#include "AliMUONTrackExtrap.h"
#include "AliMUONTrackParam.h"
#include "AliMUONConstants.h"
+#include "AliMUONReconstructor.h"
#include "AliMagF.h"
#include <TMath.h>
-#include <TMatrixD.h>
#include <TGeoManager.h>
#include <Riostream.h>
/// \endcond
const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
+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(const AliMagF* magField)
+{
+ /// set magnetic field
+
+ // set field map
+ fgkField = magField;
+ if (!fgkField) {
+ cout<<"E-AliMUONTrackExtrap::SetField: fgkField = 0x0"<<endl;
+ return;
+ }
+
+ // set field on/off flag
+ fgFieldON = (fgkField->Factor() == 0.) ? kFALSE : kTRUE;
+
+ // set field at the centre of the dipole
+ if (fgFieldON) {
+ Float_t b[3] = {0.,0.,0.}, x[3] = {50.,50.,(Float_t) fgkSimpleBPosition};
+ fgkField->Field(x,b);
+ fgSimpleBValue = (Double_t) b[0];
+ } else fgSimpleBValue = 0.;
+
+}
+
+//__________________________________________________________________________
Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
{
/// Returns impact parameter at vertex in bending plane (cm),
if (bendingMomentum == 0.) return 1.e10;
- Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
- Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
- Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
- if (fgkField) fgkField->Field(x,b);
- else {
+ if (!fgkField) {
cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
exit(-1);
}
- Double_t simpleBValue = (Double_t) b[0];
- return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / bendingMomentum);
+ const Double_t kCorrectionFactor = 0.9; // impact parameter is 10% overestimated
+
+ return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
}
- //__________________________________________________________________________
-Double_t AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
+//__________________________________________________________________________
+Double_t
+AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam)
{
/// Returns signed bending momentum in bending plane (GeV/c),
/// the sign being the sign of the charge for particles moving forward in Z,
if (impactParam == 0.) return 1.e10;
- Double_t simpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
- Double_t simpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
- Float_t b[3], x[3] = {0.,0.,(Float_t) simpleBPosition};
- if (fgkField) fgkField->Field(x,b);
- else {
+ if (!fgkField) {
cout<<"F-AliMUONTrackExtrap::GetField: fgkField = 0x0"<<endl;
exit(-1);
}
- Double_t simpleBValue = (Double_t) b[0];
- return (-0.0003 * simpleBValue * simpleBLength * simpleBPosition / impactParam);
+ 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)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
{
/// Track parameters (and their covariances if any) linearly extrapolated to the plane at "zEnd".
/// On return, results from the extrapolation are updated in trackParam.
paramCov(2,3) += dZ * paramCov(3,3);
paramCov(3,2) = paramCov(2,3);
trackParam->SetCovariances(paramCov);
+
+ // Update the propagator if required
+ if (updatePropagator) {
+ TMatrixD jacob(5,5);
+ jacob.UnitMatrix();
+ jacob(0,1) = dZ;
+ jacob(2,3) = dZ;
+ trackParam->UpdatePropagator(jacob);
+ }
+
}
}
- //__________________________________________________________________________
+//__________________________________________________________________________
void 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 (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
+ if (!fgFieldON) AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
+ else if (fgkUseHelix) AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
else AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
}
- //__________________________________________________________________________
+//__________________________________________________________________________
void AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
{
/// Track parameter extrapolation to the plane at "Z" using Helix algorithm.
stepNumber++;
ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
- // better use TArray ????
+ // better use TArray ????
for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
}
// check fgkMaxStepNumber ????
RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
}
- //__________________________________________________________________________
+//__________________________________________________________________________
void AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd)
{
/// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm.
dZ = zEnd - trackParam->GetZ();
// step lenght assuming linear trajectory
step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
- trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
+ trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
do { // reduce step lenght while zEnd oversteped
if (stepNumber > fgkMaxStepNumber) {
trackParam->SetZ(zEnd);
}
- //__________________________________________________________________________
+//__________________________________________________________________________
void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
{
/// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam.
v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
}
- //__________________________________________________________________________
+//__________________________________________________________________________
void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
{
/// Set track parameters in trackParam from Geant3 parameters pointed to by "v3",
trackParam->SetNonBendingSlope(v3[3]/v3[5]);
}
- //__________________________________________________________________________
+//__________________________________________________________________________
void AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
{
/// Track parameters and their covariances extrapolated to the plane at "zEnd".
if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
+ if (!fgFieldON) { // linear extrapolation if no magnetic field
+ AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd,updatePropagator);
+ 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;
// Get reference to the parameter covariance matrix
const TMatrixD& kParamCov = trackParam->GetCovariances();
-
+
// Extrapolate track parameters to "zEnd"
ExtrapToZ(trackParam,zEnd);
TMatrixD dParam(5,1);
for (Int_t i=0; i<5; i++) {
// Skip jacobian calculation for parameters with no associated error
- if (kParamCov(i,i) == 0.) continue;
+ if (kParamCov(i,i) <= 0.) continue;
// Small variation of parameter i only
for (Int_t j=0; j<5; j++) {
// Update the propagator if required
if (updatePropagator) trackParam->UpdatePropagator(jacob);
-
}
- //__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapToStation(AliMUONTrackParam* trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut)
-{
- /// 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::ExtrapToStation: Starting Z ("<<trackParamIn->GetZ()
- <<") in between z1 ("<<z1<<") and z2 ("<<z2<<") of station(0..)"<<station<<endl;
- exit(-1);
- }
- 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;
-}
-
- //__________________________________________________________________________
-void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx)
-{
- /// Extrapolation to the vertex (at the z position "zVtx") without Branson and energy loss corrections.
- /// Returns the track parameters resulting from the extrapolation in the current TrackParam.
- /// Include multiple Coulomb scattering effects in trackParam covariances.
-
- if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
-
- if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
- cout<<"W-AliMUONTrackExtrap::ExtrapToVertexUncorrected: Starting Z ("<<trackParam->GetZ()
- <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
- exit(-1);
- }
-
- // 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());
- }
-
- // Then add MCS effect in absorber to the parameters covariances
- AliMUONTrackParam trackParamIn(*trackParam);
- ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
- Double_t trackXYZIn[3];
- trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
- trackXYZIn[1] = trackParamIn.GetBendingCoor();
- trackXYZIn[2] = trackParamIn.GetZ();
- Double_t trackXYZOut[3];
- trackXYZOut[0] = trackParam->GetNonBendingCoor();
- trackXYZOut[1] = trackParam->GetBendingCoor();
- trackXYZOut[2] = trackParam->GetZ();
- Double_t pathLength = 0.;
- Double_t f0 = 0.;
- Double_t f1 = 0.;
- Double_t f2 = 0.;
- Double_t meanRho = 0.;
- Double_t totalELoss = 0.;
- GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,trackParam->P(),pathLength,f0,f1,f2,meanRho,totalELoss);
- AddMCSEffectInAbsorber(trackParam,pathLength,f0,f1,f2);
-
- // finally go to the vertex
- ExtrapToZCov(trackParam,zVtx);
-
-}
-
- //__________________________________________________________________________
+//__________________________________________________________________________
void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
{
/// Add to the track parameter covariances the effects of multiple Coulomb scattering
- /// at the end of the front absorber using the absorber correction parameters
+ /// The absorber correction parameters are supposed to be calculated at the current track z-position
// 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
+ (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
Double_t covCorrSlope = alpha2 * (pathLength * f0 - f1);
Double_t varSlop = alpha2 * f0;
+ // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
+ 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);
+
+ // Set MCS covariance matrix
TMatrixD newParamCov(param->GetCovariances());
// Non bending plane
newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
// Bending plane
newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
+ // 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
+ AddMCSEffectInAbsorber(param, pathLength, f0, f1, f2);
+
+ // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
+ ExtrapToZCov(param,zVtx);
+ LinearExtrapToZ(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);
}
- //__________________________________________________________________________
-void 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)
+//__________________________________________________________________________
+void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
+{
+ /// 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);
+
+ // Add effects of energy loss fluctuation to covariances
+ newParamCov(4,4) += sigmaELoss2;
+
+ // Compute new parameters corrected for energy loss
+ Double_t nonBendingSlope = param->GetNonBendingSlope();
+ Double_t bendingSlope = param->GetBendingSlope();
+ param->SetInverseBendingMomentum(param->GetCharge() / (param->P() + eLoss) *
+ TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
+ TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
+
+ // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
+ CovP2Cov(param->GetParameters(),newParamCov);
+
+ // Set new parameter covariances
+ param->SetCovariances(newParamCov);
+}
+
+//__________________________________________________________________________
+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 between track positions trackXYZIn and trackXYZOut
+ /// 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 = 0.;
meanRho = 0.;
totalELoss = 0.;
+ sigmaELoss2 = 0.;
// Check whether the geometry is available
if (!gGeoManager) {
cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
- return;
+ return kFALSE;
}
// 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;
+ if (pathLength < TGeoShape::Tolerance()) return kFALSE;
Double_t b[3];
b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
if (!currentnode) {
cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
- return;
+ return kFALSE;
}
// loop over absorber slices and calculate absorber's parameters
currentnode = gGeoManager->Step();
if (!currentnode) {
cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
- f0 = f1 = f2 = meanRho = 0.;
- return;
+ f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
+ return kFALSE;
}
if (!gGeoManager->IsEntering()) {
// make another small step to try to enter in new absorber slice
currentnode = gGeoManager->Step();
if (!gGeoManager->IsEntering() || !currentnode) {
cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
- f0 = f1 = f2 = meanRho = 0.;
- return;
+ f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
+ return kFALSE;
}
localPathLength += 0.001;
}
f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
meanRho += localPathLength * rho;
totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicA, atomicZ);
+ sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicA, atomicZ);
// prepare next step
zB = zE;
} while (remainingPathLength > TGeoShape::Tolerance());
meanRho /= pathLength;
+
+ return kTRUE;
}
- //__________________________________________________________________________
+//__________________________________________________________________________
Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
{
/// Return the angular dispersion square due to multiple Coulomb scattering
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);
+ (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
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
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);
+ 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 pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
Double_t pathLength2 = pathLength * pathLength;
Double_t varSlop = theta02;
Double_t covCorrSlope = pathLength * theta02 / 2.;
- // Add effects of multiple Coulomb scattering in track parameter covariances
+ // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeX
+ 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);
+
+ // Set MCS covariance matrix
TMatrixD newParamCov(param->GetCovariances());
// Non bending plane
newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
// Bending plane
newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
+ // 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::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx,
- Bool_t CorrectForMCS, Bool_t CorrectForEnergyLoss)
+//__________________________________________________________________________
+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)
{
- /// Extrapolation to the vertex.
- /// Returns the track parameters resulting from the extrapolation of the current TrackParam.
- /// Changes parameters according to Branson correction through the absorber and energy loss
+ /// 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<<"F-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
- <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
- exit(-1);
- }
-
- // Check if correction required
- if (!CorrectForMCS && !CorrectForEnergyLoss) {
- ExtrapToZ(trackParam,zVtx);
+ 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;
+
<<") 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;
- ExtrapToZ(trackParam,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;
- ExtrapToZ(trackParam,zVtx);
+ <<") 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;
+
<<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
} else {
- ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
+ if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
+ else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
}
- // Get absorber correction parameters assuming linear propagation from vertex to the track position
+ // 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];
- 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]);
+ 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 = 0.;
- Double_t f0 = 0.;
- Double_t f1 = 0.;
- Double_t f2 = 0.;
- Double_t meanRho = 0.;
- Double_t deltaP = 0.;
- GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,deltaP);
-
- // Correct for half of energy loss
- Double_t nonBendingSlope, bendingSlope;
- Double_t charge = TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
- if (CorrectForEnergyLoss) {
- pTot += 0.5 * deltaP;
- nonBendingSlope = trackParam->GetNonBendingSlope();
- bendingSlope = trackParam->GetBendingSlope();
- trackParam->SetInverseBendingMomentum(charge / pTot *
- TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
- TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
+ Double_t pathLength, f0, f1, f2, meanRho, deltaP, sigmaDeltaP2;
+ if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,deltaP,sigmaDeltaP2)) {
+ cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
+ if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
+ else ExtrapToZ(trackParam,zVtx);
+ return;
}
- if (CorrectForMCS) {
- // Position of the Branson plane (spectro. (z<0))
- Double_t zB = (f1>0.) ? trackXYZIn[2] - f2/f1 : 0.;
+ // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
+ if (correctForMCS) {
- // Get track position in the Branson plane corrected for magnetic field effect
- ExtrapToZ(trackParam,zVtx);
- Double_t xB = trackParam->GetNonBendingCoor() + (zB - zVtx) * trackParam->GetNonBendingSlope();
- Double_t yB = trackParam->GetBendingCoor() + (zB - zVtx) * trackParam->GetBendingSlope();
-
- // Get track slopes corrected for multiple scattering (spectro. (z<0))
- nonBendingSlope = (zB<0.) ? (xB - xVtx) / (zB - zVtx) : trackParam->GetNonBendingSlope();
- bendingSlope = (zB<0.) ? (yB - yVtx) / (zB - zVtx) : trackParam->GetBendingSlope();
+ if (correctForEnergyLoss) {
+
+ // Correct for multiple scattering and energy loss
+ CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
+ CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
+ trackXYZIn[2], pathLength, f0, f1, f2);
+ CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
+
+ } else {
+
+ // Correct for multiple scattering
+ CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
+ trackXYZIn[2], pathLength, f0, f1, f2);
+ }
- // Set track parameters at vertex
- trackParam->SetNonBendingCoor(xVtx);
- trackParam->SetBendingCoor(yVtx);
- trackParam->SetZ(zVtx);
- trackParam->SetNonBendingSlope(nonBendingSlope);
- trackParam->SetBendingSlope(bendingSlope);
} else {
- ExtrapToZ(trackParam,zVtx);
- nonBendingSlope = trackParam->GetNonBendingSlope();
- bendingSlope = trackParam->GetBendingSlope();
+
+ if (correctForEnergyLoss) {
+
+ // Correct for energy loss add multiple scattering dispersion in covariance matrix
+ CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
+ AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
+ ExtrapToZCov(trackParam, trackXYZIn[2]);
+ CorrectELossEffectInAbsorber(trackParam, 0.5*deltaP, 0.5*sigmaDeltaP2);
+ ExtrapToZCov(trackParam, zVtx);
+
+ } else {
+
+ // add multiple scattering dispersion in covariance matrix
+ AddMCSEffectInAbsorber(trackParam, pathLength, f0, f1, f2);
+ ExtrapToZCov(trackParam, zVtx);
+
+ }
+
}
- // Correct for second half of energy loss
- if (CorrectForEnergyLoss) pTot += 0.5 * deltaP;
-
- // Set track parameters at vertex
- trackParam->SetInverseBendingMomentum(charge / pTot *
- TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
- TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
-
}
- //__________________________________________________________________________
+//__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToVertex(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 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
trackXYZIn[1] = yVtx;
trackXYZIn[2] = zVtx;
Double_t pTot = trackParam->P();
- Double_t pathLength = 0.;
- Double_t f0 = 0.;
- Double_t f1 = 0.;
- Double_t f2 = 0.;
- Double_t meanRho = 0.;
- Double_t totalELoss = 0.;
- GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss);
+ Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
+ GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
return totalELoss;
}
- //__________________________________________________________________________
+//__________________________________________________________________________
Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
{
/// Returns the mean total momentum energy loss of muon with total momentum='pTotal'
Double_t w = k * rho * pathLength * atomicZ / atomicA / beta2;
if (beta2/(1-beta2)>3.5*3.5)
- return w * (log(2.*eMass*3.5/(i*atomicZ)) + 0.5*log(beta2/(1-beta2)) - beta2);
-
+ return w * (log(2.*eMass*3.5/(i*atomicZ)) + 0.5*log(beta2/(1-beta2)) - beta2);
+
return w * (log(2.*eMass*beta2/(1-beta2)/(i*atomicZ)) - beta2);
}
+//__________________________________________________________________________
+Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicA, Double_t atomicZ)
+{
+ /// 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 = 0.105658369; // 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 * atomicZ / atomicA / 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::GetField(Double_t *Position, Double_t *Field)
+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;
}
Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
-
+
return;
}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff