Changed default OCDB from 2009 to 2010
[u/mrichter/AliRoot.git] / MUON / AliMUONTrackExtrap.cxx
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c04e3238 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
56316147 18//-----------------------------------------------------------------------------
19// Class AliMUONTrackExtrap
20// ------------------------
21// Tools for track extrapolation in ALICE dimuon spectrometer
22// Author: Philippe Pillot
23//-----------------------------------------------------------------------------
c04e3238 24
c04e3238 25#include "AliMUONTrackExtrap.h"
26#include "AliMUONTrackParam.h"
27#include "AliMUONConstants.h"
0e894e58 28#include "AliMUONReconstructor.h"
8cde4af5 29
ecdf58c4 30#include "AliMagF.h"
31#include "AliExternalTrackParam.h"
8cde4af5 32
f7a1cc68 33#include <TGeoGlobalMagField.h>
8cde4af5 34#include <TGeoManager.h>
f7a1cc68 35#include <TMath.h>
ecdf58c4 36#include <TDatabasePDG.h>
c04e3238 37
ea94c18b 38#include <Riostream.h>
39
78649106 40/// \cond CLASSIMP
c04e3238 41ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
78649106 42/// \endcond
c04e3238 43
9f093251 44const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
45const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
46 Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
47 Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
4284483e 48const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
208f139e 49const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
4284483e 50const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
51const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
208f139e 52
690d2205 53//__________________________________________________________________________
f7a1cc68 54void AliMUONTrackExtrap::SetField()
9f093251 55{
cddcc1f3 56 /// set field on/off flag;
57 /// set field at the centre of the dipole
f7a1cc68 58 const Double_t x[3] = {50.,50.,fgkSimpleBPosition};
59 Double_t b[3] = {0.,0.,0.};
60 TGeoGlobalMagField::Instance()->Field(x,b);
61 fgSimpleBValue = b[0];
62 fgFieldON = fgSimpleBValue ? kTRUE : kFALSE;
9f093251 63
64}
65
66//__________________________________________________________________________
208f139e 67Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
68{
69 /// Returns impact parameter at vertex in bending plane (cm),
70 /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
71 /// using simple values for dipole magnetic field.
72 /// The sign of "BendingMomentum" is the sign of the charge.
73
74 if (bendingMomentum == 0.) return 1.e10;
75
6b191dea 76 const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
9f093251 77
78 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
208f139e 79}
80
690d2205 81//__________________________________________________________________________
9bdbee64 82Double_t
83AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
208f139e 84{
85 /// Returns signed bending momentum in bending plane (GeV/c),
86 /// the sign being the sign of the charge for particles moving forward in Z,
87 /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
88 /// using simple values for dipole magnetic field.
89
90 if (impactParam == 0.) return 1.e10;
91
9f093251 92 const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
93
9bdbee64 94 if (fgFieldON)
95 {
96 return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
97 }
98 else
99 {
100 return AliMUONConstants::GetMostProbBendingMomentum();
101 }
208f139e 102}
c04e3238 103
690d2205 104//__________________________________________________________________________
3fe6651e 105void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
019df241 106{
3fe6651e 107 /// Track parameters linearly extrapolated to the plane at "zEnd".
019df241 108 /// On return, results from the extrapolation are updated in trackParam.
109
110 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
111
112 // Compute track parameters
113 Double_t dZ = zEnd - trackParam->GetZ();
114 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
115 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
116 trackParam->SetZ(zEnd);
3fe6651e 117}
118
119//__________________________________________________________________________
120void AliMUONTrackExtrap::LinearExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
121{
122 /// Track parameters and their covariances linearly extrapolated to the plane at "zEnd".
123 /// On return, results from the extrapolation are updated in trackParam.
019df241 124
3fe6651e 125 if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
126
127 // No need to propagate the covariance matrix if it does not exist
128 if (!trackParam->CovariancesExist()) {
129 cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl;
130 // Extrapolate linearly track parameters to "zEnd"
131 LinearExtrapToZ(trackParam,zEnd);
132 return;
019df241 133 }
134
3fe6651e 135 // Compute track parameters
136 Double_t dZ = zEnd - trackParam->GetZ();
137 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
138 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
139 trackParam->SetZ(zEnd);
140
141 // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd"
142 TMatrixD jacob(5,5);
143 jacob.UnitMatrix();
144 jacob(0,1) = dZ;
145 jacob(2,3) = dZ;
146
147 // Extrapolate track parameter covariances to "zEnd"
148 TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob);
149 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
150 trackParam->SetCovariances(tmp2);
151
152 // Update the propagator if required
153 if (updatePropagator) trackParam->UpdatePropagator(jacob);
019df241 154}
155
690d2205 156//__________________________________________________________________________
4ea3f013 157Bool_t AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
c04e3238 158{
4284483e 159 /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
160 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 161 if (!fgFieldON) {
162 AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
163 return kTRUE;
164 }
165 else if (fgkUseHelix) return AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
166 else return AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
4284483e 167}
168
690d2205 169//__________________________________________________________________________
4ea3f013 170Bool_t AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
4284483e 171{
172 /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
c04e3238 173 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 174 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
c04e3238 175 Double_t forwardBackward; // +1 if forward, -1 if backward
176 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
177 else forwardBackward = -1.0;
dade8580 178 Double_t v3[7], v3New[7]; // 7 in parameter ????
179 Int_t i3, stepNumber;
c04e3238 180 // For safety: return kTRUE or kFALSE ????
181 // Parameter vector for calling EXTRAP_ONESTEP
4284483e 182 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
c04e3238 183 // sign of charge (sign of fInverseBendingMomentum if forward motion)
184 // must be changed if backward extrapolation
208f139e 185 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
c04e3238 186 // Extrapolation loop
187 stepNumber = 0;
208f139e 188 while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
c04e3238 189 stepNumber++;
4284483e 190 ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
dade8580 191 if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
690d2205 192 // better use TArray ????
208f139e 193 for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
c04e3238 194 }
208f139e 195 // check fgkMaxStepNumber ????
c04e3238 196 // Interpolation back to exact Z (2nd order)
197 // should be in function ???? using TArray ????
dade8580 198 Double_t dZ12 = v3New[2] - v3[2]; // 1->2
c04e3238 199 if (TMath::Abs(dZ12) > 0) {
dade8580 200 Double_t dZ1i = zEnd - v3[2]; // 1-i
201 Double_t dZi2 = v3New[2] - zEnd; // i->2
202 Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
203 Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
204 Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
205 Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
206 v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
207 v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
208 v3[2] = zEnd; // Z
c04e3238 209 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
210 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
211 // (PX, PY, PZ)/PTOT assuming forward motion
208f139e 212 v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
dade8580 213 v3[3] = xPrimeI * v3[5]; // PX/PTOT
214 v3[4] = yPrimeI * v3[5]; // PY/PTOT
c04e3238 215 } else {
4284483e 216 cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
c04e3238 217 }
4284483e 218 // Recover track parameters (charge back for forward motion)
dade8580 219 RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
4ea3f013 220 return kTRUE;
c04e3238 221}
222
690d2205 223//__________________________________________________________________________
4ea3f013 224Bool_t AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
4284483e 225{
226 /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
227 /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
4ea3f013 228 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
4284483e 229 Double_t forwardBackward; // +1 if forward, -1 if backward
230 if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
231 else forwardBackward = -1.0;
232 // sign of charge (sign of fInverseBendingMomentum if forward motion)
233 // must be changed if backward extrapolation
234 Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
235 Double_t v3[7], v3New[7];
236 Double_t dZ, step;
237 Int_t stepNumber = 0;
238
4ea3f013 239 // Extrapolation loop (until within tolerance or the track turn around)
4284483e 240 Double_t residue = zEnd - trackParam->GetZ();
4ea3f013 241 Bool_t uturn = kFALSE;
242 Bool_t tooManyStep = kFALSE;
4284483e 243 while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
4ea3f013 244
4284483e 245 dZ = zEnd - trackParam->GetZ();
246 // step lenght assuming linear trajectory
247 step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
690d2205 248 trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
4284483e 249 ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
4ea3f013 250
4284483e 251 do { // reduce step lenght while zEnd oversteped
252 if (stepNumber > fgkMaxStepNumber) {
253 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
4ea3f013 254 tooManyStep = kTRUE;
4284483e 255 break;
256 }
257 stepNumber ++;
258 step = TMath::Abs(step);
259 AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New);
260 residue = zEnd - v3New[2];
261 step *= dZ/(v3New[2]-trackParam->GetZ());
262 } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
4ea3f013 263
264 if (v3New[5]*v3[5] < 0) { // the track turned around
265 cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: The track turned around"<<endl;
266 uturn = kTRUE;
267 break;
268 } else RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
269
4284483e 270 }
271
272 // terminate the extropolation with a straight line up to the exact "zEnd" value
4ea3f013 273 if (uturn) {
274
275 // track ends +-100 meters away in the bending direction
276 dZ = zEnd - v3[2];
277 Double_t bendingSlope = TMath::Sign(1.e4,-fgSimpleBValue*trackParam->GetInverseBendingMomentum()) / dZ;
278 Double_t pZ = TMath::Abs(1. / trackParam->GetInverseBendingMomentum()) / TMath::Sqrt(1.0 + bendingSlope * bendingSlope);
279 Double_t nonBendingSlope = TMath::Sign(TMath::Abs(v3[3]) * v3[6] / pZ, trackParam->GetNonBendingSlope());
280 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + dZ * nonBendingSlope);
281 trackParam->SetNonBendingSlope(nonBendingSlope);
282 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + dZ * bendingSlope);
283 trackParam->SetBendingSlope(bendingSlope);
284 trackParam->SetZ(zEnd);
285
286 return kFALSE;
287
288 } else {
289
290 // track extrapolated normally
291 trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
292 trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
293 trackParam->SetZ(zEnd);
294
295 return !tooManyStep;
296
297 }
298
4284483e 299}
300
690d2205 301//__________________________________________________________________________
4284483e 302void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
c04e3238 303{
dade8580 304 /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
c04e3238 305 /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
306 /// to know whether the particle is going forward (+1) or backward (-1).
dade8580 307 v3[0] = trackParam->GetNonBendingCoor(); // X
308 v3[1] = trackParam->GetBendingCoor(); // Y
309 v3[2] = trackParam->GetZ(); // Z
c04e3238 310 Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
311 Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
dade8580 312 v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
313 v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
314 v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
315 v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
c04e3238 316}
317
690d2205 318//__________________________________________________________________________
dade8580 319void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
c04e3238 320{
dade8580 321 /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
c04e3238 322 /// assumed to be calculated for forward motion in Z.
323 /// "InverseBendingMomentum" is signed with "charge".
dade8580 324 trackParam->SetNonBendingCoor(v3[0]); // X
325 trackParam->SetBendingCoor(v3[1]); // Y
326 trackParam->SetZ(v3[2]); // Z
60e55aee 327 Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
c04e3238 328 trackParam->SetInverseBendingMomentum(charge/pYZ);
dade8580 329 trackParam->SetBendingSlope(v3[4]/v3[5]);
330 trackParam->SetNonBendingSlope(v3[3]/v3[5]);
c04e3238 331}
332
690d2205 333//__________________________________________________________________________
4ea3f013 334Bool_t AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
208f139e 335{
336 /// Track parameters and their covariances extrapolated to the plane at "zEnd".
337 /// On return, results from the extrapolation are updated in trackParam.
338
4ea3f013 339 if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same z
208f139e 340
9f093251 341 if (!fgFieldON) { // linear extrapolation if no magnetic field
3fe6651e 342 AliMUONTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator);
4ea3f013 343 return kTRUE;
9f093251 344 }
345
ea94c18b 346 // No need to propagate the covariance matrix if it does not exist
347 if (!trackParam->CovariancesExist()) {
348 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
349 // Extrapolate track parameters to "zEnd"
4ea3f013 350 return ExtrapToZ(trackParam,zEnd);
ea94c18b 351 }
352
208f139e 353 // Save the actual track parameters
354 AliMUONTrackParam trackParamSave(*trackParam);
ea94c18b 355 TMatrixD paramSave(trackParamSave.GetParameters());
356 Double_t zBegin = trackParamSave.GetZ();
357
358 // Get reference to the parameter covariance matrix
359 const TMatrixD& kParamCov = trackParam->GetCovariances();
9bf6860b 360
208f139e 361 // Extrapolate track parameters to "zEnd"
4ea3f013 362 // Do not update the covariance matrix if the extrapolation failed
363 if (!ExtrapToZ(trackParam,zEnd)) return kFALSE;
208f139e 364
ea94c18b 365 // Get reference to the extrapolated parameters
366 const TMatrixD& extrapParam = trackParam->GetParameters();
208f139e 367
368 // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
4ea3f013 369 Bool_t extrapStatus = kTRUE;
208f139e 370 TMatrixD jacob(5,5);
ea94c18b 371 jacob.Zero();
372 TMatrixD dParam(5,1);
6b191dea 373 Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
208f139e 374 for (Int_t i=0; i<5; i++) {
375 // Skip jacobian calculation for parameters with no associated error
18abc511 376 if (kParamCov(i,i) <= 0.) continue;
ea94c18b 377
208f139e 378 // Small variation of parameter i only
379 for (Int_t j=0; j<5; j++) {
380 if (j==i) {
ea94c18b 381 dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
6b191dea 382 dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
ea94c18b 383 } else dParam(j,0) = 0.;
208f139e 384 }
ea94c18b 385
208f139e 386 // Set new parameters
ea94c18b 387 trackParamSave.SetParameters(paramSave);
388 trackParamSave.AddParameters(dParam);
389 trackParamSave.SetZ(zBegin);
390
208f139e 391 // Extrapolate new track parameters to "zEnd"
4ea3f013 392 if (!ExtrapToZ(&trackParamSave,zEnd)) {
393 cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Bad covariance matrix"<<endl;
394 extrapStatus = kFALSE;
395 }
ea94c18b 396
208f139e 397 // Calculate the jacobian
ea94c18b 398 TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
399 jacobji *= 1. / dParam(i,0);
400 jacob.SetSub(0,i,jacobji);
208f139e 401 }
402
403 // Extrapolate track parameter covariances to "zEnd"
ea94c18b 404 TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
405 TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
406 trackParam->SetCovariances(tmp2);
407
408 // Update the propagator if required
409 if (updatePropagator) trackParam->UpdatePropagator(jacob);
4ea3f013 410
411 return extrapStatus;
208f139e 412}
413
690d2205 414//__________________________________________________________________________
37a615ac 415void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2)
8cde4af5 416{
417 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
37a615ac 418 /// signedPathLength must have the sign of (zOut - zIn) where all other parameters are assumed to be given at zOut.
8cde4af5 419
420 // absorber related covariance parameters
421 Double_t bendingSlope = param->GetBendingSlope();
422 Double_t nonBendingSlope = param->GetNonBendingSlope();
423 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
424 Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
690d2205 425 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
37a615ac 426 Double_t pathLength = TMath::Abs(signedPathLength);
8cde4af5 427 Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
37a615ac 428 Double_t covCorrSlope = TMath::Sign(1.,signedPathLength) * alpha2 * (pathLength * f0 - f1);
8cde4af5 429 Double_t varSlop = alpha2 * f0;
430
690d2205 431 // Set MCS covariance matrix
ea94c18b 432 TMatrixD newParamCov(param->GetCovariances());
8cde4af5 433 // Non bending plane
ea94c18b 434 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
435 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
8cde4af5 436 // Bending plane
ea94c18b 437 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
438 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 439
440 // Set momentum related covariances if B!=0
441 if (fgFieldON) {
442 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
443 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
444 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
445 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
446 // Inverse bending momentum (due to dependences with bending and non bending slopes)
447 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
448 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
449 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
450 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
451 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
452 }
ea94c18b 453
454 // Set new covariances
455 param->SetCovariances(newParamCov);
690d2205 456}
457
458//__________________________________________________________________________
459void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
460 Double_t xVtx, Double_t yVtx, Double_t zVtx,
461 Double_t errXVtx, Double_t errYVtx,
462 Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
463{
464 /// Correct parameters and corresponding covariances using Branson correction
465 /// - input param are parameters and covariances at the end of absorber
466 /// - output param are parameters and covariances at vertex
467 /// Absorber correction parameters are supposed to be calculated at the current track z-position
468
469 // Position of the Branson plane (spectro. (z<0))
470 Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
471
37a615ac 472 // Add MCS effects to current parameter covariances (spectro. (z<0))
473 AddMCSEffectInAbsorber(param, -pathLength, f0, f1, f2);
690d2205 474
475 // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
476 ExtrapToZCov(param,zVtx);
3fe6651e 477 LinearExtrapToZCov(param,zB);
690d2205 478
479 // compute track parameters at vertex
480 TMatrixD newParam(5,1);
481 newParam(0,0) = xVtx;
482 newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
483 newParam(2,0) = yVtx;
484 newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
485 newParam(4,0) = param->GetCharge() / param->P() *
486 TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
487 TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
488
489 // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
490 TMatrixD paramCovP(param->GetCovariances());
491 Cov2CovP(param->GetParameters(),paramCovP);
492
493 // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
494 TMatrixD paramCovVtx(5,5);
495 paramCovVtx.Zero();
496 paramCovVtx(0,0) = errXVtx * errXVtx;
497 paramCovVtx(1,1) = paramCovP(0,0);
498 paramCovVtx(2,2) = errYVtx * errYVtx;
499 paramCovVtx(3,3) = paramCovP(2,2);
500 paramCovVtx(4,4) = paramCovP(4,4);
501 paramCovVtx(1,3) = paramCovP(0,2);
502 paramCovVtx(3,1) = paramCovP(2,0);
503 paramCovVtx(1,4) = paramCovP(0,4);
504 paramCovVtx(4,1) = paramCovP(4,0);
505 paramCovVtx(3,4) = paramCovP(2,4);
506 paramCovVtx(4,3) = paramCovP(4,2);
507
508 // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
509 TMatrixD jacob(5,5);
510 jacob.UnitMatrix();
511 jacob(1,0) = - 1. / (zB - zVtx);
512 jacob(1,1) = 1. / (zB - zVtx);
513 jacob(3,2) = - 1. / (zB - zVtx);
514 jacob(3,3) = 1. / (zB - zVtx);
8cde4af5 515
690d2205 516 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
517 TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
518 TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
519
520 // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
521 CovP2Cov(newParam,newParamCov);
522
523 // Set parameters and covariances at vertex
524 param->SetParameters(newParam);
525 param->SetZ(zVtx);
526 param->SetCovariances(newParamCov);
8cde4af5 527}
528
690d2205 529//__________________________________________________________________________
530void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
531{
532 /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
533
534 // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
535 TMatrixD newParamCov(param->GetCovariances());
536 Cov2CovP(param->GetParameters(),newParamCov);
537
690d2205 538 // Compute new parameters corrected for energy loss
ecdf58c4 539 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
540 Double_t p = param->P();
541 Double_t e = TMath::Sqrt(p*p + muMass*muMass);
542 Double_t eCorr = e + eLoss;
543 Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
690d2205 544 Double_t nonBendingSlope = param->GetNonBendingSlope();
545 Double_t bendingSlope = param->GetBendingSlope();
ecdf58c4 546 param->SetInverseBendingMomentum(param->GetCharge() / pCorr *
690d2205 547 TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
548 TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
549
ecdf58c4 550 // Add effects of energy loss fluctuation to covariances
551 newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
552
690d2205 553 // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
554 CovP2Cov(param->GetParameters(),newParamCov);
555
556 // Set new parameter covariances
557 param->SetCovariances(newParamCov);
558}
559
560//__________________________________________________________________________
18abc511 561Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
562 Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
563 Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
8cde4af5 564{
565 /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
690d2205 566 /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
8cde4af5 567 // pathLength: path length between trackXYZIn and trackXYZOut (cm)
568 // f0: 0th moment of z calculated with the inverse radiation-length distribution
569 // f1: 1st moment of z calculated with the inverse radiation-length distribution
570 // f2: 2nd moment of z calculated with the inverse radiation-length distribution
571 // meanRho: average density of crossed material (g/cm3)
84f061ef 572 // totalELoss: total energy loss in absorber
8cde4af5 573
574 // Reset absorber's parameters
575 pathLength = 0.;
576 f0 = 0.;
577 f1 = 0.;
578 f2 = 0.;
579 meanRho = 0.;
84f061ef 580 totalELoss = 0.;
690d2205 581 sigmaELoss2 = 0.;
8cde4af5 582
583 // Check whether the geometry is available
584 if (!gGeoManager) {
585 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
18abc511 586 return kFALSE;
8cde4af5 587 }
588
589 // Initialize starting point and direction
590 pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
591 (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
592 (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
18abc511 593 if (pathLength < TGeoShape::Tolerance()) return kFALSE;
8cde4af5 594 Double_t b[3];
595 b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
596 b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
597 b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
598 TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
599 if (!currentnode) {
600 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
18abc511 601 return kFALSE;
8cde4af5 602 }
603
604 // loop over absorber slices and calculate absorber's parameters
605 Double_t rho = 0.; // material density (g/cm3)
606 Double_t x0 = 0.; // radiation-length (cm-1)
84f061ef 607 Double_t atomicA = 0.; // A of material
608 Double_t atomicZ = 0.; // Z of material
fa5e35be 609 Double_t atomicZoverA = 0.; // Z/A of material
8cde4af5 610 Double_t localPathLength = 0;
611 Double_t remainingPathLength = pathLength;
612 Double_t zB = trackXYZIn[2];
613 Double_t zE, dzB, dzE;
614 do {
615 // Get material properties
616 TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
617 rho = material->GetDensity();
618 x0 = material->GetRadLen();
84f061ef 619 atomicA = material->GetA();
620 atomicZ = material->GetZ();
fa5e35be 621 if(material->IsMixture()){
622 TGeoMixture * mixture = (TGeoMixture*)material;
623 atomicZoverA = 0.;
624 Double_t sum = 0.;
625 for (Int_t iel=0;iel<mixture->GetNelements();iel++){
626 sum += mixture->GetWmixt()[iel];
627 atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
628 }
629 atomicZoverA/=sum;
630 }
631 else atomicZoverA = atomicZ/atomicA;
8cde4af5 632
633 // Get path length within this material
634 gGeoManager->FindNextBoundary(remainingPathLength);
635 localPathLength = gGeoManager->GetStep() + 1.e-6;
636 // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
637 if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
638 else {
639 currentnode = gGeoManager->Step();
640 if (!currentnode) {
641 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 642 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
643 return kFALSE;
8cde4af5 644 }
645 if (!gGeoManager->IsEntering()) {
646 // make another small step to try to enter in new absorber slice
647 gGeoManager->SetStep(0.001);
648 currentnode = gGeoManager->Step();
649 if (!gGeoManager->IsEntering() || !currentnode) {
650 cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
18abc511 651 f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
652 return kFALSE;
8cde4af5 653 }
654 localPathLength += 0.001;
655 }
656 }
657
658 // calculate absorber's parameters
659 zE = b[2] * localPathLength + zB;
660 dzB = zB - trackXYZIn[2];
661 dzE = zE - trackXYZIn[2];
662 f0 += localPathLength / x0;
663 f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
664 f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
665 meanRho += localPathLength * rho;
fa5e35be 666 totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA);
667 sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicZoverA);
8cde4af5 668
669 // prepare next step
670 zB = zE;
671 remainingPathLength -= localPathLength;
672 } while (remainingPathLength > TGeoShape::Tolerance());
673
674 meanRho /= pathLength;
18abc511 675
676 return kTRUE;
8cde4af5 677}
678
690d2205 679//__________________________________________________________________________
ea94c18b 680Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
681{
682 /// Return the angular dispersion square due to multiple Coulomb scattering
683 /// through a material of thickness "dZ" and of radiation length "x0"
684 /// assuming linear propagation and using the small angle approximation.
685
686 Double_t bendingSlope = param.GetBendingSlope();
687 Double_t nonBendingSlope = param.GetNonBendingSlope();
688 Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
690d2205 689 (1.0 + bendingSlope * bendingSlope) /
690 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
ea94c18b 691 // Path length in the material
692 Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
693 // relativistic velocity
694 Double_t velo = 1.;
695 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
696 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
697
698 return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
699}
700
690d2205 701//__________________________________________________________________________
8cde4af5 702void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
208f139e 703{
704 /// Add to the track parameter covariances the effects of multiple Coulomb scattering
37a615ac 705 /// through a material of thickness "Abs(dZ)" and of radiation length "x0"
208f139e 706 /// assuming linear propagation and using the small angle approximation.
37a615ac 707 /// dZ = zOut - zIn (sign is important) and "param" is assumed to be given zOut.
708 /// If x0 <= 0., assume dZ = pathLength/x0 and consider the material thickness as negligible.
208f139e 709
710 Double_t bendingSlope = param->GetBendingSlope();
711 Double_t nonBendingSlope = param->GetNonBendingSlope();
690d2205 712 Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
713 Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
714 (1.0 + bendingSlope * bendingSlope) /
715 (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
208f139e 716 // Path length in the material
37a615ac 717 Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
718 Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength) / x0 : TMath::Abs(signedPathLength);
208f139e 719 // relativistic velocity
720 Double_t velo = 1.;
721 // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
37a615ac 722 Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0));
723 theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0;
208f139e 724
37a615ac 725 Double_t varCoor = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.;
208f139e 726 Double_t varSlop = theta02;
37a615ac 727 Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02 / 2. : 0.;
ea94c18b 728
690d2205 729 // Set MCS covariance matrix
ea94c18b 730 TMatrixD newParamCov(param->GetCovariances());
208f139e 731 // Non bending plane
ea94c18b 732 newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
733 newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
208f139e 734 // Bending plane
ea94c18b 735 newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
736 newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
c24543a2 737
738 // Set momentum related covariances if B!=0
739 if (fgFieldON) {
740 // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
741 Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
742 Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
743 (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
744 // Inverse bending momentum (due to dependences with bending and non bending slopes)
745 newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
746 newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
747 newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
748 newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
749 newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
750 }
208f139e 751
ea94c18b 752 // Set new covariances
753 param->SetCovariances(newParamCov);
208f139e 754}
755
690d2205 756//__________________________________________________________________________
757void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
758 Double_t xVtx, Double_t yVtx, Double_t zVtx,
759 Double_t errXVtx, Double_t errYVtx,
760 Bool_t correctForMCS, Bool_t correctForEnergyLoss)
c04e3238 761{
690d2205 762 /// Main method for extrapolation to the vertex:
763 /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
764 /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
765 /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
766 /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
767 /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
768 /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
c04e3238 769
8cde4af5 770 if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
c04e3238 771
8cde4af5 772 if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
690d2205 773 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
774 <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
fac70e25 775 return;
776 }
777
8cde4af5 778 // Check the vertex position relatively to the absorber
ea94c18b 779 if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 780 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 781 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
ea94c18b 782 } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
8cde4af5 783 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
690d2205 784 <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
785 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
786 else ExtrapToZ(trackParam,zVtx);
8cde4af5 787 return;
788 }
789
790 // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
ea94c18b 791 if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
8cde4af5 792 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 793 <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
794 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
795 else ExtrapToZ(trackParam,zVtx);
8cde4af5 796 return;
ea94c18b 797 } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
8cde4af5 798 cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
690d2205 799 <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
c04e3238 800 } else {
690d2205 801 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
802 else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
c04e3238 803 }
c04e3238 804
690d2205 805 // Get absorber correction parameters assuming linear propagation in absorber
8cde4af5 806 Double_t trackXYZOut[3];
807 trackXYZOut[0] = trackParam->GetNonBendingCoor();
808 trackXYZOut[1] = trackParam->GetBendingCoor();
809 trackXYZOut[2] = trackParam->GetZ();
810 Double_t trackXYZIn[3];
690d2205 811 if (correctForMCS) { // assume linear propagation until the vertex
812 trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
813 trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
814 trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
815 } else {
816 AliMUONTrackParam trackParamIn(*trackParam);
817 ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
818 trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
819 trackXYZIn[1] = trackParamIn.GetBendingCoor();
820 trackXYZIn[2] = trackParamIn.GetZ();
821 }
84f061ef 822 Double_t pTot = trackParam->P();
ecdf58c4 823 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
824 if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
18abc511 825 cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
826 if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
827 else ExtrapToZ(trackParam,zVtx);
828 return;
829 }
8cde4af5 830
690d2205 831 // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
832 if (correctForMCS) {
fac70e25 833
690d2205 834 if (correctForEnergyLoss) {
835
836 // Correct for multiple scattering and energy loss
ecdf58c4 837 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 838 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
839 trackXYZIn[2], pathLength, f0, f1, f2);
ecdf58c4 840 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 841
842 } else {
843
844 // Correct for multiple scattering
845 CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
846 trackXYZIn[2], pathLength, f0, f1, f2);
847 }
fac70e25 848
fac70e25 849 } else {
690d2205 850
851 if (correctForEnergyLoss) {
852
18abc511 853 // Correct for energy loss add multiple scattering dispersion in covariance matrix
ecdf58c4 854 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
37a615ac 855 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 856 ExtrapToZCov(trackParam, trackXYZIn[2]);
ecdf58c4 857 CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
690d2205 858 ExtrapToZCov(trackParam, zVtx);
859
860 } else {
861
18abc511 862 // add multiple scattering dispersion in covariance matrix
37a615ac 863 AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
690d2205 864 ExtrapToZCov(trackParam, zVtx);
865
866 }
867
fac70e25 868 }
8cde4af5 869
fac70e25 870}
871
690d2205 872//__________________________________________________________________________
873void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
874 Double_t xVtx, Double_t yVtx, Double_t zVtx,
875 Double_t errXVtx, Double_t errYVtx)
876{
877 /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
878 /// Add branson correction resolution and energy loss fluctuation to parameter covariances
879 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
880}
881
882//__________________________________________________________________________
883void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
884 Double_t xVtx, Double_t yVtx, Double_t zVtx,
885 Double_t errXVtx, Double_t errYVtx)
886{
887 /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
888 /// Add branson correction resolution to parameter covariances
889 ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
890}
891
892//__________________________________________________________________________
893void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
894{
895 /// Extrapolate track parameters to vertex, corrected for energy loss effects only
896 /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
897 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
898}
899
900//__________________________________________________________________________
901void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
902{
903 /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
904 /// Add dispersion due to multiple scattering to parameter covariances
905 ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
906}
907
908//__________________________________________________________________________
fac70e25 909Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
910{
911 /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
912
913 if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
8cde4af5 914
fac70e25 915 // Check whether the geometry is available
916 if (!gGeoManager) {
917 cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
918 return 0.;
919 }
920
921 // Get encountered material correction parameters assuming linear propagation from vertex to the track position
922 Double_t trackXYZOut[3];
923 trackXYZOut[0] = trackParam->GetNonBendingCoor();
924 trackXYZOut[1] = trackParam->GetBendingCoor();
925 trackXYZOut[2] = trackParam->GetZ();
926 Double_t trackXYZIn[3];
927 trackXYZIn[0] = xVtx;
928 trackXYZIn[1] = yVtx;
929 trackXYZIn[2] = zVtx;
84f061ef 930 Double_t pTot = trackParam->P();
18abc511 931 Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
690d2205 932 GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
fac70e25 933
ecdf58c4 934 // total momentum corrected for energy loss
935 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
936 Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
937 Double_t eCorr = e + totalELoss;
938 Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
939
940 return pTotCorr - pTot;
c04e3238 941}
942
690d2205 943//__________________________________________________________________________
fa5e35be 944Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
c04e3238 945{
84f061ef 946 /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
947 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 948 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
84f061ef 949
ecdf58c4 950 // mean exitation energy (GeV)
951 Double_t i;
952 if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
953 else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
690d2205 954
fa5e35be 955 return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA);
c04e3238 956}
957
690d2205 958//__________________________________________________________________________
fa5e35be 959Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
690d2205 960{
961 /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
962 /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
ecdf58c4 963 Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
690d2205 964 //Double_t eMass = 0.510998918e-3; // GeV
965 Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
966 Double_t p2=pTotal*pTotal;
967 Double_t beta2=p2/(p2 + muMass*muMass);
968
fa5e35be 969 Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution
690d2205 970 Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
971
972 //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
973
974 return sigma2;
975}
976
977//__________________________________________________________________________
978void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
979{
980 /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
981 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
982
983 // charge * total momentum
984 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
985 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
986
987 // Jacobian of the opposite transformation
988 TMatrixD jacob(5,5);
989 jacob.UnitMatrix();
990 jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
991 jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
992 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
993 jacob(4,4) = - qPTot / param(4,0);
994
995 // compute covariances in new coordinate system
996 TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
997 cov.Mult(jacob,tmp);
998}
999
1000//__________________________________________________________________________
1001void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
1002{
1003 /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
1004 /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
1005
1006 // charge * total momentum
1007 Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
1008 TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
1009
1010 // Jacobian of the transformation
1011 TMatrixD jacob(5,5);
1012 jacob.UnitMatrix();
1013 jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1014 jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
1015 (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1016 jacob(4,4) = - param(4,0) / qPTot;
1017
1018 // compute covariances in new coordinate system
1019 TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
1020 covP.Mult(jacob,tmp);
1021}
1022
c04e3238 1023 //__________________________________________________________________________
1024void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
1025{
71a2d3aa 1026/// <pre>
c04e3238 1027/// ******************************************************************
1028/// * *
1029/// * Performs the tracking of one step in a magnetic field *
1030/// * The trajectory is assumed to be a helix in a constant field *
1031/// * taken at the mid point of the step. *
1032/// * Parameters: *
1033/// * input *
1034/// * STEP =arc length of the step asked *
1035/// * VECT =input vector (position,direction cos and momentum) *
1036/// * CHARGE= electric charge of the particle *
1037/// * output *
1038/// * VOUT = same as VECT after completion of the step *
1039/// * *
2060b217 1040/// * ==>Called by : USER, GUSWIM *
c04e3238 1041/// * Author m.hansroul ********* *
1042/// * modified s.egli, s.v.levonian *
1043/// * modified v.perevoztchikov
1044/// * *
1045/// ******************************************************************
71a2d3aa 1046/// </pre>
c04e3238 1047
1048// modif: everything in double precision
1049
1050 Double_t xyz[3], h[4], hxp[3];
1051 Double_t h2xy, hp, rho, tet;
1052 Double_t sint, sintt, tsint, cos1t;
1053 Double_t f1, f2, f3, f4, f5, f6;
1054
1055 const Int_t kix = 0;
1056 const Int_t kiy = 1;
1057 const Int_t kiz = 2;
1058 const Int_t kipx = 3;
1059 const Int_t kipy = 4;
1060 const Int_t kipz = 5;
1061 const Int_t kipp = 6;
1062
1063 const Double_t kec = 2.9979251e-4;
1064 //
1065 // ------------------------------------------------------------------
1066 //
1067 // units are kgauss,centimeters,gev/c
1068 //
1069 vout[kipp] = vect[kipp];
1070 if (TMath::Abs(charge) < 0.00001) {
1071 for (Int_t i = 0; i < 3; i++) {
1072 vout[i] = vect[i] + step * vect[i+3];
1073 vout[i+3] = vect[i+3];
1074 }
1075 return;
1076 }
1077 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1078 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1079 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1080
1081 //cmodif: call gufld (xyz, h) changed into:
f7a1cc68 1082 TGeoGlobalMagField::Instance()->Field(xyz,h);
c04e3238 1083
1084 h2xy = h[0]*h[0] + h[1]*h[1];
1085 h[3] = h[2]*h[2]+ h2xy;
1086 if (h[3] < 1.e-12) {
1087 for (Int_t i = 0; i < 3; i++) {
1088 vout[i] = vect[i] + step * vect[i+3];
1089 vout[i+3] = vect[i+3];
1090 }
1091 return;
1092 }
1093 if (h2xy < 1.e-12*h[3]) {
1094 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1095 return;
1096 }
1097 h[3] = TMath::Sqrt(h[3]);
1098 h[0] /= h[3];
1099 h[1] /= h[3];
1100 h[2] /= h[3];
1101 h[3] *= kec;
1102
1103 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1104 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1105 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1106
1107 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1108
1109 rho = -charge*h[3]/vect[kipp];
1110 tet = rho * step;
1111
1112 if (TMath::Abs(tet) > 0.15) {
1113 sint = TMath::Sin(tet);
1114 sintt = (sint/tet);
1115 tsint = (tet-sint)/tet;
1116 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1117 } else {
1118 tsint = tet*tet/36.;
1119 sintt = (1. - tsint);
1120 sint = tet*sintt;
1121 cos1t = 0.5*tet;
1122 }
1123
1124 f1 = step * sintt;
1125 f2 = step * cos1t;
1126 f3 = step * tsint * hp;
1127 f4 = -tet*cos1t;
1128 f5 = sint;
1129 f6 = tet * cos1t * hp;
1130
1131 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1132 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1133 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1134
1135 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1136 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1137 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1138
1139 return;
1140}
1141
1142 //__________________________________________________________________________
1143void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
1144{
71a2d3aa 1145/// <pre>
c04e3238 1146/// ******************************************************************
1147/// * *
1148/// * Tracking routine in a constant field oriented *
1149/// * along axis 3 *
1150/// * Tracking is performed with a conventional *
1151/// * helix step method *
1152/// * *
2060b217 1153/// * ==>Called by : USER, GUSWIM *
c04e3238 1154/// * Authors R.Brun, M.Hansroul ********* *
1155/// * Rewritten V.Perevoztchikov
1156/// * *
1157/// ******************************************************************
71a2d3aa 1158/// </pre>
c04e3238 1159
1160 Double_t hxp[3];
1161 Double_t h4, hp, rho, tet;
1162 Double_t sint, sintt, tsint, cos1t;
1163 Double_t f1, f2, f3, f4, f5, f6;
1164
1165 const Int_t kix = 0;
1166 const Int_t kiy = 1;
1167 const Int_t kiz = 2;
1168 const Int_t kipx = 3;
1169 const Int_t kipy = 4;
1170 const Int_t kipz = 5;
1171 const Int_t kipp = 6;
1172
1173 const Double_t kec = 2.9979251e-4;
1174
1175//
1176// ------------------------------------------------------------------
1177//
1178// units are kgauss,centimeters,gev/c
1179//
1180 vout[kipp] = vect[kipp];
1181 h4 = field * kec;
1182
1183 hxp[0] = - vect[kipy];
1184 hxp[1] = + vect[kipx];
1185
1186 hp = vect[kipz];
1187
1188 rho = -h4/vect[kipp];
1189 tet = rho * step;
1190 if (TMath::Abs(tet) > 0.15) {
1191 sint = TMath::Sin(tet);
1192 sintt = (sint/tet);
1193 tsint = (tet-sint)/tet;
1194 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1195 } else {
1196 tsint = tet*tet/36.;
1197 sintt = (1. - tsint);
1198 sint = tet*sintt;
1199 cos1t = 0.5*tet;
1200 }
1201
1202 f1 = step * sintt;
1203 f2 = step * cos1t;
1204 f3 = step * tsint * hp;
1205 f4 = -tet*cos1t;
1206 f5 = sint;
1207 f6 = tet * cos1t * hp;
1208
1209 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1210 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1211 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1212
1213 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1214 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1215 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1216
1217 return;
1218}
8cde4af5 1219
c04e3238 1220 //__________________________________________________________________________
1221void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
1222{
71a2d3aa 1223/// <pre>
c04e3238 1224/// ******************************************************************
1225/// * *
1226/// * Runge-Kutta method for tracking a particle through a magnetic *
1227/// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
1228/// * Standards, procedure 25.5.20) *
1229/// * *
1230/// * Input parameters *
1231/// * CHARGE Particle charge *
1232/// * STEP Step size *
1233/// * VECT Initial co-ords,direction cosines,momentum *
1234/// * Output parameters *
1235/// * VOUT Output co-ords,direction cosines,momentum *
1236/// * User routine called *
1237/// * CALL GUFLD(X,F) *
1238/// * *
2060b217 1239/// * ==>Called by : USER, GUSWIM *
c04e3238 1240/// * Authors R.Brun, M.Hansroul ********* *
1241/// * V.Perevoztchikov (CUT STEP implementation) *
1242/// * *
1243/// * *
1244/// ******************************************************************
71a2d3aa 1245/// </pre>
c04e3238 1246
1247 Double_t h2, h4, f[4];
1248 Double_t xyzt[3], a, b, c, ph,ph2;
1249 Double_t secxs[4],secys[4],seczs[4],hxp[3];
1250 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1251 Double_t est, at, bt, ct, cba;
1252 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1253
1254 Double_t x;
1255 Double_t y;
1256 Double_t z;
1257
1258 Double_t xt;
1259 Double_t yt;
1260 Double_t zt;
1261
1262 Double_t maxit = 1992;
1263 Double_t maxcut = 11;
1264
1265 const Double_t kdlt = 1e-4;
1266 const Double_t kdlt32 = kdlt/32.;
1267 const Double_t kthird = 1./3.;
1268 const Double_t khalf = 0.5;
1269 const Double_t kec = 2.9979251e-4;
1270
1271 const Double_t kpisqua = 9.86960440109;
1272 const Int_t kix = 0;
1273 const Int_t kiy = 1;
1274 const Int_t kiz = 2;
1275 const Int_t kipx = 3;
1276 const Int_t kipy = 4;
1277 const Int_t kipz = 5;
1278
1279 // *.
1280 // *. ------------------------------------------------------------------
1281 // *.
1282 // * this constant is for units cm,gev/c and kgauss
1283 // *
1284 Int_t iter = 0;
1285 Int_t ncut = 0;
1286 for(Int_t j = 0; j < 7; j++)
1287 vout[j] = vect[j];
1288
1289 Double_t pinv = kec * charge / vect[6];
1290 Double_t tl = 0.;
1291 Double_t h = step;
1292 Double_t rest;
1293
1294
1295 do {
1296 rest = step - tl;
1297 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1298 //cmodif: call gufld(vout,f) changed into:
f7a1cc68 1299 TGeoGlobalMagField::Instance()->Field(vout,f);
c04e3238 1300
1301 // *
1302 // * start of integration
1303 // *
1304 x = vout[0];
1305 y = vout[1];
1306 z = vout[2];
1307 a = vout[3];
1308 b = vout[4];
1309 c = vout[5];
1310
1311 h2 = khalf * h;
1312 h4 = khalf * h2;
1313 ph = pinv * h;
1314 ph2 = khalf * ph;
1315 secxs[0] = (b * f[2] - c * f[1]) * ph2;
1316 secys[0] = (c * f[0] - a * f[2]) * ph2;
1317 seczs[0] = (a * f[1] - b * f[0]) * ph2;
1318 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1319 if (ang2 > kpisqua) break;
1320
1321 dxt = h2 * a + h4 * secxs[0];
1322 dyt = h2 * b + h4 * secys[0];
1323 dzt = h2 * c + h4 * seczs[0];
1324 xt = x + dxt;
1325 yt = y + dyt;
1326 zt = z + dzt;
1327 // *
1328 // * second intermediate point
1329 // *
1330
1331 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1332 if (est > h) {
1333 if (ncut++ > maxcut) break;
1334 h *= khalf;
1335 continue;
1336 }
1337
1338 xyzt[0] = xt;
1339 xyzt[1] = yt;
1340 xyzt[2] = zt;
1341
1342 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1343 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1344
1345 at = a + secxs[0];
1346 bt = b + secys[0];
1347 ct = c + seczs[0];
1348
1349 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1350 secys[1] = (ct * f[0] - at * f[2]) * ph2;
1351 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1352 at = a + secxs[1];
1353 bt = b + secys[1];
1354 ct = c + seczs[1];
1355 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1356 secys[2] = (ct * f[0] - at * f[2]) * ph2;
1357 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1358 dxt = h * (a + secxs[2]);
1359 dyt = h * (b + secys[2]);
1360 dzt = h * (c + seczs[2]);
1361 xt = x + dxt;
1362 yt = y + dyt;
1363 zt = z + dzt;
1364 at = a + 2.*secxs[2];
1365 bt = b + 2.*secys[2];
1366 ct = c + 2.*seczs[2];
1367
1368 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1369 if (est > 2.*TMath::Abs(h)) {
1370 if (ncut++ > maxcut) break;
1371 h *= khalf;
1372 continue;
1373 }
1374
1375 xyzt[0] = xt;
1376 xyzt[1] = yt;
1377 xyzt[2] = zt;
1378
1379 //cmodif: call gufld(xyzt,f) changed into:
f7a1cc68 1380 TGeoGlobalMagField::Instance()->Field(xyzt,f);
c04e3238 1381
1382 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1383 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1384 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1385
1386 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1387 secys[3] = (ct*f[0] - at*f[2])* ph2;
1388 seczs[3] = (at*f[1] - bt*f[0])* ph2;
1389 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1390 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1391 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1392
1393 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1394 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1395 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1396
1397 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1398 if (ncut++ > maxcut) break;
1399 h *= khalf;
1400 continue;
1401 }
1402
1403 ncut = 0;
1404 // * if too many iterations, go to helix
1405 if (iter++ > maxit) break;
1406
1407 tl += h;
1408 if (est < kdlt32)
1409 h *= 2.;
1410 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1411 vout[0] = x;
1412 vout[1] = y;
1413 vout[2] = z;
1414 vout[3] = cba*a;
1415 vout[4] = cba*b;
1416 vout[5] = cba*c;
1417 rest = step - tl;
1418 if (step < 0.) rest = -rest;
1419 if (rest < 1.e-5*TMath::Abs(step)) return;
1420
1421 } while(1);
1422
1423 // angle too big, use helix
1424
1425 f1 = f[0];
1426 f2 = f[1];
1427 f3 = f[2];
1428 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1429 rho = -f4*pinv;
1430 tet = rho * step;
1431
1432 hnorm = 1./f4;
1433 f1 = f1*hnorm;
1434 f2 = f2*hnorm;
1435 f3 = f3*hnorm;
1436
1437 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1438 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1439 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1440
1441 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1442
1443 rho1 = 1./rho;
1444 sint = TMath::Sin(tet);
1445 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1446
1447 g1 = sint*rho1;
1448 g2 = cost*rho1;
1449 g3 = (tet-sint) * hp*rho1;
1450 g4 = -cost;
1451 g5 = sint;
1452 g6 = cost * hp;
1453
1454 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1455 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1456 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1457
1458 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1459 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1460 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1461
1462 return;
1463}
8cde4af5 1464