New class AliMUONTrackExtrap containing static method for tack extrapolation (Philipp...
authormartinez <martinez@f7af4fe6-9843-0410-8265-dc069ae4e863>
Fri, 27 Oct 2006 07:58:23 +0000 (07:58 +0000)
committermartinez <martinez@f7af4fe6-9843-0410-8265-dc069ae4e863>
Fri, 27 Oct 2006 07:58:23 +0000 (07:58 +0000)
MUON/AliMUONTrackExtrap.cxx [new file with mode: 0644]
MUON/AliMUONTrackExtrap.h [new file with mode: 0644]

diff --git a/MUON/AliMUONTrackExtrap.cxx b/MUON/AliMUONTrackExtrap.cxx
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+/**************************************************************************
+ * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
+ *                                                                        *
+ * Author: The ALICE Off-line Project.                                    *
+ * Contributors are mentioned in the code where appropriate.              *
+ *                                                                        *
+ * Permission to use, copy, modify and distribute this software and its   *
+ * documentation strictly for non-commercial purposes is hereby granted   *
+ * without fee, provided that the above copyright notice appears in all   *
+ * copies and that both the copyright notice and this permission notice   *
+ * appear in the supporting documentation. The authors make no claims     *
+ * about the suitability of this software for any purpose. It is          *
+ * provided "as is" without express or implied warranty.                  *
+ **************************************************************************/
+
+/* $Id$ */
+
+///////////////////////////////////////////////////
+//
+// Tools
+// for
+// track
+// extrapolation
+// in
+// ALICE
+// dimuon
+// spectrometer
+//
+///////////////////////////////////////////////////
+
+#include <Riostream.h>
+
+#include "AliMUONTrackExtrap.h" 
+#include "AliMUONTrackParam.h"
+#include "AliMUONConstants.h"
+#include "AliMagF.h" 
+#include "AliLog.h" 
+#include "AliTracker.h"
+
+ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
+
+const AliMagF* AliMUONTrackExtrap::fgkField = 0x0;
+
+  //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
+{
+  /// Track parameter extrapolation to the plane at "Z".
+  /// 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
+  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 ????
+  // For safety: return kTRUE or kFALSE ????
+  // Parameter vector for calling EXTRAP_ONESTEP
+  SetGeant3ParametersFromTrackParam(trackParam, vGeant3, forwardBackward);
+  // 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 ????
+  // Extrapolation loop
+  stepNumber = 0;
+  while (((-forwardBackward * (vGeant3[2] - zEnd)) <= 0.0) &&  // spectro. z<0
+        (stepNumber < maxStepNumber)) {
+    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];}
+  }
+  // check maxStepNumber ????
+  // Interpolation back to exact Z (2nd order)
+  // should be in function ???? using TArray ????
+  Double_t dZ12 = vGeant3New[2] - vGeant3[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 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
+  } else {
+    cout<<"W-AliMUONTrackExtrap::ExtrapToZ: Extrap. to Z not reached, Z = "<<zEnd<<endl;
+  }
+  // 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)
+{
+  /// Set vector of Geant3 parameters pointed to by "vGeant3" 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
+  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
+}
+
+  //__________________________________________________________________________
+void AliMUONTrackExtrap::SetTrackParamFromGeant3Parameters(Double_t *vGeant3, Double_t charge, AliMUONTrackParam* trackParam)
+{
+  /// Set track parameters in trackParam from Geant3 parameters pointed to by "vGeant3",
+  /// 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->SetInverseBendingMomentum(charge/pYZ);
+  trackParam->SetBendingSlope(vGeant3[4]/vGeant3[5]);
+  trackParam->SetNonBendingSlope(vGeant3[3]/vGeant3[5]);
+}
+
+  //__________________________________________________________________________
+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::ExtrapToStationAliError: 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::ExtrapToVertex(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
+{
+  /// 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);
+}
+
+
+//  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)
+{
+  /// 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;
+  }
+
+  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;
+  }
+
+  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);
+
+  
+  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 ???
+
+  trackParam->SetBendingCoor(xVtx);
+  trackParam->SetNonBendingCoor(yVtx);
+  trackParam->SetZ(zVtx);
+
+}
+
+  //__________________________________________________________________________
+Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta)
+{
+  /// 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;
+    } else {
+      deltaP = 3.0714 + 0.011767 *pTotal;
+    }
+    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;
+    }
+    deltaP *= 0.9; // AZ
+  }
+  pTotalCorrected = pTotal + deltaP / TMath::Cos(theta);
+  return pTotalCorrected;
+}
+
+  //__________________________________________________________________________
+void AliMUONTrackExtrap::FieldCorrection(AliMUONTrackParam *trackParam, Double_t zEnd)
+{
+  /// 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);
+  }
+  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));
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout)
+{
+///    ******************************************************************
+///    *                                                                *
+///    *  Performs the tracking of one step in a magnetic field         *
+///    *  The trajectory is assumed to be a helix in a constant field   *
+///    *  taken at the mid point of the step.                           *
+///    *  Parameters:                                                   *
+///    *   input                                                        *
+///    *     STEP =arc length of the step asked                         *
+///    *     VECT =input vector (position,direction cos and momentum)   *
+///    *     CHARGE=  electric charge of the particle                   *
+///    *   output                                                       *
+///    *     VOUT = same as VECT after completion of the step           *
+///    *                                                                *
+///    *    ==>Called by : <USER>, GUSWIM                               *
+///    *       Author    m.hansroul  *********                          *
+///    *       modified  s.egli, s.v.levonian                           *
+///    *       modified  v.perevoztchikov
+///    *                                                                *
+///    ******************************************************************
+
+// modif: everything in double precision
+
+    Double_t xyz[3], h[4], hxp[3];
+    Double_t h2xy, hp, rho, tet;
+    Double_t sint, sintt, tsint, cos1t;
+    Double_t f1, f2, f3, f4, f5, f6;
+
+    const Int_t kix  = 0;
+    const Int_t kiy  = 1;
+    const Int_t kiz  = 2;
+    const Int_t kipx = 3;
+    const Int_t kipy = 4;
+    const Int_t kipz = 5;
+    const Int_t kipp = 6;
+
+    const Double_t kec = 2.9979251e-4;
+    //
+    //    ------------------------------------------------------------------
+    //
+    //       units are kgauss,centimeters,gev/c
+    //
+    vout[kipp] = vect[kipp];
+    if (TMath::Abs(charge) < 0.00001) {
+      for (Int_t i = 0; i < 3; i++) {
+       vout[i] = vect[i] + step * vect[i+3];
+       vout[i+3] = vect[i+3];
+      }
+      return;
+    }
+    xyz[0]    = vect[kix] + 0.5 * step * vect[kipx];
+    xyz[1]    = vect[kiy] + 0.5 * step * vect[kipy];
+    xyz[2]    = vect[kiz] + 0.5 * step * vect[kipz];
+
+    //cmodif: call gufld (xyz, h) changed into:
+    GetField (xyz, h);
+    h2xy = h[0]*h[0] + h[1]*h[1];
+    h[3] = h[2]*h[2]+ h2xy;
+    if (h[3] < 1.e-12) {
+      for (Int_t i = 0; i < 3; i++) {
+       vout[i] = vect[i] + step * vect[i+3];
+       vout[i+3] = vect[i+3];
+      }
+      return;
+    }
+    if (h2xy < 1.e-12*h[3]) {
+      ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
+      return;
+    }
+    h[3] = TMath::Sqrt(h[3]);
+    h[0] /= h[3];
+    h[1] /= h[3];
+    h[2] /= h[3];
+    h[3] *= kec;
+
+    hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
+    hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
+    hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
+    hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
+
+    rho = -charge*h[3]/vect[kipp];
+    tet = rho * step;
+
+    if (TMath::Abs(tet) > 0.15) {
+      sint = TMath::Sin(tet);
+      sintt = (sint/tet);
+      tsint = (tet-sint)/tet;
+      cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
+    } else {
+      tsint = tet*tet/36.;
+      sintt = (1. - tsint);
+      sint = tet*sintt;
+      cos1t = 0.5*tet;
+    }
+
+    f1 = step * sintt;
+    f2 = step * cos1t;
+    f3 = step * tsint * hp;
+    f4 = -tet*cos1t;
+    f5 = sint;
+    f6 = tet * cos1t * hp;
+    vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
+    vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
+    vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
+    vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
+    vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
+    vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
+    return;
+}
+
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout)
+{
+///    ******************************************************************
+///    *                                                                *
+///    *       Tracking routine in a constant field oriented            *
+///    *       along axis 3                                             *
+///    *       Tracking is performed with a conventional                *
+///    *       helix step method                                        *
+///    *                                                                *
+///    *    ==>Called by : <USER>, GUSWIM                               *
+///    *       Authors    R.Brun, M.Hansroul  *********                 *
+///    *       Rewritten  V.Perevoztchikov
+///    *                                                                *
+///    ******************************************************************
+
+    Double_t hxp[3];
+    Double_t h4, hp, rho, tet;
+    Double_t sint, sintt, tsint, cos1t;
+    Double_t f1, f2, f3, f4, f5, f6;
+
+    const Int_t kix  = 0;
+    const Int_t kiy  = 1;
+    const Int_t kiz  = 2;
+    const Int_t kipx = 3;
+    const Int_t kipy = 4;
+    const Int_t kipz = 5;
+    const Int_t kipp = 6;
+
+    const Double_t kec = 2.9979251e-4;
+
+// 
+//     ------------------------------------------------------------------
+// 
+//       units are kgauss,centimeters,gev/c
+// 
+    vout[kipp] = vect[kipp];
+    h4 = field * kec;
+
+    hxp[0] = - vect[kipy];
+    hxp[1] = + vect[kipx];
+    hp = vect[kipz];
+
+    rho = -h4/vect[kipp];
+    tet = rho * step;
+    if (TMath::Abs(tet) > 0.15) {
+      sint = TMath::Sin(tet);
+      sintt = (sint/tet);
+      tsint = (tet-sint)/tet;
+      cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
+    } else {
+      tsint = tet*tet/36.;
+      sintt = (1. - tsint);
+      sint = tet*sintt;
+      cos1t = 0.5*tet;
+    }
+
+    f1 = step * sintt;
+    f2 = step * cos1t;
+    f3 = step * tsint * hp;
+    f4 = -tet*cos1t;
+    f5 = sint;
+    f6 = tet * cos1t * hp;
+    vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
+    vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
+    vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
+    vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
+    vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
+    vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
+
+    return;
+}
+ //__________________________________________________________________________
+void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout)
+{
+///    ******************************************************************
+///    *                                                                *
+///    *  Runge-Kutta method for tracking a particle through a magnetic *
+///    *  field. Uses Nystroem algorithm (See Handbook Nat. Bur. of     *
+///    *  Standards, procedure 25.5.20)                                 *
+///    *                                                                *
+///    *  Input parameters                                              *
+///    *       CHARGE    Particle charge                                *
+///    *       STEP      Step size                                      *
+///    *       VECT      Initial co-ords,direction cosines,momentum     *
+///    *  Output parameters                                             *
+///    *       VOUT      Output co-ords,direction cosines,momentum      *
+///    *  User routine called                                           *
+///    *       CALL GUFLD(X,F)                                          *
+///    *                                                                *
+///    *    ==>Called by : <USER>, GUSWIM                               *
+///    *       Authors    R.Brun, M.Hansroul  *********                 *
+///    *                  V.Perevoztchikov (CUT STEP implementation)    *
+///    *                                                                *
+///    *                                                                *
+///    ******************************************************************
+
+    Double_t h2, h4, f[4];
+    Double_t xyzt[3], 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;
+    Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
+    
+    Double_t x;
+    Double_t y;
+    Double_t z;
+    
+    Double_t xt;
+    Double_t yt;
+    Double_t zt;
+
+    Double_t maxit = 1992;
+    Double_t maxcut = 11;
+
+    const Double_t kdlt   = 1e-4;
+    const Double_t kdlt32 = kdlt/32.;
+    const Double_t kthird = 1./3.;
+    const Double_t khalf  = 0.5;
+    const Double_t kec = 2.9979251e-4;
+
+    const Double_t kpisqua = 9.86960440109;
+    const Int_t kix  = 0;
+    const Int_t kiy  = 1;
+    const Int_t kiz  = 2;
+    const Int_t kipx = 3;
+    const Int_t kipy = 4;
+    const Int_t kipz = 5;
+  
+    // *.
+    // *.    ------------------------------------------------------------------
+    // *.
+    // *             this constant is for units cm,gev/c and kgauss
+    // *
+    Int_t iter = 0;
+    Int_t ncut = 0;
+    for(Int_t j = 0; j < 7; j++)
+      vout[j] = vect[j];
+
+    Double_t  pinv   = kec * charge / vect[6];
+    Double_t tl = 0.;
+    Double_t h = step;
+    Double_t rest;
+
+    do {
+      rest  = step - tl;
+      if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
+      //cmodif: call gufld(vout,f) changed into:
+
+      GetField(vout,f);
+
+      // *
+      // *             start of integration
+      // *
+      x      = vout[0];
+      y      = vout[1];
+      z      = vout[2];
+      a      = vout[3];
+      b      = vout[4];
+      c      = vout[5];
+
+      h2     = khalf * h;
+      h4     = khalf * h2;
+      ph     = pinv * h;
+      ph2    = khalf * ph;
+      secxs[0] = (b * f[2] - c * f[1]) * ph2;
+      secys[0] = (c * f[0] - a * f[2]) * ph2;
+      seczs[0] = (a * f[1] - b * f[0]) * ph2;
+      ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
+      if (ang2 > kpisqua) break;
+
+      dxt    = h2 * a + h4 * secxs[0];
+      dyt    = h2 * b + h4 * secys[0];
+      dzt    = h2 * c + h4 * seczs[0];
+      xt     = x + dxt;
+      yt     = y + dyt;
+      zt     = z + dzt;
+      // *
+      // *              second intermediate point
+      // *
+
+      est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
+      if (est > h) {
+       if (ncut++ > maxcut) break;
+       h *= khalf;
+       continue;
+      }
+      xyzt[0] = xt;
+      xyzt[1] = yt;
+      xyzt[2] = zt;
+
+      //cmodif: call gufld(xyzt,f) changed into:
+      GetField(xyzt,f);
+
+      at     = a + secxs[0];
+      bt     = b + secys[0];
+      ct     = c + seczs[0];
+
+      secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
+      secys[1] = (ct * f[0] - at * f[2]) * ph2;
+      seczs[1] = (at * f[1] - bt * f[0]) * ph2;
+      at     = a + secxs[1];
+      bt     = b + secys[1];
+      ct     = c + seczs[1];
+      secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
+      secys[2] = (ct * f[0] - at * f[2]) * ph2;
+      seczs[2] = (at * f[1] - bt * f[0]) * ph2;
+      dxt    = h * (a + secxs[2]);
+      dyt    = h * (b + secys[2]);
+      dzt    = h * (c + seczs[2]);
+      xt     = x + dxt;
+      yt     = y + dyt;
+      zt     = z + dzt;
+      at     = a + 2.*secxs[2];
+      bt     = b + 2.*secys[2];
+      ct     = c + 2.*seczs[2];
+
+      est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
+      if (est > 2.*TMath::Abs(h)) {
+       if (ncut++ > maxcut) break;
+       h *= khalf;
+       continue;
+      }
+      xyzt[0] = xt;
+      xyzt[1] = yt;
+      xyzt[2] = zt;
+
+      //cmodif: call gufld(xyzt,f) changed into:
+      GetField(xyzt,f);
+
+      z      = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
+      y      = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
+      x      = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
+
+      secxs[3] = (bt*f[2] - ct*f[1])* ph2;
+      secys[3] = (ct*f[0] - at*f[2])* ph2;
+      seczs[3] = (at*f[1] - bt*f[0])* ph2;
+      a      = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
+      b      = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
+      c      = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
+
+      est    = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
+       + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
+       + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
+
+      if (est > kdlt && TMath::Abs(h) > 1.e-4) {
+       if (ncut++ > maxcut) break;
+       h *= khalf;
+       continue;
+      }
+
+      ncut = 0;
+      // *               if too many iterations, go to helix
+      if (iter++ > maxit) break;
+
+      tl += h;
+      if (est < kdlt32) 
+       h *= 2.;
+      cba    = 1./ TMath::Sqrt(a*a + b*b + c*c);
+      vout[0] = x;
+      vout[1] = y;
+      vout[2] = z;
+      vout[3] = cba*a;
+      vout[4] = cba*b;
+      vout[5] = cba*c;
+      rest = step - tl;
+      if (step < 0.) rest = -rest;
+      if (rest < 1.e-5*TMath::Abs(step)) return;
+
+    } while(1);
+
+    // angle too big, use helix
+
+    f1  = f[0];
+    f2  = f[1];
+    f3  = f[2];
+    f4  = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
+    rho = -f4*pinv;
+    tet = rho * step;
+    hnorm = 1./f4;
+    f1 = f1*hnorm;
+    f2 = f2*hnorm;
+    f3 = f3*hnorm;
+
+    hxp[0] = f2*vect[kipz] - f3*vect[kipy];
+    hxp[1] = f3*vect[kipx] - f1*vect[kipz];
+    hxp[2] = f1*vect[kipy] - f2*vect[kipx];
+    hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
+
+    rho1 = 1./rho;
+    sint = TMath::Sin(tet);
+    cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
+
+    g1 = sint*rho1;
+    g2 = cost*rho1;
+    g3 = (tet-sint) * hp*rho1;
+    g4 = -cost;
+    g5 = sint;
+    g6 = cost * hp;
+    vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
+    vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
+    vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
+    vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
+    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;
+}
+
diff --git a/MUON/AliMUONTrackExtrap.h b/MUON/AliMUONTrackExtrap.h
new file mode 100644 (file)
index 0000000..4e58af5
--- /dev/null
@@ -0,0 +1,62 @@
+#ifndef ALIMUONTRACKEXTRAP_H
+#define ALIMUONTRACKEXTRAP_H
+/* Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
+ * See cxx source for full Copyright notice                               */
+
+/*$Id$*/
+// Revision of includes 07/05/2004
+
+/// \ingroup rec
+/// \class AliMUONTrackExtrap
+/// \brief Track parameters in ALICE dimuon spectrometer
+///
+//////////////////////////////////////////////////////////////
+/// Tools for track extrapolation in ALICE dimuon spectrometer
+//////////////////////////////////////////////////////////////
+
+#include <TObject.h>
+
+class AliMagF;
+class AliMUONTrackParam;
+
+class AliMUONTrackExtrap : public TObject 
+{
+ public:
+       /// Constructor
+  AliMUONTrackExtrap() : TObject(){};
+       /// Destructor
+  virtual ~AliMUONTrackExtrap(){};
+  
+       /// set field map
+  static void SetField(const AliMagF* magField) {fgkField = magField;}
+  
+  static void ExtrapToZ(AliMUONTrackParam *trackParam, Double_t Z);
+  static void ExtrapToStation(AliMUONTrackParam *trackParamIn, Int_t station, AliMUONTrackParam *trackParamOut);
+  static void ExtrapToVertex(AliMUONTrackParam *trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx);
+  
+  static void ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout);
+  
+  
+ private:
+  static const AliMagF* fgkField;     //!< field map
+
+  // Functions
+  AliMUONTrackExtrap(const AliMUONTrackExtrap& trackExtrap);
+  AliMUONTrackExtrap& operator=(const AliMUONTrackExtrap& trackExtrap);
+
+  static void SetGeant3ParametersFromTrackParam(AliMUONTrackParam* trackParam, Double_t *vGeant3, Double_t forwardBackward);
+  static void SetTrackParamFromGeant3Parameters(Double_t *vGeant3, Double_t Charge, AliMUONTrackParam* trackParam);
+  
+  static void BransonCorrection(AliMUONTrackParam *trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx);
+  static Double_t TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta);
+  static void FieldCorrection(AliMUONTrackParam *trackParam, Double_t Z);
+  
+  static void ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout);
+  static void ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout);
+
+  static void GetField(Double_t *Position, Double_t *Field);
+  
+  ClassDef(AliMUONTrackExtrap, 0) // Tools for track extrapolation in ALICE dimuon spectrometer
+};
+       
+#endif