/* $Id$ */
-///////////////////////////////////////////////////
-//
-// Tools
-// for
-// track
-// extrapolation
-// in
-// ALICE
-// dimuon
-// spectrometer
-//
-///////////////////////////////////////////////////
-
-#include <Riostream.h>
+//-----------------------------------------------------------------------------
+// Class AliMUONTrackExtrap
+// ------------------------
+// Tools for track extrapolation in ALICE dimuon spectrometer
+// Author: Philippe Pillot
+//-----------------------------------------------------------------------------
#include "AliMUONTrackExtrap.h"
#include "AliMUONTrackParam.h"
#include "AliMUONConstants.h"
-#include "AliMagF.h"
-#include "AliLog.h"
-#include "AliTracker.h"
+#include "AliMUONReconstructor.h"
+
+#include "AliMagF.h"
+#include "AliExternalTrackParam.h"
+
+#include <TGeoGlobalMagField.h>
+#include <TGeoManager.h>
+#include <TMath.h>
+#include <TDatabasePDG.h>
+#include <Riostream.h>
+
+/// \cond CLASSIMP
ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
+/// \endcond
+
+const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
+const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
+ Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
+ Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
+const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
+const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
+const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
+const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::SetField()
+{
+ /// set field on/off flag;
+ /// set field at the centre of the dipole
+ const Double_t x[3] = {50.,50.,fgkSimpleBPosition};
+ Double_t b[3] = {0.,0.,0.};
+ TGeoGlobalMagField::Instance()->Field(x,b);
+ fgSimpleBValue = b[0];
+ fgFieldON = (TMath::Abs(fgSimpleBValue) > 1.e-10) ? kTRUE : kFALSE;
+
+}
-const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
+//__________________________________________________________________________
+Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
+{
+ /// Returns impact parameter at vertex in bending plane (cm),
+ /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
+ /// using simple values for dipole magnetic field.
+ /// The sign of "BendingMomentum" is the sign of the charge.
+
+ if (bendingMomentum == 0.) return 1.e10;
+
+ const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
+
+ return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
+}
- //__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
+//__________________________________________________________________________
+Double_t
+AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
{
- /// Track parameter extrapolation to the plane at "Z".
+ /// Returns signed bending momentum in bending plane (GeV/c),
+ /// the sign being the sign of the charge for particles moving forward in Z,
+ /// from the impact parameter "ImpactParam" at vertex in bending plane (cm),
+ /// using simple values for dipole magnetic field.
+
+ if (impactParam == 0.) return 1.e10;
+
+ const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
+
+ if (fgFieldON)
+ {
+ return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
+ }
+ else
+ {
+ return AliMUONConstants::GetMostProbBendingMomentum();
+ }
+}
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
+{
+ /// Track parameters linearly extrapolated to the plane at "zEnd".
+ /// On return, results from the extrapolation are updated in trackParam.
+
+ if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
+
+ // Compute track parameters
+ Double_t dZ = zEnd - trackParam->GetZ();
+ trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
+ trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
+ trackParam->SetZ(zEnd);
+}
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::LinearExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
+{
+ /// Track parameters and their covariances linearly extrapolated to the plane at "zEnd".
+ /// On return, results from the extrapolation are updated in trackParam.
+
+ if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
+
+ // No need to propagate the covariance matrix if it does not exist
+ if (!trackParam->CovariancesExist()) {
+ cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl;
+ // Extrapolate linearly track parameters to "zEnd"
+ LinearExtrapToZ(trackParam,zEnd);
+ return;
+ }
+
+ // Compute track parameters
+ Double_t dZ = zEnd - trackParam->GetZ();
+ trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
+ trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
+ trackParam->SetZ(zEnd);
+
+ // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd"
+ TMatrixD jacob(5,5);
+ jacob.UnitMatrix();
+ jacob(0,1) = dZ;
+ jacob(2,3) = dZ;
+
+ // Extrapolate track parameter covariances to "zEnd"
+ TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob);
+ TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
+ trackParam->SetCovariances(tmp2);
+
+ // Update the propagator if required
+ if (updatePropagator) trackParam->UpdatePropagator(jacob);
+}
+
+//__________________________________________________________________________
+Bool_t AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
+{
+ /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm.
+ /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
+ if (!fgFieldON) {
+ AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
+ return kTRUE;
+ }
+ else if (fgkUseHelix) return AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
+ else return AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
+}
+
+//__________________________________________________________________________
+Bool_t AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
+{
+ /// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
/// On return, the track parameters resulting from the extrapolation are updated in trackParam.
- if (trackParam->GetZ() == zEnd) return; // nothing to be done if same Z
+ if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
Double_t forwardBackward; // +1 if forward, -1 if backward
if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
else forwardBackward = -1.0;
- Double_t vGeant3[7], vGeant3New[7]; // 7 in parameter ????
- Int_t iGeant3, stepNumber;
- Int_t maxStepNumber = 5000; // in parameter ????
+ Double_t v3[7], v3New[7]; // 7 in parameter ????
+ Int_t i3, stepNumber;
// For safety: return kTRUE or kFALSE ????
// Parameter vector for calling EXTRAP_ONESTEP
- SetGeant3ParametersFromTrackParam(trackParam, vGeant3, forwardBackward);
+ ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
// sign of charge (sign of fInverseBendingMomentum if forward motion)
// must be changed if backward extrapolation
- Double_t chargeExtrap = forwardBackward *
- TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
- Double_t stepLength = 6.0; // in parameter ????
+ Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
// Extrapolation loop
stepNumber = 0;
- while (((-forwardBackward * (vGeant3[2] - zEnd)) <= 0.0) && // spectro. z<0
- (stepNumber < maxStepNumber)) {
+ while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
stepNumber++;
- // Option for switching between helix and Runge-Kutta ????
- //ExtrapOneStepRungekutta(chargeExtrap, stepLength, vGeant3, vGeant3New);
- ExtrapOneStepHelix(chargeExtrap, stepLength, vGeant3, vGeant3New);
- if ((-forwardBackward * (vGeant3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
- // better use TArray ????
- for (iGeant3 = 0; iGeant3 < 7; iGeant3++)
- {vGeant3[iGeant3] = vGeant3New[iGeant3];}
+ ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
+ if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
+ // better use TArray ????
+ for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
}
- // check maxStepNumber ????
+ // check fgkMaxStepNumber ????
// Interpolation back to exact Z (2nd order)
// should be in function ???? using TArray ????
- Double_t dZ12 = vGeant3New[2] - vGeant3[2]; // 1->2
+ Double_t dZ12 = v3New[2] - v3[2]; // 1->2
if (TMath::Abs(dZ12) > 0) {
- Double_t dZ1i = zEnd - vGeant3[2]; // 1-i
- Double_t dZi2 = vGeant3New[2] - zEnd; // i->2
- Double_t xPrime = (vGeant3New[0] - vGeant3[0]) / dZ12;
- Double_t xSecond = ((vGeant3New[3] / vGeant3New[5]) - (vGeant3[3] / vGeant3[5])) / dZ12;
- Double_t yPrime = (vGeant3New[1] - vGeant3[1]) / dZ12;
- Double_t ySecond = ((vGeant3New[4] / vGeant3New[5]) - (vGeant3[4] / vGeant3[5])) / dZ12;
- vGeant3[0] = vGeant3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
- vGeant3[1] = vGeant3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
- vGeant3[2] = zEnd; // Z
+ Double_t dZ1i = zEnd - v3[2]; // 1-i
+ Double_t dZi2 = v3New[2] - zEnd; // i->2
+ Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
+ Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
+ Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
+ Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
+ v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
+ v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
+ v3[2] = zEnd; // Z
Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
// (PX, PY, PZ)/PTOT assuming forward motion
- vGeant3[5] =
- 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
- vGeant3[3] = xPrimeI * vGeant3[5]; // PX/PTOT
- vGeant3[4] = yPrimeI * vGeant3[5]; // PY/PTOT
+ v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
+ v3[3] = xPrimeI * v3[5]; // PX/PTOT
+ v3[4] = yPrimeI * v3[5]; // PY/PTOT
+ } else {
+ cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
+ }
+ // Recover track parameters (charge back for forward motion)
+ RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
+ return kTRUE;
+}
+
+//__________________________________________________________________________
+Bool_t AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
+{
+ /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
+ /// On return, the track parameters resulting from the extrapolation are updated in trackParam.
+ if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
+ Double_t forwardBackward; // +1 if forward, -1 if backward
+ if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
+ else forwardBackward = -1.0;
+ // sign of charge (sign of fInverseBendingMomentum if forward motion)
+ // must be changed if backward extrapolation
+ Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
+ Double_t v3[7], v3New[7];
+ Double_t dZ, step;
+ Int_t stepNumber = 0;
+
+ // Extrapolation loop (until within tolerance or the track turn around)
+ Double_t residue = zEnd - trackParam->GetZ();
+ Bool_t uturn = kFALSE;
+ Bool_t trackingFailed = kFALSE;
+ Bool_t tooManyStep = kFALSE;
+ while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
+
+ dZ = zEnd - trackParam->GetZ();
+ // step lenght assuming linear trajectory
+ step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
+ trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
+ ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
+
+ do { // reduce step lenght while zEnd oversteped
+ if (stepNumber > fgkMaxStepNumber) {
+ cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
+ tooManyStep = kTRUE;
+ break;
+ }
+ stepNumber ++;
+ step = TMath::Abs(step);
+ if (!AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New)) {
+ trackingFailed = kTRUE;
+ break;
+ }
+ residue = zEnd - v3New[2];
+ step *= dZ/(v3New[2]-trackParam->GetZ());
+ } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
+
+ if (trackingFailed) break;
+ else if (v3New[5]*v3[5] < 0) { // the track turned around
+ cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: The track turned around"<<endl;
+ uturn = kTRUE;
+ break;
+ } else RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
+
+ }
+
+ // terminate the extropolation with a straight line up to the exact "zEnd" value
+ if (trackingFailed || uturn) {
+
+ // track ends +-100 meters away in the bending direction
+ dZ = zEnd - v3[2];
+ Double_t bendingSlope = TMath::Sign(1.e4,-fgSimpleBValue*trackParam->GetInverseBendingMomentum()) / dZ;
+ Double_t pZ = TMath::Abs(1. / trackParam->GetInverseBendingMomentum()) / TMath::Sqrt(1.0 + bendingSlope * bendingSlope);
+ Double_t nonBendingSlope = TMath::Sign(TMath::Abs(v3[3]) * v3[6] / pZ, trackParam->GetNonBendingSlope());
+ trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + dZ * nonBendingSlope);
+ trackParam->SetNonBendingSlope(nonBendingSlope);
+ trackParam->SetBendingCoor(trackParam->GetBendingCoor() + dZ * bendingSlope);
+ trackParam->SetBendingSlope(bendingSlope);
+ trackParam->SetZ(zEnd);
+
+ return kFALSE;
+
} else {
- cout<<"W-AliMUONTrackExtrap::ExtrapToZ: Extrap. to Z not reached, Z = "<<zEnd<<endl;
+
+ // track extrapolated normally
+ trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
+ trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
+ trackParam->SetZ(zEnd);
+
+ return !tooManyStep;
+
}
- // Track parameters from Geant3 parameters,
- // with charge back for forward motion
- SetTrackParamFromGeant3Parameters(vGeant3, chargeExtrap * forwardBackward, trackParam);
+
}
- //__________________________________________________________________________
-void AliMUONTrackExtrap::SetGeant3ParametersFromTrackParam(AliMUONTrackParam* trackParam, Double_t *vGeant3, Double_t forwardBackward)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
{
- /// Set vector of Geant3 parameters pointed to by "vGeant3" from track parameters in trackParam.
+ /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
/// Since AliMUONTrackParam is only geometry, one uses "forwardBackward"
/// to know whether the particle is going forward (+1) or backward (-1).
- vGeant3[0] = trackParam->GetNonBendingCoor(); // X
- vGeant3[1] = trackParam->GetBendingCoor(); // Y
- vGeant3[2] = trackParam->GetZ(); // Z
+ v3[0] = trackParam->GetNonBendingCoor(); // X
+ v3[1] = trackParam->GetBendingCoor(); // Y
+ v3[2] = trackParam->GetZ(); // Z
Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
- vGeant3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
- vGeant3[5] = -forwardBackward * pZ / vGeant3[6]; // PZ/PTOT spectro. z<0
- vGeant3[3] = trackParam->GetNonBendingSlope() * vGeant3[5]; // PX/PTOT
- vGeant3[4] = trackParam->GetBendingSlope() * vGeant3[5]; // PY/PTOT
+ v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
+ v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
+ v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
+ v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
}
- //__________________________________________________________________________
-void AliMUONTrackExtrap::SetTrackParamFromGeant3Parameters(Double_t *vGeant3, Double_t charge, AliMUONTrackParam* trackParam)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
{
- /// Set track parameters in trackParam from Geant3 parameters pointed to by "vGeant3",
+ /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
/// assumed to be calculated for forward motion in Z.
/// "InverseBendingMomentum" is signed with "charge".
- trackParam->SetNonBendingCoor(vGeant3[0]); // X
- trackParam->SetBendingCoor(vGeant3[1]); // Y
- trackParam->SetZ(vGeant3[2]); // Z
- Double_t pYZ = vGeant3[6] * TMath::Sqrt(1.0 - vGeant3[3] * vGeant3[3]);
+ trackParam->SetNonBendingCoor(v3[0]); // X
+ trackParam->SetBendingCoor(v3[1]); // Y
+ trackParam->SetZ(v3[2]); // Z
+ Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
trackParam->SetInverseBendingMomentum(charge/pYZ);
- trackParam->SetBendingSlope(vGeant3[4]/vGeant3[5]);
- trackParam->SetNonBendingSlope(vGeant3[3]/vGeant3[5]);
+ trackParam->SetBendingSlope(v3[4]/v3[5]);
+ trackParam->SetNonBendingSlope(v3[3]/v3[5]);
}
- //__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut)
+//__________________________________________________________________________
+Bool_t AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
{
- /// Track parameters extrapolated from "trackParamIn" to both chambers of the station(0..) "station"
- /// are returned in the array (dimension 2) of track parameters pointed to by "TrackParamOut"
- /// (index 0 and 1 for first and second chambers).
- Double_t extZ[2], z1, z2;
- Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
- // range of station to be checked ????
- z1 = AliMUONConstants::DefaultChamberZ(2 * station);
- z2 = AliMUONConstants::DefaultChamberZ(2 * station + 1);
- // First and second Z to extrapolate at
- if ((z1 > trackParamIn->GetZ()) && (z2 > trackParamIn->GetZ())) {i1 = 0; i2 = 1;}
- else if ((z1 < trackParamIn->GetZ()) && (z2 < trackParamIn->GetZ())) {i1 = 1; i2 = 0;}
- else {
- cout<<"E-AliMUONTrackExtrap::ExtrapToStationAliError: Starting Z ("<<trackParamIn->GetZ()
- <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl;
- exit(-1);
+ /// Track parameters and their covariances extrapolated to the plane at "zEnd".
+ /// On return, results from the extrapolation are updated in trackParam.
+
+ if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same z
+
+ if (!fgFieldON) { // linear extrapolation if no magnetic field
+ AliMUONTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator);
+ return kTRUE;
}
- extZ[i1] = z1;
- extZ[i2] = z2;
- // copy of track parameters
- trackParamOut[i1] = *trackParamIn;
- // first extrapolation
- ExtrapToZ(&(trackParamOut[i1]),extZ[0]);
- trackParamOut[i2] = trackParamOut[i1];
- // second extrapolation
- ExtrapToZ(&(trackParamOut[i2]),extZ[1]);
- return;
+
+ // No need to propagate the covariance matrix if it does not exist
+ if (!trackParam->CovariancesExist()) {
+ cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
+ // Extrapolate track parameters to "zEnd"
+ return ExtrapToZ(trackParam,zEnd);
+ }
+
+ // Save the actual track parameters
+ AliMUONTrackParam trackParamSave(*trackParam);
+ TMatrixD paramSave(trackParamSave.GetParameters());
+ Double_t zBegin = trackParamSave.GetZ();
+
+ // Get reference to the parameter covariance matrix
+ const TMatrixD& kParamCov = trackParam->GetCovariances();
+
+ // Extrapolate track parameters to "zEnd"
+ // Do not update the covariance matrix if the extrapolation failed
+ if (!ExtrapToZ(trackParam,zEnd)) return kFALSE;
+
+ // Get reference to the extrapolated parameters
+ const TMatrixD& extrapParam = trackParam->GetParameters();
+
+ // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
+ Bool_t extrapStatus = kTRUE;
+ TMatrixD jacob(5,5);
+ jacob.Zero();
+ TMatrixD dParam(5,1);
+ Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
+ for (Int_t i=0; i<5; i++) {
+ // Skip jacobian calculation for parameters with no associated error
+ if (kParamCov(i,i) <= 0.) continue;
+
+ // Small variation of parameter i only
+ for (Int_t j=0; j<5; j++) {
+ if (j==i) {
+ dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
+ dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
+ } else dParam(j,0) = 0.;
+ }
+
+ // Set new parameters
+ trackParamSave.SetParameters(paramSave);
+ trackParamSave.AddParameters(dParam);
+ trackParamSave.SetZ(zBegin);
+
+ // Extrapolate new track parameters to "zEnd"
+ if (!ExtrapToZ(&trackParamSave,zEnd)) {
+ cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Bad covariance matrix"<<endl;
+ extrapStatus = kFALSE;
+ }
+
+ // Calculate the jacobian
+ TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
+ jacobji *= 1. / dParam(i,0);
+ jacob.SetSub(0,i,jacobji);
+ }
+
+ // Extrapolate track parameter covariances to "zEnd"
+ TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
+ TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
+ trackParam->SetCovariances(tmp2);
+
+ // Update the propagator if required
+ if (updatePropagator) trackParam->UpdatePropagator(jacob);
+
+ return extrapStatus;
}
- //__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2)
{
- /// Extrapolation to the vertex.
- /// Returns the track parameters resulting from the extrapolation in the current TrackParam.
- /// Changes parameters according to Branson correction through the absorber
-
- Double_t zAbsorber = -503.0; // to be coherent with the Geant absorber geometry !!!!
- // spectro. (z<0)
- // Extrapolates track parameters upstream to the "Z" end of the front absorber
- ExtrapToZ(trackParam,zAbsorber); // !!!
- // Makes Branson correction (multiple scattering + energy loss)
- BransonCorrection(trackParam,xVtx,yVtx,zVtx);
- // Makes a simple magnetic field correction through the absorber
- FieldCorrection(trackParam,zAbsorber);
+ /// Add to the track parameter covariances the effects of multiple Coulomb scattering
+ /// signedPathLength must have the sign of (zOut - zIn) where all other parameters are assumed to be given at zOut.
+
+ // absorber related covariance parameters
+ Double_t bendingSlope = param->GetBendingSlope();
+ Double_t nonBendingSlope = param->GetNonBendingSlope();
+ Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
+ Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
+ (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
+ Double_t pathLength = TMath::Abs(signedPathLength);
+ Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
+ Double_t covCorrSlope = TMath::Sign(1.,signedPathLength) * alpha2 * (pathLength * f0 - f1);
+ Double_t varSlop = alpha2 * f0;
+
+ // Set MCS covariance matrix
+ TMatrixD newParamCov(param->GetCovariances());
+ // Non bending plane
+ newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
+ newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
+ // Bending plane
+ newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
+ newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
+
+ // Set momentum related covariances if B!=0
+ if (fgFieldON) {
+ // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
+ Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
+ Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
+ (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
+ // Inverse bending momentum (due to dependences with bending and non bending slopes)
+ newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
+ newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
+ newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
+ newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
+ newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
+ }
+
+ // Set new covariances
+ param->SetCovariances(newParamCov);
}
+//__________________________________________________________________________
+void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param,
+ Double_t xVtx, Double_t yVtx, Double_t zVtx,
+ Double_t errXVtx, Double_t errYVtx,
+ Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
+{
+ /// Correct parameters and corresponding covariances using Branson correction
+ /// - input param are parameters and covariances at the end of absorber
+ /// - output param are parameters and covariances at vertex
+ /// Absorber correction parameters are supposed to be calculated at the current track z-position
+
+ // Position of the Branson plane (spectro. (z<0))
+ Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
+
+ // Add MCS effects to current parameter covariances (spectro. (z<0))
+ AddMCSEffectInAbsorber(param, -pathLength, f0, f1, f2);
+
+ // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
+ ExtrapToZCov(param,zVtx);
+ LinearExtrapToZCov(param,zB);
+
+ // compute track parameters at vertex
+ TMatrixD newParam(5,1);
+ newParam(0,0) = xVtx;
+ newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
+ newParam(2,0) = yVtx;
+ newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
+ newParam(4,0) = param->GetCharge() / param->P() *
+ TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
+ TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
+
+ // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
+ TMatrixD paramCovP(param->GetCovariances());
+ Cov2CovP(param->GetParameters(),paramCovP);
+
+ // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
+ TMatrixD paramCovVtx(5,5);
+ paramCovVtx.Zero();
+ paramCovVtx(0,0) = errXVtx * errXVtx;
+ paramCovVtx(1,1) = paramCovP(0,0);
+ paramCovVtx(2,2) = errYVtx * errYVtx;
+ paramCovVtx(3,3) = paramCovP(2,2);
+ paramCovVtx(4,4) = paramCovP(4,4);
+ paramCovVtx(1,3) = paramCovP(0,2);
+ paramCovVtx(3,1) = paramCovP(2,0);
+ paramCovVtx(1,4) = paramCovP(0,4);
+ paramCovVtx(4,1) = paramCovP(4,0);
+ paramCovVtx(3,4) = paramCovP(2,4);
+ paramCovVtx(4,3) = paramCovP(4,2);
+
+ // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
+ TMatrixD jacob(5,5);
+ jacob.UnitMatrix();
+ jacob(1,0) = - 1. / (zB - zVtx);
+ jacob(1,1) = 1. / (zB - zVtx);
+ jacob(3,2) = - 1. / (zB - zVtx);
+ jacob(3,3) = 1. / (zB - zVtx);
+
+ // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
+ TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
+ TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
+
+ // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
+ CovP2Cov(newParam,newParamCov);
+
+ // Set parameters and covariances at vertex
+ param->SetParameters(newParam);
+ param->SetZ(zVtx);
+ param->SetCovariances(newParamCov);
+}
-// Keep this version for future developments
- //__________________________________________________________________________
-// void AliMUONTrackExtrap::BransonCorrection(AliMUONTrackParam* trackParam)
-// {
-// /// Branson correction of track parameters
-// // the entry parameters have to be calculated at the end of the absorber
-// Double_t zEndAbsorber, zBP, xBP, yBP;
-// Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
-// Int_t sign;
-// // Would it be possible to calculate all that from Geant configuration ????
-// // and to get the Branson parameters from a function in ABSO module ????
-// // with an eventual contribution from other detectors like START ????
-// // Radiation lengths outer part theta > 3 degres
-// static Double_t x01[9] = { 18.8, // C (cm)
-// 10.397, // Concrete (cm)
-// 0.56, // Plomb (cm)
-// 47.26, // Polyethylene (cm)
-// 0.56, // Plomb (cm)
-// 47.26, // Polyethylene (cm)
-// 0.56, // Plomb (cm)
-// 47.26, // Polyethylene (cm)
-// 0.56 }; // Plomb (cm)
-// // inner part theta < 3 degres
-// static Double_t x02[3] = { 18.8, // C (cm)
-// 10.397, // Concrete (cm)
-// 0.35 }; // W (cm)
-// // z positions of the materials inside the absober outer part theta > 3 degres
-// static Double_t z1[10] = { 90, 315, 467, 472, 477, 482, 487, 492, 497, 502 };
-// // inner part theta < 3 degres
-// static Double_t z2[4] = { 90, 315, 467, 503 };
-// static Bool_t first = kTRUE;
-// static Double_t zBP1, zBP2, rLimit;
-// // Calculates z positions of the Branson's planes: zBP1 for outer part and zBP2 for inner part (only at the first call)
-// if (first) {
-// first = kFALSE;
-// Double_t aNBP = 0.0;
-// Double_t aDBP = 0.0;
-// Int_t iBound;
-//
-// for (iBound = 0; iBound < 9; iBound++) {
-// aNBP = aNBP +
-// (z1[iBound+1] * z1[iBound+1] * z1[iBound+1] -
-// z1[iBound] * z1[iBound] * z1[iBound] ) / x01[iBound];
-// aDBP = aDBP +
-// (z1[iBound+1] * z1[iBound+1] - z1[iBound] * z1[iBound] ) / x01[iBound];
-// }
-// zBP1 = (2.0 * aNBP) / (3.0 * aDBP);
-// aNBP = 0.0;
-// aDBP = 0.0;
-// for (iBound = 0; iBound < 3; iBound++) {
-// aNBP = aNBP +
-// (z2[iBound+1] * z2[iBound+1] * z2[iBound+1] -
-// z2[iBound] * z2[iBound ] * z2[iBound] ) / x02[iBound];
-// aDBP = aDBP +
-// (z2[iBound+1] * z2[iBound+1] - z2[iBound] * z2[iBound]) / x02[iBound];
-// }
-// zBP2 = (2.0 * aNBP) / (3.0 * aDBP);
-// rLimit = z2[3] * TMath::Tan(3.0 * (TMath::Pi()) / 180.);
-// }
-//
-// pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
-// sign = 1;
-// if (trackParam->GetInverseBendingMomentum() < 0) sign = -1;
-// pZ = pYZ / (TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()));
-// pX = pZ * trackParam->GetNonBendingSlope();
-// pY = pZ * trackParam->GetBendingSlope();
-// pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
-// xEndAbsorber = trackParam->GetNonBendingCoor();
-// yEndAbsorber = trackParam->GetBendingCoor();
-// radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
-//
-// if (radiusEndAbsorber2 > rLimit*rLimit) {
-// zEndAbsorber = z1[9];
-// zBP = zBP1;
-// } else {
-// zEndAbsorber = z2[3];
-// zBP = zBP2;
-// }
-//
-// xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
-// yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
-//
-// // new parameters after Branson and energy loss corrections
-// pZ = pTotal * zBP / TMath::Sqrt(xBP * xBP + yBP * yBP + zBP * zBP);
-// pX = pZ * xBP / zBP;
-// pY = pZ * yBP / zBP;
-// trackParam->SetBendingSlope(pY/pZ);
-// trackParam->SetNonBendingSlope(pX/pZ);
-//
-// pT = TMath::Sqrt(pX * pX + pY * pY);
-// theta = TMath::ATan2(pT, pZ);
-// pTotal = TotalMomentumEnergyLoss(rLimit, pTotal, theta, xEndAbsorber, yEndAbsorber);
-//
-// trackParam->SetInverseBendingMomentum((sign / pTotal) *
-// TMath::Sqrt(1.0 +
-// trackParam->GetBendingSlope() * trackParam->GetBendingSlope() +
-// trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()) /
-// TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()));
-//
-// // vertex position at (0,0,0)
-// // should be taken from vertex measurement ???
-// trackParam->SetBendingCoor(0.);
-// trackParam->SetNonBendingCoor(0.);
-// trackParam->SetZ(0.);
-// }
-
-void AliMUONTrackExtrap::BransonCorrection(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
{
- /// Branson correction of track parameters
- // the entry parameters have to be calculated at the end of the absorber
- // simplified version: the z positions of Branson's planes are no longer calculated
- // but are given as inputs. One can use the macros MUONTestAbso.C and DrawTestAbso.C
- // to test this correction.
- // Would it be possible to calculate all that from Geant configuration ????
- // and to get the Branson parameters from a function in ABSO module ????
- // with an eventual contribution from other detectors like START ????
- // change to take into account the vertex postition (real, reconstruct,....)
-
- Double_t zBP, xBP, yBP;
- Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
- Int_t sign;
- static Bool_t first = kTRUE;
- static Double_t zBP1, zBP2, rLimit, thetaLimit, zEndAbsorber;
- // zBP1 for outer part and zBP2 for inner part (only at the first call)
- if (first) {
- first = kFALSE;
-
- zEndAbsorber = -503; // spectro (z<0)
- thetaLimit = 3.0 * (TMath::Pi()) / 180.;
- rLimit = TMath::Abs(zEndAbsorber) * TMath::Tan(thetaLimit);
- zBP1 = -450; // values close to those calculated with EvalAbso.C
- zBP2 = -480;
- }
+ /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances
+
+ // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
+ TMatrixD newParamCov(param->GetCovariances());
+ Cov2CovP(param->GetParameters(),newParamCov);
+
+ // Compute new parameters corrected for energy loss
+ Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
+ Double_t p = param->P();
+ Double_t e = TMath::Sqrt(p*p + muMass*muMass);
+ Double_t eCorr = e + eLoss;
+ Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
+ Double_t nonBendingSlope = param->GetNonBendingSlope();
+ Double_t bendingSlope = param->GetBendingSlope();
+ param->SetInverseBendingMomentum(param->GetCharge() / pCorr *
+ TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
+ TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
+
+ // Add effects of energy loss fluctuation to covariances
+ newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
+
+ // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
+ CovP2Cov(param->GetParameters(),newParamCov);
+
+ // Set new parameter covariances
+ param->SetCovariances(newParamCov);
+}
- pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
- sign = 1;
- if (trackParam->GetInverseBendingMomentum() < 0) sign = -1;
- pZ = trackParam->Pz();
- pX = trackParam->Px();
- pY = trackParam->Py();
- pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
- xEndAbsorber = trackParam->GetNonBendingCoor();
- yEndAbsorber = trackParam->GetBendingCoor();
- radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
-
- if (radiusEndAbsorber2 > rLimit*rLimit) {
- zBP = zBP1;
- } else {
- zBP = zBP2;
+//__________________________________________________________________________
+Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
+ Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
+ Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
+{
+ /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber
+ /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important)
+ // pathLength: path length between trackXYZIn and trackXYZOut (cm)
+ // f0: 0th moment of z calculated with the inverse radiation-length distribution
+ // f1: 1st moment of z calculated with the inverse radiation-length distribution
+ // f2: 2nd moment of z calculated with the inverse radiation-length distribution
+ // meanRho: average density of crossed material (g/cm3)
+ // totalELoss: total energy loss in absorber
+
+ // Reset absorber's parameters
+ pathLength = 0.;
+ f0 = 0.;
+ f1 = 0.;
+ f2 = 0.;
+ meanRho = 0.;
+ totalELoss = 0.;
+ sigmaELoss2 = 0.;
+
+ // Check whether the geometry is available
+ if (!gGeoManager) {
+ cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
+ return kFALSE;
}
-
- xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
- yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
-
- // new parameters after Branson and energy loss corrections
-// Float_t zSmear = zBP - gRandom->Gaus(0.,2.); // !!! possible smearing of Z vertex position
-
- Float_t zSmear = zBP ;
- pZ = pTotal * (zSmear-zVtx) / TMath::Sqrt((xBP-xVtx) * (xBP-xVtx) + (yBP-yVtx) * (yBP-yVtx) +( zSmear-zVtx) * (zSmear-zVtx) );
- pX = pZ * (xBP - xVtx)/ (zSmear-zVtx);
- pY = pZ * (yBP - yVtx) / (zSmear-zVtx);
- trackParam->SetBendingSlope(pY/pZ);
- trackParam->SetNonBendingSlope(pX/pZ);
-
+ // Initialize starting point and direction
+ pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
+ (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
+ (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
+ if (pathLength < TGeoShape::Tolerance()) return kFALSE;
+ Double_t b[3];
+ b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
+ b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
+ b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
+ TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
+ if (!currentnode) {
+ cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
+ return kFALSE;
+ }
- pT = TMath::Sqrt(pX * pX + pY * pY);
- theta = TMath::ATan2(pT, TMath::Abs(pZ));
- pTotal = TotalMomentumEnergyLoss(thetaLimit, pTotal, theta);
-
- trackParam->SetInverseBendingMomentum((sign / pTotal) *
- TMath::Sqrt(1.0 +
- trackParam->GetBendingSlope() * trackParam->GetBendingSlope() +
- trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()) /
- TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()));
-
- // vertex position at (0,0,0)
- // should be taken from vertex measurement ???
+ // loop over absorber slices and calculate absorber's parameters
+ Double_t rho = 0.; // material density (g/cm3)
+ Double_t x0 = 0.; // radiation-length (cm-1)
+ Double_t atomicA = 0.; // A of material
+ Double_t atomicZ = 0.; // Z of material
+ Double_t atomicZoverA = 0.; // Z/A of material
+ Double_t localPathLength = 0;
+ Double_t remainingPathLength = pathLength;
+ Double_t zB = trackXYZIn[2];
+ Double_t zE, dzB, dzE;
+ do {
+ // Get material properties
+ TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
+ rho = material->GetDensity();
+ x0 = material->GetRadLen();
+ atomicA = material->GetA();
+ atomicZ = material->GetZ();
+ if(material->IsMixture()){
+ TGeoMixture * mixture = (TGeoMixture*)material;
+ atomicZoverA = 0.;
+ Double_t sum = 0.;
+ for (Int_t iel=0;iel<mixture->GetNelements();iel++){
+ sum += mixture->GetWmixt()[iel];
+ atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
+ }
+ atomicZoverA/=sum;
+ }
+ else atomicZoverA = atomicZ/atomicA;
+
+ // Get path length within this material
+ gGeoManager->FindNextBoundary(remainingPathLength);
+ localPathLength = gGeoManager->GetStep() + 1.e-6;
+ // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
+ if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
+ else {
+ currentnode = gGeoManager->Step();
+ if (!currentnode) {
+ cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
+ f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
+ return kFALSE;
+ }
+ if (!gGeoManager->IsEntering()) {
+ // make another small step to try to enter in new absorber slice
+ gGeoManager->SetStep(0.001);
+ currentnode = gGeoManager->Step();
+ if (!gGeoManager->IsEntering() || !currentnode) {
+ cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
+ f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
+ return kFALSE;
+ }
+ localPathLength += 0.001;
+ }
+ }
+
+ // calculate absorber's parameters
+ zE = b[2] * localPathLength + zB;
+ dzB = zB - trackXYZIn[2];
+ dzE = zE - trackXYZIn[2];
+ f0 += localPathLength / x0;
+ f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
+ f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
+ meanRho += localPathLength * rho;
+ totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA);
+ sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicZoverA);
+
+ // prepare next step
+ zB = zE;
+ remainingPathLength -= localPathLength;
+ } while (remainingPathLength > TGeoShape::Tolerance());
+
+ meanRho /= pathLength;
+
+ return kTRUE;
+}
- trackParam->SetBendingCoor(xVtx);
- trackParam->SetNonBendingCoor(yVtx);
- trackParam->SetZ(zVtx);
+//__________________________________________________________________________
+Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
+{
+ /// Return the angular dispersion square due to multiple Coulomb scattering
+ /// through a material of thickness "dZ" and of radiation length "x0"
+ /// assuming linear propagation and using the small angle approximation.
+
+ Double_t bendingSlope = param.GetBendingSlope();
+ Double_t nonBendingSlope = param.GetNonBendingSlope();
+ Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
+ (1.0 + bendingSlope * bendingSlope) /
+ (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
+ // Path length in the material
+ Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
+ // relativistic velocity
+ Double_t velo = 1.;
+ // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
+ Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
+
+ return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
+}
+//__________________________________________________________________________
+void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
+{
+ /// Add to the track parameter covariances the effects of multiple Coulomb scattering
+ /// through a material of thickness "Abs(dZ)" and of radiation length "x0"
+ /// assuming linear propagation and using the small angle approximation.
+ /// dZ = zOut - zIn (sign is important) and "param" is assumed to be given zOut.
+ /// If x0 <= 0., assume dZ = pathLength/x0 and consider the material thickness as negligible.
+
+ Double_t bendingSlope = param->GetBendingSlope();
+ Double_t nonBendingSlope = param->GetNonBendingSlope();
+ Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
+ Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
+ (1.0 + bendingSlope * bendingSlope) /
+ (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
+ // Path length in the material
+ Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
+ Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength) / x0 : TMath::Abs(signedPathLength);
+ // relativistic velocity
+ Double_t velo = 1.;
+ // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
+ Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0));
+ theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0;
+
+ Double_t varCoor = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.;
+ Double_t varSlop = theta02;
+ Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02 / 2. : 0.;
+
+ // Set MCS covariance matrix
+ TMatrixD newParamCov(param->GetCovariances());
+ // Non bending plane
+ newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
+ newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
+ // Bending plane
+ newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
+ newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
+
+ // Set momentum related covariances if B!=0
+ if (fgFieldON) {
+ // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
+ Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
+ Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
+ (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
+ // Inverse bending momentum (due to dependences with bending and non bending slopes)
+ newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
+ newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
+ newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
+ newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
+ newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
+ }
+
+ // Set new covariances
+ param->SetCovariances(newParamCov);
}
- //__________________________________________________________________________
-Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
+ Double_t xVtx, Double_t yVtx, Double_t zVtx,
+ Double_t errXVtx, Double_t errYVtx,
+ Bool_t correctForMCS, Bool_t correctForEnergyLoss)
{
- /// Returns the total momentum corrected from energy loss in the front absorber
- // One can use the macros MUONTestAbso.C and DrawTestAbso.C
- // to test this correction.
- // Momentum energy loss behaviour evaluated with the simulation of single muons (april 2002)
- Double_t deltaP, pTotalCorrected;
-
- // Parametrization to be redone according to change of absorber material ????
- // See remark in function BransonCorrection !!!!
- // The name is not so good, and there are many arguments !!!!
- if (theta < thetaLimit ) {
- if (pTotal < 20) {
- deltaP = 2.5938 + 0.0570 * pTotal - 0.001151 * pTotal * pTotal;
+ /// Main method for extrapolation to the vertex:
+ /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam
+ /// Changes parameters and covariances according to multiple scattering and energy loss corrections:
+ /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances
+ /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances
+ /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances
+ /// if correctForEnergyLoss=kFALSE: do nothing about energy loss
+
+ if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
+
+ if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
+ cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
+ <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
+ return;
+ }
+
+ // Check the vertex position relatively to the absorber
+ if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
+ cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
+ <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
+ } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
+ cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
+ <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
+ if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
+ else ExtrapToZ(trackParam,zVtx);
+ return;
+ }
+
+ // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
+ if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
+ cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
+ <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
+ if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
+ else ExtrapToZ(trackParam,zVtx);
+ return;
+ } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
+ cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
+ <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
+ } else {
+ if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
+ else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
+ }
+
+ // Get absorber correction parameters assuming linear propagation in absorber
+ Double_t trackXYZOut[3];
+ trackXYZOut[0] = trackParam->GetNonBendingCoor();
+ trackXYZOut[1] = trackParam->GetBendingCoor();
+ trackXYZOut[2] = trackParam->GetZ();
+ Double_t trackXYZIn[3];
+ if (correctForMCS) { // assume linear propagation until the vertex
+ trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
+ trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
+ trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
+ } else {
+ AliMUONTrackParam trackParamIn(*trackParam);
+ ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
+ trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
+ trackXYZIn[1] = trackParamIn.GetBendingCoor();
+ trackXYZIn[2] = trackParamIn.GetZ();
+ }
+ Double_t pTot = trackParam->P();
+ Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
+ if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
+ cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
+ if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
+ else ExtrapToZ(trackParam,zVtx);
+ return;
+ }
+
+ // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
+ if (correctForMCS) {
+
+ if (correctForEnergyLoss) {
+
+ // Correct for multiple scattering and energy loss
+ CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
+ CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
+ trackXYZIn[2], pathLength, f0, f1, f2);
+ CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
+
} else {
- deltaP = 3.0714 + 0.011767 *pTotal;
+
+ // Correct for multiple scattering
+ CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
+ trackXYZIn[2], pathLength, f0, f1, f2);
}
- deltaP *= 0.75; // AZ
+
} else {
- if (pTotal < 20) {
- deltaP = 2.1207 + 0.05478 * pTotal - 0.00145079 * pTotal * pTotal;
- } else {
- deltaP = 2.6069 + 0.0051705 * pTotal;
+
+ if (correctForEnergyLoss) {
+
+ // Correct for energy loss add multiple scattering dispersion in covariance matrix
+ CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
+ AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
+ ExtrapToZCov(trackParam, trackXYZIn[2]);
+ CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
+ ExtrapToZCov(trackParam, zVtx);
+
+ } else {
+
+ // add multiple scattering dispersion in covariance matrix
+ AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
+ ExtrapToZCov(trackParam, zVtx);
+
}
- deltaP *= 0.9; // AZ
+
}
- pTotalCorrected = pTotal + deltaP / TMath::Cos(theta);
- return pTotalCorrected;
+
}
- //__________________________________________________________________________
-void AliMUONTrackExtrap::FieldCorrection(AliMUONTrackParam *trackParam, Double_t zEnd)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam,
+ Double_t xVtx, Double_t yVtx, Double_t zVtx,
+ Double_t errXVtx, Double_t errYVtx)
{
- /// Correction of the effect of the magnetic field in the absorber
- // Assume a constant field along Z axis.
- Float_t b[3],x[3];
- Double_t bZ;
- Double_t pYZ,pX,pY,pZ,pT;
- Double_t pXNew,pYNew;
- Double_t c;
-
- pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
- c = TMath::Sign(1.0,trackParam->GetInverseBendingMomentum()); // particle charge
-
- pZ = trackParam->Pz();
- pX = trackParam->Px();
- pY = trackParam->Py();
- pT = TMath::Sqrt(pX*pX+pY*pY);
-
- if (TMath::Abs(pZ) <= 0) return;
- x[2] = zEnd/2;
- x[0] = x[2]*trackParam->GetNonBendingSlope();
- x[1] = x[2]*trackParam->GetBendingSlope();
-
- // Take magn. field value at position x.
- if (fgkField) fgkField->Field(x,b);
- else {
- cout<<"F-AliMUONTrackExtrap::FieldCorrection: fgkField = 0x0"<<endl;
- exit(-1);
+ /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects
+ /// Add branson correction resolution and energy loss fluctuation to parameter covariances
+ ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
+}
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam,
+ Double_t xVtx, Double_t yVtx, Double_t zVtx,
+ Double_t errXVtx, Double_t errYVtx)
+{
+ /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only
+ /// Add branson correction resolution to parameter covariances
+ ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
+}
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx)
+{
+ /// Extrapolate track parameters to vertex, corrected for energy loss effects only
+ /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances
+ ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
+}
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
+{
+ /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections
+ /// Add dispersion due to multiple scattering to parameter covariances
+ ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
+}
+
+//__________________________________________________________________________
+Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
+{
+ /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation
+
+ if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
+
+ // Check whether the geometry is available
+ if (!gGeoManager) {
+ cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
+ return 0.;
}
- bZ = b[2];
-
- // Transverse momentum rotation
- // Parameterized with the study of DeltaPhi = phiReco - phiGen as a function of pZ.
- Double_t phiShift = c*0.436*0.0003*bZ*zEnd/pZ;
- // Rotate momentum around Z axis.
- pXNew = pX*TMath::Cos(phiShift) - pY*TMath::Sin(phiShift);
- pYNew = pX*TMath::Sin(phiShift) + pY*TMath::Cos(phiShift);
-
- trackParam->SetBendingSlope(pYNew/pZ);
- trackParam->SetNonBendingSlope(pXNew/pZ);
- trackParam->SetInverseBendingMomentum(c/TMath::Sqrt(pYNew*pYNew+pZ*pZ));
-
+ // Get encountered material correction parameters assuming linear propagation from vertex to the track position
+ Double_t trackXYZOut[3];
+ trackXYZOut[0] = trackParam->GetNonBendingCoor();
+ trackXYZOut[1] = trackParam->GetBendingCoor();
+ trackXYZOut[2] = trackParam->GetZ();
+ Double_t trackXYZIn[3];
+ trackXYZIn[0] = xVtx;
+ trackXYZIn[1] = yVtx;
+ trackXYZIn[2] = zVtx;
+ Double_t pTot = trackParam->P();
+ Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
+ GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
+
+ // total momentum corrected for energy loss
+ Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
+ Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
+ Double_t eCorr = e + totalELoss;
+ Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
+
+ return pTotCorr - pTot;
+}
+
+//__________________________________________________________________________
+Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
+{
+ /// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
+ /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
+ Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
+
+ // mean exitation energy (GeV)
+ Double_t i;
+ if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
+ else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
+
+ return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA);
+}
+
+//__________________________________________________________________________
+Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
+{
+ /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal'
+ /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ'
+ Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
+ //Double_t eMass = 0.510998918e-3; // GeV
+ Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
+ Double_t p2=pTotal*pTotal;
+ Double_t beta2=p2/(p2 + muMass*muMass);
+
+ Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution
+ Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
+
+ //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
+
+ return sigma2;
+}
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::Cov2CovP(const TMatrixD ¶m, TMatrixD &cov)
+{
+ /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot)
+ /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
+
+ // charge * total momentum
+ Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
+ TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
+
+ // Jacobian of the opposite transformation
+ TMatrixD jacob(5,5);
+ jacob.UnitMatrix();
+ jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
+ jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
+ (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
+ jacob(4,4) = - qPTot / param(4,0);
+
+ // compute covariances in new coordinate system
+ TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
+ cov.Mult(jacob,tmp);
+}
+
+//__________________________________________________________________________
+void AliMUONTrackExtrap::CovP2Cov(const TMatrixD ¶m, TMatrixD &covP)
+{
+ /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz)
+ /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
+
+ // charge * total momentum
+ Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
+ TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
+
+ // Jacobian of the transformation
+ TMatrixD jacob(5,5);
+ jacob.UnitMatrix();
+ jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
+ jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
+ (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
+ jacob(4,4) = - param(4,0) / qPTot;
+
+ // compute covariances in new coordinate system
+ TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
+ covP.Mult(jacob,tmp);
}
//__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
+void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
{
+/// <pre>
/// ******************************************************************
/// * *
/// * Performs the tracking of one step in a magnetic field *
/// * output *
/// * VOUT = same as VECT after completion of the step *
/// * *
-/// * ==>Called by : <USER>, GUSWIM *
+/// * ==>Called by : USER, GUSWIM *
/// * Author m.hansroul ********* *
/// * modified s.egli, s.v.levonian *
/// * modified v.perevoztchikov
/// * *
/// ******************************************************************
+/// </pre>
// modif: everything in double precision
xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
//cmodif: call gufld (xyz, h) changed into:
- GetField (xyz, h);
+ TGeoGlobalMagField::Instance()->Field(xyz,h);
h2xy = h[0]*h[0] + h[1]*h[1];
h[3] = h[2]*h[2]+ h2xy;
}
//__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
+void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, const Double_t *vect, Double_t *vout)
{
+/// <pre>
/// ******************************************************************
/// * *
/// * Tracking routine in a constant field oriented *
/// * Tracking is performed with a conventional *
/// * helix step method *
/// * *
-/// * ==>Called by : <USER>, GUSWIM *
+/// * ==>Called by : USER, GUSWIM *
/// * Authors R.Brun, M.Hansroul ********* *
/// * Rewritten V.Perevoztchikov
/// * *
/// ******************************************************************
+/// </pre>
Double_t hxp[3];
Double_t h4, hp, rho, tet;
return;
}
+
//__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
+Bool_t AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, const Double_t* vect, Double_t* vout)
{
+/// <pre>
/// ******************************************************************
/// * *
/// * Runge-Kutta method for tracking a particle through a magnetic *
/// * User routine called *
/// * CALL GUFLD(X,F) *
/// * *
-/// * ==>Called by : <USER>, GUSWIM *
+/// * ==>Called by : USER, GUSWIM *
/// * Authors R.Brun, M.Hansroul ********* *
/// * V.Perevoztchikov (CUT STEP implementation) *
/// * *
/// * *
/// ******************************************************************
+/// </pre>
Double_t h2, h4, f[4];
- Double_t xyzt[3], a, b, c, ph,ph2;
+ Double_t xyzt[3] = {FLT_MAX, FLT_MAX, FLT_MAX};
+ Double_t a, b, c, ph,ph2;
Double_t secxs[4],secys[4],seczs[4],hxp[3];
Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
Double_t est, at, bt, ct, cba;
rest = step - tl;
if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
//cmodif: call gufld(vout,f) changed into:
-
- GetField(vout,f);
+ TGeoGlobalMagField::Instance()->Field(vout,f);
// *
// * start of integration
xyzt[2] = zt;
//cmodif: call gufld(xyzt,f) changed into:
- GetField(xyzt,f);
+ TGeoGlobalMagField::Instance()->Field(xyzt,f);
at = a + secxs[0];
bt = b + secys[0];
xyzt[2] = zt;
//cmodif: call gufld(xyzt,f) changed into:
- GetField(xyzt,f);
+ TGeoGlobalMagField::Instance()->Field(xyzt,f);
z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
vout[5] = cba*c;
rest = step - tl;
if (step < 0.) rest = -rest;
- if (rest < 1.e-5*TMath::Abs(step)) return;
+ if (rest < 1.e-5*TMath::Abs(step)) return kTRUE;
} while(1);
// angle too big, use helix
+ cout<<"W-AliMUONTrackExtrap::ExtrapOneStepRungekutta: Ruge-Kutta failed: switch to helix"<<endl;
f1 = f[0];
f2 = f[1];
f3 = f[2];
f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
+ if (f4 < 1.e-10) {
+ cout<<"E-AliMUONTrackExtrap::ExtrapOneStepRungekutta: magnetic field at (";
+ cout<<xyzt[0]<<", "<<xyzt[1]<<", "<<xyzt[2]<<") = "<<f4<<": giving up"<<endl;
+ return kFALSE;
+ }
rho = -f4*pinv;
tet = rho * step;
vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
- return;
-}
-//___________________________________________________________
- void AliMUONTrackExtrap::GetField(Double_t *Position, Double_t *Field)
-{
- /// interface for arguments in double precision (Why ? ChF)
- Float_t x[3], b[3];
-
- x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
-
- if (fgkField) fgkField->Field(x,b);
- else {
- cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
- exit(-1);
- }
-
- Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
-
- return;
+ return kTRUE;
}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff