 00000000000..67e4beb83c8 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/RandomNumbers.xml @@ -0,0 +1,140 @@ + + +

Random Numbers

+ +This page describes the random-number generator in PYTHIA and +how it can be replaced by an external one. + +

Internal random numbers

+ +The Rndm class generates random numbers, using the +Marsaglia-Zaman-Tsang algorithm Mar90. + +

+Random numbers R uniformly distributed in +0 < R < 1 are obtained with +

+   Rndm::flat();
+
+There are also methods to generate according to an exponential, to +x * exp(-x), to a Gaussian, or picked among a set of +possibilites, which make use of flat(). + +

+If the random number generator is not initialized before, it will be +so the first time it is asked to generate a random number, and then +with the default seed, 19780503. This means that, by default, all runs +will use identically the same random number sequence. This is +convenient for debugging purposes, but dangerous if you intend to +run several "identical" jobs to boost statistics. You can initialize, +or reinitialize, with your own choice of seed with a +

+   Rndm::init(seed);
+
+Here values 0 < seed < 900 000 000 gives so many +different random number sequences, while seed = 0 will call +the Stdlib time(0) function to provide a "random" +seed, and seed < 0 will revert back to +the default seed. + +

+The Pythia class defines a +flag and a mode, that allows the seed to be set in +the Pythia::init call. That would be the standard way for a +user to pick the random number sequence in a run. + +

External random numbers

+ +RndmEngine is a base class for the external handling of +random-number generation. The user-written derived class is called +if a pointer to it has been handed in with the +pythia.rndmEnginePtr() method. Since the default +Marsaglia-Zaman-Tsang algorithm is quite good, chances are that any +replacement would be a step down, but this may still be required by +consistency with other program elements in big experimental frameworks. + +

+There is only one pure virtual method in RndmEngine, to +generate one random number flat in the range between 0 and 1: +

+  virtual double flat() = 0;
+
+Note that methods for initialization are not provided in the base +class, in part since input parameters may be specific to the generator +used, in part since initialization can as well be taken care of +externally to the Pythia code. + +

+An example illustrating how to run with an external random number +generator is provided in main24.cc. + +

The methods

+ +We here collect a more complete and formal overview of the methods. + + +construct a random number generator, but does not initialize it. + + + +construct a random number generator, and initialize it for the +given seed number. + + + +pass in pointer for external random number generation. + + + +initialize, or reinitialize, the random number generator for the given +seed number. Not necessary if the seed was already set in the constructor. + + + +generate next random number uniformly between 0 and 1. + + + +generate random numbers according to exp(-x). + + + +generate random numbers according to x exp(-x). + + + +generate random numbers according to exp(-x^2/2). + + + +generate a pair of random numbers according to +exp( -(x^2 + y^2) / 2). Is faster than two calls +to gauss(). + + + +pick one option among vector of (positive) probabilities. + + + +save the current state of the random number generator to a binary +file. This involves two integers and 100 double-precision numbers. +Intended for debug purposes. Note that binary files may be +platform-dependent and thus not transportable. + + + +set the state of the random number generator by reading in a binary +file saved by the above command. Comments as above. + + + +if you want to construct an external random number generator +(or generator interface) then you must implement this method +in your class derived from the RndmEningen base class, +to give a random number between 0 and 1. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ResonanceDecays.xml b/PYTHIA8/pythia8140/xmldoc/ResonanceDecays.xml new file mode 100644 index 00000000000..d78173634ba --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ResonanceDecays.xml @@ -0,0 +1,317 @@ + + +

Resonance Decays

+ +The ResonanceDecays class performs the sequential decays of +all resonances formed in the hard process. Note the important distinction +between "resonances" and other "particles" made in PYTHIA. +
    +
  • +The list of resonances contains gamma^*/Z^0, W^+-, top, +the Higgs, and essentially all new particles of Beyond-the-Standard-Model +physics: further Higgses, sfermions, gauginos, techniparticles, and so on. +The partial widths to different decay channels are perturbatively +calculable, given the parameters of the respective model, and branching +ratios may be allowed to vary across a (reasonably broad) resonance peak. +Usually resonances are short-lived, and therefore it makes sense to consider +their decays immediately after the primary hard process has been set up. +Furthermore, in several cases the decay angular distributions are encoded +as part of the specific process, e.g. the W decays differently in +f fbar -> W^+-, f fbar -> W^+ W^- and +h^0 -> W^+ W^- . All of these particles are (in PYTHIA) only +produced as part of the hard process itself, i.e. they are not produced +in showers or hadronization processes. Therefore the restriction to +specific decay channels can be consistently taken into account as a +corresponding reduction in the cross section of a process. Finally, note +that all of these resonances have an on-shell mass above 20 GeV, with the +exception of some hypothetical weakly interacting and stable particles +such as the gravitino. +
    • +
  • +The other particles include normal hadrons and the Standard-Model leptons, +including the tau^+-. These can be produced in the normal +hadronization and decay description, which involve unknown nonperturbative +parameters and multistep chains that cannot be predicted beforehand: +a hard process like g g -> g g can develop a shower with a +g -> b bbar branching, where the b hadronizes to a +B^0bar that oscillates to a B^0 that decays to a +tau^+. Therefore any change of branching ratios - most of which +are determined from data rather than from first principles anyway - +will not be taken into account in the cross section of a process. +Exceptions exist, but most particles in this class are made to decay +isotropically. Finally, note that all of these particles have a mass +below 20 GeV. +
    • +
+ +There is one ambiguous case in this classification, namely the photon. +The gamma^*/Z^0 combination contains a low-mass peak when +produced in a hard process. On the other hand, photons can participate +in shower evolution, and therefore a photon originally assumed +massless can be assigned an arbitrarily high mass when it is allowed +to branch into a fermion pair. In some cases this could lead to +doublecounting, e.g. between processes such as +f fbar -> (gamma^*/Z^0) (gamma^*/Z^0), +f fbar -> (gamma^*/Z^0) gamma and +f fbar -> gamma gamma. Here it make sense to limit the +lower mass allowed for the gamma^*/Z^0 combination, +in 23:mMin, to be the same as the upper limit allowed +for an off-shell photon in the shower evolution, in +TimeShower:mMaxGamma. By default this matching is done +at 10 GeV. + +

+In spite of the above-mentioned differences, the resonances and the +other particles are all stored in one common +particle data table, so as to offer a +uniform interface to setting and +getting properties such as name, mass, charge and decay modes, +also for the particle properties +in the event record. Some methods are specific to resonances, however, +in particular for the calculation of partial widths and thereby of +branching ratio. For resonances these can be calculated dynamically, +set up at initialization for the nominal mass and then updated to the +current mass when these are picked according to a Breit-Wigner resonance +shape. + +

Resonance Decays and Cross Sections

+ +As already hinted above, you have the possibility to set the allowed +decay channels of resonances, see +Particle Data Scheme description. +For instance, if you study the process q qbar -> H^0 Z^0 +you could specify that the Z^0 should decay only to +lepton pairs, the H^0 only to W^+ W^-, the +W^+ only to a muon and a neutrino, while the W^- +can decay to anything. Unfortunately there are limits to the +flexibility: you cannot set a resonance to have different properties +in different places of a process, e.g. if instead +H^0 -> Z^0 Z^0 in the above process then the three +Z^0's would all obey the same rules. + +

+The restrictions on the allowed final states of a process is directly +reflected in the cross section of it. That is, if some final states +are excluded then the cross section is reduced accordingly. Such +restrictions are built up recursively in cases of sequential decay +chains. The restrictions are also reflected in the compositions of +those events that actually do get to be generated. For instance, +the relative rates of H^0 -> W^+ W^- and +H^0 -> Z^0 Z^0 are shifted when the allowed sets of +W^+- and Z^0 decay channels are changed. + +

+We remind that only those particles that Pythia treat as resonances +enjoy this property, and only those that are considered as part of the +hard process and its assocaited resonance decays. + +

+There is one key restriction on resonances: + +Minimal allowed width of a resonance, in GeV. If the width falls below +this number the resonance is considered stable and will not be allowed +to decay. This is mainly intended as a technical parameter, to avoid +disasters in cases where no open decay channels exists at all. It could +be used for real-life decisions as well, however, but then typically +would have to be much bigger than the default value. Special caution +would be needed if coloured resonance particles were made stable, since +the program would not necessarily know how to hadronize them, and +therefore fail at that stage. + + +

Special properties and methods for resonances

+ +The method ParticleData::isResonance(id) allows you to +query whether a given particle species is considered a resonance or not. +You can also change the default value of this flag in the normal way, +e.g. pythia.readString("id:isResonance = true"). + +

+An option with a forced width can be set with the +id:doForceWidth flag as above, and queried with +ParticleData::doForceWidth(id). It is by default +off, and should normally so remain. If switched +on then the width stored in id:mWidth is +strictly used to describe the Breit-Wigner of the resonance. This is +unlike the normal behaviour of standard resonances such as the +Z^0, W^+-, t or h^0, which have +explicit decay-widths formulae encoded, in classes derived from the +ResonanceWidths +base class. These formulae are used, e.g., to derive all the Higgs partial +widths as a function of the Higgs mass you choose, and at initialization +overwrites the existing total width value. The reason for forcing the +width to another value specified by you would normally more have to do +with experimental issues than with physics ones, e.g. how sensitive your +detector would be to changes in the Higgs width by a factor of two. +A warning is that such a rescaling could modify the cross section of +a process correspondingly for some processes, while leaving it +(essentially) unchanged for others (as would seem most logical), +depending on how these were encoded. A further warning is that, +if you use this facility for Z^0 or Z'^0 with +gamma^*/Z^0 or gamma^*/Z^0/Z'^0 interference on, +then also the handling of this interference is questionable. +So, if you need to use the width-rescaling option, be extremely cautios. + +

+If a resonance does not have a class of its own, with hardcoded equations +for all relevant partial widths, then a simpler object will be created +at initialization. This object will take the total width and branching +ratios as is (with the optional variations explained in the next section), +and thus the rescaling approach brings no further freedom. + +

+Mainly for internal usage, the +ParticleData contain +some special methods that are only meaningful for resonances: +

    +
  • resInit(...) to initialize a resonance, possibly +including a recalculation of the nominal width to match the nominal +mass;
    • +
  • resWidth(...) to calculate the partial and total widths +at the currently selected mass;
    • +
  • resWidthOpen(...) to calculate the partial and total +widths of those channels left open by user switches, at the currently +selected mass;
    • +
  • resWidthStore(...) to calculate the partial and total +widths of those channels left open by user switches, at the currently +selected mass, and store those as input for a subsequent selection of +decay channel;
    • +
  • resOpenFrac(...) to return the fraction of the total +width that is open by the decay channel selection made by users (based on +the choice of onMode +for the various decay channels, recursively calculated for sequential +decays);
    • +
  • resWidthRescaleFactor(...) returns the factor by which +the internally calculated PYTHIA width has to be rescaled to give the +user-enforced width;
    • +
  • resWidthChan(...) to return the width for one particular +channel (currently only used for Higgs decays, to obtain instate coupling +from outstate width).
    • +
+These methods actually provide an interface to the classes derived from +the ResonanceWidths base class, to describe various +resonances. + +

Modes for Matrix Element Processing

+ +The meMode() value for a decay mode is used to specify +nonisotropic decays or the conversion of +a parton list into a set of hadrons in some channels of normal +particles. For resonances it can also take a third function, namely +to describe how the branching ratios and widths of a resonance should +be rescaled as a function of the current mass of the decaying resonance. +The rules are especially useful when new channels are added to an +existing particle, or a completely new resonance added. + +
    +
  • 0 : channels for which hardcoded partial-width expressions are +expected to exist in the derived class of the respective resonance. +Should no such code exist then the partial width defaults to zero. +
    • +
  • 1 - 99 : same as 0, but normally not used for resonances.
    • +
  • 100 : calculate the partial width of the channel from its stored +branching ratio times the stored total width. This value remains unchanged +when the resonance fluctuates in mass. Specifically there are no +threshold corrections. That is, if the resonance fluctuates down in +mass, to below the nominal threshold, it is assumed that one of the +daughters could also fluctuate down to keep the channel open. (If not, +there may be problems later on.) +
    • +
  • 101 : calculate the partial width of the channel from its stored +branching ratio times the stored total width. Multiply by a step threshold, +i.e. the channel is switched off when the sum of the daughter on-shell +masses is above the current mother mass.
    • +
  • 102 : calculate the partial width of the channel from its stored +branching ratio times the stored total width. Multiply by a smooth +threshold factor +beta = sqrt( (1 - m_1^2/m_2 - m_2^2/m^2)^2 - 4 m_1^2 m_2^2/m^4) +for two-body decays and sqrt(1 - Sum_i m_i / m) for multibody +ones. The former correctly encodes the size of the phase space but +misses out on any nontrivial matrix-element behaviour, while the latter +obviously is a very crude simplification of the correct phase-space +expression. Specifically, it is thereby assumed that the stored branching +ratio and total width did not take into account such a factor.
    • +
  • 103 : use the same kind of behaviour and threshold factor as for +102 above, but assume that such a threshold factor has been used when +the default branching ratio and total width were calculated, so that one +should additionally divide by the on-shell threshold factor. Specifically, +this will give back the stored branching ratios for on-shell mass, +unlike the 102 option. To avoid division by zero, or in general +unreasonably big rescaling factors, a lower limit +minThreshold (see below) on the value of the on-shell +threshold factor is imposed. (In cases where a big rescaling is +intentional, code 102 would be more appropriate.)
    • +
+ + +Used uniquely for meMode = 103 to set the minimal value +assumed for the threshold factor, +sqrt( (1 - m_1^2/m_2 - m_2^2/m^2)^2 - 4 m_1^2 m_2^2/m^4) +for two-body decays and sqrt(1 - Sum_i m_i / m) for multibody +ones. Thus the inverse of this number sets an upper limit for how +much the partial width of a channel can increase from the on-shell +value to the value for asymptotically large resonance masses. Is mainly +intended as a safety measure, to avoid unintentionally large rescalings. + + +

+All of these meMode's may coexist for the same resonance. +This would be the case e.g. if you want to add a few new channels to an +already existing resonance, where the old partial widths come hardcoded +while the new ones are read in from an external file. The typical example +would be an MSSM Higgs sector, where partial widths to SM particles are +already encoded, meMode = 0, while decay rates to sparticles +are read in from some external calculation and maybe would be best +approximated by using meMode = 103. Indeed the default +particle table in PYTHIA uses 103 for all channels that are expected +to be provided by external input. + +

+Some further clarification may be useful. At initialization the existing +total width and on-shell branching ratios will be updated. For channels +with meMode < 100 the originally stored branching ratios +are irrelevant, since the existing code will anyway be used to calculate +the partial widths from scratch. For channels with meMode = 100 +or bigger, instead the stored branching ratio is used together with the +originally stored total width to define the correct on-shell partial width. +The sum of partial widths then gives the new total width, and from there +new branching ratios are defined. + +

+In these operations the original sum of branching ratios need not be +normalized to unity. For instance, you may at input have a stored total +width of 1 GeV and a sum of branching ratios of 2. After initialization +the width will then have been changed to 2 GeV and the sum of branching +ratios rescaled to unity. This might happen e.g. if you add a few channels +to an existing resonance, without changing the branching ratios of the +existing channels or the total width of the resonance. + +

+In order to simulate the Breit-Wigner shape correctly, it is important +that all channels that contribute to the total width are included in the +above operations. This must be kept separate from the issue of which +channels you want to have switched on for a particular study, to be +considered next. + +

+ +In the event-generation process, when an off-shell resonance mass has been +selected, the width and branching ratios are re-evaluated for this new mass. +At this stage also the effects of restrictions on allowed decay modes are +taken into account, as set by the onMode switch for each +separate decay channel. Thus a channel may be on or off, with different +choices of open channels between the particle and its antiparticle. +In addition, even when a channel is on, the decay may be into another +resonance with its selection of allowed channels. It is these kinds of +restrictions that lead to the Gamma_out possibly being +smaller than Gamma_tot. As a reminder, the Breit-Wigner for +decays behaves like Gamma_out / ((s - m^2)^2 + s * Gamma_tot^2), +where the width in the numerator is only to those channels being studied, +but the one in the denominator to all channels of the particle. These +ever-changing numbers are not directly visible to the user, but are only +stored in a work area. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SUSYLesHouchesAccord.xml b/PYTHIA8/pythia8140/xmldoc/SUSYLesHouchesAccord.xml new file mode 100644 index 00000000000..a8ad3653fd2 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SUSYLesHouchesAccord.xml @@ -0,0 +1,106 @@ + + +

SUSY Les Houches Accord

+ +The PYTHIA 8 program does not contain an internal spectrum calculator +(a.k.a. RGE package) to provide supersymmetric couplings, mixing angles, +masses and branching ratios. Thus the SUSY Les Houches Accord (SLHA) +Ska04All08 is the only way of +inputting SUSY models, and SUSY processes cannot be run unless such an +input has taken place. + +

+Most of the SUSY implementation in PYTHIA 8 is compatible with both the +SLHA1 and SLHA2 conventions (with the exception of R-parity violation and +the NMSSM extension in the latter case). Internally, PYTHIA 8 uses the +SLHA2 conventions and translates SLHA1 input to these when necessary. +See the section on SUSY Processes for more information. + +

+When reading LHEF files, Pythia automatically looks for SLHA information +between <slha>...</slha> tags in the header of such +files. When running Pythia without LHEF input (or if reading an LHEF +file that does not contain SLHA information in the header), a separate +file containing SLHA information may be specified using +SLHA:file (see below). + +

+With the so-called QNUMBERS extension Alw07, the +SLHA input format can also be used for more general BSM models, although +the implementation of this extension is not yet complete in PYTHIA 8. + +

+Finally, the SLHA input capability can of course also be used to input +SLHA-formatted MASS and DECAY tables for other particles, such as the top +quark, furnishing a less sophisticated but more universal complement to the +standard PYTHIA 8-specific methods for inputting such information (for the +latter, see the section on Particle Data +and the scheme to modify it). This +may at times not be desirable, so a few options can be used to curb the right +of SLHA to overwrite particle data. + +

+The reading-in of information from SLHA or LHEF files is handled by the +SusyLesHouches class, while the subsequent calculation of +derived quantities of direct application to SUSY processes is done in the +CoupSUSY class. + +

SLHA Switches and Parameters

+ + +Controls from where SLHA information is read. + + + + + + +Name of an SLHA (or LHEF) file containing the SUSY/BSM model definition, +spectra, and (optionally) decay tables. Default void +signals that no such file has been assigned. + + + +Some programs write SLHA output also for SM particles where normally +one would not want to have masses and decay modes changed unwittingly. +Therefore, by default, known SM particles are ignored in SLHA files. +To be more specific, particle data for identity codes in the ranges +1 - 24 and 81 - 999,999 are ignored. Notably this includes Z^0, +W^+- and t. The SM Higgs is modified by the SLHA input, +as is other codes in the range 25 - 80 and 1,000,000 - . If you +switch off this flag then also SM particles are modified by SLHA input. + + + +This parameter provides an alternative possibility to ignore SLHA input +for all particles with identity codes below 1,000,000 (which mainly +means SM particle, but also includes e.g. the Higgses in +two-Higgs-doublet scenarios) whose default masses in PYTHIA lie below +some threshold value, given by this parameter. The default value of +100.0 allows SLHA input to modify the top quark, but not, e.g., the +Z^0 and W^+- bosons. + + + +Controls amount of text output written by the SLHA interface, with a +value of 0 corresponding to the most quiet mode. + + +

Internal SLHA Variables

+ +The following variables are used internally by PYTHIA as local copies +of SLHA information. User changes will generally have no effect, since +these variables will be reset by the SLHA reader during initialization. + + +Corresponds to SLHA block MODSEL entry 3. + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SUSYProcesses.xml b/PYTHIA8/pythia8140/xmldoc/SUSYProcesses.xml new file mode 100644 index 00000000000..8ce0d21eb96 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SUSYProcesses.xml @@ -0,0 +1,241 @@ + + +

SUSY Processes

+ +The implementation of SUSY processes is currently still in a development +stage, so careful case-by-case validations against other codes are +strongly recommended and should be considered mandatory. +Please notify the authors (peter.skands@cern.ch) +of any significant deviations (i.e., larger than 10%). In some cases, +limited preliminary validations have +already been carried out by the authors. This is remarked on process by +process below. + +

+Here is collected processes involving supersymmetric particle +production, with the exception of the (extended) Higgs sector. +Since the number of separate but closely related processes is so big, +there will not be switches for each separate process but only for a +reasonable set of subgroups. However, the general +switches SUSY:idA and SUSY:idB may be used in +conjunction with any of these groups to provide some additional +flexibility to concentrate on processes involving only specific (s)particle +final states, see below. + +
Important note: +In order to simulate SUSY processes it is required to read in the +couplings and masses relevant for the scenario to be studied. This +is done with the help of the SUSY Les Houches Accord (SLHA), including +the SLHA2 extensions and generalizations. (Internally, the SLHA2 +conventions are used. SLHA1 spectra are automatically translated into +SLHA2 notation during initialization.) The +reading of a relevant SLHA file must be set up, as described +on this page. + +

+Note also that lepton and photon initial states are not yet available. Only +quark/gluon-initiated 2->2 processes have been implemented. Likewise, direct +slepton production has not yet been implemented (i.e., 2->2 processes +involving sleptons in the final state). Sleptons will of course still be +produced through cascade decays of heavier (s)particles. + +

+Finally, note that these cross sections will be correctly folded with open +branching fractions of cascade decays, but at present any difference between +particle and antiparticle decay tables is not taken into account. This +possibility will be included in a future update. + + +Common switch for production of supersymmetric particles, i.e. +particles with R-parity -1. + + + +Option to limit the sum over possible outgoing states in SUSY +2 -> 2 processes to ones including a specific particle +identity code. The default corresponds to summing over all possible +indices. A non-zero value of SUSY:idA selects only processes +that contain the state corresponding to that particular particle identity +code in the fundamental 2 -> 2 scattering process (symmetrized +over particle/antiparticle). It is the user's responsibility to ensure +that (a subset of) the processes be to simulated actually include this +particle at the 2 -> 2 level; thus, asking for the lightest +neutralino (code 1000021) to be present in a squark-squark production +process will give no match. + + + +As for SUSY:idA, but requires an additional particle +with PDG code SUSY:idB to be present in the 2->2 +process. Thus, using SUSY:idA and SUSY:idB +a specific subprocess can be selected. Again only the absolute sign is +used, i.e. the summation over particle and antiparticle is retained. + + +

Gluino Pair Production

+ + +Pair production of gluinos by gluon-gluon initial states. Does not +depend on flavour violation. This cross section has been validated against +Pythia 6 for SPS1a. + + + +Pair production of gluinos by quark-antiquark annihilation and +t-channel squark exchange. So far, these cross sections assume the +squark CKM is aligned with the quark CKM and that all quantities are +real, so effects of non-minimal flavour violation and/or CP violation +are not yet included. This cross section has been validated against +Pythia 6 for SPS1a. + + +

Associated Squark-Gluino Production

+ + +Associated production of a squark with a gluino. Only implemented for the +flavor-diagonal case. These cross sections have been validated against +Pythia 6 for SPS1a. Note: these cross sections are so far +limited to the SLHA1 flavor structure. They will not give correct results if +used with an SLHA2 spectrum. + + +

Squark Pair Production

+ + +Pair production of a scalar quark together with a scalar antiquark by +gluon annhilation via s-channel gluon exhange, t- and u-channel squark +exchange, and the direct 4-point coupling. +The cross section expression follows +Boz07 and has been validated against Pythia 6. + + + +Pair production of a scalar quark together with a scalar antiquark +by quark-antiquark annihilation. +For same-isospin ~q~q* production (i.e., ~u~u*, ~u~c*, ...), +the s-channel gluon, photon, and Z and +t-channel gluino contributions have so far been implemented (i.e., the +t-channel neutralino contributions are neglected). +For opposite-isospin ~q~q* production (~u~d*, ~u~s*, ...), +the s-channel W and t-channel gluino +contributions have been implemented (i.e., the t-channel neutralino +contributions are neglected). +The cross section expressions follow Boz07 +and should thus be valid also in the case of non-minimal flavour +violation and/or CP violation. These cross sections have been validated +against Pythia 6 for SPS1a, +for ~t1~t1*, ~t2~t2*, ~b1~b1*, ~b2~b2*, and ~b1~b2* (+c.c.) production. +For ~t1~t2* (+c.c.), +there is currently a factor 2 between Pythia 6 and this implementation; +pending resolution. The FLV and CPV cases have not yet been validated. + + + +When switched on this flag switches off all but the s-channel +gluon contribution in the +calculation of same-isospin squark-antisquark production cross +sections. Intended for reference only. For the most +accurate physics simulation, leave this flag in the off +position. + + + +Pair production of scalar quarks (squark-squark and its charge +conjugate process; for squark-antisquark production see above) +by t- and u-channel gluino, neutralino, and + chargino exchange. The cross section expressions follow Boz07 +and should thus be valid also in the case of non-minimal flavour +violation and/or CP violation. Note: Pythia 6 only included the gluino exchange + contribution, which typically dominates due to the size of the strong +coupling; for counterchecks, +the flag SUSY:qq2squarksquark:gluinoOnly +below can be switched on to eliminate the chargino and neutralino +contributions. These cross sections have been validated against Pythia 6 for +SPS1a, for ~b1~b1, ~b1~b2, and ~b2~b2 production, with 5-10% differences +observed. + + + +When switched on this flag causes the t- or u-channel +neutralino and chargino contributions to be ignored in the +calculation of squark pair production cross sections. Intended for reference +only. For the most +accurate physics simulation, leave this flag in the off +position. + + +

Neutralino and Chargino Pair Production

+ + +Pair production of neutralinos by quark-antiquark annihilation. With +four neutralino species this gives ten separate processes, codes +1201 - 1210. The cross section expressions follow Boz07 and +should thus be valid also in the case of non-minimal flavour +violation and/or CP violation. These cross sections have been validated +against Pythia 6 for SPS1a and against the code +XSUSY (based on Boz07) for a non-minimal FLV case. +Validation of CPV cases has not yet been carried out. + + + +Associated chargino-neutralino production by quark-antiquark +annihilation. With four neutralino species, two chargino ones, and +maintaining charge conjugate proceeses separate, this gives 16 +separate processes, codes 1221 - 1236. The cross section expressions +follow Boz07 and should thus be valid also in the case of +non-minimal flavour violation and/or CP violation. These cross sections have +been validated against Pythia 6 for SPS1a and against the code +XSUSY (based on Boz07) for a non-minimal FLV case. Validation of + CPV cases has not yet been carried out. + + + +Pair production of charginos by quark-antiquark annihilation. With +two chargino species and maintaining mutually charge conjugate +processes separate, this gives four separate processes, codes +1241 - 1244. The cross section expressions follow Boz07 +and should thus be valid also in the case of non-minimal flavour +violation and/or CP violation. These cross sections have +been validated +against Pythia 6 for SPS1a and against the code +XSUSY (based on Boz07) for a non-minimal FLV case. Validation of + CPV cases has not yet been carried out. + + +

Associated Neutralino/Chargino + Squark/Gluino Production

+ + +Pair production of neutralinos from quark-gluon initial states. +The cross section expressions follow Boz07 and +should thus be valid also in the case of non-minimal flavour +violation and/or CP violation. Note: these cross sections are in a +development stage and have not yet been validated. + + + +Associated chargino-squark production from quark-gluon initial states. +annihilation. The cross section expressions +follow Boz07 and should thus be valid also in the case of +non-minimal flavour violation and/or CP violation. Note: these cross sections +are in a development stage and have not yet been validated. + + + +Associated neutralino-gluino production by quark-antiquark +annihilation. Status: not implemented yet. + + + +Associated chargino-gluino production by quark-antiquark +annihilation. Status: not implemented yet. + + +

Slepton Production

+ +No 2->2 slepton pair production or associated slepton production +cross sections have been implemented yet. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SampleMainPrograms.xml b/PYTHIA8/pythia8140/xmldoc/SampleMainPrograms.xml new file mode 100644 index 00000000000..523e9f8b57c --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SampleMainPrograms.xml @@ -0,0 +1,181 @@ + + +

Sample Main Programs

+ +Descriptions of available classes, methods and settings are all +very good and useful. Ultimately they are necessary for you to +be able to fine-tune your runs to the task at hand. To get going, +however, nothing helps like having explicit examples to study. +This is what is provided in the examples subdirectory, +along with instructions how they should be run: +
    + +
  • main01.cc : a simple study of the charged multiplicity +for jet events at the LHC. (Brief example fitting on one slide.)
    • + +
  • main02.cc : a simple study of the pT spectrum +of Z bosons at the Tevatron. (Brief example fitting on one slide.)
    • + +
  • main03.cc : a simple single-particle analysis of jet +events, where input is set by main03.cmnd "cards file".
    • + +
  • main04.cc : a simple study of several different kinds +of events, with the choice to be made in the main04.cmnd +"cards file".
    • + +
  • main05.cc : generation of QCD jet events at the LHC, +with jet analysis using the CellJet cone-jet finder.
    • + +
  • main06.cc : tests of cross sections for elastic and +diffractive topologies, using main06.cmnd to pick process.
    • + +
  • main07.cc : tests of cross sections for minimum-bias +events, using main07.cmnd to pick options.
    • + +
  • main08.cc : generation of the QCD jet cross section +by splitting the run into subruns, each in its own pT bin, +and adding the results properly reweighted. Two options, with limits +set either in the main program or by subrun specification in the +main08.cmnd file.
    • + +
  • main09.cc : generation of LEP1 hadronic events, i.e. +e^+e^- -> gamma*/Z^0 -> q qbar, with charged multiplicity, +sphericity, thrust and jet analysis.
    • + +
  • main10.cc : illustration how userHooks can be used +interact directly with the event-generation process.
    • + +
  • main11.cc : generation of two predetermined hard +interactions in each event.
    • + +
  • main12.cc : a study of top events, fed in from the +Les Houches Event File ttbar.lhe, here generated by +PYTHIA 6.4. This file currently only contains 100 events +so as not to make the distributed PYTHIA package too big, and so serves +mainly as a demonstration of the principles involved.
    • + +
  • main13.cc : a more sophisticated variant of +main12.cc, where two Les Houches Event Files +(ttbar.lhe and ttbar2.lhe) successively +are used as input. Also illustrating some other aspects, like the +capability to mix in internally generated events.
    • + +
  • main14.cc : a systematic comparison of several +cross section values with their corresponding values in PYTHIA 6.4, +the latter available as a table in the code.
    • + +
  • main15.cc : loop over several tries, either to redo +B decays only or to redo the complete hadronization chain of an event. +Since much of the generation process is only made once this is a way +to increase efficiency.
    • + +
  • main16.cc : put all user analysis code into a class +of its own, separate from the main program; provide the "cards file" +name as a command-line argument.
    • + +
  • main17.cc : collect the Pythia calls in a wrapper class, +thereby simplifying the main program; provide the "cards file" name +as a command-line argument.
    • + +
  • main18.cc : shows how to write an event filter class, +where you keep a vector of pointers to the subset of particles you +want to study further. The event record itself remains unchanged.
    • + +
  • main19.cc : use several instances of Pythia, one for +signal events and others for a variable number of pileup and "beam-gas" +events, combined into one common event record.
    • + +
  • main20.cc : shows how PYTHIA 8 can write a Les Houches +Event File, using facilities potentially useful also for other programs +to write an LHEF.
    • + +
  • main21.cc : an example how a single particle or various +parton-level configurations can be input directly for hadronization, +without being tied to the full process-generation machinery, e.g. to +study the hadronization of junction topologies.
    • + +
  • main22.cc : tests of internally implemented cross sections +for Supersymmetric particle production, with SYSY spectrum defined in +sps1a.spc and settings in main22.cmnd.
    • + +
  • main23.cc : shows how an external decay handler can +be linked to handle the decays of some particles.
    • + +
  • main24.cc : shows how an external random number +generator can be linked to replace the internal one.
    • + +
  • main25.cc : shows how an external process can be +implemented as a new class derived from a PYTHIA base class, and then +handed in for generation as with a normal internal process.
    • + +
  • main26.cc : shows how an external resonance can be +implemented as a new class derived from a PYTHIA base class, and be +used in an external process, both of which are then handed in for +generation as with a normal internal resonance and process.
    • + +
  • main27.cc : shows how an external beam momentum spread +and vertex location generator can be implemented as a new class derived +from a PYTHIA base class, and then handed in for internal use.
    • + +
  • main28.cc : test program for processes in scenarios +with large extra dimensions or unparticles. + +
  • main29.cc : set up a fictitious production process +to a generic resonance, where you easily can compose your own list +of (two-body) decay modes to a variety of final states. Also traces +decay chains down to truly stable particles: gamma, e+-, p/pbar and +neutrinos. Suitable for astroparticle applications, like neutralino +pair annihilation, where cross sections are calculated separately +in another program. + +
  • main30.cc : production of Kaluza-Klein gamma/Z +states in TeV-sized extra dimensions. + +
  • main31.cc : similar to main01, except that the +event record is output in the HepMC event record format. Requires +that HepMC is properly linked.
    • + +
  • main32.cc : a streamlined version for the generation +of events that are then stored in HepMC format, without any event +analysis. That is, all physics studies will have to be done afterwards. +The name of the input "cards file" (e.g. main32.cmnd) +and output HepMC event file are to be provided as command-line arguments. +Requires that HepMC is properly linked.
    • + +
  • main41.cc : a test of the shape of parton densities, +as a check prior to using a given PDF set in a generator. Requires +that LHAPDF is properly linked.
    • + +
  • main42.cc : compares the charged multiplicity +distribution, and a few other minimum-bias physics aspects, between +default PYTHIA PDF and another one. Requires that LHAPDF is properly +linked.
    • + +
  • main43.cc : tests the possibility to do backwards +evolution from an incoming photon at the hard interaction. Requires +that you link to a LHAPDF set that includes the photon PDF.
    • + +
  • main44.cc : exemplifies how you create your own +PDF set and link it in for use in the process generation.
    • + +
  • main51.cc : exemplifies how you can link in runtime +generation of hard processes from PYTHIA 6, using the Les Houches +Accord facilities. This example is deprecated, since PYTHIA 8 by now +contains essentially all hard processes found in PYTHIA 6.
    • + +
  • main61.cc : an example how the FastJet jet finding +package can be linked to allow an analysis of the final state, +in this case for a study of W + jet production.
    • + +
  • main71.cc : exemplifies an improved matching of +parton showers to LHEF-style input based on the POWHEG approach, +in this particular case for the POWHEG-hvq program applied to top +pair production Cor10. The small sample of input events +is stored in the powheg-hvq.lhe file. +
    • + +
+ + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SaveSettings.xml b/PYTHIA8/pythia8140/xmldoc/SaveSettings.xml new file mode 100644 index 00000000000..5ceb3675e94 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SaveSettings.xml @@ -0,0 +1,150 @@ + + +

Save Settings

+ +The information on this webpage is only valid if you access the PHP +dynamic webpages via a web browser, and does not apply to the static +HTML equivalents. With PHP, all of the settings in the PYTHIA program +are represented by radio buttons or fill-in boxes, that makes it easy +for you to construct a file with your desired changes. This file can +then be read into PYTHIA by your main program to steer the whole run. + +

Basic instructions

+ +The functionality of the PHP option is described in the following. + +

+
+ +
+ +

    + +

  • +To begin with, you must specify a (temporary) file name in the +box above. If the filename already exists on the server, you will be +requested to pick a new name.
    • + +

  • +Once you have Submitted your filename, you can browse through the +pages and make your selections. The values currently selected when you +load the page are the default values.
    • + +

  • +When you have finished making your changes to a particular page, +you must click on Save Settings at the bottom of +the page. This will write the changes to your temporary file. If you make +a mistake, just repeat the procedure for that category again.
    + +

  • +When you have finished all the changes you need, return to this page +and click Finish File.
    • + +

  • +You will then get up a link, that you are asked to right-click +with your mouse (or equivalent).
    • + +

  • +In the menu that appears, pick the option Save Link As +(or equivalent).
    • + +

  • +You will now get up a file browser, for you to pick and Save +the location and file name (the latter by default the same as the +temporary file name).
    • + +

  • +At any time, if you click the RESET button, your temporary +file will be erased and you can start anew.
    • + +

  • +Before you use a file, be sure to check it visually to confirm +that you saved what you intended to. Minor corrections are easily made +in a text editor. +
    • + +
+ +

+

Supplementary notes

+ + +The documentation files exist in three versions. +
    + +

  1. +As a set of .xml files, in the xmldoc/ +subdirectory. These are the master copies that no user ever should +touch, but that are used to generate the variants below.
    2. + +

  2. +As a set of .html files, in the htmldoc/ +subdirectory. You can open your own locally installed copy of the +Welcome.html file in your web browser and thereafter +navigate among all the pages. You can learn which parameters are free +to be changed, but not change anything, except by brute-force +cut-and-paste to a file of your own.
    3. + +

  3. +As a set of .php files, in the phpdoc/ +subdirectory. For these files to provide the functionality described +above they have to accessed via a webserver. The one where you have +your homepage should work fine. Alternatively you can use pages already +available on another server.
    4. + +
+ +

+A few further comments about the operation of the PHP option: +

    + +

  • +To set up the PHP files on your webserver, you have to install the whole +phpdoc/ subdirectory there. In addition to the +.php code this includes a few more files, plus a +subdirectory named files where the temporary files +are stored. This subdirectory must have public write access to work +(chmod a+w files if not).
    • + +

  • +The "temporary" files stored in files actually remain +unless the RESET button is used. The good news is that this makes +it possible to recover a file that otherwise might be lost. The bad +news is that the files directory may need to be cleaned +up from time to time. (But typically the files are pretty small, so +this should not be a major problem.)
    • + +

  • +When you click the Save Settings button on the bottom of a page +all changed settings are written on the temporary file in the format +
    +name-of-flag/mode/parameter/word = value
+
    +with one variable per line. Thereafter all the settings on the page +are restored to their default values.
    • + +

  • +You can return to a page to do some further changes and save those. +If you change the same parameter twice, it is the last value that +counts. (Both values are stored in the file, with the more recent +lower down, and then PYTHIA does the changes sequentially.) However +remember that unchanged values are not stored, so if you want to +restore some default value it may be simpler to edit the file +afterwards.
    • + +

  • +The changeable flags/modes/parameters/words are mainly in the +"Setup Run Tasks" section of the index, but a few (less +frequently used ones) can also be found lower down, in the +"Study Output" and "Link to Other Programs" pages. + +

  • +It is not (yet) possible to modify particle data within the PHP-based +setup approach. This is a more difficult task, since e.g. the +modifications one may want to do in a decay table can be quite +interrelated. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SemiInternalProcesses.xml b/PYTHIA8/pythia8140/xmldoc/SemiInternalProcesses.xml new file mode 100644 index 00000000000..30ffd321861 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SemiInternalProcesses.xml @@ -0,0 +1,477 @@ + + +

    Semi-Internal Processes

    + +Normally users are expected to implement new processes via the +Les Houches Accord. Then +you do all flavour, colour and phase-space selection externally, +before your process-level events are input for further processing +by PYTHIA. However, it is also possible to implement a +new process in exactly the same way as the internal PYTHIA +ones, thus making use of the internal phase space selection machinery +to sample an externally provided cross-section expression. +This page gives a brief summary how to do that. If you additionally +want to introduce a new resonance species, with its own internal +width calculations, you will find further instructions +here. + +

    +Should you actually go ahead, it is strongly recommended to shop around +for a similar process that has already been implemented, and to use that +existing code as a template. Look for processes with the same combinations +of incoming flavours and colour flows, rather than the shape of the +cross section itself. With a reasonable such match the task should be +of medium difficulty, without it more demanding. + +

    +PYTHIA is rather good at handling the phase space of +2 -> 1 and 2 -> 2 processes, is more primitive for +2 -> 3 ones and does not at all address higher multiplicities. +This limits the set of processes that you can implement in this +framework. The produced particles may be resonances, however, so it is +possible to end up with bigger "final" multiplicities through sequential +decays, and to include further matrix-element weighting in those decays. + +

    +There are two steps involved in implementing a process: +
    1) writing a new class, where the matrix elements are implemented, +including information on incoming and outgoing flavours and colours, and +
    2) making the process available. +
    We consider these two aspects in turn. An example where it all comes +together is found in main25.cc. + +

    The Cross Section Class

    + +The matrix-element information has to be encoded in a new class. +The relevant code could either be put before the main program in the +same file, or be stored separately, e.g. in a matched pair +of .h and .cc files. The latter may be more +convenient, in particular if the cross sections are lengthy, or if you +intend to build up your own little process library, but of course +requires that these additional files are correctly compiled and linked. + +

    +The class has to be derived either from +Sigma1Process, for 2 -> 1 processes, from +Sigma2Process, for 2 -> 2 ones, or from +Sigma3Process, for 2 -> 3 ones. (The +Sigma0Process class is used for elastic, diffractive +and minimum-bias events, and is not recommended for use beyond that.) +These are in their turn derived from the SigmaProcess +base class. + +

    +The class can implement a number of methods. Some of these are +compulsory, others strongly recommended, and the rest are to be +used only when the need arises to override the default behaviour. +The methods are: + +

    +A constructor for the derived class obviously must be available. +Here you are quite free to allow a list of arguments, to set +the parameters of your model, or even to create a set of closely +related but distinct processes. For instance, g g -> Q Qbar, +Q = c or b, is only coded once, and then the +constructor takes the quark code (4 or 5) as argument, +to allow the proper amount of differentiation. + +

    +A destructor is only needed if you plan to delete the process +before the natural end of the run, and require some special behaviour +at that point. If you call such a destructor you will leave a pointer +dangling inside the Pythia object you gave it in to, +if that still exists. + + +is called once during initalization, and can then be used to set up +parameters, such as masses and couplings, and perform calculations +that need not be repeated for each new event, thereby saving time. +This method needs not be implemented, since in principle all +calculations can be done in sigmaHat below. + + + +is called once a kinematical configuration has been determined, but +before the two incoming flavours are known. This routine can therefore +be used to perform calculations that otherwise might have to be repeated +over and over again in sigmaHat below. For instance +a flavour-independent cross section calculation for a q g +initial state would be repeated 20 times in sigmaHat, +five times for the five quark flavours allowed in the incoming beams, +times twice to include antiquarks, times twice since the (anti)quark +could be in either of the two beams. You could therefore calculate the +result once only and store it as a private data member of the class. +It is optional whether you want to use this method, however, or put +everything in sigmaHat. + + + +is the key method for cross section calculations and returns a cross section +value, as further described below. It is called when also a preliminary set +of incoming flavours has been picked, in addition to the kinematical ones +already available for sigmaKin. Typically sigmaHat +is called inside a loop over all allowed incoming flavour combinations, +stored in id1 and id2, with fixed kinematics, +as already illustrated above. The sum over the different flavour combinations +provides the total cross section, while their relative size is used to make +a selection of a specific incomimg state. +
    For a 2 -> 1 process, the returned value should be +sigmaHat(sHat), where mH (= mHat), +sH (= sHat) and sH2 (= sHat^2) +are available to be used. +
    For a 2 -> 2 process, instead +d(sigmaHat)/d(tHat) should be returned, based on +provided mH, sH, sH2, tH, tH2, uH, uH2, m3, s3, m4, s4 and +pT2 values (s3 = m3*m3 etc.). Overload the +convertME() method below if you instead plan to return +|M|^2. +
    For a 2 -> 3 process, instead |M|^2 should be +returned, with normalization such that |M|^2 / (2 sHat) integrated +over the three-body phase space gives the cross section. Here no standard +set of variables exist. Instead the obvious ones, +mH, sH, m3, s3, m4, s4, m5, s5, are complemented by the +four-vectors p3cm, p4cm, p5cm, from which further invariants +may be calculated. The four-vectors are defined in the CM frame of the +subcollision, with incoming partons along the +-z axis. +
    In either case, alpha_s and alpha_em have already +been calculated, and are stored in alpS and alpEM. +Also other standard variables may be used, like +CoupEW::sin2thetaW(), and related flavour-dependent +vector and axial couplings in CoupEW and CKM combinations +in VCKM. +
    In case some of the final-state particles are resonances, their +squared masses have already been selected according to a Breit-Wigner +with a linearly running width Gamma(m) = Gamma(m_0) * m / m_0. +More precisely, the mass spectrum is weighted according to +w_BW(m^2) d(m^2), where + +w_BW(m^2) = (1/pi) * (m * Gamma(m)) / ( (m^2 - m_0^2)^2 + (m * Gamma(m))^2 ) . + +If you would like to have another expression, the above weights are stored +in runBW3, runBW4 and runBW5, +respectively. If you divide out one of these factors, you just remain with +a phase space selection d(m^2) for this particle, +and can multiply on your desired shape factor instead. Unfortunately, the +Monte Carlo efficiency will drop if your new mass distribution differs +dramatically from the input one. Therefore it does make sense to adjust the +database value of the width to be slightly (but not too much) broader +than the distribution you have in mind. Also note that, already by default, +the wings of the Breit-Wigner are oversampled (with a compensating lower +internal weight) by partly sampling like (a + b/m^2 + c/m^4) d(m^2), +where the last term is only used for gamma^*/Z^0. +
    As alternative to the kinematics variables defined above, to be used +for cross section calculations, also the two arrays mME[5] +and pME[5] can be used, for masses and four-momenta, +respectively. Here indices 0 and 1 are the two incoming beams, and 2 +and onwards the outgoing particles. (Note that this differs from the normal +internal labelling, where slot 0 is left empty.) The four-momenta are +defined in the rest frame of the subcollision, and do not represent the +final kinematics. Furthermore, for 2 -> 2 processes of massive +identical particles (or antiparticles) in the final state, such as +t tbar or W^+ W^-, the kinematics is here adjusted +so that the two particles have the same mass, formed as a suitable +average of the actual Breit-Wigner-distributed masses. This allows the +evaluation of matrix-element expressions that only have meaning if the +two have the same mass. +     + + +is called only once an initial state and a kinematical configuration has +been picked. This routine must set the complete flavour information and +the colour flow of the process. This may involve further random choices, +between different possible final-state flavours or between possible +competing colour flows. Private data members of the class may be used to +retain some information from the previous steps above. +
    When this routine is called the two incoming flavours have already +been selected and are available in id1 and id2, +whereas the one, two or three outgoing ones either are fixed for a given +process or can be determined from the instate (e.g. whether a W^+ +or W^- was produced). There is also a standard method in +VCKM to pick a final flavour from an initial one with CKM +mixing. Once you have figured out the value of +id3 and, the case being, id4 and +id5, you store these values permanently by a call +setId( id1, id2, id3, id4, id5), where the last two may be +omitted if irrelevant. +
    Correspondingly, the colours are stored with +setColAcol( col1, acol1, col2, acol2, col3, acol3, col4, acol4, +col5, acol5), where the final ones may be omitted if irrelevant. +Les Houches style colour tags are used, but starting with number 1 +(and later shifted by the currently requested offset). The +input is grouped particle by particle, with the colour index before the +anticolour one. You may need to select colour flow dynamically, depending +on the kinematics, when several distinct possibilities exist. Trivial +operations, like swapping colours and anticolours, can be done with +existing methods. +
    When the id3Mass() and id4Mass() +methods have been used, the order of the outgoing particles may be +inconsistent with the way the tHat and uHat +variables have been defined. A typical example would be a process like +q g -> q' W with tHat defined between incoming and +outgoing quark, but where id3Mass() = 24 and so the +process is to be stored as q g -> W q'. One should then put +the variable swapTU = true in setIdColAcol() +for each event where the tHat and uHat variables +should be swapped before the event kinematics is reconstructed. This +variable is automatically restored to false for each new +event. +     + + +is called to allow a reweighting of the simultaneous flavour choices of +resonance decay products. Is currently only used for the +q qbar -> gamma*/Z^0 gamma*/Z^0 process, and will likely not +be of interest for you. + + + +is called when the basic process has one or several resonances, after each +set of related resonances in process[i], +iResBeg <= i <= iResEnd, +has been allowed to decay. The calculated weight, to be normalized +to the range between 0 and 1, is used to decide whether to accept the +decay(s) or try for a new decay configuration. The base-class version of +this method returns unity, i.e. gives isotropic decays by default. +This method may be called repeatedly for a single event. For instance, in +q qbar -> H^0 Z^0 with H^0 -> W^+ W^-, a first call +would be made after the H^0 and Z^0 decays, and then +depend only on the Z^0 decay angles since the H^0 +decays isotropically. The second call would be after the W^+ W^- +decays and then involve correlations between the four daughter fermions. + + + +returns the name of the process, as you want it to be shown in listings. + + + +returns an integer identifier of the process. This has no internal function, +but is only intended as a service for the user to rapidly (and hopefully +uniquely) identify which process occured in a given event. Numbers below +10000 are reserved for internal PYTHIA use. + + + +this string specifies the combinations of incoming partons that are +allowed for the process under consideration, and thereby which incoming +flavours id1 and id2 the sigmaHat() +calls will be looped over. It is always possible to pick a wider flavour +selection than strictly required and then put to zero cross sections in +the superfluous channels, but of course this may cost some extra execution +time. Currently allowed options are: +
    * gg: two gluons. +
    * qg: one (anti)quark and one gluon. +
    * qq: any combination of two quarks, two antiquarks or +a quark and an antiquark. +
    * qqbarSame: a quark and its antiquark; +this is a subset of the above qq option. +
    * ff: any combination of two fermions, two antifermions +or a fermion and an antifermion; is the same as qq for +hadron beams but also allows processes to work with lepton beams. +
    * ffbarSame: a fermion and its antifermion; is the +same as qqbarSame for hadron beams but also allows processes +to work with lepton beams. +
    * ffbarChg: a fermion and an antifermion that combine +to give charge +-1. +
    * fgm: a fermion and a photon (gamma). +
    * ggm: a gluon and a photon. +
    * gmgm: two photons. +     + + +it is assumed that cross sections normally come in dimensions such that +they, when integrated over the relevant phase space, obtain the dimension +GeV^-2, and therefore need to be converted to mb. If the cross section +is already encoded as mb then convert2mb() should be +overloaded to instead return false. + + + +it is assumed that 2 -> 2 cross sections are encoded as +d(sigmaHat)/d(tHat) in the SigmaProcess::sigmaHat() +methods. If convertME() is overloaded to instead return +true then the return value is instead assumed to be the +squared matrix element |M|^2, and +SigmaProcess::sigmaHatWrap(...) converts to +d(sigmaHat)/d(tHat). +This switch has no effect on 2 -> 1 and 2 -> 3 processes. +In the former one always needs to encode sigmaHat(sHat), +in the latter always |M|^2. + + + + + + + +are the one, two or three final-state flavours, where masses are to be +selected before the matrix elements are evaluated. Only the absolute value +should be given. For massless particles, like gluons and photons, one need +not give anything, i.e. one defaults to 0. The same goes for normal light +quarks, where masses presumably are not implemented in the matrix elements. +Later on, these quarks can still (automatically) obtain constituent masses, +once a u, d or s flavour has been selected. + + + + + +are the codes of up to two s-channel resonances contributing to +the matrix elements. These are used by the program to improve the phase-space +selection efficiency, by partly sampling according to the relevant +Breit-Wigners. Massless resonances (the gluon and photon) need not be +specified. + + + +normally the choice of renormalization and factorization scales in +2 -> 2 and 2 -> 3 processes is based on the assumption +that t- and u-channel exchanges dominates the +cross section. In cases such as f fbar -> gamma* -> f' fbar' a +2 -> 2 process actually ought to be given scales as a +2 -> 1 one, in the sense that it proceeds entirely through +an s-channel resonance. This can be achieved if you override the +default false to return true. See further the +page on couplings and scales. + + + +normally no intermediate state is shown in the event record for +2 -> 2 and 2 -> 3 processes. However, in case +that idSChannel is overloaded to return a nonzero value, +an intermediate particle with that identity code is inserted into the +event record, to make it a 2 -> 1 -> 2 or 2 -> 1 -> 3 +process. Thus if both isSChannel and idSChannel +are overloaded, a process will behave and look like it proceeded through +a resonance. The one difference is that the implementation of the +matrix element is not based on the division into a production and a +decay of an intermediate resonance, but is directly describing the +transition from the initial to the final state. + + + + + +the non-QCD 2 -> 3 phase space selection machinery is rather +primitive, as already mentioned. The efficiency can be improved in +processes that proceed though t-channel exchanges, such as +q qbar' -> H^0 q qbar' via Z^0 Z^0 fusion, if the identity +of the t-channel-exchanged particles on the two side of the +event are provided. Only the absolute value is of interest. + + + + + +in the above kind of 2 -> 3 phase-space selection, the +sampling of pT^2 is done with one part flat, one part weighted +like 1 / (pT^2 + m_R^2) and one part like +1 / (pT^2 + m_R^2)^2. The above values provide the relative +amount put in the latter two channels, respectively, with the first +obtaining the rest. Thus the sum of tChanFracPow1() and +tChanFracPow2() must be below unity. The final results +should be independent of these numbers, but the Monte Carlo efficiency +may be quite low for a bad choice. Here m_R is the mass of the +exchanged resonance specified by idTchan1() or +idTchan2(). Note that the order of the final-state +listing is important in the above q qbar' -> H^0 q qbar' example, +i.e. the H^0 must be returned by id3Mass(), +since it is actually the pT^2 of the latter two that are +selected independently, with the first pT then fixed +by transverse-momentum conservation. + + + +in 2 -> 3 processes the phase space selection used here +involves a twofold ambiguity basically corresponding to a flipping of +the positions of last two outgoing particles. These are assumed equally +likely by default, false, but for processes proceeding entirely +through t-channel exchange the Monte Carlo efficiency can be +improved by making a preselection based on the relative propagator +weights, true. + + + +allows a possibility to override the global mode +WeakZ0:gmZmode +for a specific process. The global mode normally is used to switch off +parts of the gamma^*/Z^0 propagator for test purposes. The +above local mode is useful for processes where a Z^0 really is +that and nothing more, such as q qbar -> H^0 Z^0. The default +value -1 returned by gmZmode() ensures that the global +mode is used, while 0 gives full gamma^*/Z^0 interference, +1 gamma^* only and 2 Z^0 only. + + +

    Access to a process

    + +Once you have implemented a class, it is straightforward to make use of +it in a run. Assume you have written a new class MySigma, +which inherits from Sigma1Process, Sigma2Process +or Sigma3Process, which in their turn inherit from +SigmaProcess. You then create an instance of this class +and hand it in to a pythia object with +
    +      SigmaProcess* mySigma = new MySigma();
+      pythia.setSigmaPtr( mySigma); 
+
    +If you have several processes you can repeat the procedure any number +of times. When pythia.init(...) is called these processes +are initialized along with any internal processes you may have switched on, +and treated in exactly the same manner. The pythia.next() +will therefore generate a mix of the different kinds of processes without +distinction. See also the Program Flow +description. + +

    +If the code should be of good quality and general usefulness, it would +be simple to include it as a permanently available process in the +standard program distribution. The final step of that integration ought to +be left for the PYTHIA authors, but here is a description of what is +required. + +

    +A flag has to be defined, that allows the process to be switched on; +by default it should always be off. The name of the flag should be +chosen of the type model:process. Here the +model would be related to the general scenario considered, +e.g. Compositeness, while process would +specify instate and outstate, separated by a 2 (= to), e.g. +ug2u*g. +When several processes are implemented and "belong together" it is +also useful to define a model:all switch that affects +all the separate processes. + +

    +The flags should normally be stored in the ProcessSelection.xml +file or one of its daughters for a specific kind of processes. This is to +make them easily found by users. You could create and use your own +.xml file, so long as you then add that name to the +list of files in the Index.xml file. (If not, +the flags would never be created and the program would not work.) + +

    +In the ProcessContainer.c file, the +SetupContainers::init() method needs to be expanded to +create instances of the processes switched on. This code is fairly +repetitive, and should be easy to copy and modify from the code +already there. The basic structure is +
    (i) check whether a process is requested by the user and, if so, +
    (ii) create an instance of the matrix-element class, +
    (iii)create a container for the matrix element and its associated +phase-space handling, and +
    (iv) add the container to the existing process list. + +

    +Two minor variations are possible. One is that a set of related +processes are lumped inside the the same initial check, i.e. are +switched on all together. The second is that the matrix-element +constructor may take arguments, as specified by you (see above). +If so, the same basic matrix element may be recycled for a set of +related processes, e.g. one for a composite u and one for +a composite d. Obviously these variations may be combined. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SemiInternalResonances.xml b/PYTHIA8/pythia8140/xmldoc/SemiInternalResonances.xml new file mode 100644 index 00000000000..1299c35bee4 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SemiInternalResonances.xml @@ -0,0 +1,209 @@ + + +

    Semi-Internal Resonances

    + +The introduction of a new +semi-internal process may also involve a new particle, +not currently implemented in PYTHIA. Often it is then enough to +use the standard machinery +to introduce a new particle (id:all = ...) and new +decay channels (id:addChannel = ...). By default this +only allows you to define a fixed total width and fixed branching +ratios. Using meMode +values 100 or bigger provides the possibility of a very +simple threshold behaviour. + +

    +If you want to have complete freedom, however, there are two +ways to go. One is that you make the resonance decay part of the +hard process itself, either using the +Les Houches interface or +a semi-internal process. The other is for you to create a new +ResonanceWidths object, where you write the code +needed for a calculation of the partial width of a particular +channel. + +

    +Here we will explain what is involved in setting up a resonance. +Should you actually go ahead with this, it is strongly recommended +to use an existing resonance as a template, to get the correct +structure. There also exists a sample main program, +main26.cc, that illustrates how you could combine +a new process and a new resonance. + +

    +There are three steps involved in implementing a new resonance: +
    1) providing the standard particle information, as already +outlined above (id:all = ..., +id:addChannel = ...), except that now branching +ratios need not be specified, since they anyway will be overwritten +by the dynamically calculated values. +
    2) writing the class that calculates the partial widths. +
    3) handing in a pointer to an instance of this class to PYTHIA. +
    We consider the latter two aspects in turn. + +

    The ResonanceWidths Class

    + +The resonance-width calculation has to be encoded in a new class. +The relevant code could either be put before the main program in the +same file, or be stored separately, e.g. in a matched pair +of .h and .cc files. The latter may be more +convenient, in particular if the calculations are lengthy, or +likely to be used in many different runs, but of course requires +that these additional files are correctly compiled and linked. + +

    +The class has to be derived from the ResonanceWidths +base class. It can implement a number of methods. The constructor +and the calcWidth ones are always needed, while others +are for convenience. Much of the administrativ machinery is handled +by methods in the base class. + +

    Thus, in particular, you must implement expressions for all +possible final states, whether switched on in the current run or not, +since all contribute to the total width needed in the denominator of +the Breit-Wigner expression. Then the methods in the base class take +care of selecting only allowed channels where that is required, and +also of including effects of closed channels in secondary decays. +These methods can be accessed indirectly via the +res... +methods of the normal +particle database. + +

    +A constructor for the derived class obviously must be available. +Here you are quite free to allow a list of arguments, to set +the parameters of your model. The constructor must call the +base-class initBasic(idResIn) method, where the argument +idResIn is the PDG-style identity code you have chosen +for the new resonance. When you create several related resonances +as instances of the same class you would naturally make +idResIn an argument of the constructor; for the +PYTHIA classes this convention is used also in cases when it is +not needed. +
    The initBasic(...) method will +hook up the ResonanceWidths object with the corresponding +entry in the generic particle database, i.e. with the normal particle +information you set up in point 1) above. It will store, in base-class +member variables, a number of quantities that you later may find useful: +
    idRes : the identity code you provide; +
    hasAntiRes : whether there is an antiparticle; +
    mRes : resonance mass; +
    GammaRes resonance width; +
    m2Res : the squared mass; +
    GamMRat : the ratio of width to mass. + +

    +A destructor is only needed if you plan to delete the resonance +before the natural end of the run, and require some special behaviour +at that point. If you call such a destructor you will leave a pointer +dangling inside the Pythia object you gave it in to, +if that still exists. + + +is called once during initialization, and can then be used to set up +further parameters specific to this particle species, such as couplings, +and perform calculations that need not be repeated for each new event, +thereby saving time. This method needs not be implemented. + + + +is called once a mass has been chosen for the resonance, but before +a specific final state is considered. This routine can therefore +be used to perform calculations that otherwise might have to be repeated +over and over again in calcWidth below. It is optional +whether you want to use this method, however, or put +everything in calcWidth(). +
    The optional argument will have the value true when +the resonance is initialized, and then be false throughout +the event generation, should you wish to make a distinction. +In PYTHIA such a distinction is made for gamma^*/Z^0 and +gamma^*/Z^0/Z'^0, owing to the necessity of a special +description of interference effects, but not for other resonances. +
    In addition to the base-class member variables already described +above, mHat contains the current mass of the resonance. +At initialization this agrees with the nominal mass mRes, +but during the run it will not (in general). +     + + +is the key method for width calculations and returns a partial width +value, as further described below. It is called for a specific +final state, typically in a loop over all allowed final states, +subsequent to the calcPreFac(...) call above. +Information on the final state is stored in a number of base-class +variables, for you to use in your calculations: +
    iChannel : the channel number in the list of +possible decay channels; +
    mult : the number of decay products; +
    id1, id2, id3 : the identity code of up to the first +three decay products, arranged in descending order of the absolute value +of the identity code; +
    id1Abs, id2Abs, id3Abs : the absolute value of the +above three identity codes; +
    mHat : the current resonance mass, which is the same +as in the latest calcPreFac(...) call; +
    mf1, mf2, mf3 : masses of the above decay products; +
    mr1, mr2, mr3 : squared ratio of the product masses +to the resonance mass; +
    ps : is only meaningful for two-body decays, where it +gives the phase-space factor +ps = sqrt( (1. - mr1 - mr2)^2 - 4. * mr1 * mr2 ); +
    In two-body decays the third slot is zero for the above properties. +Should there be more than three particles in the decay, you would have +to take care of the subsequent products yourself, e.g. using +
    particlePtr->decay[iChannel].product(j); +
    to extract the j'th decay products (with +j = 0 for the first, etc.). Currently we are not aware +of any such examples. +
    The base class also contains methods for alpha_em and +alpha_strong evaluation, and can access many standard-model +couplings; see the existing code for examples. +
    The result of your calculation should be stored in +
    widNow : the partial width of the current channel, +expressed in GeV. +     + + +is not normally used. In PYTHIA the only exception is Higgs decays, +where it is used to define the width (except for colour factors) +associated with a specific incoming/outgoing state. It allows the +results of some loop expressions to be pretabulated. + + +

    Access to resonance widths

    + +Once you have implemented a class, it is straightforward to +make use of it in a run. Assume you have written a new class +MyResonance, which inherits from +ResonanceWidths. You then create an instance of +this class and hand it in to a pythia object with +
    +      ResonanceWidths* myResonance = new MyResonance();
+      pythia.setResonancePtr( myResonance); 
+
    +If you have several resonances you can repeat the procedure any number +of times. When pythia.init(...) is called these resonances +are initialized along with all the internal resonances, and treated in +exactly the same manner. See also the Program +Flow +description. + +

    +If the code should be of good quality and general usefulness, +it would be simple to include it as a permanently available process +in the standard program distribution. The final step of that integration +ought to be left for the PYTHIA authors, but basically all that is +needed is to add one line in +ParticleData::initResonances, where one creates an +instance of the resonance in the same way as for the resonances already +there. In addition, the particle data and decay table for the new +resonance has to be added to the permanent +particle database, and the code itself +to include/ResonanceWidths.h and +src/ResonanceWidths.cc. + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SettingsScheme.xml b/PYTHIA8/pythia8140/xmldoc/SettingsScheme.xml new file mode 100644 index 00000000000..655c9748ff9 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SettingsScheme.xml @@ -0,0 +1,420 @@ + + +

    The Settings Scheme

    + +The Settings class keeps track of all the flags, modes, +parameters and words used during the event generation. As such, it +serves all the Pythia program elements from one central +repository. Accessing it allows the user to modify the generator +behaviour. + +

    +Each Pythia object has a public member settings +of the Settings class. Therefore you access the +settings methods as pythia.settings.command(argument), +assuming that pythia is an instance of the Pythia +class. Further, for the most frequent user tasks, Pythia +methods have been defined, so that pythia.command(argument) +would work, see further below. + +

    +The central section on this page is the Operation one. The preceding +concepts section is there mainly to introduce the basic structure and +the set of properties that can be accessed. The subsequent sections +provide a complete listing of the existing public methods, which most +users probably will have little interaction with. + +

    Concepts

    + +We distinguish four kinds of user-modifiable variables, by the way +they have to be stored: +
      +
    1. Flags are on/off switches, and are stored as bool.
      2. +
    2. Modes corresponds to a finite enumeration of separate options, + and are stored as int.
      3. +
    3. Parameters take a continuum of values, and are stored as +double. The shorthand notation parm is used in the C++ +code and XML tags, so that all four kinds are represented by +four-letter type names.
      4. +
    4. Words are simple character strings and are stored as +string. No blanks or double quotation marks (") may +appear inside a word, the former to simplify parsing of an input file +and the latter not to cause conflicts with XML attribute delimiters. +Currently the main application is to store file names.
      5. +
    + +

    +In general, each variable stored in Settings is associated +with four kinds of information: +

      +
    • The variable name, of the form class:name +(or file:name, usually these agree), e.g. +TimeShower:pTmin. The class/file part usually identifies +the .xml file where the variable is defined, and the part of +the program where it is used, but such a connection cannot be strictly +upheld, since e.g. the same variable may be used in a few different +cases (even if most of them are not).
      • +
    • The default value, set in the original declaration, and intended +to represent a reasonable choice.
      • +
    • The current value, which differs from the default when the user so +requests.
      • +
    • An allowed range of values, represented by meaningful +minimum and maximum values. This has no sense for a flag +or a word (and is not used there), is usually rather +well-defined for a mode, but less so for a parm. +Often the allowed range exaggerates the degree of our current knowledge, +so as not to restrict too much what the user can do. One may choose +not to set the lower or upper limit, in which case the range is +open-ended.
      • +
    + +

    +Technically, the Settings class is implemented with the +help of four separate maps, one for each kind of variable, with the +variable name used as key. + +

    Operation

    + +The normal flow of setting values is: + +
      + +

    1. +When a Pythia object pythia is created, +the member pythia.settings is asked to scan the files +listed in the Index.xml file in the xmldoc +subdirectory. + +

      +In all of the files scanned, lines beginning with +<flag, <mode, <parm +or <word are identified, and the information on +such a line is used to define a new flag, mode, parameter or word. +To exemplify, consider a line +

      +<parm name="TimeShower:pTmin" default="0.5" min="0.1" max="2.0">
+
      +which appears in the TimeShower.xml file, and there +defines a parameter TimeShower:pTmin with default value +0.5 GeV and allowed variation in the range 0.1 - 2.0 GeV. The min +and max values are optional. +Important: the values in the .xml files should +not be changed, except by the PYTHIA authors. Any changes should be +done with the help of the methods described below. +
      2. + +

    2. +Between the creation of the Pythia object and the +init call for it, you may use several alternative +methods to modify some of the default values. + +

      +a) Inside your main program you can directly set values with +

      +    pythia.readString(string) 
+
      +where both the variable name and the value are contained inside +the character string, separated by blanks and/or a =, e.g. +
      +    pythia.readString("TimeShower:pTmin = 1.0"); 
+
      +The match of the name to the database is case-insensitive. Names +that do not match an existing variable are ignored. A warning is +printed, however. Strings beginning with a non-alphanumeric character, +like # or !, are assumed to be comments and are not processed at all. +Values below the minimum or above the maximum are set at +the respective border. For bool values, the following +notation may be used interchangeably: +true = on = yes = ok = 1, while everything else gives +false (including but not limited to +false, off, no and 0).
      + +

      +b) The Pythia readString(string) method +actually does not do changes itself, but sends on the string either +to the Settings class or to ParticleData. +The former holds if the string begins with a letter, the latter +if it begins with a digit. If desired, it is possible to communicate +directly with the corresponding Settings method: +

      +    pythia.settings.readString("TimeShower:pTmin = 1.0"); 
+
      +In this case, changes intended for ParticleData +would not be understood. + +

      +c) Underlying the settings.readString(string) method are +the settings-type-sensitive commands in the Settings, that +are split by names containing flag, mode, +parm or word. Thus, the example now reads +

      +    pythia.settings.parm("TimeShower:pTmin", 1.0); 
+
      +Such a form could be convenient e.g. if a parameter is calculated +at the beginning of the main program, and thus is available as a +variable rather than as a character string. +Note that Boolean values must here be given as true or +false i.e. there is less flexibility than with the +previous methods. + +

      +At the same level, there are several different methods available. +These are included in the full description below, but normally the user +should have no need for them. + +

      +d) A simpler and more useful way is to collect all your changes +in a separate file, with one line per change, e.g. +

      +    TimeShower:pTmin = 1.0
+
      +Each line is read in as a string and processed with the methods already +introduced. + +The file can be read by the +
      +    pythia.readFile(fileName); 
+
      +method (or an istream instead of a fileName). +The file can freely mix commands to the Settings and +ParticleData classes, and so is preferable. Lines with +settings are handled by calls to the +pythia.settings.readString(string) method. +
      3. + +

    3. +In the pythia.init(...) call, many of the various other program +elements are initialized, making use of the current values in the database. +Once initialized, the common Settings database is likely not +consulted again by these routines. It is therefore not productive to do +further changes in mid-run: at best nothing changes, at worst you may +set up inconsistencies. + +

      +A routine reInit(fileName) is provided, and can be used to +zero all the maps and reinitialize them from scratch. Such a call might be +useful if several subruns are to be made with widely different parameter +sets - normally the maps are only built from scratch once, namely when the +Pythia() object is created. A more economical alternative is +offered by resetAll(), however, which sets all variables back +to their default values. +

      4. + +

    4. +You may at any time obtain a listing of all variables in the +database by calling +
      +    pythia.settings.listAll();
+
      +The listing is strictly alphabetical, which at least means that names +from the same file are kept together, but otherwise may not be so +well-structured: important and unimportant ones will appear mixed. +A more relevant alternative is +
      +    pythia.settings.listChanged();
+
      +where you will only get those variables that differ from their +defaults. Or you can use +
      +    pythia.settings.list("string");
+
      +where only those variables with names that contain the string +(case-insensitive match) are listed. Thus, with a string +shower, the shower-related variables would be shown. +
      5. + +

    5. +The above listings are in a tabular form that cannot be read +back in. Assuming you want to save all changed settings (maybe because +you read in changes from several files), you can do that by calling +
      +    pythia.settings.writeFile(fileName);
+
      +This file could then directly be read in by +readFile(fileName) in a subsequent (identical) run. +Some variants of this command are listed below. +
      6. +
    + +

    Methods

    + +The complete list of methods and arguments is as follows. Most of the +ones of interest to the user have already been mentioned above. +Others can be used, but the same functionality is better achieved +by higher-level routines. Some are part of the internal machinery, +and should not be touched by user. + +

    +Note that there is no Settings::readFile(...) method. +The intention is that you should use Pythia::readFile(...). +It parses and decides which individual lines should be sent on to +Settings::readString(...). + + +the constructor, which takes no arguments. Internal. + + + +initialize pointer to error-message database. Internal. + + + +read in the settings database. + +read in the settings from all the files listed in this file, and +assumed to be located in the same subdirectory. + + +By default nothing is done if the method has already been called once. +If true the further settings read in are added to the current database. + + +stream for error printout. + +Note: The method returns false if it fails. + + + +overwrite the existing database. + +read in the settings from all the files listed in this file, and +assumed to be located in the same subdirectory. + + +stream for error printout. + +Note: The method returns false if it fails. + + + +read in a string, and change the relevant quantity in the database. +It is normally used indirectly, via +Pythia::readString(...) and +Pythia::readFile(...). + +the string to be interpreted as an instruction. + + +write a warning message or not whenever the instruction does not make +sense, e.g. if the variable does not exist in the databases. + + +stream for error printout. + +Note: the method returns false if it fails to +make sense out of the input string. + + + + + +write current settings to a file or to an ostream. + +file or stream on which settings are written. + + +normally only settings that have been changed are written, +but if true then all settings are output. + +Note: the method returns false if it fails. + + + + + + + +list all or changed settings, or a group of them. + +list all those settings where the name contains +the match (sub)string (case-insensitive). + + +output stream for the listing. + + + + +reset all current values to their defaults. + + + + + + + + + +return true if an entry of the given name and kind +exists, else false. + + + + + + + + + +add an entry of the respective kind to the database. The name and default +value always has to be supplied, for Mode and +Word additionally if lower and/or upper limits are to be +imposed and, if so, what those limit are. + + + + + + + + + +return the current value of the respective setting. If the name +does not exist in the database, a value false, +0, 0. and " " +is returned, respectively. + + + + + + + + + +change the current value of the respective setting to the provided +new value. If lower or upper limits have been set, input values +outside the allowed range are reinterpreted as being a the nearest +limit. + + + + + +as above, but do not check lower and upper limits, so that the current +value can be put outside the intended borders. + + + + + + + + + +reset the current value to the default one. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/SpacelikeShowers.xml b/PYTHIA8/pythia8140/xmldoc/SpacelikeShowers.xml new file mode 100644 index 00000000000..1d17567a254 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/SpacelikeShowers.xml @@ -0,0 +1,340 @@ + + +

    Spacelike Showers

    + +The PYTHIA algorithm for spacelike initial-state showers is +based on the recent article Sjo05, where a +transverse-momentum-ordered backwards evolution scheme is introduced. +This algorithm is a further development of the virtuality-ordered one +presented in Sj085, with matching to first-order matrix +element for Z^0, W^+- and Higgs (in the +m_t -> infinity limit) production as introduced in +Miu99. + +

    +The normal user is not expected to call SpaceShower +directly, but only have it called from Pythia, +via PartonLevel. Some of the parameters below, +in particular SpaceShower:alphaSvalue, +would be of interest for a tuning exercise, however. + +

    Main variables

    + +The maximum pT to be allowed in the shower evolution is +related to the nature of the hard process itself. It involves a +delicate balance between not doublecounting and not leaving any +gaps in the coverage. The best procedure may depend on information +only the user has: how the events were generated and mixed (e.g. with +Les Houches Accord external input), and how they are intended to be +used. Therefore a few options are available, with a sensible default +behaviour. + + +Way in which the maximum shower evolution scale is set to match the +scale of the hard process itself. + + + +Note 1: These options only apply to the hard interaction. +Emissions off subsequent multiple interactions are always constrainted +to be below the factorization scale of the process itself. +Note 2: Some processes contain matrix-element matching +to the first emission; this is the case notably for single +gamma^*/Z^0, W^+- and H^0 production. Then default +and option 2 give the correct result, while option 1 should never +be used. + + + +In cases where the above pTmaxMatch rules would imply +that pT_max = pT_factorization, pTmaxFudge +introduces a multiplicative factor f such that instead +pT_max = f * pT_factorization. Only applies to the hardest +interaction in an event, cf. below. It is strongly suggested that +f = 1, but variations around this default can be useful to +test this assumption. + + + +A multiplicative factor f such that +pT_max = f * pT_factorization, as above, but here for the +non-hardest interactions (when multiple interactions are allowed). + + + +These options only take effect when a process is allowed to radiate up +to the kinematical limit by the above pTmaxMatch choice, +and no matrix-element corrections are available. Then, in many processes, +the fall-off in pT will be too slow by one factor of pT^2. +That is, while showers have an approximate dpT^2/pT^2 shape, often +it should become more like dpT^2/pT^4 at pT values above +the scale of the hard process. Whether this actually is the case +depends on the particular process studied, e.g. if t-channel +gluon exchange is likely to dominate. If so, the options below could +provide a reasonable high-pT behaviour without requiring +higher-order calculations. + + + +Note: These options only apply to the hard interaction. +Emissions off subsequent multiple interactions are always constrainted +to be below the factorization scale of the process itself. + + + +In cases 1 and 2 above, where a dampening is imposed at around the +factorization or renormalization scale, respectively, this allows the +pT scale of dampening of radiation by a half to be shifted +by this factor relative to the default Q_fac or Q_ren. +This number ought to be in the neighbourhood of unity, but variations +away from this value could do better in some processes. + + +

    +The amount of QCD radiation in the shower is determined by + +The alpha_strong value at scale M_Z^2. +Default value is picked equal to the one used in CTEQ 5L. + + +

    +The actual value is then regulated by the running to the scale +pT^2, at which it is evaluated + +Order at which alpha_strong runs, + + + + + +

    +QED radiation is regulated by the alpha_electromagnetic +value at the pT^2 scale of a branching. + + +The running of alpha_em. + + + + + +

    +There are two complementary ways of regularizing the small-pT +divergence, a sharp cutoff and a smooth dampening. These can be +combined as desired but it makes sense to coordinate with how the +same issue is handled in multiple interactions. + + +Regularize the pT -> 0 divergence using the same sharp cutoff +and smooth dampening parameters as used to describe multiple interactions. +That is, the MultipleInteractions:pT0Ref, +MultipleInteractions:ecmRef, +MultipleInteractions:ecmPow and +MultipleInteractions:pTmin parameters are used to regularize +all ISR QCD radiation, rather than the corresponding parameters below. +This is a sensible physics ansatz, based on the assumption that colour +screening effects influence both MI and ISR in the same way. Photon +radiation is regularized separately in either case. +Warning: if a large pT0 is picked for multiple +interactions, such that the integrated interaction cross section is +below the nondiffractive inelastic one, this pT0 will +automatically be scaled down to cope. Information on such a rescaling +does NOT propagate to SpaceShower, however. + + +

    +The actual pT0 parameter used at a given CM energy scale, +ecmNow, is obtained as + + pT0 = pT0(ecmNow) = pT0Ref * (ecmNow / ecmRef)^ecmPow + +where pT0Ref, ecmRef and ecmPow are the +three parameters below. + + +Regularization of the divergence of the QCD emission probability for +pT -> 0 is obtained by a factor pT^2 / (pT0^2 + pT^2), +and by using an alpha_s(pT0^2 + pT^2). An energy dependence +of the pT0 choice is introduced by the next two parameters, +so that pT0Ref is the pT0 value for the reference +cm energy, pT0Ref = pT0(ecmRef). + + + +The ecmRef reference energy scale introduced above. + + + +The ecmPow energy rescaling pace introduced above. + + + +Lower cutoff in pT, below which no further ISR branchings +are allowed. Normally the pT0 above would be used to +provide the main regularization of the branching rate for +pT -> 0, in which case pTmin is used mainly for +technical reasons. It is possible, however, to set pT0Ref = 0 +and use pTmin to provide a step-function regularization, +or to combine them in intermediate approaches. Currently pTmin +is taken to be energy-independent. + + + +Parton shower cut-off pT for photon coupling to a coloured +particle. + + + +Parton shower cut-off mass for pure QED branchings. +Assumed smaller than (or equal to) pTminChgQ. + + + +Force emissions, after the first, to be ordered in rapidity, +i.e. in terms of decreasing angles in a backwards-evolution sense. +Could be used to probe sensitivity to unordered emissions. +Only affects QCD emissions. + + +

    Further variables

    + +These should normally not be touched. Their only function is for +cross-checks. + +

    +There are three flags you can use to switch on or off selected +branchings in the shower: + + +Allow a QCD shower; on/off = true/false. + + + +Allow quarks to radiate photons; on/off = true/false. + + + +Allow leptons to radiate photons; on/off = true/false. + + +

    +There are three further possibilities to simplify the shower: + + +Use of matrix element corrections; on/off = true/false. + + + +Azimuthal asymmetry induced by gluon polarization; on/off = true/false. + + + +Azimuthal asymmetry induced by interference; on/off = true/false. + + + +Size of asymmetry induced by interference. Natural value of order 0.5; +expression would blow up for a value of 1. + + + +Number of allowed quark flavours in g -> q qbar branchings, +when kinematically allowed, and thereby also in incoming beams. +Changing it to 4 would forbid g -> b bbar, etc. + + +

    Technical notes

    + +Almost everything is equivalent to the algorithm in [1]. Minor changes +are as follows. +
      +
    • +It is now possible to have a second-order running alpha_s, +in addition to fixed or first-order running. +
      • +
    • +The description of heavy flavour production in the threshold region +has been modified, so as to be more forgiving about mismatches +between the c/b masses used in Pythia relative to those +used in a respective PDF parametrization. The basic idea is that, +in the threshold region of a heavy quark Q, Q = c/b, +the effect of subsequent Q -> Q g branchings is negligible. +If so, then + + f_Q(x, pT2) = integral_mQ2^pT2 dpT'2/pT'2 * alpha_s(pT'2)/2pi + * integral P(z) g(x', pT'2) delta(x - z x') + +so use this to select the pT2 of the g -> Q Qbar +branching. In the old formalism the same kind of behaviour should +be obtained, but by a cancellation of a 1/f_Q that diverges +at the theshold and a Sudakov that vanishes. +
      +The strategy therefore is that, once pT2 < f * mQ2, with +f a parameter of the order of 2, a pT2 is chosen +like dpT2/pT2 between mQ2 and f * mQ2, a +nd a z flat in the allowed range. Thereafter acceptance +is based on the product of three factors, representing the running +of alpha_strong, the splitting kernel (including the mass term) +and the gluon density weight. At failure, a new pT2 is chosen +in the same range, i.e. is not required to be lower since no Sudakov +is involved. +
      • +
    • +The QED algorithm now allows for hadron beams with non-zero photon +content. The backwards-evolution of a photon in a hadron is identical +to that of a gluon, with CF -> eq^2 and CA -> 0. +Note that this will only work in conjunction with +parton distribution that explicitly include photons as part of the +hadron structure (such as the MRST2004qed set). Since Pythia's +internal sets do not allow for photon content in hadrons, it is thus +necessary to use the LHAPDF interface to make use of this feature. The +possibility of a fermion backwards-evolving to a photon has not yet +been included, nor has photon backwards-evolution in lepton beams. +
      • +
    + +     + + + diff --git a/PYTHIA8/pythia8140/xmldoc/StandardModelParameters.xml b/PYTHIA8/pythia8140/xmldoc/StandardModelParameters.xml new file mode 100644 index 00000000000..e997ae173b8 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/StandardModelParameters.xml @@ -0,0 +1,285 @@ + + +

    Standard-Model Parameters

    + +

    The strong coupling

    + +The AlphaStrong class is used to provide a first- or +second-order running alpha_strong (or, trivially, a +zeroth-order fixed one). Formulae are the standard ones found in +Yao06. The second-order expression used, eq. (9.5), +may be somewhat different in other approaches (with differences +formally of higher order), so do not necessarily expect perfect +agreement, especially not at small Q^2 scales. The starting +alpha_strong value is defined at the M_Z mass scale. +The Lambda values are matched at the b and c +flavour thresholds, such that alpha_strong is continuous. +For second-order matching an approximate iterative method is used. + +

    +Since we allow alpha_strong to vary separately for +hard processes, timelike showers, spacelike showers and multiple +interactions, the relevant values can be set in each of these classes. +The default behaviour is everywhere first-order running. + +

    +The alpha_strong calculation is initialized by +init( value, order), where value +is the alpha_strong value at M_Z and order +is the order of the running, 0, 1 or 2. Thereafter the value can be +calculated by alphaS(scale2), where +scale2 is the Q^2 scale in GeV^2. + +

    +For applications inside shower programs, a second-order alpha_s +value can be obtained as the product of the two functions +alphaS1Ord(scale2) and alphaS2OrdCorr(scale2), +where the first gives a simple first-order running (but with the +second-order Lambda) and the second the correction factor, +below unity, for the second-order terms. This allows a compact handling +of evolution equations. + +

    The electromagnetic coupling

    + +The AlphaEM class is used to generate a running +alpha_em. The input StandardModel:alphaEMmZ +value at the M_Z mass is matched to a low-energy behaviour +with running starting at the electron mass threshold. The matching +is done by fitting an effective running coefficient in the region +betweeen the light-quark treshold and the charm/tau threshold. This +procedure is approximate, but good enough for our purposes. + +

    +Since we allow alpha_em to vary separately for +hard processes, timelike showers, spacelike showers and multiple +interactions, the choice between using a fixed or a running +alpha_em can be made in each of these classes. +The default behaviour is everywhere first-order running. +The actual values assumed at zero momentum transfer and +at M_Z are only set here, however. + + +The alpha_em value at vanishing momentum transfer +(and also below m_e). + + + +The alpha_em value at the M_Z mass scale. +Default is taken from Yao06. + + +

    +The alpha_em calculation is initialized by +init(order), where order is the order of +the running, 0 or 1, with -1 a special option to use the fix value +provided at M_Z. Thereafter the value can be +calculated by alphaEM(scale2), where +scale2 is the Q^2 scale in GeV^2. + +

    The electroweak couplings

    + +There are two degrees of freedom that can be set, related to the +electroweak mixing angle: + + +The sine-squared of the weak mixing angle, as used in all Z^0 +and W^+- masses and couplings, except for the vector couplings +of fermions to the Z^0, see below. Default is the MSbar value +from Yao06. + + + +The sine-squared of the weak mixing angle, as used to derive the vector +couplings of fermions to the Z^0, in the relation +v_f = a_f - 4 e_f sin^2(theta_W)bar. Default is the +effective-angle value from Yao06. + + +

    The quark weak-mixing matrix

    + +The absolute values of the Cabibbo-Kobayashi-Maskawa matrix elements are +set by the following nine real values taken from Yao06 - +currently the CP-violating phase is not taken into account in this +parametrization. It is up to the user to pick a consistent unitary +set of new values whenever changes are made. + + +The V_ud CKM matrix element. + + + +The V_us CKM matrix element. + + + +The V_ub CKM matrix element. + + + +The V_cd CKM matrix element. + + + +The V_cs CKM matrix element. + + + +The V_cb CKM matrix element. + + + +The V_td CKM matrix element. + + + +The V_ts CKM matrix element. + + + +The V_tb CKM matrix element. + + +

    The CoupSM class

    + +The Pythia class contains a +public instance coupSM of the CoupSM class. +This class contains one instance each of the AlphaStrong +and AlphaEM classes, and additionally stores the weak couplings +and the quark mixing matrix mentioned above. This class is used especially +in the calculation of cross sections and resonance widths, but could also +be used elsewhere. Specifically, as already mentioned, there are separate +AlphaStrong and AlphaEM instances for timelike +and spacelike showers and for multiple interactions, while weak couplings +and the quark mixing matrix are only stored here. With the exception of the +first two methods below, which are for internal use, the subsequent ones +could also be used externally. + + +the constructor does nothing. Internal. + + + +this is where the AlphaStrong and AlphaEM +instances are initialized, and weak couplings and the quark mixing matrix +are read in and set. This is based on the values stored on this page and +among the Couplings and Scales. +Internal. + + + +the alpha_strong value at the quadratic scale scale2. + + + +a first-order overestimate of the full second-order alpha_strong +value at the quadratic scale scale2. + + + +a multiplicative correction factor, below unity, that brings the +first-order overestimate above into agreement with the full second-order +alpha_strong value at the quadratic scale scale2. + + + + + + + +the three-, four-, and five-flavour Lambda scale. + + + +the alpha_em value at the quadratic scale scale2. + + + + + +the sine-squared and cosine-squared of the weak mixing angle, as used in +the gauge-boson sector. + + + +the sine-squared of the weak mixing angle, as used to derive the vector +couplings of fermions to the Z^0. + + + +the electrical charge of a fermion, by the absolute sign of the PDF code, +i.e. idAbs must be in the range between 1 and 18. + + + + + +the vector and axial charges of a fermion, by the absolute sign of the PDF +code (a_f = +-1, v_f = a_f - 4. * sin2thetaWbar * e_f). + + + + + + + +the weak isospin, left- and righthanded charges of a fermion, by the +absolute sign of the PDF code (t^3_f = a_f/2, l_f = (v_f + a_f)/2, +r_f = (v_f - a_f)/2; you may find other conventions in the literature +that differ by a factor of 2). + + + + + + + + + + + +common quadratic combinations of the above couplings: +e_f^2, v_f^2, a_f^2, e_f * v_f, v_f^2 + a_f^2. + + + + + +the CKM mixing element,or the square of it, for +up-type generation index genU +(1 = u, 2 = c, 3 = t, 4 = t') and +down-type generation index genD +(1 = d, 2 = s, 3 = b, 4 = b'). + + + + + +the CKM mixing element,or the square of it, for +flavours id1 and id2, both in the +range from -18 to +18. The sign is here not +checked (so it can be used both for u + dbar -> W+ +and u -> d + W+, say), but impossible flavour combinations +evaluate to zero. The neutrino sector is numbered by flavor +eigenstates, so there is no mixing in the lepton-neutrino system. + + + +the sum of squared CKM mixing element that a given flavour can couple to, +excluding the top quark and fourth generation. Is close to unity +for the first two generations. Returns unity for the lepton-neutrino +sector. + + + +picks a random CKM partner quark or lepton (with the same sign as +id) according to the respective squared elements, again +excluding the top quark and fourth generation from the list of +possibilities. Unambiguous choice for the lepton-neutrino sector. + + +     + + diff --git a/PYTHIA8/pythia8140/xmldoc/TimelikeShowers.xml b/PYTHIA8/pythia8140/xmldoc/TimelikeShowers.xml new file mode 100644 index 00000000000..5cf03552c22 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/TimelikeShowers.xml @@ -0,0 +1,424 @@ + + +

    Timelike Showers

    + +The PYTHIA algorithm for timelike final-state showers is based on +the recent article Sjo05, where a transverse-momentum-ordered +evolution scheme is introduced. This algorithm is influenced by +the previous mass-ordered algorithm in PYTHIA Ben87 and by +the dipole-emission formulation in Ariadne Gus86. From the +mass-ordered algorithm it inherits a merging procedure for first-order +gluon-emission matrix elements in essentially all two-body decays +in the standard model and its minimal supersymmetric extension +Nor01. + +

    +The normal user is not expected to call TimeShower directly, +but only have it called from Pythia. Some of the parameters +below, in particular TimeShower:alphaSvalue, would be of +interest for a tuning exercise, however. + +

    Main variables

    + +Often the maximum scale of the FSR shower evolution is understood from the +context. For instance, in a resonace decay half the resonance mass sets an +absolute upper limit. For a hard process in a hadronic collision the choice +is not as unique. Here the factorization +scale has been chosen as the maximum evolution scale. This would be +the pT for a 2 -> 2 process, supplemented by mass terms +for massive outgoing particles. For some special applications we do allow +an alternative. + + +Way in which the maximum shower evolution scale is set to match the +scale of the hard process itself. + + + +Note: These options only apply to the hard interaction. +Emissions off subsequent multiple interactions are always constrainted +to be below the factorization scale of the process itself. They also +assume you use interleaved evolution, so that FSR is in direct +competition with ISR for the hardest emission. If you already +generated a number of ISR partons at low pT, it would not +make sense to have a later FSR shower up to the kinematical for all +of them. + + + +In cases where the above pTmaxMatch rules would imply +that pT_max = pT_factorization, pTmaxFudge +introduces a multiplicative factor f such that instead +pT_max = f * pT_factorization. Only applies to the hardest +interaction in an event, cf. below. It is strongly suggested that +f = 1, but variations around this default can be useful to +test this assumption. +Note:Scales for resonance decays are not affected, but can +be set separately by user hooks. + + + +A multiplicative factor f such that +pT_max = f * pT_factorization, as above, but here for the +non-hardest interactions (when multiple interactions are allowed). + + + +These options only take effect when a process is allowed to radiate up +to the kinematical limit by the above pTmaxMatch choice, +and no matrix-element corrections are available. Then, in many processes, +the fall-off in pT will be too slow by one factor of pT^2. +That is, while showers have an approximate dpT^2/pT^2 shape, often +it should become more like dpT^2/pT^4 at pT values above +the scale of the hard process. This argument is more obvious for ISR, +but is taken over unchanged for FSR to have a symmetric description. + + + +Note: These options only apply to the hard interaction. +Emissions off subsequent multiple interactions are always constrainted +to be below the factorization scale of the process itself. + + + +In cases 1 and 2 above, where a dampening is imposed at around the +factorization or renormalization scale, respectively, this allows the +pT scale of dampening of radiation by a half to be shifted +by this factor relative to the default Q_fac or Q_ren. +This number ought to be in the neighbourhood of unity, but variations +away from this value could do better in some processes. + + +

    +The amount of QCD radiation in the shower is determined by + +The alpha_strong value at scale M_Z^2. The default +value corresponds to a crude tuning to LEP data, to be improved. + + +

    +The actual value is then regulated by the running to the scale +pT^2, at which the shower evaluates alpha_strong + + +Order at which alpha_strong runs, + + + + + +

    +QED radiation is regulated by the alpha_electromagnetic +value at the pT^2 scale of a branching. + + +The running of alpha_em. + + + + + +

    +The rate of radiation if divergent in the pT -> 0 limit. Here, +however, perturbation theory is expected to break down. Therefore an +effective pT_min cutoff parameter is introduced, below which +no emissions are allowed. The cutoff may be different for QCD and QED +radiation off quarks, and is mainly a technical parameter for QED +radiation off leptons. + + +Parton shower cut-off pT for QCD emissions. + + + +Parton shower cut-off pT for photon coupling to coloured particle. + + + +Parton shower cut-off pT for pure QED branchings. +Assumed smaller than (or equal to) pTminChgQ. + + +

    +Shower branchings gamma -> f fbar, where f is a +quark or lepton, in part compete with the hard processes involving +gamma^*/Z^0 production. In order to avoid overlap it makes +sense to correlate the maximum gamma mass allowed in showers +with the minumum gamma^*/Z^0 mass allowed in hard processes. +In addition, the shower contribution only contains the pure +gamma^* contribution, i.e. not the Z^0 part, so +the mass spectrum above 50 GeV or so would not be well described. + + +Maximum invariant mass allowed for the created fermion pair in a +gamma -> f fbar branching in the shower. + + +

    Interleaved evolution

    + +Multiple interactions (MI) and initial-state showers (ISR) are +always interleaved, as follows. Starting from the hard interaction, +the complete event is constructed by a set of steps. In each step +the pT scale of the previous step is used as starting scale +for a downwards evolution. The MI and ISR components each make +their respective Monte Carlo choices for the next lower pT +value. The one with larger pT is allowed to carry out its +proposed action, thereby modifying the conditions for the next steps. +This is relevant since the two components compete for the energy +contained in the beam remnants: both an interaction and an emission +take avay some of the energy, leaving less for the future. The end +result is a combined chain of decreasing pT values, where +ones associated with new interactions and ones with new emissions +are interleaved. + +

    +There is no corresponding requirement for final-state radiation (FSR) +to be interleaved. Such an FSR emission does not compete directly for +beam energy (but see below), and also can be viewed as occuring after +the other two components in some kind of time sense. Interleaving is +allowed, however, since it can be argued that a high-pT FSR +occurs on shorter time scales than a low-pT MI, say. +Backwards evolution of ISR is also an example that physical time +is not the only possible ordering principle, but that one can work +with conditional probabilities: given the partonic picture at a +specific pT resolution scale, what possibilities are open +for a modified picture at a slightly lower pT scale, either +by MI, ISR or FSR? Complete interleaving of the three components also +offers advantages if one aims at matching to higher-order matrix +elements above some given scale. + + +If on, final-state emissions are interleaved in the same +decreasing-pT chain as multiple interactions and initial-state +emissions. If off, final-state emissions are only addressed after the +multiple interactions and initial-state radiation have been considered. + + +

    +As an aside, it should be noted that such interleaving does not affect +showering in resonance decays, such as a Z^0. These decays are +only introduced after the production process has been considered in full, +and the subsequent FSR is carried out inside the resonance, with +preserved resonance mass. + +

    +One aspect of FSR for a hard process in hadron collisions is that often +colour diples are formed between a scattered parton and a beam remnant, +or rather the hole left behind by an incoming partons. If such holes +are allowed as dipole ends and take the recoil when the scattered parton +undergoes a branching then this translates into the need to take some +amount of remnant energy also in the case of FSR, i.e. the roles of +ISR and FSR are not completely decoupled. The energy taken away is +bokkept by increasing the x value assigned to the incoming +scattering parton, and a reweighting factor +x_new f(x_new, pT^2) / x_old f(x_old, pT^2) +in the emission probability ensures that not unphysically large +x_new values are reached. Usually such x changes are +small, and they can be viewed as a higher-order effect beyond the +accuracy of the leading-log initial-state showers. + +

    +This choice is not unique, however. As an alternative, if nothing else +useful for cross-checks, one could imagine that the FSR is completely +decoupled from the ISR and beam remnants. + + +If on, the final-state shower is allowed to borrow energy from +the beam remnants as described above, thereby changing the mass of the +scattering subsystem. If off, the partons in the scattering subsystem +are constrained to borrow energy from each other, such that the total +four-momentum of the system is preserved. This flag has no effect +on resonance decays, where the shower always preserves the resonance +mass, cf. the comment above about showers for resonances never being +interleaved. + + + +When beam recoil is allowed there is still some ambiguity how far +into the beam end of the dipole that emission should be allowed. +It is dampened in the beam region, but probably not enough. +When on an additional suppression factor +4 pT2_hard / (4 pT2_hard + m2) is multiplied on to the +emission probability. Here pT_hard is the transverse momentum +of the radiating parton and m the off-shell mass it acquires +by the branching, m2 = pT2/(z(1-z)). Note that +m2 = 4 pT2_hard is the kinematical limit for a scattering +at 90 degrees without beam recoil. + + +

    Radiation off octet onium states

    + +In the current implementation, charmonium and bottomonium production +can proceed either through colour singlet or colour octet mechanisms, +both of them implemented in terms of 2 -> 2 hard processes +such as g g -> (onium) g. +In the former case the state does not radiate and the onium therefore +is produced in isolation, up to normal underlying-event activity. In +the latter case the situation is not so clear, but it is sensible to +assume that a shower can evolve. (Assuming, of course, that the +transverse momentum of the onium state is sufficiently high that +radiation is of relevance.) + +

    +There could be two parts to such a shower. Firstly a gluon (or even a +quark, though less likely) produced in a hard 2 -> 2 process +can undergo showering into many gluons, whereof one branches into the +heavy-quark pair. Secondly, once the pair has been produced, each quark +can radiate further gluons. This latter kind of emission could easily +break up a semibound quark pair, but might also create a new semibound +state where before an unbound pair existed, and to some approximation +these two effects should balance in the onium production rate. +The showering "off an onium state" as implemented here therefore should +not be viewed as an accurate description of the emission history +step by step, but rather as an effective approach to ensure that the +octet onium produced "in the hard process" is embedded in a realistic +amount of jet activity. +Of course both the isolated singlet and embedded octet are likely to +be extremes, but hopefully the mix of the two will strike a reasonable +balance. However, it is possible that some part of the octet production +occurs in channels where it should not be accompanied by (hard) radiation. +Therefore reducing the fraction of octet onium states allowed to radiate +is a valid variation to explore uncertainties. + +

    +If an octet onium state is chosen to radiate, the simulation of branchings +is based on the assumption that the full radiation is provided by an +incoherent sum of radiation off the quark and off the antiquark of the +onium state. Thus the splitting kernel is taken to be the normal +q -> q g one, multiplied by a factor of two. Obviously this is +a simplification of a more complex picture, averaging over factors pulling +in different directions. Firstly, radiation off a gluon ought +to be enhanced by a factor 9/4 relative to a quark rather than the 2 +now used, but this is a minor difference. Secondly, our use of the +q -> q g branching kernel is roughly equivalent to always +following the harder gluon in a g -> g g branching. This could +give us a bias towards producing too hard onia. A soft gluon would have +little phase space to branch into a heavy-quark pair however, so the +bias may not be as big as it would seem at first glance. Thirdly, +once the gluon has branched into a quark pair, each quark carries roughly +only half of the onium energy. The maximum energy per emitted gluon should +then be roughly half the onium energy rather than the full, as it is now. +Thereby the energy of radiated gluons is exaggerated, i.e. onia become too +soft. So the second and the third points tend to cancel each other. + +

    +Finally, note that the lower cutoff scale of the shower evolution depends +on the onium mass rather than on the quark mass, as it should be. Gluons +below the octet-onium scale should only be part of the octet-to-singlet +transition. + + +Allow colour-octet charmonium and bottomonium states to radiate gluons. +0 means that no octet-onium states radiate, 1 that all do, with possibility +to interpolate between these two extremes. + + + +The colour factor used used in the splitting kernel for those octet onium +states that are allowed to radiate, normalized to the q -> q g +splitting kernel. Thus the default corresponds to twice the radiation +off a quark. The physically preferred range would be between 1 and 9/4. + + +

    Further variables

    + +There are several possibilities you can use to switch on or off selected +branching types in the shower, or in other respects simplify the shower. +These should normally not be touched. Their main function is for +cross-checks. + + +Allow a QCD shower, i.e. branchings q -> q g, g -> g g +and g -> q qbar; on/off = true/false. + + + +Number of allowed quark flavours in g -> q qbar branchings +(phase space permitting). A change to 4 would exclude +g -> b bbar, etc. + + + +Allow quarks to radiate photons, i.e. branchings q -> q gamma; +on/off = true/false. + + + +Allow leptons to radiate photons, i.e. branchings l -> l gamma; +on/off = true/false. + + + +Allow photons to branch into lepton or quark pairs, i.e. branchings +gamma -> l+ l- and gamma -> q qbar; +on/off = true/false. + + + +Number of allowed quark flavours in gamma -> q qbar branchings +(phase space permitting). A change to 4 would exclude +g -> b bbar, etc. + + + +Number of allowed lepton flavours in gamma -> l+ l- branchings +(phase space permitting). A change to 2 would exclude +gamma -> tau+ tau-, and a change to 1 also +gamma -> mu+ mu-. + + + +Use of matrix element corrections where available; on/off = true/false. + + + +Azimuthal asymmetry induced by gluon polarization; on/off = true/false. + + +     + + diff --git a/PYTHIA8/pythia8140/xmldoc/TopProcesses.xml b/PYTHIA8/pythia8140/xmldoc/TopProcesses.xml new file mode 100644 index 00000000000..d35e5d40722 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/TopProcesses.xml @@ -0,0 +1,48 @@ + + +

    Top Processes

    + +Different ways to produce top quarks, singly or in pairs. + + +Common switch for the group of top production. + + + +Scatterings g g -> t tbar. +Code 601. + + + +Scatterings q qbar -> t tbar by gluon exchange. +Code 602. + + + +Scatterings q q' -> t q'' by t-channel exchange +of a W^+- boson. +Code 603. + + + +Scatterings f fbar -> t tbar by s-channel exchange +of a gamma^*/Z^0 boson. +Code 604. + + + +Scatterings f fbar' -> t q'' by s-channel exchange +of a W^+- boson. +Code 605. + + + +Scatterings gamma gamma -> t tbar. +Code 606. + + + +     + + + diff --git a/PYTHIA8/pythia8140/xmldoc/TotalCrossSections.xml b/PYTHIA8/pythia8140/xmldoc/TotalCrossSections.xml new file mode 100644 index 00000000000..03d1778653f --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/TotalCrossSections.xml @@ -0,0 +1,161 @@ + + +

    Total Cross Sections

    + +The SigmaTotal class returns the total, elastic, diffractive +and nondiffractive cross sections in hadronic collisions, and also the +slopes of the d(sigma)/dt distributions. The parametrizations +used are from Sch94, Sch97 which borrows some of the total cross +sections from Don92. + +

    +There are strong indications that the currently implemented diffractive +cross section parametrizations, which should be in reasonable agreement +with data at lower energies, overestimate the diffractive rate at larger +values. If you wish to explore this (or other) aspect, it is possible to +override the cross section values in two different ways. The first offers +(almost) complete freedom, but needs to be defined separately for each +CM energy, while the second introduces a simpler parametrized damping. +The two cannot be combined. Furthermore the Coulomb term for elastic +scattering, which by default is off, can be switched on. + +

    +The allowed combinations of incoming particles are p + p, +pbar + p, pi+ + p, pi- + p, +pi0/rho0 + p, phi + p, J/psi + p, +rho + rho, rho + phi, rho + J/psi, +phi + phi, phi + J/psi, J/psi + J/psi. +The strong emphasis on vector mesons is related to the description +of gamma + p and gamma + gamma interactions in a +Vector Dominance Model framework (which will not be available for some +time to come, so this is a bit of overkill). Nevertheless, the sections +below, with allowed variations, are mainly intended to make sense for +p + p. + +

    Set cross sections

    + + +Allow a user to set own cross sections by hand; on/off = true/false. + + +

    +When SigmaTotal:setOwn = on, the user is expected to set +values for the corresponding cross sections: + + +Total cross section in mb. + + + +Elastic cross section in mb. + + + +Single Diffractive cross section A + B -> X + B in mb. + + + +Single Diffractive cross section A + B -> A + X in mb. + + + +Double Diffractive cross section A + B -> X_1 + X_2 in mb. + + +

    +Note that the total cross section subtracted by the elastic and various +diffractive ones gives the inelastic nondiffractive cross section, +which therefore is not set separately. If this cross section evaluates +to be negative the internal parametrizations are used instead of the +ones here. However, since the nondiffractive inelastic cross section +is what makes up the minimum-bias event class, and plays a major role +in the description of multiple interactions, it is important that a +consistent set is used. + +

    Dampen diffractive cross sections

    + + +Allow a user to dampen diffractive cross sections; on/off = true/false. + + +

    +When SigmaDiffractive:dampen = on, the three diffractive +cross sections are damped so that they never can exceed the respective +values below. Specifically, if the standard parametrization gives +the cross section sigma_old(s) and a fixed sigma_max +is set, the actual cross section becomes sigma_new(s) += sigma_old(s) * sigma_max / (sigma_old(s) + sigma_max). +This reduces to sigma_old(s) at low energies and to +sigma_max at high ones. Note that the asymptotic value +is approached quite slowly, however. + + +The above sigma_max for A + B -> X + B in mb. + + + +The above sigma_max for A + B -> X + B in mb. + + + +The above sigma_max for A + B -> X + B in mb. + + +

    +As above, a reduced diffractive cross section automatically translates +into an increased nondiffractive one, such that the total (and elastic) +cross section remains fixed. + + +

    Set elastic cross section

    + +

    +In the above option the t slopes are based on the internal +parametrizations. In addition there is no Coulomb-term contribution +to the elastic (or total) cross section, which of course becomes +infinite if this contribution is included. If you have switched on +SigmaTotal:setOwn you can further switch on a machinery +to include the Coulomb term, including interference with the conventional +strong-interaction Pomeron one Ber87. Then the elastic cross +section is no longer taken from SigmaTotal:sigmaEl but +derived from the parameters below and SigmaTotal:sigmaTot, +using the optical theorem. The machinery is only intended to be used for +p p and pbar p collisions. The description of +diffractive events, and especially their slopes, remains unchanged. + + +Allow a user to set parameters for the normalization and shape of the +elastic cross section the by hand; yes/no = true/false. + + + +the slope b of the strong-interaction term exp(bt), +in units of GeV^-2. + + + +the ratio of the real to the imaginary parts of the nuclear scattering +amplitude. + + + +the main parameter of the electric form factor +G(t) = lambda^2 / (lambda + |t|)^2, in units of GeV^2. + + + +since the Coulomb contribution is infinite a lower limit on +|t| must be set to regularize the divergence, +in units of GeV^2. + + + +The Coulomb term is taken to contain a phase factor +exp(+- i alpha phi(t)), with + for p p and - for +pbar p, where phi(t) = - phaseConst - ln(-B t/2). +This constant is model dependent Cah82. + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/Tunes.xml b/PYTHIA8/pythia8140/xmldoc/Tunes.xml new file mode 100644 index 00000000000..2ad10ceb9d7 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Tunes.xml @@ -0,0 +1,168 @@ + + +

    Tunes

    + +Since some physics aspects cannot be derived from first principles, +this program contains many parameters that represent a true +uncertainty in our understanding of nature. Particularly afflicted +are the areas of hadronization and multiple interactions, which both +involve nonperturbative QCD physics. + +

    +Technically, PYTHIA parameters can be varied independently of each +other, but the physical requirement of a sensible description of a set +of data leads to correlations and anticorrelations between the +parameters. Hence the need to produce tunes, not of one parameter at +a time, but simultaneously for a group of them. A well-known such +example is parton densities, where combined tunes to a wide range of data +have been produced, that can then be obtained prepackaged. + +

    +Given the many PYTHIA parameters to be tuned, it is convenient to +divide the task into subtasks. Firstly, if we assume jet universality, +hadronization and final-state parton showers should be tuned to +e^+e^- annihilation data, notably from LEP1, since this +offers the cleanest environment. Secondly, with such parameters fixed, +hadron collider data should be studied to pin down multiple interactions +and other further aspects, such as initial-state radiation. Ideally this +would be done separately for diffractive and non-diffractive events, +although it is not possible to have a clean separation. (Thirdly +would come anything else, such as physics with photon beams, which +involve further parameters, but that is beyond the current scope.) + +

    +The first step in this program has now been taken, with a tune to LEP1 +data by Hendrik Hoeth, using the Rivet + Professor framework. Starting +with version 8.125 it defines the default values for hadronization +parameters and timelike showers. + +

    +The situation is worse for multiple interactions, where PYTHIA 8 is more +different from PYTHIA 6. Nevertheless, a first simple tune is now +available, appropriately called "Tune 1", and became default starting with +version 8.127. + +

    +It was noted, in particular by Hendrik Hoeth, that the +program had a tension between parameters needed to describe minimum-bias +and underlying-event activity. Therefore some further physics features +have been introduced in the code itself, which are made default as of +8.140. This version also includes two new draft tunes, 2C and 2M, based +on the CTEQ 6L1 and the MRST LO** PDF sets, respectively. These have been +made by hand, as a prequel to complete Professor-style tunings. + +

    +The very first data to come out of the LHC shows a higher rapidity plateau +than predicted for current PYTHIA 6 tunes, also for the lower energies. +This may suggest some tension in the data. Therefore two alternatives, +3C and 3M, have been produced by a few brute-force changes of 2C and 2M. +This includes a reduced admixture of diffractive topologies and a steeper +multiplicity variation with energy. + +

    +In the future we hope to see further PYTHIA 8 tunes appear. Like with +parton distributions, there is likely to be several tunes, because +different sets of data will pull in different directions, by imperfections +in the model or in the data, and by differences in the chosen +tuning strategies. We therefore propose to collect some of these tunes +here, in a prepackaged form. Of course, in all cases it is a matter +of setting values for parameters already defined elsewhere, so the +tunes offer no new functionality, only a more convenient setup. + +

    +You should be aware that the evolution of the program will not guarantee +complete backwards compatibility between versions. Most obviously this +concerns bug fixes. But also for some other major changes, like the +introduction of the new diffractive machinery, the default behaviour +of old tunes has been changed retroactively. (Which should be fine for +diffraction, since previous tunes were not based on data strongly +influenced by diffraction.) + +

    +If you set either the Tune:ee and Tune:pp +modes below non-zero then all parameters used in the respective tune +will be set accordingly when pythia.init(...) is called. +You can check this by calling pythia.settings.listChanged() +before and after initialization; before only the tune modes are +nondefault, afterwards all the non-default-valued parameters in the +tune appear. Therefore you cannot directly combine a tune option with +your own choices for some of the parameters used in the tune, since +the values you set before pythia.init(...) would be +overwritten at that point. + +

    +Instead you can yourself call the method that sets up the tunes, +pythia.initTunes(int eeTune, int ppTune). +Here eeTune and ppTune encode the same +options as the already-introduced Tune:ee and +Tune:pp. So the procedure would be first to call +pythia.initTunes(...), then do the further changes +you wish, and finally initialize with Tune:ee and +Tune:pp both zero. + + +Choice of tune to e^+e^- data, mainly for the hadronization +and timelike-showering aspects of PYTHIA. + + + + + + + +Choice of tune to pp / ppbar data, mainly for the +initial-state-radiation, multiple-interactions and beam-remnants +aspects of PYTHIA. + + + + + + + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/UpdateHistory.xml b/PYTHIA8/pythia8140/xmldoc/UpdateHistory.xml new file mode 100644 index 00000000000..5713ac33ef9 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/UpdateHistory.xml @@ -0,0 +1,884 @@ + + +

    Update History

    + +These update notes describe major updates relative to the baseline +PYTHIA 8.100 version. However, they are less extensive than the +corresponding update notes for PYTHIA 6. There are three main +reasons for this: + +
      + +
    • The manual contained on these html/php pages is kept up to date. +(However, the "Brief Introduction" may not always be.)
      • + +
    • 8.1 is a quite new code, so there are many minor changes that, +if all were to be documented, would hide the key ones.
      • + +
    • 8.1 is not yet used for "mission critical" applications, +so there is less need to trace changed behaviour.
      • + +
    + +

    Main news by version

    + +
      + +
    • 8.105: 24 February 2008 +
        + +
      • New option to initialize with arbitrary beam directions
        +pythia.init( idA, idB, pxA, pyA, pzA, pxB, pyB, pzB)
        • + +
      • Added capability to set beam energy spread +and beam vertex. +
        +Warning: as a consequence, the old Beams group of +settings has been moved to BeamRemnants, and +Beams is now instead used for machine beam parameters. +Therefore also some Main settings of this character have been +regrouped, as follows: + + + + + + + + + + + + + + + + +
        8.100 setting has been moved to
        Main:idA Beams:idA
        Main:idB Beams:idB
        Main:inCMframe (Beams:frameType)
        Main:eCM Beams:eCM
        Main:eA Beams:eA
        Main:eB Beams:eB
        Main:LHEF Beams:LHEF
        • + +
      • The forceHadronLevel() method introduced for standalone +hadronization.
        • + +
      • main15.cc illustrated how either full hadronization or +only decays of some particles can be looped over for the rest of the +event retained.
        • + +
      • The LHAevnt and LHAinit classes have been +joined into a new LHAup one, with new options that allow +the writing of a Les Houches Event File.
        • + +
      • The SusyLesHouches class updated to handle +SLHA version 2.
        • + +
      • Updated HepMC conversion routine.
        • + +
      • The static ErrorMsg class has been removed and +its functionality moved into the non-static Info class, +in the renamed Info file.
        • + +
      • Further reduction of the use of static, with related code changes. +This should allow to have several almost independent Pythia +instances. Some static classes still remain, however, notably for +random number generation and particle properties.
        • + +
      • Limited capability to use two different Pythia instances +for signal + pileup event generation, see main19.cc for an +example.
        • + +
      • In the Event class the = and +=+ methods have been overloaded to allow the copying +or appending of event records. Illustrated in main19.cc.
        • + +
      • The html and php page formatting improved with +cascading style sheets.
        • + +
      • Several minor improvements and new options, including updated configure +scripts.
        • + +
      +
      • + +
    • 8.108: 1 May 2008 +
        + +
      • Correction in the event record, so that the beam particles in line +1 and 2 do not have any mother according to the motherList +method. Previously the "system" entry in line 0 was counted as their +mother, which gave rise to an unexpected extra vertex in the conversion +to the HepMC format.
        • + +
      • Support for HepMC version 1 is removed, to simplify the code and +reflect the evolution of the field.
        • + +
      • Status codes are stored in HepMC only as 1 for existing and 2 for +decayed or fragmented particles (whereas previously the original PYTHIA +codes were used for the latter).
        • + +
      • Parton densities are stored in HepMC as xf(x,Q^2) +rather than the f(x,Q^2) used in (some) previous versions.
        • + +
      • The SusyLesHouches class has ben updated so that reading is fully +compatible with the SLHA2 standard.
        • + +
      • Improved handling of the Higgs width, relevant for massive and thereby +broad resonance shapes.
        • + +
      • The matrix elements for neutralino pair production have now been +completed and checked.
        • + +
      • Ensure that alpha_strong does not blow up, by introducing +a minimal scale somewhat above Lambda_3 (roughly where +alpha_strong = 10).
        • + +
      • New methods isValence1() and isValence2() +in the Info class.
        • + +
      • Protection against division by zero in calculation of decay vertex +(for zero-mass gluons with zero lifetime, where there should be no +displacement).
        • + +
      • A new compilation option -Wshadow is introduced and +code is rewritten at all places where this option gave warnings.
        • + +
      • Minor library correction to allow compilation with gcc 4.3.0.
        • + +
      +
      • + +
    • 8.114: 22 October 2008 +
        + +
      • New rescattering description operational (but still experimental) +for the case that FSR is not interleaved, but saved until after MI, +ISR and beam remnants have been handled. This involves much new code +in several classes.
        • + +
      • A new class PartonSystems is introduced to +keep track of which partons in the event record belong to which +subcollision system, plus some further information on each subsystem. +It takes over functionality previously found as part of the +Event class, but leaves room for future growth.
        • + +
      • Add optional model, wherein an increased pT0 turnoff scale +for MI and ISR is used for above-average active events, i.e. events that +already have several MI's or ISR emissions.
        • + +
      • Freeze GRV 94L distribution at small Q^2 to avoid blowup.
        • + +
      • The pythia.readFile(...) method can now alternatively take +an istream as argument instead of a filename.
        • + +
      • Minor bug correction in PartonLevel.cc; the bug could +(rarely) give a segmentation fault.
        • + +
      +
      • + +
    • 8.120: 10 March 2009 +
        + +
      • New rescattering description further developed, but not yet +recommended for normal usage.
        • + +
      • Include new processes for Large Extra Dimensions and Unparticles, +contributed by Stefan Ask. New test program main28.cc +illustrates.
        • + +
      • Include further SUSY processes: neutralino-chargino and +chargino-chargino pairs. The processes should be valid also +in the case of non-minimal flavour violation and/or CP violation. +Expanded machinery to keep track of SUSY parameters.
        • + +
      • Include backwards evolution of incoming photon as part of the +SpaceShower initial-state radiation description. This +allows you to simulate hard collisions where one of the incoming +partons is a photon. New test program main43.cc +illustrates.
        • + +
      • Allow separate mass and transverse momentum cuts when two hard +subprocesses are generated in the same event.
        • + +
      • The default value for the border between short- and long-lived +paticles has been changed from 1 mm to 10 mm, to better conform with +LHC standards, see here. +The default is still to let all unstable particles decay.
        • + +
      • New ISR matrix-element correction to f -> f gamma +in single W production.
        • + +
      • New method Event::statusHepMC returns the status +code according to the HepMC conventions agreed in February 2009. +The interface to HepMC now writes out status according to this +convention.
        • + +
      • Add capability to link to FastJet, with expanded configure script +and Makefile, and with main61.cc as new example.
        • + +
      • Update of Makefile.msc, with added support for latest +Visual C++ Express edition and use of regexp to check nmake version.
        • + +
      • Update of LHAFortran.h and +Pythia6Interface.h, to make the interface to Fortran +routines work also under Windows. (Thanks to Anton Karneyeu.) + +
      • Updated and expanded worksheet.
        • + +
      • The manual pages in the xmldoc directory, and thereby +also those of the htmldoc and phpdoc +directories, have been significantly updated and expanded. In particular, +in many places the class of each method is explicitly shown, as well as +the type of the return value and of the arguments. This upgrade is not +yet completed, but already covers the more relevant sections.
        • + +
      • The unary minus operator in the Vec4() returns a +reference to a four-vector with all components negated, but leaves +the original four-vector unchanged. Previously the four-vector itself +was flipped.
        • + +
      • The pPlus() and pMinus() methods of a +four-vector and an event-record particle are renamed pPos() +and pNeg(), respectively.
        • + +
      • Include a further loop in ProcessLevel, so that a new +process is generated in case of failures of a less severe nature.
        • + +
      • Introduce warning message for unexpected meMode in +ResonanceWidths.
        • + +
      • Les Houches event reading framework has been rearranged for +more flexibility. Some bugs corrected. Specifically, when scale +is not set (scale = -1. in the Les Houches standard), +PYTHIA did not attempt to set this scale itself, which typically +lead to there not being any ISR or FSR. Now the +rules for normal +1-, 2- and 3-body final states are applied, with a trivial +extension of the 3-body rules for higher multiplicities.
        • + +
      • Correct bug in the handling of parton densities, whereby it was +not possible to switch to a new set, once a first initialization +had been done.
        • + +
      • Correct bugs when several Pythia::init initialization +calls are made in the same run, specifically in the case that pointers +to external processes have been handed in. + +
      • Changes in main03.cmnd and main04.cmnd +so that some nonstandard options are commented ou rather than active. +Related comments inserted also in some other .cmnd files, +but there without any change in program execution.
        • + +
      • A few further minor bug fixes.
        • + +
      • Update year to 2009.
        • + +
      +
      • + +
    • 8.125: 16 June 2009 +
        + +
      • Hadronization and timlike-shower parameter default values updated +according to a tune to LEP1 data by Hendrik Hoeth, using the +Rivet + Professor framework.
        • + +
      • Many further SUSY production processes. SLHA readin expanded to cover +also masses and decay modes. Example main22.cc updated, while +main33.cc now superfluous and removed.
        • + +
      • Also further processes for extra dimensions.
        • + +
      • Stefan Ask joins as coauthor.
        • + +
      • The TimeShower::shower(...) method has gained +a new argument, that forces the shower evolution to stop after +a given number of branchings. A new method +TimeShower::pTLastInShower() permits the last evolution +pT to be read out. These extensions can be useful +for matching studies. +
        • + +
      • New optional argument isInterleaved added to +TimeShower::branch(...). Is false by default, but +true when called from the parton level for interleaved evolution +of several parton systems, optionally also with ISR and MI.
        • + +
      • New methods UserHooks::canSetResonanceScale() +and UserHooks:scaleResonance(...) allows an optional +user choice of the maximum shower scale in resonance decays.
        • + +
      • A new method SpaceShower::doRestart() has been +added, to help distinguish cases when a +SpaceShower::branch(...) failure forces a complete +restart of the evolution from ones where only the intended +current branching has been vetoed. + +
      • When multiple interactions are initialized, it is now +possible to reduce both pT0 and pTmin +if necessary to find a valid solution where +sigma_jet > sigma_nondiffractive. Previously +only the former would be reduced, which could lead to +infinite loops if too large a pTmin was used. +Thanks to Sami Kama for pointing out the problem. +
        • + +
      • The rescattering machinery is now essentially completed, and can +be used also by others than the authors. For now, however, it can only +be recommended for dedicated studies, not e.g. for generic tunes. +
        • + +
      • Timelike and spacelike showers, and beam remnant handling, +are modified to handle rescattering partons. Specifically, a new machinery +is introduced to trace the recoils from the combination of rescattering +with showers and primordial kT. Can assign space- or timelike +virtualities to intermediate particles to have energy and momentum +conserved locally. This affects the PartonLevel, +MultipleInteractions, TimeShower, +SpaceShower and BeamRemnants classes. +Further details to appear in the upcoming article on rescattering. +(Another change is a reversal to pre-8.114 order for non-interleaved FSR, +wherein also FSR is treated before beam remnants are attached.) +
        • + +
      • Four new status codes introduced, as part of the rescattering +description: +
        45 : incoming rescattered parton, with changed kinematics owing +to ISR in the mother system (cf. status 34); +
        46 : incoming copy of recoiler when this is a rescattered parton +(cf. status 42); +
        54 : copy of a recoiler, when in the initial state of a different +system from the radiator; +
        55 : copy of a recoiler, when in the final state of a different +system from the radiator. +
        • + +
      • New method Info::tooLowPTmin() can tell whether the +pTmin scales for showers or multiple interactions are too low. +
        • + +
      • Pion beams allowed, both pi^+, pi^- and +pi^0. New machinery for the latter, where the valence +flavour content is chosen to be either d dbar or +u ubar for each new event. One internal pion PDF +implemented, with others from LHAPDF.
        • + +
      • Treatment of Pomeron-proton collisions begun.
        • + +
      • Phase-space handling of hard processes and multiple interactions +slightly expanded to better allow for harder PDF's than proton ones, +e.g. for Pomerons.
        • + +
      • The program documentation has been expanded with an +alphabetical index of all methods that are described on the +webpages, see the Program Methods +page. Also other sections of the documentation have been +updated and expanded, including the worksheet.
        • + +
      • Several list methods have been made +const. For the listing of events two new methods +have been added, Event::list() and +Event::list(bool showScaleAndVertex, +bool showMothersAndDaughters = false), +that correspond to special cases of the general method.
        • + +
      • A new method Pythia::LHAeventSkip(int nSkip) +permits a skip-ahead of the reading of external Les Houches +Events, without the necessity to generate the intervening +nSkip events in full. Makes use of the new +LHAup::skipEvent(int nSkip) method to perform +the operations. Mainly intended for debug purposes. + +
      • The ClusterJet jet finder now saves the last +five clustering scales. Also a minor bug fix. Thanks to Nils +Lavesson for this contribution.
        • + +
      • The Particle::m2() method now returns a negative +number when the stored mass m is negative, as used to +indicate spacelike virtualities. Also the +Particle::eCalc(), Particle::mT() and +Particle::mT2() methods have been modified. +
        • + +
      • The << method to print our a four-vector has +been expanded with a fifth number, the invariant length, with a minus +sign for spacelike vectors, and provided within brackets to allow +a simple visual distinction.
        • + +
      • New methods Rndm::dumpState(string fileName) and +Rndm::readState(string fileName) allows to write or +read the state of the random number generator to or from a binary file. +
        • + +
      • New method double GammaReal(double x) returns the +value of the Gamma function for arbitrary real argument. +Some cross sections for extra-dimensional processes rewritten to +make use of it. +
        • + +
      • New example program main29.cc shows how +to set up a fictitious process of a heavy system decaying +to two particles or partons, with decays traced to stable +particles, as relevant for astroparticle applications.
        • + +
      • Main programs that illustrate the HepMC interface have +been updated to use version 2.04, including units and excluding +deprecated output formats.
        • + +
      • The main32.cc example extended also to handle +Les Houches Event Files.
        • + +
      • The Makefile has been modified so that "make clean" only +removes the current compilation and library fles, while +"make distclean" gives a more extensive reset and cleanup. +Thanks to Nils Lavesson for this contribution. Some other +minor Makefile corrections.
        • + +
      • Several main programs that use the +Main:timesToShow mode have been corrected so as +not to crash if this is set to zero. Also some other cosmetics +changes in main programs that do not affect the running.
        • + +
      • Bug correction, in that previously a veto with user hooks +was not propagated from parton showers inside resonance decays. +
        • + +
      • Minor bug fix in TimeShower for kinematics with +unequal beam-particle masses.
        • + +
      • Bug fix so that PartonLevel:MI = off also works for +minimum-bias events.
        • + +
      • Minor bug fix in the impact-parameter selection of multiple +interactions. Thanks to Sami Kama for pointing it out.
        • + +
      • String fragmentation for junction topology protected against +numerical instability in boost.
        • + +
      • Bug correction in the handling of particle decays to partons, +where the scale of the partons was set before the partons had been +added to some arrays, leading to indexation out of bounds. +Thanks to Vladislav Burylov for discovering this bug. +
        • + +
      • Bug correction in the handling of particles with inhibited decay, +where the decay vertex would be too far displaced, which could lead to +infinite loop. Thanks to Sami Kama for debugging this.
        • + +
      • Check to avoid infinite loop in matrix-element handling of +two-body decays.
        • + +
      • Bug correction to avoid infinite loops in Dalitz decay treatment. +Some changes in the decay handling logic to allow a new try when the +decay of a particle fails.
        • + +
      • Minor correction, so the pointer to the Info class +is set also for user-written classes derived from LHAup. +
        • + +
      • Correction for typo in the matrix element of the +Sigma3ff2HchgchgfftWW class, for doubly charged Higgs +production. Thanks to Merlin Kole for spotting it.
        • + +
      • Updated colour bookkeeping in junction-antijunction annihilation +avoids later problems in Pythia::check().
        • + +
      • Minor updates of the Makefile.msc file to work with +Visual Studio 2008. Thanks to David Bailey for these modifications.
        • + +
      • Ensure that nInit in the BeamParticle +class is set also for unresolved lepton beams.
        • + +
      • The VetoEvolution class, derived from +UserHooks, is obsolete and has been removed.
        • + +
      +
      • + +
    • 8.130: 15 September 2009 +
        + +
      • New machinery that allows multiple interactions inside diffractive +systems. Also new optional Pomeron flux factors and Pomeron PDFs. +New page on diffraction added, where +further details are collected. Still not tuned, so to be used with +caution.
        • + +
      • Make Peter Skands' "Tune 1" parameters for ISR and MI default. +The older simpler tune is still available as an option, see +Tune:pp. +
        • + +
      • New possible choices for a second hard process: charmonium, +bottomonium, top pair and single top.
        • + +
      • New code for pair production of generic colour-triplet scalar, +fermion or vector. Largely written by Johan Bijnens, partly recycling +existing code.
        • + +
      • Add user hooks possibility to veto event after a given number +of multiple interactions.
        • + +
      • Add instructions how PYTHIA 8 can be used from inside ROOT. +Thanks to Andreas Morsch for providing the text and Rene Brun +for a simple example.
        • + +
      • The main21.cc example extended with an option +for a single-particle gun.
        • + +
      • Improvements and bug fixes in rescattering framework.
        • + +
      • New method Hist::table(string fileName) provides a +more direct way to print a two-column table of histogram contents +into a file than the current Hist::table(ostream& os = cout). +
        • + +
      • Modify reading of external files so that a line only consisting of +control characters counts as empty, the same way as a line only consisting +of blanks already did. This includes carriage return, tabs and a few more, +the ones represented by \n \t \v \b \r \f \a. Applies to +Les Houches Event files, settings files and particle data files.
        • + +
      • Fix it so that the read-in of a Les Houches Event File for the +hardest process can be combined with the faciliy to select a specified +second hard process.
        • + +
      • New empty base class method LHAup::fileFound() +allows the derived class LHAupLHEF to signal more +clearly that a failed initialization is caused by a failure to open +the desired file.
        • + +
      • Check that a pointer to an LHAup object has been set +in Pythia::LHAeventList() and +Pythia::LHAeventSkip(...) calls.
        • + +
      • Updated configure and Makefile, e.g. to build shared libraries +on Mac OS X.
        • + +
      • The options with a direct link to hard-process generation +in PYTHIA 6 has been removed. It is hardly ever used but +complicates the build structure. (Owing to its usefulness for some +debug work, it was reinstated in a limited form in version 8.135. +Thus main51.cc now contains the complete interface, +previously in separate files, and commented-out lines in +examples/Makefile suggest how PYTHIA 6 could be linked.) +
        • + +
      • New argument to Info::errorMsg(...) allows to +show all error messages of a specific kind rather than only the +first one, e.g. for initialization.
        • + +
      • Correction in decay table of righthanded Majorana neutrinos. +Thanks to Arnaud Ferrari and Vladimir Savinov.
        • + +
      • Correction in expressions in the manual for H^+- couplings +to an h^0, H^0 or A^0 and a W^+-. +Thanks to Rikard Enberg.
        • + +
      • Fix for accessing uninitialized memory, caused by accessing the +daughters of the incoming beams before these daughters actually existed. +Thanks to David Bailey and Sami Kama. +
        • + +
      • Uninitialized photon PDF inside the proton could give crazy results +for processes with incoming photons. Thanks to Adam Davison.
        • + +
      • Bug fix such that finite lifetimes can be set also for particles +produced in the hard process. To exemplify, the bug affected +tau leptons produced in Z^0 and W^+- +decays. Thanks to Troels Petersen.
        • + +
      • Bug fix in TimeShower, that beamOffset +could remain uninitialized. Thanks to Sami Kama.
        • + +
      • Minor correction to resonance decays: fail if the allowed mass +range of a Breit-Wigner resonance is a small fraction of the total +area under the resonance curve.
        • + +
      • Correction when all three valence quarks were kicked out from a +proton and could give false messages that beam momentum had been +used up.
        • + +
      • Clarify status codes needed for hadron-level standalone runs in +order to avoid error messages, and modify the main21.cc +example accordingly.
        • + +
      • Minor corrections in the processes for extra dimensions.
        • + +
      • Some other minor additions to existing facilities +and minor bug fixes.
        • + +
      +
      • + +
    • 8.135: 10 January 2010 +
        + +
      • All usage of static member methods inside Pythia8 has now been +eliminated. This simplifies for you to have several simultaneous +Pythia instances that are run with different conditions. +The three main classes affected by this are the Settings +and ParticleData databases and the Rndm +random-number generator. You can no longer address the methods of these +classes directly, but have to address them via the settings, +particleData and rndm instances in the +respective Pythia object. Also some other smaller pieces +of code are affected, e.g. Standard Model and SUSY couplings +(the latter in new files). +Note 1: The documentation has been updated accordingly +on these webpages, but the "A Brief Introduction to PYTHIA 8.1" +still refers to the old behaviour of version 8.100. +Note 2: the interface to the external LHAPDF library remains +static, since LHAPDF is written in Fortran and thus by definition +static. +Note 3: if you want to have momentum smearing in +CellJet you now need to send in a pointer to a +random-number generator. +
        • + +
      • Ten new proton PDF sets are made available internally: +MRST LO* (2007), MRST LO** (2008), MSTW 2008 LO (central member), +MSTW 2008 NLO (central member), CTEQ6L, CTEQ6L1, CTEQ6.6 (NLO, +central member), CT09MC1, CT09MC2, and CT09MCS, see +PDF Selection. The Pomeron PDF data +files have been renamed for consistency. Thanks to Tomas Kasemets +for help with this Kas10. +
        • + +
      • New parameters TimeShower:pTmaxFudgeMI and +SpaceShower:pTmaxFudgeMI introduced, to give the same +functionality for multiple interactions that +TimeShower:pTmaxFudge and SpaceShower:pTmaxFudge +do for the hardest.
        • + +
      • A few extensions of the UserHooks framework. +New methods UserHooks:canVetoISREmission() and +UserHooks::doVetoISREmission(...) allows the latest +initial-state emission to be studied before being finalized, +with the possibility to veto it. +Similarly Userhooks:canVetoFSREmission() and +UserHooks::doVetoFSREmission(...) can be used to +veto the latest final-state emission.
        • + +
      • A number of loop counters have been introduced in the +Info class, that offers some further information on +the progress of the event generation, for use e.g. in conjunction +with the UserHooks facility.
        • + +
      • The Pythia::initTunes(...) method is made public, so that +it can be called before the normal call from Pythia::init(...). +That way it is possible to start out from a given tune and change a few +of the parameters. +
        • + +
      • Bug corrected in LHAFortran.h for hard-process input +from Fortran commonblock. This did not work properly when the input +was used in combination with a second hard process generated internally. +Thanks to Mikhail Kirsanov and Roberto Chierici. + +
      • Insertion of missing initialization of isInit in the +Settings and ParticleData constructors, and +nInit for BeamParticle. +Thanks to Leif Lönnblad.
        • + +
      • Updated Makefile.msc for Windows users.
        • + +
      • Fix of some non-optimal use of booleans, that give warnings on +a Windows compiler. Thanks to Anton Karneyeu.
        • + +
      • New options for the +SUSY Les Houches Accord such that, by default, +particle and decay data are not overwritten for known Standard Model +particles (including Z^0, W^+- and t, +but excluding the Higgs).
        • + +
      • Bug fix in SusyLesHouches, where the reading of SLHA +information embedded in an LHEF would not stop at the end of the header +section.
        • + +
      • Bug correction for undefined secondary widths where decay products +together are heavier than the mother. Also unit default secondary width +values in the DecayChannel constructor.
        • + +
      • Documentation updated, including change of current year to 2010.
        • + +
      +
      • + +
    • 8.140: 16 July 2010 +
        + +
      • Four new draft tunes available.
        • + +
      • Introduction of a new scenario for production of Hidden-Valley +particles, and interleaved showering in the QCD and HV sectors, see +the new Hidden Valleys +description. A longer physics writeup is available Car10. +
        • + +
      • Implementation of 2 -> 3 phase space selection intended +for QCD processes with massless partons. A new set of matching +phase space cut parameters. +The ten different QCD 2 -> 3 +processes have been implemented making use of this new +possibility, so far without a complete handling of possible colour +flows, however.
        • + +
      • New processes have been added for +contact interactions in +q q -> q q and q qbar -> q qbar scattering.
        • + +
      • A process has been added for TeV^-1 Sized +Extra Dimensions, which +involves the electroweak KK gauge bosons, i.e. gamma_{KK}/Z_{KK}, +in one TeV^-1 sized extra dimension; see main30.cc for +an example. This scenario is described in Bel10. Thanks to +Noam Hod and coworkers for contributing this code.
        • + +
      • In the Randall-Sundrum extra-dimensional scenario a new option has +been added where SM fields can exist in the bulk rather than only on +a brane. (Still under development.) Furthermore production of a +Kaluza-Klein gluon state has been added, and the main28.cc +test program extended.
        • + +
      • The scenario for monojets in Large Extra Dimensions has been expanded +with an alternative for scalar graviton exchange instead of tensor one. +
        • + +
      • New parameters for maximum scale of +timelike showers, +TimeShower:pTmaxMatch, and the dampening of hard radiation, +TimeShower:pTdampMatch and TimeShower:pTdampFudge, +by analogy with corresponding ones for spacelike showers. Also new method +TimeShower:limitPTmax(...) to implement alternative procedures. +For dipoles stretched to the beam the new switch +TimeShower:dampenBeamRecoil allows to dampen radiation +close to the beam direction, with a changed default behaviour.
        • + +
      • Azimuthal anisotropies from coherence arguments have been introduced +for the spacelike parton showers, see SpaceShower:phiIntAsym +and SpaceShower:strengthIntAsym. +Also azimuthal anisotropies from gluon polarization have been introduced +for the spacelike parton showers, see SpaceShower:phiPolAsym, +and updated for timelike parton showers, see +TimeShower:phiPolAsym.
        • + +
      • Improvements for the matching to POWHEG LHEF-style input illustrated +by the new main71.cc example. See also Cor10.
        • + +
      • A set of new processes gamma gamma -> f fbar, with f +quarks or leptons. Code for equivalent photon flux around an unresolved +proton, with more to come. Thanks to Oystein Alvestad. +
        • + +
      • A new option has been included to dampen the growth of the diffractive +cross sections, see Total Cross +Sections.
        • + +
      • A new method virtual int SigmaProcess::idSChannel() +has been introduced. If overloaded to return a nonzero value then a +2 -> n process will appear listed as a 2 -> 1 -> n one. +That is, an intermediate resonance with the requested identity will be +inserted in the event record, even without appearing in the calculation +of the matrix element proper. Thanks to Noam Hod for idea and code.
        • + +
      • A new method SigmaProcess::convertM2() has been introduced +to optionally allow the SigmaProcess::sigmaHat() to return +the squared matrix element rather than d(sigmaHat)/d(tHat) for + 2 -> 2 processes. Furthermore kinematics is stored in the new +mME and pME vectors for alternative cross +section encodings.
        • + +
      • Different encoding of the f fbar -> Z W cross section, +contributed by Merlin Kole, based on the cross section of +Brown, Sahdev and Mikaelian. Gives a distinctly different cross section +than the previous based on EHLQ (including their bug fix). +In particular the problem with negative cross sections is now fixed.
        • + +
      • Minor updates: pass xmlPath to new MSTW and CTEQ PDFs; +reset beams earlier to give cleaner documentation.
        • + +
      • The H1 Fit B LO parametrization to the Pomeron PDF has been included, +and made new default for Pomerons. Thanks to Paul Newman for providing +the data files.
        • + +
      • Three changes, in principle unrelated, but with the common objective +to make the generation of a given event depend only on the values +determined during the initialization stage and on the state of the +random-number generator when the event is begun. The new default +should ensure a reproducible stop-and-restart behaviour, convenient +for debug purposes. Thanks to Michael Schmelling for stressing the +desire for such a behaviour. +
        (i) Introduction of a new option +PhaseSpace:increaseMaximum that allows to switch between +two strategies for handling the (hopefully rare) cases when the +assumed maximum of the cross section function is exceeded during the +event generation, with a changed default behaviour. In the old +default the maximum could be increased if it was exceeded during the run, +thereby introducing a memory of the previously generated events. +
        (ii) Updated handling of random numbers with Gaussian distributions. +The gauss() method now only generates one value at a time. +Instead the new gauss2() method returns a pair of Gauss +numbers, with related time savings. In the old approach one Gaussian +number could be buffered, which introduced a memory. +
        (iii) Minor bug fix in MiniStringFragmentation, where +the popcorn baryon state was not reset for each new system, again +giving a (flawed) memory.
        • + +
      • New directory rootexample with a simple code example +how to use ROOT for histogramming in PYTHIA runs. See +ROOT Usage for details. Thanks to Rene Brun. +
        • + +
      • In the HepMCinterface the checks for unhadronized +quarks and gluons are not performed if hadronization has been switched +off.
        • + +
      • The UserHooks::initPtr(...) has been expanded so that +pointers to more classes (beam particles, random number, couplings, etc.) +are sent in, thereby increasing the scope of possible user-written code. +Also, the UserHooks::doVetoProcessLevel(Event& process) +now allows the process event record to be modified, +even if it is not recommended. The new Info::pTnow() +method returns the current pT scale of the combined MI, ISR +and FSR evolution, which can be useful for some user hooks decisions. +
        • + +
      • Histograms of the Hist class can now be booked +with up to 1000 bins, instead of the previous maximum 100. All bins +can be written to file, but the line-printer style printing will join +nearby bins so at most 100 are printed, as before.
        • + +
      • Updated configure and Makefile +to allow 64-bit compilation and more options. Thanks to Mikhail Kirsanov, +Rene Brun and Fons Rademakers.
        • + +
      • Bug fix in ProcessLevel for colour flow checks of +junctions. Enables the decay of a neutralino to three quarks, e.g. +Thanks to Nils-Erik Bomark.
        • + +
      • Bug fixes in TimeShower, where recoil partners in resonance +decays of coloured particles, and recoil partners in QED dipoles when beams +are not allowed to take a recoil, might not be correctly identified.
        • + +
      • Bug fix in SpaceShower: when used with a fixed +alpha_strong, the threshold enhancement factor of +g -> Q Qbar became undefined. Thanks to Stefan Prestel.
        • + +
      • Bug fix in initialization of resonance widths, where the +minWidth parameter could be used uninitialized, +occasionally resulting in strange initialization problems when +kinematics needs to force at least one resonance to be off-shell.
        • + +
      • Minor updates of main06.cc, main10.cc +and main23.cc.
        • + +
      • Bug fix in mother pointer of multiple interactions in +diffractive systems.
        • + +
      +
      • + +
    + +     + + diff --git a/PYTHIA8/pythia8140/xmldoc/UserHooks.xml b/PYTHIA8/pythia8140/xmldoc/UserHooks.xml new file mode 100644 index 00000000000..68023e03421 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/UserHooks.xml @@ -0,0 +1,645 @@ + + +

    User Hooks

    + +Sometimes it may be convenient to step in during the generation +process: to modify the built-in cross sections, to veto undesirable +events or simply to collect statistics at various stages of the +evolution. There is a base class UserHooks that gives +you this access at a few selected places. This class in itself does +nothing; the idea is that you should write your own derived class +for your task. One simple derived class (SuppressSmallPT) +comes with the program, mainly as illustration, and the +main10.cc program provides a complete (toy) example how +a derived class could be set up and used. + +

    +There are six sets of routines, that give you different kinds of +freedom. They are, in no particular order: +
    (i) Ones that give you access to the event record in between +the process-level and parton-level steps, or in between the +parton-level and hadron-level ones. You can study the event record +and decide whether to veto this event. +
    (ii) Ones that allow you to set a scale at which the combined +parton-level MI+ISR+FSR downwards evolution in pT is +temporarily interrupted, so the event can be studied and either +vetoed or allowed to continue the evolution. +
    (iii) Ones that allow you to to study the event after the first +few ISR/FSR emissions, or first few MI, so the event can be vetoed +or allowed to continue the evolution. +
    (iv) Ones that allow you to study the latest initial- or +final-state emission and veto that emission, without vetoing the +event as a whole. +
    (v) Ones that give you access to the properties of the trial +hard process, so that you can modify the internal Pythia cross section +by your own correction factors. +
    (vi) Ones that let you set the scale of shower evolution, +specifically for matching in resonance decays. +
    They are described further in the following numbered subsections. + +

    +All the possibilities above can be combined freely and also be combined +with the standard flags. An event would then survive only if it survived +each of the possible veto methods. There are no hidden interdependencies +in this game, but of course some combinations may not be particularly +meaningful. For instance, if you set PartonLevel:all = off +then the doVetoPT(...) and doVetoPartonLevel(...) +locations in the code are not even reached, so they would never be called. + +

    +The effect of the vetoes of types (i), (ii) and (iii) can be studied +in the output of the +Pythia::statistics() +method. The "Selected" column represents the number of events that were +found acceptable by the internal Pythia machinery, whereas the "Accepted" +one are the events that also survived the user cuts. The cross section +is based on the latter number, and so is reduced by the amount associated +by the vetoed events. Also type (v) modifies the cross section, while +types (iv) and (vi) do not. + +

    The basic components

    + +For a derived UserHooks class to be called during the +execution, a pointer to an object of this class should be handed in +with the +
    +Pythia::setUserHooksPtr( UserHooks*) +
    method. The first step therefore is to construct your own derived +class, of course. This must contain a constructor and a destructor. The +initPtr method comes "for free", and is set up without +any intervention from you. + + + + +The constructor and destructor do not need to do anything. + + + +this (non-virtual) method is automatically called during the +initialization stage to set several useful pointers, and to set up +the workEvent below. The corresponding objects can +later be used to extract some useful information. +
    Info: +general event and run information, including some loop counters. +
    Settings: +the settings used to determine the character of the run. +
    ParticleData: +the particle data used in the event record +(including workEvent below). +
    Rndm: the random number +generator, that you could also use in your code. +
    BeamParticle: +the beamAPtr and beamBPtr beam particles +contain info on partons extracted from the two incoming beams, +on the PDFs used, and more. In cases when diffraction is simulated, +also special Pomeron beams beamPomAPtr and +beamPomBPtr are introduced, for the Pomerons residing +inside the respective proton. +
    CoupSM: +Standard Model couplings. +
    PartonSystems: +the list of partons that belong to each individual subcollision system. +
    SigmaTotal: +total/elastic/diffractive cross section parametrizations. +     + +

    +Next you overload the desired methods listed in the sections below. +These often come in pairs or triplets, where the first must return +true for the last method to be called. This latter method typically +hands you a reference to the event record, which you then can use to +decide whether or not to veto. Often the event record can be quite +lengthy and difficult to overview. The following methods and data member +can then come in handy. + + +is a protected method that you can make use of in your own methods to +extract a simplified list of the hard process, where all resonance decay +chains are omitted. Intended for the can/doVetoProcessLevel +routines. Note that the normal process-level generation does include +resonance decays. That is, if a top quark is produced in the hard process, +then also decays such as t -> b W+, W+ -> u dbar will be generated +and stored in process. The omitResonanceDecays +routine will take the input process and copy it to +workEvent (see below), minus the resonance decay chains. +All particles produced in the hard process, such as the top, will be +considered final-state ones, with positive status and no daughters, +just as it is before resonances are allowed to decay. +
    (In the PartonLevel routines, these decay chains will +initially not be copied from process to event. +Instead the combined MI, ISR and FSR evolution is done with the top +above as final particle. Only afterwards will the resonance decay chains +be copied over, with kinematics changes reflecting those of the top, and +showers in the decays carried out.) +
    +     + + + +is a protected method that you can make use of in your own methods to +extract a brief list of the current +partons of interest, with all irrelevant ones omitted. For the default +isHardest = true only the outgoing partons from the hardest +interaction (including the partons added to it by ISR and FSR) are +extracted, as relevant e.g. for doVetoPT( iPos, event) with +iPos = 0 - 4. With isHardest = false instead +the outgoing partons of the latest "subprocess" are extracted, as relevant +when iPos = 5, where it corresponds to the outgoing partons +in the currently considered decay. The resut is stored in +workEvent below. The partons are stored in slots 0 through +workEvent.size() - 1. The mother1() and +mother2() indices of a particle in this list both return 0. +The daughter1() and daughter2() indices both +return the index of the same parton in the original event record +(event; possibly process), +so that you can trace the full history, if of interest. + + + +This protected class member contains the outcome of the above +omitResonanceDecays(...) and +subEvent(...) methods. Alternatively you can use it for +whatever temporary purposes you wish. You are free to use standard +operations, e.g. to boost the event to its rest frame before analysis, +or remove particles that should not be analyzed. +The workEvent can also be sent on to a +jet clustering algorithm. + +

    (i) Interrupt between the main generation levels

    + + +In the base class this method returns false. If you redefine it +to return true then the method doVetoProcessLevel(...) +will be called immediately after a hard process (and associated +resonance decays) has been selected and stored in the +process event record. +
    At this stage, the process record typically contains +the two beams in slots 1 and 2, the two incoming partons to the hard +process in slots 3 and 4, the N (usually 1, 2 or 3) primary produced +particles in slots 5 through 4 + N, and thereafter recursively the +resonance decay chains, if any. Use the method +omitResonanceDecays(...) if you want to skip these +decay chains. There are exceptions to this structure, +for soft QCD processes (where +the partonic process may not yet have been selected at this stage), +and when a second hard process has +been requested (where two hard processes are bookkept). In general +it is useful to begin the development work by listing a few +process records, to clarify what the structure is for +the cases of interest. +     + + +can optionally be called, as described above. You can study the +process event record of the hard process. +Based on that you can decide whether to veto the event, true, or let +it continue to evolve, false. If you veto, then this event is not +counted among the accepted ones, and does not contribute to the estimated +cross section. The Pytha::next() method will begin a +completely new event, so the vetoed event will not appear in the +output of Pythia::next(). +Warning: Normally you should not modify the process +event record. However, for some matrix-element-matching procedures it may +become unavoidable. If so, be very careful, since there are many pitfalls. +Only to give one example: if you modify the incoming partons then also +the information stored in the beam particles may need to be modified. +Note: the above veto is different from setting the flag +PartonLevel:all = off. +Also in the latter case the event generation will stop after the process +level, but an event generated up to this point is considered perfectly +acceptable. It can be studied and it contributes to the cross section. +That is, PartonLevel:all = off is intended for simple studies +of hard processes, where one can save a lot of time by not generating +the rest of the story. By contrast, the doVetoProcessLevel() +method allows you to throw away uninteresting events at an early stage +to save time, but those events that do survive the veto are allowed to +develop into complete final states (unless flags have been set otherwise). + + + +In the base class this method returns false. If you redefine it +to return true then the method doVetoPartonLevel(...) +will be called immediately after the parton level has been generated +and stored in the event +event record. Thus showers, multiple interactions and beam remnants +have been set up, but hadronization and decays have not yet been +performed. This is already a fairly complete event, possibly with quite +a complex parton-level history. Therefore it is usually only meaningful +to study the hardest interaction, e.g. using subEvent(...) +introduced above, or fairly generic properties, such as the parton-level +jet structure. + + + +can optionally be called, as described above. You can study, but not +modify, the event event record of the partonic process. +Based on that you can decide whether to veto the event, true, or let +it continue to evolve, false. If you veto, then this event is not +counted among the accepted ones, and does not contribute to the estimated +cross section. The Pytha::next() method will begin a +completely new event, so the vetoed event will not appear in the +output of Pythia::next(). +Note: the above veto is different from setting the flag +HadronLevel:all = off. +Also in the latter case the event generation will stop after the parton +level, but an event generated up to this point is considered perfectly +acceptable. It can be studied and it contributes to the cross section. +That is, HadronLevel:all = off is intended for simple +studies of complete partonic states, where one can save time by not +generating the complete hadronic final state. By contrast, the +doVetoPartonLevel() method allows you to throw away +uninteresting events to save time that way, but those events that +do survive the veto are allowed to develop into complete final states +(unless flags have been set otherwise). + + +

    (ii) Interrupt during the parton-level evolution, at a +pT scale

    + +During the parton-level evolution, multiple interactions (MI), +initial-state radiation (ISR) and final-state radiation (FSR) +are normally evolved downwards in +one interleaved evolution sequence of decreasing pT values. +For some applications, e.g matrix-element-matching approaches, it +may be convenient to stop the evolution temporarily when the "hard" +emissions have been considered, but before continuing with the more +time-consuming soft activity. Based on these hard partons one can make +a decision whether the event at all falls in the intended event class, +e.g. has the "right" number of parton-level jets. If yes then, as for +the methods above, the evolution will continue all the way up to a +complete event. Also as above, if no, then the event will not be +considered in the final cross section. + +

    +Recall that the new or modified partons resulting from a MI, ISR or FSR +step are always appended to the end of the then-current event record. +Previously existing partons are not touched, except for the +status, mother and daughter +values, which are updated to reflect the modified history. It is +therefore straightforward to find the partons associated with the most +recent occurence. +
    An MI results in four new partons being appended, two incoming +and two outgoing ones. +
    An ISR results in the whole affected system being copied down, +with one of the two incoming partons being replaced by a new one, and +one more outgoing parton. +
    An FSR results in three new partons, two that come from the +branching and one that takes the recoil. +
    The story becomes more messy when rescattering is allowed as part +of the MI machinery. Then there will not only be a new system, as +outlined above, but additionally some existing systems will undergo +cascade effects, and be copied down with changed kinematics. + +

    +In this subsection we outline the possibility to interrupt at a given +pT scale, in the next to interrupt after a given number of +emissions. + + +In the base class this method returns false. If you redefine it +to return true then the method doVetoPT(...) will +interrupt the downward evolution at scaleVetoPT(). + + +In the base class this method returns 0. You should redefine it +to return the pT scale at which you want to study the event. + + + +can optionally be called, as described above. You can study, but not +modify, the event event record of the partonic process. +Based on that you can decide whether to veto the event, true, or let +it continue to evolve, false. If you veto, then this event is not +counted among the accepted ones, and does not contribute to the estimated +cross section. The Pytha::next() method will begin a +completely new event, so the vetoed event will not appear in the +output of Pythia::next(). + is the position/status when the routine is +called, information that can help you decide your course of action: + when no MI, ISR or FSR occured above the veto scale; + + when inside the interleaved MI + ISR + FSR evolution, +after an MI process; + + when inside the interleaved MI + ISR + FSR evolution, +after an ISR emission; + + when inside the interleaved MI + ISR + FSR evolution, +after an FSR emission; + + for the optional case where FSR is deferred from the +interleaved evolution and only considered separately afterward (then +alternative 3 would never occur); + + is for subsequent resonance decays, and is called once +for each decaying resonance in a chain such as t -> b W, W -> u dbar. + + + the event record contains a list of all partons +generated so far, also including intermediate ones not part of the +"current final state", and also those from further multiple interactions. +This may not be desirable for comparisons with matrix-element calculations. +You may want to make use of the subEvent(...) method below to +obtain a simplified event record workEvent. + + + +

    (iii) Interrupt during the parton-level evolution, after a step

    + +These options are closely related to the ones above in section (ii), so +we do not repeat the introduction, nor the possibilities to study the +event record, also by using subEvent(...) and +workEvent. +What is different is that the methods in this section give access to the +event as it looks like after each of the first few steps in the downwards +evolution, irrespectively of the pT scales of these branchings. +Furthermore, it is here assumed that the focus normally is on the hardest +subprocess, so that ISR/FSR emissions associated with additional MI's +are not considered. For MI studies, however, a separate simpler +alternative is offered to consider the event after a given number +of interactions. + + +In the base class this method returns false. If you redefine it +to return true then the method doVetoStep(...) will +interrupt the downward ISR and FSR evolution the first +numberVetoStep() times. + + +Returns the number of steps n each of ISR and FSR, for the +hardest interaction, that you want to be able to study. That is, +the method will be called after the first n ISR emissions, +irrespective of the number of FSR ones at the time, and after the +first n FSR emissions, irespective of the number of ISR ones. +The number of steps defaults to the first one only, but you are free +to pick another value. Note that double diffraction is handled as two +separate Pomeron-proton collisions, and thus has two sequences of +emissions. + + + +can optionally be called, as described above. You can study, but not +modify, the event event record of the partonic process. +Based on that you can decide whether to veto the event, true, or let +it continue to evolve, false. If you veto, then this event is not +counted among the accepted ones, and does not contribute to the estimated +cross section. The Pytha::next() method will begin a +completely new event, so the vetoed event will not appear in the +output of Pythia::next(). + is the position/status when the routine is +called, information that can help you decide your course of action. +Agrees with options 2 - 5 of the doVetoPT(...) routine +above, while options 0 and 1 are not relevant here. + + is the number of ISR emissions in the hardest +process so far. For resonance decays, iPos = 5, it is 0. + + is the number of FSR emissions in the hardest +process so far. For resonance decays, iPos = 5, it is the +number of emissions in the currently studied system. + + the event record contains a list of all partons +generated so far, also including intermediate ones not part of the +"current final state", and also those from further multiple interactions. +This may not be desirable for comparisons with matrix-element calculations. +You may want to make use of the subEvent(...) method above to +obtain a simplified event record. + + + + +In the base class this method returns false. If you redefine it +to return true then the method doVetoMIStep(...) will +interrupt the downward MI evolution the first +numberVetoMIStep() times. + + +Returns the number of steps in the MI evolution that you want to be +able to study, right after each new step has been taken and the +subcollision has been added to the event record. The number of steps +defaults to the first one only, but you are free to pick another value. +Note that the hardest interaction of an events counts as the first +multiple interaction. For most hard processes it thus at the first +step offers nothing not available with the VetoProcessLevel +functionality above. For the minimum-bias and diffractive systems the +hardest interaction is not selected at the process level, however, so +there a check after the first multiple interaction offers new +functionality. Note that double diffraction is handled as two separate +Pomeron-proton collisions, and thus has two sequences of interactions. +Also, if you have set up a second hard process then a check is made +after these first two, and the first interaction coming from the MI +machinery would have sequence number 3. + + + +can optionally be called, as described above. You can study, but not +modify, the event event record of the partonic process. +Based on that you can decide whether to veto the event, true, or let +it continue to evolve, false. If you veto, then this event is not +counted among the accepted ones, and does not contribute to the estimated +cross section. The Pytha::next() method will begin a +completely new event, so the vetoed event will not appear in the +output of Pythia::next(). + is the number of MI subprocesses has occured +so far. + + the event record contains a list of all partons +generated so far, also including intermediate ones not part of the +"current final state", e.g. leftovers from the ISR and FSR evolution +of previously generated systems. The most recently added one has not +had time to radiate, of course. + + + +

    (iv) Veto emissions

    + +The methods in this group are intended to allow the veto of an emission +in ISR or FSR, without affecting the evolution in any other way. +If an emission is vetoed, the event record is "rolled back" to the +way it was before the emission occured, and the evolution in pT +is continued downwards from the rejected value. The decision can be +based on full knowledge of the kinematics of the branching. + + +In the base class this method returns false. If you redefine it +to return true then the method doVetoISREmission(...) +will interrupt the initial-state shower immediately after each +emission and allow that emission to be vetoed. + + +can optionally be called, as described above. You can study, but not +modify, the event event record of the partonic process. +Based on that you can decide whether to veto the emission, true, or +not, false. If you veto, then the latest emission is removed from +the event record. In either case the evolution of the shower will +continue from the point where it was left off. + is the size of the event record before the +latest emission was added to it. It will also become the new size if +the emission is vetoed. + + the event record contains a list of all partons +generated so far. Of special interest are the ones associated with the +most recent emission, which are stored in entries from sizeOld +through event.size() - 1 inclusive. If you veto the emission +these entries will be removed, and the history info in the remaining +partons will be restored to a state as if the emission had never occured. + + + + +In the base class this method returns false. If you redefine it +to return true then the method doVetoFSREmission(...) +will interrupt the final-state shower immediately after each +emission and allow that emission to be vetoed. + + +can optionally be called, as described above. You can study, but not +modify, the event event record of the partonic process. +Based on that you can decide whether to veto the emission, true, or +not, false. If you veto, then the latest emission is removed from +the event record. In either case the evolution of the shower will +continue from the point where it was left off. + is the size of the event record before the +latest emission was added to it. It will also become the new size if +the emission is vetoed. + + the event record contains a list of all partons +generated so far. Of special interest are the ones associated with the +most recent emission, which are stored in entries from sizeOld +through event.size() - 1 inclusive. If you veto the emission +these entries will be removed, and the history info in the remaining +partons will be restored to a state as if the emission had never occured. + + + +

    (v) Modify cross-sections

    + + +In the base class this method returns false. If you redefine it +to return true then the method multiplySigmaBy(...) will +allow you to modify the cross section weight assigned to the current +event. + + + +when called this method should provide the factor by which you want to +see the cross section weight of the current event modified by. If you +return unity then the normal cross section is obtained. Note that, unlike +the methods above, these modifications do not lead to a difference between +the number of "selected" events and the number of "accepted" ones, +since the modifications occur already before the "selected" level. +The integrated cross section of a process is modified, of course. +Note that the cross section is only modifiable for normal hard processes. +It does not affect the cross section in further multiple interactions, +nor in elastic/diffractive/minimum-bias events. +: +what makes this routine somewhat tricky to write is that the +hard-process event has not yet been constructed, so one is restricted +to use the information available in the phase-space and cross-section +objects currently being accessed. Which of their methods are applicable +depends on the process, in particular the number of final-state particles. +The multiplySigmaBy code in UserHooks.cc +contains explicit instructions about which methods provide meaningful +information, and so offers a convenient starting point. + +: this flag is true when the method is +called from within the event-generation machinery and false +when it is called at the initialization stage of the run, when the +cross section is explored to find a maximum for later Monte Carlo usage. +Cross-section modifications should be independent of this flag, +for consistency, but if multiplySigmaBy(...) is used to +collect statistics on the original kinematics distributions before cuts, +then it is important to be able to exclude the initialization stage +from comparisons. + + + +

    +One derived class is supplied as an example how this facility can be used +to reweight cross sections in the same spirit as is done with QCD cross +sections for the minimum-bias/underlying-event description: + +suppress small-pT production for 2 -> 2 processes +only, while leaving other processes unaffected. The basic suppression +factor is pT^4 / ((k*pT0)^2 + pT^2)^2, where pT +refers to the current hard subprocess and pT0 is the same +energy-dependent dampening scale as used for +multiple interactions. +This class contains canModifySigma() and +multiplySigmaBy() methods that overload the base class ones. + + + The optional arguments of the constructor provides further variability. + +corresponds to the additional factor k in the above formula. +It is by default equal to 1 but can be used to explore deviations from +the expected value. + + +if this number n is bigger than the default 0, the +corresponding number of alpha_strong factors is also +reweighted from the normal renormalization scale to a modified one, +i.e. a further suppression factor +( alpha_s((k*pT0)^2 + Q^2_ren) / alpha_s(Q^2_ren) )^n +is introduced. + + +regulates which kind of new alpha_strong value is evaluated +for the numerator in the above expression. It is by default the same +as set for multiple interactions (i.e. same starting value at +M_Z and same order of running), but if false +instead the one for hard subprocesses. The denominator +alpha_s(Q^2_ren) is always the value used for the "original", +unweighted cross section. + + + +

    (vi) Modify scale in shower evolution

    + +The choice of maximum shower scale in resonance decays is normally not a +big issue, since the shower here is expected to cover the full phase +space. In some special cases a matching scheme is intended, where hard +radiation is covered by matrix elements, and only softer by showers. The +below two methods support such an approach. Note that the two methods +are not used in the TimeShower class itself, but when +showers are called from the PartonLevel generation. Thus +user calls directly to TimeShower are not affected. + + +In the base class this method returns false. If you redefine it +to return true then the method scaleResonance(...) +will set the initial scale of downwards shower evolution. + + +can optionally be called, as described above. You should return the maximum +scale, in GeV, from which the shower evolution will begin. The base class +method returns 0, i.e. gives no shower evolution at all. +You can study, but not modify, the event event record +of the partonic process to check which resonance is decaying, and into what. + is the location in the event record of the +resonance that decayed to the particles that now will shower. + + the event record contains a list of all partons +generated so far, specifically the decaying resonance and its immediate +decay products. + + + +     + + diff --git a/PYTHIA8/pythia8140/xmldoc/Version.xml b/PYTHIA8/pythia8140/xmldoc/Version.xml new file mode 100644 index 00000000000..20564d4e6ed --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Version.xml @@ -0,0 +1,19 @@ + + +

    Version

    + +The settings on this page should not be changed by the ordinary user, +but appear here for documentation purposes, and so that they can +form part of the standard databases and be queried accordingly. + + +Version and subversion number, with three significant decimals. + + + +Last date of change of current (sub)version, in format yyyymmdd. + + +     + + diff --git a/PYTHIA8/pythia8140/xmldoc/Welcome.xml b/PYTHIA8/pythia8140/xmldoc/Welcome.xml new file mode 100644 index 00000000000..1ab4bc66fea --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/Welcome.xml @@ -0,0 +1,14 @@ + + + + + + + + + + + + diff --git a/PYTHIA8/pythia8140/xmldoc/ct09mc1.pds b/PYTHIA8/pythia8140/xmldoc/ct09mc1.pds new file mode 100644 index 00000000000..0a97d7ca3ff --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ct09mc1.pds @@ -0,0 +1,6440 @@ +PDF Table for Fit #: fl6msrv + Ordr, Nfl, lambda Qmass 1, 2, 3, 4, 5, 6 + 1. 5. 0.1668 0.001 0.001 0.200 1.300 4.650 172.000 + IPD0, IHDN, IKNL, NfMx, Nfval, KF, Nelmt + 1 1 1 5 2 12 57300 + NX, NT, JT, NG, NTL(NG+1) + 190 24 1 2 24 +(NTL(I), NTN(I), TLN(I), DTN(I), I =1, NG) + 0 6 7.19603E-01 8.04674E-02 + 6 18 1.20241E+00 7.69817E-02 +QINI, QMAX, (QV(I), TV(I), I =0, NT) + 1.30000E+00 1.00000E+05 + 1.30000E+00 7.19603E-01 + 1.54410E+00 8.00071E-01 + 1.86068E+00 8.80538E-01 + 2.27748E+00 9.61006E-01 + 2.83526E+00 1.04147E+00 + 3.59503E+00 1.12194E+00 + 4.65000E+00 1.20241E+00 + 6.06898E+00 1.27939E+00 + 8.09160E+00 1.35637E+00 + 1.10395E+01 1.43335E+00 + 1.54405E+01 1.51033E+00 + 2.21836E+01 1.58732E+00 + 3.28092E+01 1.66430E+00 + 5.00682E+01 1.74128E+00 + 7.90344E+01 1.81826E+00 + 1.29400E+02 1.89524E+00 + 2.20389E+02 1.97222E+00 + 3.91696E+02 2.04921E+00 + 7.28945E+02 2.12619E+00 + 1.42569E+03 2.20317E+00 + 2.94218E+03 2.28015E+00 + 6.43417E+03 2.35713E+00 + 1.49799E+04 2.43411E+00 + 3.73160E+04 2.51110E+00 + 1.00000E+05 2.58808E+00 +XMIN, XCR, (XV(I), I =1, NX) + 1.00000E-08 1.50000E+00 + 1.00000E-08 1.17803E-08 1.38778E-08 1.63489E-08 1.92599E-08 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1.01517E+00 9.06937E-01 8.10685E-01 7.24869E-01 6.48315E-01 + 5.79976E-01 5.18936E-01 4.64389E-01 4.15624E-01 3.72011E-01 3.32991E-01 + 2.98067E-01 2.66793E-01 2.38770E-01 2.13639E-01 1.91077E-01 1.70801E-01 + 1.52540E-01 1.36073E-01 1.21202E-01 1.07754E-01 9.55931E-02 8.45660E-02 + 7.46080E-02 6.56093E-02 5.74914E-02 5.01841E-02 4.36238E-02 3.77516E-02 + 3.25131E-02 2.78574E-02 2.37368E-02 2.01060E-02 1.69228E-02 1.41469E-02 + 1.17404E-02 9.66735E-03 7.89385E-03 6.38821E-03 5.12016E-03 4.06129E-03 + 3.18713E-03 2.47090E-03 1.89149E-03 1.42842E-03 1.06320E-03 7.79212E-04 + 5.61783E-04 3.98061E-04 2.76974E-04 1.89129E-04 1.26700E-04 8.32879E-05 + 5.37856E-05 3.41836E-05 2.14750E-05 1.33946E-05 8.35347E-06 5.24488E-06 + 3.33291E-06 2.14693E-06 1.39738E-06 9.12131E-07 5.91159E-07 3.76350E-07 + 2.32946E-07 1.38664E-07 7.84720E-08 4.15311E-08 2.00410E-08 8.43420E-09 + 2.84114E-09 6.53323E-10 7.39317E-11 0.00000E+00 + diff --git a/PYTHIA8/pythia8140/xmldoc/ct09mc2.pds b/PYTHIA8/pythia8140/xmldoc/ct09mc2.pds new file mode 100644 index 00000000000..65ce7dbd896 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ct09mc2.pds @@ -0,0 +1,6440 @@ +PDF Table for Fit #: fl6msrv + Ordr, Nfl, lambda Qmass 1, 2, 3, 4, 5, 6 + 2. 5. 0.2268 0.001 0.001 0.200 1.300 4.650 172.000 + IPD0, IHDN, IKNL, NfMx, Nfval, KF, Nelmt + 1 1 1 5 2 12 57300 + NX, NT, JT, NG, NTL(NG+1) + 190 24 1 2 24 +(NTL(I), NTN(I), TLN(I), DTN(I), I =1, NG) + 0 7 5.57275E-01 7.83026E-02 + 7 17 1.10539E+00 8.58403E-02 +QINI, QMAX, (QV(I), TV(I), I =0, NT) + 1.30000E+00 1.00000E+05 + 1.30000E+00 5.57275E-01 + 1.49866E+00 6.35577E-01 + 1.74779E+00 7.13880E-01 + 2.06404E+00 7.92182E-01 + 2.47076E+00 8.70485E-01 + 3.00126E+00 9.48788E-01 + 3.70389E+00 1.02709E+00 + 4.65000E+00 1.10539E+00 + 6.09576E+00 1.19123E+00 + 8.18731E+00 1.27707E+00 + 1.12911E+01 1.36291E+00 + 1.60268E+01 1.44875E+00 + 2.34741E+01 1.53459E+00 + 3.55786E+01 1.62043E+00 + 5.59725E+01 1.70627E+00 + 9.17063E+01 1.79212E+00 + 1.57052E+02 1.87796E+00 + 2.82247E+02 1.96380E+00 + 5.34606E+02 2.04964E+00 + 1.07227E+03 2.13548E+00 + 2.28911E+03 2.22132E+00 + 5.23059E+03 2.30716E+00 + 1.28707E+04 2.39300E+00 + 3.43324E+04 2.47884E+00 + 1.00000E+05 2.56468E+00 +XMIN, XCR, (XV(I), I =1, NX) + 1.00000E-08 1.50000E+00 + 1.00000E-08 1.17803E-08 1.38778E-08 1.63489E-08 1.92599E-08 2.26892E-08 + 2.67291E-08 3.14884E-08 3.70950E-08 4.36999E-08 5.14807E-08 6.06469E-08 + 7.14452E-08 8.41659E-08 9.91515E-08 1.16805E-07 1.37602E-07 1.62101E-07 + 1.90962E-07 2.24961E-07 2.65013E-07 3.12195E-07 3.67777E-07 4.33253E-07 + 5.10385E-07 6.01248E-07 7.08284E-07 8.34965E-07 9.83595E-07 1.15868E-06 + 1.36492E-06 1.60787E-06 1.89406E-06 2.23117E-06 2.62841E-06 3.09641E-06 + 3.64773E-06 4.29722E-06 5.06234E-06 5.96367E-06 7.02548E-06 8.27631E-06 + 9.74982E-06 1.14856E-05 1.35304E-05 1.59392E-05 1.87766E-05 2.21191E-05 + 2.60564E-05 3.06942E-05 3.61571E-05 4.25918E-05 5.01709E-05 5.90977E-05 + 6.96115E-05 8.19937E-05 9.65758E-05 1.13747E-04 1.33967E-04 1.57774E-04 + 1.85802E-04 2.18795E-04 2.57627E-04 3.03325E-04 3.57094E-04 4.20343E-04 + 4.94725E-04 5.82239E-04 6.85007E-04 8.05733E-04 9.47515E-04 1.11390E-03 + 1.30904E-03 1.53770E-03 1.80543E-03 2.11857E-03 2.48437E-03 2.91111E-03 + 3.40814E-03 3.98598E-03 4.65639E-03 5.43234E-03 6.32831E-03 7.35986E-03 + 8.54125E-03 9.89379E-03 1.14309E-02 1.31758E-02 1.51436E-02 1.73523E-02 + 1.98189E-02 2.25606E-02 2.55851E-02 2.89092E-02 3.25397E-02 3.64826E-02 + 4.07414E-02 4.53168E-02 5.02071E-02 5.54085E-02 6.09151E-02 6.67197E-02 + 7.28133E-02 7.91861E-02 8.58274E-02 9.27257E-02 9.98695E-02 1.07243E-01 + 1.14848E-01 1.22661E-01 1.30677E-01 1.38873E-01 1.47265E-01 1.55821E-01 + 1.64539E-01 1.73408E-01 1.82435E-01 1.91589E-01 2.00875E-01 2.10284E-01 + 2.19811E-01 2.29449E-01 2.39192E-01 2.49036E-01 2.58974E-01 2.69003E-01 + 2.79118E-01 2.89315E-01 2.99590E-01 3.09940E-01 3.20361E-01 3.30848E-01 + 3.41402E-01 3.52019E-01 3.62695E-01 3.73426E-01 3.84208E-01 3.95063E-01 + 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1.85178E-05 + 1.44926E-05 1.12880E-05 8.71724E-06 6.65279E-06 5.00816E-06 3.71199E-06 + 2.70394E-06 1.93194E-06 1.35094E-06 9.22210E-07 6.12767E-07 3.94898E-07 + 2.45798E-07 1.46862E-07 8.35791E-08 4.47158E-08 2.20033E-08 9.56434E-09 + 3.38526E-09 8.31475E-10 1.00056E-10 0.00000E+00 + diff --git a/PYTHIA8/pythia8140/xmldoc/ct09mcs.pds b/PYTHIA8/pythia8140/xmldoc/ct09mcs.pds new file mode 100644 index 00000000000..eb05eff58dd --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ct09mcs.pds @@ -0,0 +1,6440 @@ +PDF Table for Fit #: cp6ls14 + Ordr, Nfl, lambda Qmass 1, 2, 3, 4, 5, 6 + 2. 5. 0.2268 0.001 0.001 0.200 1.400 4.750 172.000 + IPD0, IHDN, IKNL, NfMx, Nfval, KF, Nelmt + 1 1 1 5 2 12 57300 + NX, NT, JT, NG, NTL(NG+1) + 190 24 1 3 24 +(NTL(I), NTN(I), TLN(I), DTN(I), I =1, NG) + 0 1 5.57275E-01 4.15705E-02 + 1 6 5.98845E-01 8.55946E-02 + 7 17 1.11241E+00 8.54274E-02 +QINI, QMAX, (QV(I), TV(I), I =0, NT) + 1.30000E+00 1.00000E+05 + 1.30000E+00 5.57275E-01 + 1.40000E+00 5.98845E-01 + 1.64727E+00 6.84440E-01 + 1.96658E+00 7.70034E-01 + 2.38526E+00 8.55629E-01 + 2.94342E+00 9.41223E-01 + 3.70108E+00 1.02682E+00 + 4.75000E+00 1.11241E+00 + 6.23021E+00 1.19784E+00 + 8.37178E+00 1.28327E+00 + 1.15499E+01 1.36869E+00 + 1.63983E+01 1.45412E+00 + 2.40214E+01 1.53955E+00 + 3.64069E+01 1.62498E+00 + 5.72629E+01 1.71040E+00 + 9.37788E+01 1.79583E+00 + 1.60488E+02 1.88126E+00 + 2.88130E+02 1.96669E+00 + 5.45004E+02 2.05211E+00 + 1.09118E+03 2.13754E+00 + 2.32426E+03 2.22297E+00 + 5.29613E+03 2.30840E+00 + 1.29876E+04 2.39382E+00 + 3.45020E+04 2.47925E+00 + 1.00000E+05 2.56468E+00 +XMIN, XCR, (XV(I), I =1, NX) + 1.00000E-08 1.50000E+00 + 1.00000E-08 1.17803E-08 1.38778E-08 1.63489E-08 1.92599E-08 2.26892E-08 + 2.67291E-08 3.14884E-08 3.70950E-08 4.36999E-08 5.14807E-08 6.06469E-08 + 7.14452E-08 8.41659E-08 9.91515E-08 1.16805E-07 1.37602E-07 1.62101E-07 + 1.90962E-07 2.24961E-07 2.65013E-07 3.12195E-07 3.67777E-07 4.33253E-07 + 5.10385E-07 6.01248E-07 7.08284E-07 8.34965E-07 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1.68416E-01 1.84794E-01 2.01731E-01 2.19016E-01 + 2.36948E-01 2.55242E-01 2.73927E-01 2.92954E-01 3.12340E-01 3.32036E-01 + 3.52019E-01 3.72282E-01 3.92772E-01 4.13533E-01 4.34326E-01 4.55495E-01 + 4.76836E-01 4.98342E-01 5.20006E-01 5.41818E-01 5.63773E-01 5.85861E-01 + 6.08077E-01 6.30459E-01 6.52800E-01 6.75387E-01 6.98063E-01 7.20830E-01 + 7.43683E-01 7.66623E-01 7.89636E-01 8.12791E-01 8.35940E-01 8.59175E-01 + 8.82485E-01 9.05866E-01 9.29311E-01 9.52817E-01 9.76387E-01 1.00000E+00 +Parton Distribution Table: + 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 + 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 + 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 + 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 + 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 + 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 + 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 + 0.00000E+00 0.00000E+00 0.00000E+00 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7.54275E-02 5.89608E-02 + 4.56200E-02 3.48977E-02 2.63602E-02 1.96328E-02 1.43947E-02 + 1.03707E-02 7.32962E-03 5.05994E-03 3.41616E-03 2.23612E-03 + 1.41685E-03 8.64446E-04 5.04582E-04 2.79418E-04 1.45450E-04 + 6.99926E-05 3.07289E-05 1.19772E-05 4.01020E-06 1.10444E-06 + 2.35759E-07 3.64994E-08 3.21967E-09 0.00000E+00 9.13651E+07 + 6.60183E+07 4.64500E+07 3.26601E+07 2.29443E+07 1.61046E+07 + 1.12937E+07 7.91261E+06 5.53854E+06 3.87305E+06 2.70572E+06 + 1.88833E+06 1.31652E+06 9.16904E+05 6.37911E+05 4.43330E+05 + 3.07767E+05 2.13421E+05 1.47833E+05 1.02287E+05 7.06963E+04 + 4.88083E+04 3.36615E+04 2.31910E+04 1.59615E+04 1.09739E+04 + 7.54238E+03 5.15078E+03 3.53769E+03 2.42969E+03 1.66923E+03 + 1.14769E+03 7.89689E+02 5.44533E+02 3.76625E+02 2.61605E+02 + 1.82653E+02 1.28385E+02 9.09820E+01 6.51030E+01 4.71067E+01 + 3.45095E+01 2.56216E+01 1.92803E+01 1.47243E+01 1.13933E+01 + 8.92762E+00 7.07576E+00 5.66466E+00 4.57443E+00 3.72147E+00 + 3.04579E+00 2.50777E+00 2.07005E+00 1.71457E+00 1.42288E+00 + 1.18213E+00 9.82502E-01 8.15993E-01 6.78183E-01 5.61591E-01 + 4.64282E-01 3.82688E-01 3.14364E-01 2.57083E-01 2.09212E-01 + 1.69323E-01 1.36168E-01 1.08800E-01 8.61847E-02 6.78328E-02 + 5.27793E-02 4.06450E-02 3.09429E-02 2.32583E-02 1.72355E-02 + 1.25719E-02 9.00948E-03 6.33280E-03 4.34700E-03 2.91771E-03 + 1.89821E-03 1.19511E-03 7.24322E-04 4.19853E-04 2.30804E-04 + 1.19230E-04 5.69190E-05 2.47869E-05 9.58467E-06 3.18707E-06 + 8.74235E-07 1.86959E-07 2.92339E-08 2.65384E-09 0.00000E+00 diff --git a/PYTHIA8/pythia8140/xmldoc/ctq66.00.pds b/PYTHIA8/pythia8140/xmldoc/ctq66.00.pds new file mode 100644 index 00000000000..1460d4192ef --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/ctq66.00.pds @@ -0,0 +1,5099 @@ +PDF Table for Fit #: p82a3 + Ordr, Nfl, lambda Qmass 1, 2, 3, 4, 5, 6 + 2. 5. 0.2262 0.001 0.001 0.200 1.300 4.500 175.000 + IPD0, IHDN, IKNL, NfMx, Nfval, KF, Nelmt + 1 1 2 5 2 12 45300 + NX, NT, JT, NG, NTL(NG+1) + 150 24 1 2 24 +(NTL(I), NTN(I), TLN(I), DTN(I), I =1, NG) + 0 7 5.58779E-01 7.66540E-02 + 7 17 1.09536E+00 8.64425E-02 +QINI, QMAX, (QV(I), TV(I), I =0, NT) + 1.30000E+00 1.00000E+05 + 1.30000E+00 5.58779E-01 + 1.49431E+00 6.35433E-01 + 1.73684E+00 7.12087E-01 + 2.04307E+00 7.88741E-01 + 2.43457E+00 8.65395E-01 + 2.94191E+00 9.42049E-01 + 3.60899E+00 1.01870E+00 + 4.50000E+00 1.09536E+00 + 5.89476E+00 1.18180E+00 + 7.91236E+00 1.26824E+00 + 1.09066E+01 1.35468E+00 + 1.54759E+01 1.44113E+00 + 2.26644E+01 1.52757E+00 + 3.43551E+01 1.61401E+00 + 5.40692E+01 1.70045E+00 + 8.86525E+01 1.78690E+00 + 1.51992E+02 1.87334E+00 + 2.73584E+02 1.95978E+00 + 5.19288E+02 2.04622E+00 + 1.04437E+03 2.13267E+00 + 2.23717E+03 2.21911E+00 + 5.13351E+03 2.30555E+00 + 1.26969E+04 2.39199E+00 + 3.40794E+04 2.47844E+00 + 1.00000E+05 2.56488E+00 +XMIN, XCR, (XV(I), I =1, NX) + 1.00000E-08 2.00000E+00 + 1.00000E-08 1.21431E-08 1.47455E-08 1.79056E-08 2.17430E-08 2.64028E-08 + 3.20612E-08 3.89322E-08 4.72758E-08 5.74075E-08 6.97106E-08 8.46503E-08 + 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alphaS(MZ) = 0.12032 + # alphaSorder,alphaSnfmax = 0, 5 + # nExtraFlavours = 0 + + xg xd xu xs xc xb xdv xuv xsv + 8.0090E+00 1.3182E+00 1.3280E+00 6.5619E-01 0.0000E+00 0.0000E+00 5.8017E-03 1.5621E-02 0.0000E+00 + 1.3658E+01 1.3573E+00 1.3671E+00 7.0073E-01 0.0000E+00 0.0000E+00 5.8891E-03 1.5771E-02 0.0000E+00 + 1.9234E+01 1.4059E+00 1.4159E+00 7.5351E-01 0.0000E+00 0.0000E+00 5.9561E-03 1.5886E-02 0.0000E+00 + 3.0629E+01 1.5247E+00 1.5347E+00 8.7863E-01 0.0000E+00 0.0000E+00 6.0622E-03 1.6067E-02 0.0000E+00 + 3.0629E+01 1.5247E+00 1.5347E+00 8.7863E-01 2.9834E-07 0.0000E+00 6.0622E-03 1.6067E-02 0.0000E+00 + 3.9149E+01 1.6266E+00 1.6367E+00 9.8425E-01 1.1276E-01 0.0000E+00 6.1268E-03 1.6176E-02 0.0000E+00 + 5.0924E+01 1.7791E+00 1.7892E+00 1.1411E+00 2.7542E-01 0.0000E+00 6.2025E-03 1.6304E-02 0.0000E+00 + 6.2763E+01 1.9433E+00 1.9534E+00 1.3088E+00 4.4809E-01 0.0000E+00 6.2677E-03 1.6414E-02 0.0000E+00 + 7.5692E+01 2.1324E+00 2.1426E+00 1.5014E+00 6.4529E-01 0.0000E+00 6.3304E-03 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b/PYTHIA8/pythia8140/xmldoc/mrstlostarstar.00.dat new file mode 100644 index 00000000000..389f433ebd7 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/mrstlostarstar.00.dat @@ -0,0 +1,3035 @@ + # Tue Oct 27 14:26:24 2009 + # MSTW 2008 LO PDF grid for central fit. + # distance(t),tolerance(T) = 0. 0. + # mCharm = 1.43 + # mBottom = 4.30 + # alphaS(1GeV) = 0.40768 + # alphaS(MZ) = 0.11517 + # alphaSorder,alphaSnfmax = 0, 5 + # nExtraFlavours = 0 + + xg xd xu xs xc xb xdv xuv xsv + 1.2042E+01 1.3018E+00 1.3129E+00 6.4816E-01 0.0000E+00 0.0000E+00 5.5017E-03 1.6579E-02 0.0000E+00 + 1.8147E+01 1.3513E+00 1.3625E+00 7.0214E-01 -2.4286E-17 -2.4286E-17 5.5603E-03 1.6674E-02 0.0000E+00 + 2.3965E+01 1.4062E+00 1.4173E+00 7.6048E-01 -1.2924E-16 -1.2924E-16 5.6072E-03 1.6750E-02 -2.2204E-16 + 3.5512E+01 1.5303E+00 1.5415E+00 8.9026E-01 -5.5077E-16 -5.5077E-16 5.6849E-03 1.6875E-02 -1.1102E-15 + 3.5512E+01 1.5303E+00 1.5415E+00 8.9026E-01 2.9995E-07 -5.5077E-16 5.6849E-03 1.6875E-02 -1.1102E-15 + 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-1.7637E-06 6.6763E-07 -1.4905E-06 -1.7509E-06 5.6424E-06 -1.7672E-06 + 1.9284E-14 -2.1997E-08 5.6420E-06 -1.7728E-06 6.6763E-07 -1.4973E-06 -1.7509E-06 5.6424E-06 -1.7672E-06 + 1.9284E-14 -3.0541E-08 5.6335E-06 -1.7814E-06 6.6763E-07 -1.5037E-06 -1.7509E-06 5.6424E-06 -1.7672E-06 + 1.9284E-14 -3.8435E-08 5.6256E-06 -1.7893E-06 6.6763E-07 -1.5097E-06 -1.7509E-06 5.6424E-06 -1.7672E-06 + 1.9284E-14 -4.9983E-08 5.6140E-06 -1.8008E-06 6.6763E-07 -1.5183E-06 -1.7509E-06 5.6424E-06 -1.7672E-06 + 1.9284E-14 -5.6721E-08 5.6073E-06 -1.8075E-06 6.6763E-07 -1.5234E-06 -1.7509E-06 5.6424E-06 -1.7672E-06 diff --git a/PYTHIA8/pythia8140/xmldoc/mstw2008lo.00.dat b/PYTHIA8/pythia8140/xmldoc/mstw2008lo.00.dat new file mode 100644 index 00000000000..421080710a3 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/mstw2008lo.00.dat @@ -0,0 +1,3035 @@ + # Thu Nov 6 19:08:12 2008 + # MSTW 2008 LO PDF grid for central fit. + # distance(t),tolerance(T) = 0. 0. + # mCharm = 1.40 + # mBottom = 4.75 + # alphaS(1GeV) = 0.68183 + # alphaS(MZ) = 0.13939 + # alphaSorder,alphaSnfmax = 0, 5 + # nExtraFlavours = 0 + + xg xd xu xs xc xb xdv xuv xsv + 1.3241E+02 1.1742E+00 1.1767E+00 4.8673E-01 0.0000E+00 0.0000E+00 1.9861E-04 2.6691E-03 -7.2535E-04 + 1.3796E+02 1.7390E+00 1.7415E+00 1.0578E+00 0.0000E+00 0.0000E+00 2.1538E-04 2.7734E-03 -7.3571E-04 + 1.4346E+02 2.1713E+00 2.1739E+00 1.4948E+00 0.0000E+00 0.0000E+00 2.2894E-04 2.8541E-03 -7.4354E-04 + 1.5307E+02 2.7759E+00 2.7786E+00 2.1057E+00 0.0000E+00 0.0000E+00 2.4858E-04 2.9662E-03 -7.5416E-04 + 1.5307E+02 2.7759E+00 2.7786E+00 2.1057E+00 1.4899E-06 0.0000E+00 2.4858E-04 2.9662E-03 -7.5416E-04 + 1.6275E+02 3.3097E+00 3.3125E+00 2.6446E+00 6.0851E-01 0.0000E+00 2.6627E-04 3.0628E-03 -7.6309E-04 + 1.7447E+02 3.8472E+00 3.8500E+00 3.1868E+00 1.1915E+00 0.0000E+00 2.8409E-04 3.1567E-03 -7.7157E-04 + 1.8667E+02 4.3367E+00 4.3396E+00 3.6804E+00 1.7187E+00 0.0000E+00 3.0008E-04 3.2382E-03 -7.7880E-04 + 2.0037E+02 4.8348E+00 4.8378E+00 4.1823E+00 2.2517E+00 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diff --git a/PYTHIA8/pythia8140/xmldoc/mstw2008nlo.00.dat b/PYTHIA8/pythia8140/xmldoc/mstw2008nlo.00.dat new file mode 100644 index 00000000000..b7e447c89e6 --- /dev/null +++ b/PYTHIA8/pythia8140/xmldoc/mstw2008nlo.00.dat @@ -0,0 +1,3035 @@ + # Mon Nov 10 16:35:59 2008 + # MSTW 2008 NLO PDF grid for central fit. + # distance(t),tolerance(T) = 0. 0. + # mCharm = 1.40 + # mBottom = 4.75 + # alphaS(1GeV) = 0.49128 + # alphaS(MZ) = 0.12018 + # alphaSorder,alphaSnfmax = 1, 5 + # nExtraFlavours = 0 + + xg xd xu xs xc xb xdv xuv xsv + -1.0407E+01 1.3098E+00 1.3144E+00 4.6749E-01 0.0000E+00 0.0000E+00 7.5402E-06 4.6422E-03 -7.3203E-04 + -1.0583E+01 1.2372E+00 1.2419E+00 4.0558E-01 0.0000E+00 0.0000E+00 1.5377E-05 4.7693E-03 -7.4388E-04 + -1.0365E+01 1.2000E+00 1.2048E+00 3.7621E-01 0.0000E+00 0.0000E+00 2.1813E-05 4.8647E-03 -7.5265E-04 + -9.3612E+00 1.1792E+00 1.1842E+00 3.6560E-01 0.0000E+00 0.0000E+00 3.1249E-05 4.9930E-03 -7.6430E-04 + -9.3612E+00 1.1792E+00 1.1842E+00 3.6560E-01 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