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AliMUONTrackExtrap.cxx
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4  * Author: The ALICE Off-line Project. *
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15 
16 /* $Id$ */
17 
18 //-----------------------------------------------------------------------------
19 // Class AliMUONTrackExtrap
20 // ------------------------
21 // Tools for track extrapolation in ALICE dimuon spectrometer
22 // Author: Philippe Pillot
23 //-----------------------------------------------------------------------------
24 
25 #include "AliMUONTrackExtrap.h"
26 #include "AliMUONTrackParam.h"
27 #include "AliMUONConstants.h"
28 #include "AliMUONReconstructor.h"
29 
30 #include "AliMagF.h"
31 #include "AliExternalTrackParam.h"
32 
33 #include <TGeoGlobalMagField.h>
34 #include <TGeoManager.h>
35 #include <TMath.h>
36 #include <TDatabasePDG.h>
37 
38 #include <Riostream.h>
39 
40 using std::endl;
41 using std::cout;
43 ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context
45 
46 const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ());
47 const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL());
48  Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.;
49  Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE;
50 const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE;
51 const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000;
52 const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.;
53 const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002;
54 
55 //__________________________________________________________________________
56 void AliMUONTrackExtrap::SetField()
57 {
60  const Double_t x[3] = {50.,50.,fgkSimpleBPosition};
61  Double_t b[3] = {0.,0.,0.};
62  TGeoGlobalMagField::Instance()->Field(x,b);
63  fgSimpleBValue = b[0];
64  fgFieldON = (TMath::Abs(fgSimpleBValue) > 1.e-10) ? kTRUE : kFALSE;
65 
66 }
67 
68 //__________________________________________________________________________
70 {
75 
76  if (bendingMomentum == 0.) return 1.e10;
77 
78  const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated
79 
80  return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum);
81 }
82 
83 //__________________________________________________________________________
84 Double_t
86 {
91 
92  if (impactParam == 0.) return 1.e10;
93 
94  const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated
95 
96  if (fgFieldON)
97  {
98  return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam);
99  }
100  else
101  {
103  }
104 }
105 
106 //__________________________________________________________________________
108 {
111 
112  if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
113 
114  // Compute track parameters
115  Double_t dZ = zEnd - trackParam->GetZ();
116  trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
117  trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
118  trackParam->SetZ(zEnd);
119 }
120 
121 //__________________________________________________________________________
122 void AliMUONTrackExtrap::LinearExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
123 {
126 
127  if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z
128 
129  // No need to propagate the covariance matrix if it does not exist
130  if (!trackParam->CovariancesExist()) {
131  cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl;
132  // Extrapolate linearly track parameters to "zEnd"
133  LinearExtrapToZ(trackParam,zEnd);
134  return;
135  }
136 
137  // Compute track parameters
138  Double_t dZ = zEnd - trackParam->GetZ();
139  trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ);
140  trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ);
141  trackParam->SetZ(zEnd);
142 
143  // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd"
144  TMatrixD jacob(5,5);
145  jacob.UnitMatrix();
146  jacob(0,1) = dZ;
147  jacob(2,3) = dZ;
148 
149  // Extrapolate track parameter covariances to "zEnd"
150  TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob);
151  TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
152  trackParam->SetCovariances(tmp2);
153 
154  // Update the propagator if required
155  if (updatePropagator) trackParam->UpdatePropagator(jacob);
156 }
157 
158 //__________________________________________________________________________
159 Bool_t AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd)
160 {
163  if (!fgFieldON) {
164  AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd);
165  return kTRUE;
166  }
167  else if (fgkUseHelix) return AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd);
168  else return AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd);
169 }
170 
171 //__________________________________________________________________________
172 Bool_t AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd)
173 {
176  if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
177  Double_t forwardBackward; // +1 if forward, -1 if backward
178  if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
179  else forwardBackward = -1.0;
180  Double_t v3[7], v3New[7]; // 7 in parameter ????
181  Int_t i3, stepNumber;
182  // For safety: return kTRUE or kFALSE ????
183  // Parameter vector for calling EXTRAP_ONESTEP
184  ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
185  // sign of charge (sign of fInverseBendingMomentum if forward motion)
186  // must be changed if backward extrapolation
187  Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
188  // Extrapolation loop
189  stepNumber = 0;
190  while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0
191  stepNumber++;
192  ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New);
193  if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0
194  // better use TArray ????
195  for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];}
196  }
197  // check fgkMaxStepNumber ????
198  // Interpolation back to exact Z (2nd order)
199  // should be in function ???? using TArray ????
200  Double_t dZ12 = v3New[2] - v3[2]; // 1->2
201  if (TMath::Abs(dZ12) > 0) {
202  Double_t dZ1i = zEnd - v3[2]; // 1-i
203  Double_t dZi2 = v3New[2] - zEnd; // i->2
204  Double_t xPrime = (v3New[0] - v3[0]) / dZ12;
205  Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12;
206  Double_t yPrime = (v3New[1] - v3[1]) / dZ12;
207  Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12;
208  v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
209  v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
210  v3[2] = zEnd; // Z
211  Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
212  Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
213  // (PX, PY, PZ)/PTOT assuming forward motion
214  v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
215  v3[3] = xPrimeI * v3[5]; // PX/PTOT
216  v3[4] = yPrimeI * v3[5]; // PY/PTOT
217  } else {
218  cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl;
219  }
220  // Recover track parameters (charge back for forward motion)
221  RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam);
222  return kTRUE;
223 }
224 
225 //__________________________________________________________________________
227 {
230  if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z
231  Double_t forwardBackward; // +1 if forward, -1 if backward
232  if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0
233  else forwardBackward = -1.0;
234  // sign of charge (sign of fInverseBendingMomentum if forward motion)
235  // must be changed if backward extrapolation
236  Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum());
237  Double_t v3[7], v3New[7];
238  Double_t dZ, step;
239  Int_t stepNumber = 0;
240 
241  // Extrapolation loop (until within tolerance or the track turn around)
242  Double_t residue = zEnd - trackParam->GetZ();
243  Bool_t uturn = kFALSE;
244  Bool_t trackingFailed = kFALSE;
245  Bool_t tooManyStep = kFALSE;
246  while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) {
247 
248  dZ = zEnd - trackParam->GetZ();
249  // step lenght assuming linear trajectory
250  step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() +
251  trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope());
252  ConvertTrackParamForExtrap(trackParam, forwardBackward, v3);
253 
254  do { // reduce step lenght while zEnd oversteped
255  if (stepNumber > fgkMaxStepNumber) {
256  cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl;
257  tooManyStep = kTRUE;
258  break;
259  }
260  stepNumber ++;
261  step = TMath::Abs(step);
262  if (!AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New)) {
263  trackingFailed = kTRUE;
264  break;
265  }
266  residue = zEnd - v3New[2];
267  step *= dZ/(v3New[2]-trackParam->GetZ());
268  } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue);
269 
270  if (trackingFailed) break;
271  else if (v3New[5]*v3[5] < 0) { // the track turned around
272  cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: The track turned around"<<endl;
273  uturn = kTRUE;
274  break;
275  } else RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam);
276 
277  }
278 
279  // terminate the extropolation with a straight line up to the exact "zEnd" value
280  if (trackingFailed || uturn) {
281 
282  // track ends +-100 meters away in the bending direction
283  dZ = zEnd - v3[2];
284  Double_t bendingSlope = TMath::Sign(1.e4,-fgSimpleBValue*trackParam->GetInverseBendingMomentum()) / dZ;
285  Double_t pZ = TMath::Abs(1. / trackParam->GetInverseBendingMomentum()) / TMath::Sqrt(1.0 + bendingSlope * bendingSlope);
286  Double_t nonBendingSlope = TMath::Sign(TMath::Abs(v3[3]) * v3[6] / pZ, trackParam->GetNonBendingSlope());
287  trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + dZ * nonBendingSlope);
288  trackParam->SetNonBendingSlope(nonBendingSlope);
289  trackParam->SetBendingCoor(trackParam->GetBendingCoor() + dZ * bendingSlope);
290  trackParam->SetBendingSlope(bendingSlope);
291  trackParam->SetZ(zEnd);
292 
293  return kFALSE;
294 
295  } else {
296 
297  // track extrapolated normally
298  trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope());
299  trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope());
300  trackParam->SetZ(zEnd);
301 
302  return !tooManyStep;
303 
304  }
305 
306 }
307 
308 //__________________________________________________________________________
309 void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3)
310 {
314  v3[0] = trackParam->GetNonBendingCoor(); // X
315  v3[1] = trackParam->GetBendingCoor(); // Y
316  v3[2] = trackParam->GetZ(); // Z
317  Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum());
318  Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope());
319  v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT
320  v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0
321  v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT
322  v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT
323 }
324 
325 //__________________________________________________________________________
326 void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam)
327 {
331  trackParam->SetNonBendingCoor(v3[0]); // X
332  trackParam->SetBendingCoor(v3[1]); // Y
333  trackParam->SetZ(v3[2]); // Z
334  Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3]));
335  trackParam->SetInverseBendingMomentum(charge/pYZ);
336  trackParam->SetBendingSlope(v3[4]/v3[5]);
337  trackParam->SetNonBendingSlope(v3[3]/v3[5]);
338 }
339 
340 //__________________________________________________________________________
341 Bool_t AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator)
342 {
345 
346  if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same z
347 
348  if (!fgFieldON) { // linear extrapolation if no magnetic field
349  AliMUONTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator);
350  return kTRUE;
351  }
352 
353  // No need to propagate the covariance matrix if it does not exist
354  if (!trackParam->CovariancesExist()) {
355  cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl;
356  // Extrapolate track parameters to "zEnd"
357  return ExtrapToZ(trackParam,zEnd);
358  }
359 
360  // Save the actual track parameters
361  AliMUONTrackParam trackParamSave(*trackParam);
362  TMatrixD paramSave(trackParamSave.GetParameters());
363  Double_t zBegin = trackParamSave.GetZ();
364 
365  // Get reference to the parameter covariance matrix
366  const TMatrixD& kParamCov = trackParam->GetCovariances();
367 
368  // Extrapolate track parameters to "zEnd"
369  // Do not update the covariance matrix if the extrapolation failed
370  if (!ExtrapToZ(trackParam,zEnd)) return kFALSE;
371 
372  // Get reference to the extrapolated parameters
373  const TMatrixD& extrapParam = trackParam->GetParameters();
374 
375  // Calculate the jacobian related to the track parameters extrapolation to "zEnd"
376  Bool_t extrapStatus = kTRUE;
377  TMatrixD jacob(5,5);
378  jacob.Zero();
379  TMatrixD dParam(5,1);
380  Double_t direction[5] = {-1.,-1.,1.,1.,-1.};
381  for (Int_t i=0; i<5; i++) {
382  // Skip jacobian calculation for parameters with no associated error
383  if (kParamCov(i,i) <= 0.) continue;
384 
385  // Small variation of parameter i only
386  for (Int_t j=0; j<5; j++) {
387  if (j==i) {
388  dParam(j,0) = TMath::Sqrt(kParamCov(i,i));
389  dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction
390  } else dParam(j,0) = 0.;
391  }
392 
393  // Set new parameters
394  trackParamSave.SetParameters(paramSave);
395  trackParamSave.AddParameters(dParam);
396  trackParamSave.SetZ(zBegin);
397 
398  // Extrapolate new track parameters to "zEnd"
399  if (!ExtrapToZ(&trackParamSave,zEnd)) {
400  cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Bad covariance matrix"<<endl;
401  extrapStatus = kFALSE;
402  }
403 
404  // Calculate the jacobian
405  TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam);
406  jacobji *= 1. / dParam(i,0);
407  jacob.SetSub(0,i,jacobji);
408  }
409 
410  // Extrapolate track parameter covariances to "zEnd"
411  TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob);
412  TMatrixD tmp2(jacob,TMatrixD::kMult,tmp);
413  trackParam->SetCovariances(tmp2);
414 
415  // Update the propagator if required
416  if (updatePropagator) trackParam->UpdatePropagator(jacob);
417 
418  return extrapStatus;
419 }
420 
421 //__________________________________________________________________________
422 void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2)
423 {
426 
427  // absorber related covariance parameters
428  Double_t bendingSlope = param->GetBendingSlope();
429  Double_t nonBendingSlope = param->GetNonBendingSlope();
430  Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
431  Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) /
432  (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1
433  Double_t pathLength = TMath::Abs(signedPathLength);
434  Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2);
435  Double_t covCorrSlope = TMath::Sign(1.,signedPathLength) * alpha2 * (pathLength * f0 - f1);
436  Double_t varSlop = alpha2 * f0;
437 
438  // Set MCS covariance matrix
439  TMatrixD newParamCov(param->GetCovariances());
440  // Non bending plane
441  newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
442  newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
443  // Bending plane
444  newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
445  newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
446 
447  // Set momentum related covariances if B!=0
448  if (fgFieldON) {
449  // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
450  Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
451  Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
452  (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
453  // Inverse bending momentum (due to dependences with bending and non bending slopes)
454  newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
455  newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
456  newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
457  newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
458  newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
459  }
460 
461  // Set new covariances
462  param->SetCovariances(newParamCov);
463 }
464 
465 //__________________________________________________________________________
467  Double_t xVtx, Double_t yVtx, Double_t zVtx,
468  Double_t errXVtx, Double_t errYVtx,
469  Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2)
470 {
475 
476  // Position of the Branson plane (spectro. (z<0))
477  Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.;
478 
479  // Add MCS effects to current parameter covariances (spectro. (z<0))
480  AddMCSEffectInAbsorber(param, -pathLength, f0, f1, f2);
481 
482  // Get track parameters and covariances in the Branson plane corrected for magnetic field effect
483  ExtrapToZCov(param,zVtx);
484  LinearExtrapToZCov(param,zB);
485 
486  // compute track parameters at vertex
487  TMatrixD newParam(5,1);
488  newParam(0,0) = xVtx;
489  newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx);
490  newParam(2,0) = yVtx;
491  newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx);
492  newParam(4,0) = param->GetCharge() / param->P() *
493  TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) /
494  TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0));
495 
496  // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
497  TMatrixD paramCovP(param->GetCovariances());
498  Cov2CovP(param->GetParameters(),paramCovP);
499 
500  // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system
501  TMatrixD paramCovVtx(5,5);
502  paramCovVtx.Zero();
503  paramCovVtx(0,0) = errXVtx * errXVtx;
504  paramCovVtx(1,1) = paramCovP(0,0);
505  paramCovVtx(2,2) = errYVtx * errYVtx;
506  paramCovVtx(3,3) = paramCovP(2,2);
507  paramCovVtx(4,4) = paramCovP(4,4);
508  paramCovVtx(1,3) = paramCovP(0,2);
509  paramCovVtx(3,1) = paramCovP(2,0);
510  paramCovVtx(1,4) = paramCovP(0,4);
511  paramCovVtx(4,1) = paramCovP(4,0);
512  paramCovVtx(3,4) = paramCovP(2,4);
513  paramCovVtx(4,3) = paramCovP(4,2);
514 
515  // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx)
516  TMatrixD jacob(5,5);
517  jacob.UnitMatrix();
518  jacob(1,0) = - 1. / (zB - zVtx);
519  jacob(1,1) = 1. / (zB - zVtx);
520  jacob(3,2) = - 1. / (zB - zVtx);
521  jacob(3,3) = 1. / (zB - zVtx);
522 
523  // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system
524  TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob);
525  TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp);
526 
527  // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system
528  CovP2Cov(newParam,newParamCov);
529 
530  // Set parameters and covariances at vertex
531  param->SetParameters(newParam);
532  param->SetZ(zVtx);
533  param->SetCovariances(newParamCov);
534 }
535 
536 //__________________________________________________________________________
537 void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2)
538 {
540 
541  // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system
542  TMatrixD newParamCov(param->GetCovariances());
543  Cov2CovP(param->GetParameters(),newParamCov);
544 
545  // Compute new parameters corrected for energy loss
546  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
547  Double_t p = param->P();
548  Double_t e = TMath::Sqrt(p*p + muMass*muMass);
549  Double_t eCorr = e + eLoss;
550  Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
551  Double_t nonBendingSlope = param->GetNonBendingSlope();
552  Double_t bendingSlope = param->GetBendingSlope();
553  param->SetInverseBendingMomentum(param->GetCharge() / pCorr *
554  TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) /
555  TMath::Sqrt(1.0 + bendingSlope*bendingSlope));
556 
557  // Add effects of energy loss fluctuation to covariances
558  newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2;
559 
560  // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system
561  CovP2Cov(param->GetParameters(),newParamCov);
562 
563  // Set new parameter covariances
564  param->SetCovariances(newParamCov);
565 }
566 
567 //__________________________________________________________________________
568 Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal,
569  Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2,
570  Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2)
571 {
574  // pathLength: path length between trackXYZIn and trackXYZOut (cm)
575  // f0: 0th moment of z calculated with the inverse radiation-length distribution
576  // f1: 1st moment of z calculated with the inverse radiation-length distribution
577  // f2: 2nd moment of z calculated with the inverse radiation-length distribution
578  // meanRho: average density of crossed material (g/cm3)
579  // totalELoss: total energy loss in absorber
580 
581  // Reset absorber's parameters
582  pathLength = 0.;
583  f0 = 0.;
584  f1 = 0.;
585  f2 = 0.;
586  meanRho = 0.;
587  totalELoss = 0.;
588  sigmaELoss2 = 0.;
589 
590  // Check whether the geometry is available
591  if (!gGeoManager) {
592  cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl;
593  return kFALSE;
594  }
595 
596  // Initialize starting point and direction
597  pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+
598  (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+
599  (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2]));
600  if (pathLength < TGeoShape::Tolerance()) return kFALSE;
601  Double_t b[3];
602  b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength;
603  b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength;
604  b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength;
605  TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b);
606  if (!currentnode) {
607  cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl;
608  return kFALSE;
609  }
610 
611  // loop over absorber slices and calculate absorber's parameters
612  Double_t rho = 0.; // material density (g/cm3)
613  Double_t x0 = 0.; // radiation-length (cm-1)
614  Double_t atomicA = 0.; // A of material
615  Double_t atomicZ = 0.; // Z of material
616  Double_t atomicZoverA = 0.; // Z/A of material
617  Double_t localPathLength = 0;
618  Double_t remainingPathLength = pathLength;
619  Double_t sigmaELoss = 0.;
620  Double_t zB = trackXYZIn[2];
621  Double_t zE, dzB, dzE;
622  do {
623  // Get material properties
624  TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial();
625  rho = material->GetDensity();
626  x0 = material->GetRadLen();
627  atomicA = material->GetA();
628  atomicZ = material->GetZ();
629  if(material->IsMixture()){
630  TGeoMixture * mixture = (TGeoMixture*)material;
631  atomicZoverA = 0.;
632  Double_t sum = 0.;
633  for (Int_t iel=0;iel<mixture->GetNelements();iel++){
634  sum += mixture->GetWmixt()[iel];
635  atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel];
636  }
637  atomicZoverA/=sum;
638  }
639  else atomicZoverA = atomicZ/atomicA;
640 
641  // Get path length within this material
642  gGeoManager->FindNextBoundary(remainingPathLength);
643  localPathLength = gGeoManager->GetStep() + 1.e-6;
644  // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step
645  if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength;
646  else {
647  currentnode = gGeoManager->Step();
648  if (!currentnode) {
649  cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
650  f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
651  return kFALSE;
652  }
653  if (!gGeoManager->IsEntering()) {
654  // make another small step to try to enter in new absorber slice
655  gGeoManager->SetStep(0.001);
656  currentnode = gGeoManager->Step();
657  if (!gGeoManager->IsEntering() || !currentnode) {
658  cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl;
659  f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.;
660  return kFALSE;
661  }
662  localPathLength += 0.001;
663  }
664  }
665 
666  // calculate absorber's parameters
667  zE = b[2] * localPathLength + zB;
668  dzB = zB - trackXYZIn[2];
669  dzE = zE - trackXYZIn[2];
670  f0 += localPathLength / x0;
671  f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.;
672  f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.;
673  meanRho += localPathLength * rho;
674  totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA);
675  sigmaELoss += EnergyLossFluctuation(pTotal, localPathLength, rho, atomicZoverA);
676 
677  // prepare next step
678  zB = zE;
679  remainingPathLength -= localPathLength;
680  } while (remainingPathLength > TGeoShape::Tolerance());
681 
682  meanRho /= pathLength;
683  sigmaELoss2 = sigmaELoss*sigmaELoss;
684 
685  return kTRUE;
686 }
687 
688 //__________________________________________________________________________
689 Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0)
690 {
694 
695  Double_t bendingSlope = param.GetBendingSlope();
696  Double_t nonBendingSlope = param.GetNonBendingSlope();
697  Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() *
698  (1.0 + bendingSlope * bendingSlope) /
699  (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
700  // Path length in the material
701  Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
702  // relativistic velocity
703  Double_t velo = 1.;
704  // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
705  Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0));
706 
707  return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0;
708 }
709 
710 //__________________________________________________________________________
711 void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
712 {
718 
719  Double_t bendingSlope = param->GetBendingSlope();
720  Double_t nonBendingSlope = param->GetNonBendingSlope();
721  Double_t inverseBendingMomentum = param->GetInverseBendingMomentum();
722  Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum *
723  (1.0 + bendingSlope * bendingSlope) /
724  (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope);
725  // Path length in the material
726  Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope);
727  Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength) / x0 : TMath::Abs(signedPathLength);
728  // relativistic velocity
729  Double_t velo = 1.;
730  // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory
731  Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0));
732  theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0;
733 
734  Double_t varCoor = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.;
735  Double_t varSlop = theta02;
736  Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02 / 2. : 0.;
737 
738  // Set MCS covariance matrix
739  TMatrixD newParamCov(param->GetCovariances());
740  // Non bending plane
741  newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope;
742  newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop;
743  // Bending plane
744  newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope;
745  newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop;
746 
747  // Set momentum related covariances if B!=0
748  if (fgFieldON) {
749  // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY
750  Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
751  Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope /
752  (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope);
753  // Inverse bending momentum (due to dependences with bending and non bending slopes)
754  newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope;
755  newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop;
756  newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope;
757  newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop;
758  newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop;
759  }
760 
761  // Set new covariances
762  param->SetCovariances(newParamCov);
763 }
764 
765 //__________________________________________________________________________
767  Double_t xVtx, Double_t yVtx, Double_t zVtx,
768  Double_t errXVtx, Double_t errYVtx,
769  Bool_t correctForMCS, Bool_t correctForEnergyLoss)
770 {
778 
779  if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex
780 
781  if (trackParam->GetZ() > zVtx) { // spectro. (z<0)
782  cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
783  <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl;
784  return;
785  }
786 
787  // Check the vertex position relatively to the absorber
788  if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
789  cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
790  <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
791  } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0)
792  cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx
793  <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl;
794  if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
795  else ExtrapToZ(trackParam,zVtx);
796  return;
797  }
798 
799  // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed
800  if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0)
801  cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
802  <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl;
803  if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
804  else ExtrapToZ(trackParam,zVtx);
805  return;
806  } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0)
807  cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ()
808  <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl;
809  } else {
810  if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd());
811  else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd());
812  }
813 
814  // Get absorber correction parameters assuming linear propagation in absorber
815  Double_t trackXYZOut[3];
816  trackXYZOut[0] = trackParam->GetNonBendingCoor();
817  trackXYZOut[1] = trackParam->GetBendingCoor();
818  trackXYZOut[2] = trackParam->GetZ();
819  Double_t trackXYZIn[3];
820  if (correctForMCS) { // assume linear propagation until the vertex
821  trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0)
822  trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
823  trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]);
824  } else {
825  AliMUONTrackParam trackParamIn(*trackParam);
826  ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg()));
827  trackXYZIn[0] = trackParamIn.GetNonBendingCoor();
828  trackXYZIn[1] = trackParamIn.GetBendingCoor();
829  trackXYZIn[2] = trackParamIn.GetZ();
830  }
831  Double_t pTot = trackParam->P();
832  Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
833  if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) {
834  cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl;
835  if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx);
836  else ExtrapToZ(trackParam,zVtx);
837  return;
838  }
839 
840  // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags
841  if (correctForMCS) {
842 
843  if (correctForEnergyLoss) {
844 
845  // Correct for multiple scattering and energy loss
846  CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
847  CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
848  trackXYZIn[2], pathLength, f0, f1, f2);
849  CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
850 
851  } else {
852 
853  // Correct for multiple scattering
854  CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx,
855  trackXYZIn[2], pathLength, f0, f1, f2);
856  }
857 
858  } else {
859 
860  if (correctForEnergyLoss) {
861 
862  // Correct for energy loss add multiple scattering dispersion in covariance matrix
863  CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
864  AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
865  ExtrapToZCov(trackParam, trackXYZIn[2]);
866  CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2);
867  ExtrapToZCov(trackParam, zVtx);
868 
869  } else {
870 
871  // add multiple scattering dispersion in covariance matrix
872  AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0))
873  ExtrapToZCov(trackParam, zVtx);
874 
875  }
876 
877  }
878 
879 }
880 
881 //__________________________________________________________________________
883  Double_t xVtx, Double_t yVtx, Double_t zVtx,
884  Double_t errXVtx, Double_t errYVtx)
885 {
888  ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE);
889 }
890 
891 //__________________________________________________________________________
893  Double_t xVtx, Double_t yVtx, Double_t zVtx,
894  Double_t errXVtx, Double_t errYVtx)
895 {
898  ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE);
899 }
900 
901 //__________________________________________________________________________
903 {
906  ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE);
907 }
908 
909 //__________________________________________________________________________
911 {
914  ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE);
915 }
916 
917 //__________________________________________________________________________
918 Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
919 {
921 
922  if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex
923 
924  // Check whether the geometry is available
925  if (!gGeoManager) {
926  cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl;
927  return 0.;
928  }
929 
930  // Get encountered material correction parameters assuming linear propagation from vertex to the track position
931  Double_t trackXYZOut[3];
932  trackXYZOut[0] = trackParam->GetNonBendingCoor();
933  trackXYZOut[1] = trackParam->GetBendingCoor();
934  trackXYZOut[2] = trackParam->GetZ();
935  Double_t trackXYZIn[3];
936  trackXYZIn[0] = xVtx;
937  trackXYZIn[1] = yVtx;
938  trackXYZIn[2] = zVtx;
939  Double_t pTot = trackParam->P();
940  Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2;
941  GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2);
942 
943  // total momentum corrected for energy loss
944  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
945  Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass);
946  Double_t eCorr = e + totalELoss;
947  Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass);
948 
949  return pTotCorr - pTot;
950 }
951 
952 //__________________________________________________________________________
953 Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
954 {
957  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
958 
959  // mean exitation energy (GeV)
960  Double_t i;
961  if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9;
962  else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9;
963 
964  return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA);
965 }
966 
967 //__________________________________________________________________________
968 Double_t AliMUONTrackExtrap::EnergyLossFluctuation(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
969 {
972  Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV
973  //Double_t eMass = 0.510998918e-3; // GeV
974  Double_t k = 0.307075e-3; // GeV.g^-1.cm^2
975  Double_t p2=pTotal*pTotal;
976  Double_t beta2=p2/(p2 + muMass*muMass);
977 
978  Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution
979  Double_t sigma = fwhm / TMath::Sqrt(8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma)
980 
981  //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution
982 
983  return sigma;
984 }
985 
986 //__________________________________________________________________________
987 void AliMUONTrackExtrap::Cov2CovP(const TMatrixD &param, TMatrixD &cov)
988 {
991 
992  // charge * total momentum
993  Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
994  TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
995 
996  // Jacobian of the opposite transformation
997  TMatrixD jacob(5,5);
998  jacob.UnitMatrix();
999  jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1000  jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) /
1001  (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1002  jacob(4,4) = - qPTot / param(4,0);
1003 
1004  // compute covariances in new coordinate system
1005  TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob);
1006  cov.Mult(jacob,tmp);
1007 }
1008 
1009 //__________________________________________________________________________
1010 void AliMUONTrackExtrap::CovP2Cov(const TMatrixD &param, TMatrixD &covP)
1011 {
1014 
1015  // charge * total momentum
1016  Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) /
1017  TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0);
1018 
1019  // Jacobian of the transformation
1020  TMatrixD jacob(5,5);
1021  jacob.UnitMatrix();
1022  jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1023  jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) /
1024  (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0));
1025  jacob(4,4) = - param(4,0) / qPTot;
1026 
1027  // compute covariances in new coordinate system
1028  TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob);
1029  covP.Mult(jacob,tmp);
1030 }
1031 
1032  //__________________________________________________________________________
1033 void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
1034 {
1056 
1057 // modif: everything in double precision
1058 
1059  Double_t xyz[3], h[4], hxp[3];
1060  Double_t h2xy, hp, rho, tet;
1061  Double_t sint, sintt, tsint, cos1t;
1062  Double_t f1, f2, f3, f4, f5, f6;
1063 
1064  const Int_t kix = 0;
1065  const Int_t kiy = 1;
1066  const Int_t kiz = 2;
1067  const Int_t kipx = 3;
1068  const Int_t kipy = 4;
1069  const Int_t kipz = 5;
1070  const Int_t kipp = 6;
1071 
1072  const Double_t kec = 2.9979251e-4;
1073  //
1074  // ------------------------------------------------------------------
1075  //
1076  // units are kgauss,centimeters,gev/c
1077  //
1078  vout[kipp] = vect[kipp];
1079  if (TMath::Abs(charge) < 0.00001) {
1080  for (Int_t i = 0; i < 3; i++) {
1081  vout[i] = vect[i] + step * vect[i+3];
1082  vout[i+3] = vect[i+3];
1083  }
1084  return;
1085  }
1086  xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
1087  xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
1088  xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
1089 
1090  //cmodif: call gufld (xyz, h) changed into:
1091  TGeoGlobalMagField::Instance()->Field(xyz,h);
1092 
1093  h2xy = h[0]*h[0] + h[1]*h[1];
1094  h[3] = h[2]*h[2]+ h2xy;
1095  if (h[3] < 1.e-12) {
1096  for (Int_t i = 0; i < 3; i++) {
1097  vout[i] = vect[i] + step * vect[i+3];
1098  vout[i+3] = vect[i+3];
1099  }
1100  return;
1101  }
1102  if (h2xy < 1.e-12*h[3]) {
1103  ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
1104  return;
1105  }
1106  h[3] = TMath::Sqrt(h[3]);
1107  h[0] /= h[3];
1108  h[1] /= h[3];
1109  h[2] /= h[3];
1110  h[3] *= kec;
1111 
1112  hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
1113  hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
1114  hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
1115 
1116  hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
1117 
1118  rho = -charge*h[3]/vect[kipp];
1119  tet = rho * step;
1120 
1121  if (TMath::Abs(tet) > 0.15) {
1122  sint = TMath::Sin(tet);
1123  sintt = (sint/tet);
1124  tsint = (tet-sint)/tet;
1125  cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
1126  } else {
1127  tsint = tet*tet/36.;
1128  sintt = (1. - tsint);
1129  sint = tet*sintt;
1130  cos1t = 0.5*tet;
1131  }
1132 
1133  f1 = step * sintt;
1134  f2 = step * cos1t;
1135  f3 = step * tsint * hp;
1136  f4 = -tet*cos1t;
1137  f5 = sint;
1138  f6 = tet * cos1t * hp;
1139 
1140  vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
1141  vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
1142  vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
1143 
1144  vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
1145  vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
1146  vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
1147 
1148  return;
1149 }
1150 
1151  //__________________________________________________________________________
1152 void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, const Double_t *vect, Double_t *vout)
1153 {
1168 
1169  Double_t hxp[3];
1170  Double_t h4, hp, rho, tet;
1171  Double_t sint, sintt, tsint, cos1t;
1172  Double_t f1, f2, f3, f4, f5, f6;
1173 
1174  const Int_t kix = 0;
1175  const Int_t kiy = 1;
1176  const Int_t kiz = 2;
1177  const Int_t kipx = 3;
1178  const Int_t kipy = 4;
1179  const Int_t kipz = 5;
1180  const Int_t kipp = 6;
1181 
1182  const Double_t kec = 2.9979251e-4;
1183 
1184 //
1185 // ------------------------------------------------------------------
1186 //
1187 // units are kgauss,centimeters,gev/c
1188 //
1189  vout[kipp] = vect[kipp];
1190  h4 = field * kec;
1191 
1192  hxp[0] = - vect[kipy];
1193  hxp[1] = + vect[kipx];
1194 
1195  hp = vect[kipz];
1196 
1197  rho = -h4/vect[kipp];
1198  tet = rho * step;
1199  if (TMath::Abs(tet) > 0.15) {
1200  sint = TMath::Sin(tet);
1201  sintt = (sint/tet);
1202  tsint = (tet-sint)/tet;
1203  cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
1204  } else {
1205  tsint = tet*tet/36.;
1206  sintt = (1. - tsint);
1207  sint = tet*sintt;
1208  cos1t = 0.5*tet;
1209  }
1210 
1211  f1 = step * sintt;
1212  f2 = step * cos1t;
1213  f3 = step * tsint * hp;
1214  f4 = -tet*cos1t;
1215  f5 = sint;
1216  f6 = tet * cos1t * hp;
1217 
1218  vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
1219  vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
1220  vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
1221 
1222  vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
1223  vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
1224  vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
1225 
1226  return;
1227 }
1228 
1229  //__________________________________________________________________________
1230 Bool_t AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, const Double_t* vect, Double_t* vout)
1231 {
1255 
1256  Double_t h2, h4, f[4];
1257  Double_t xyzt[3] = {FLT_MAX, FLT_MAX, FLT_MAX};
1258  Double_t a, b, c, ph,ph2;
1259  Double_t secxs[4],secys[4],seczs[4],hxp[3];
1260  Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
1261  Double_t est, at, bt, ct, cba;
1262  Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
1263 
1264  Double_t x;
1265  Double_t y;
1266  Double_t z;
1267 
1268  Double_t xt;
1269  Double_t yt;
1270  Double_t zt;
1271 
1272  Double_t maxit = 1992;
1273  Double_t maxcut = 11;
1274 
1275  const Double_t kdlt = 1e-4;
1276  const Double_t kdlt32 = kdlt/32.;
1277  const Double_t kthird = 1./3.;
1278  const Double_t khalf = 0.5;
1279  const Double_t kec = 2.9979251e-4;
1280 
1281  const Double_t kpisqua = 9.86960440109;
1282  const Int_t kix = 0;
1283  const Int_t kiy = 1;
1284  const Int_t kiz = 2;
1285  const Int_t kipx = 3;
1286  const Int_t kipy = 4;
1287  const Int_t kipz = 5;
1288 
1289  // *.
1290  // *. ------------------------------------------------------------------
1291  // *.
1292  // * this constant is for units cm,gev/c and kgauss
1293  // *
1294  Int_t iter = 0;
1295  Int_t ncut = 0;
1296  for(Int_t j = 0; j < 7; j++)
1297  vout[j] = vect[j];
1298 
1299  Double_t pinv = kec * charge / vect[6];
1300  Double_t tl = 0.;
1301  Double_t h = step;
1302  Double_t rest;
1303 
1304 
1305  do {
1306  rest = step - tl;
1307  if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
1308  //cmodif: call gufld(vout,f) changed into:
1309  TGeoGlobalMagField::Instance()->Field(vout,f);
1310 
1311  // *
1312  // * start of integration
1313  // *
1314  x = vout[0];
1315  y = vout[1];
1316  z = vout[2];
1317  a = vout[3];
1318  b = vout[4];
1319  c = vout[5];
1320 
1321  h2 = khalf * h;
1322  h4 = khalf * h2;
1323  ph = pinv * h;
1324  ph2 = khalf * ph;
1325  secxs[0] = (b * f[2] - c * f[1]) * ph2;
1326  secys[0] = (c * f[0] - a * f[2]) * ph2;
1327  seczs[0] = (a * f[1] - b * f[0]) * ph2;
1328  ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
1329  if (ang2 > kpisqua) break;
1330 
1331  dxt = h2 * a + h4 * secxs[0];
1332  dyt = h2 * b + h4 * secys[0];
1333  dzt = h2 * c + h4 * seczs[0];
1334  xt = x + dxt;
1335  yt = y + dyt;
1336  zt = z + dzt;
1337  // *
1338  // * second intermediate point
1339  // *
1340 
1341  est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
1342  if (est > h) {
1343  if (ncut++ > maxcut) break;
1344  h *= khalf;
1345  continue;
1346  }
1347 
1348  xyzt[0] = xt;
1349  xyzt[1] = yt;
1350  xyzt[2] = zt;
1351 
1352  //cmodif: call gufld(xyzt,f) changed into:
1353  TGeoGlobalMagField::Instance()->Field(xyzt,f);
1354 
1355  at = a + secxs[0];
1356  bt = b + secys[0];
1357  ct = c + seczs[0];
1358 
1359  secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
1360  secys[1] = (ct * f[0] - at * f[2]) * ph2;
1361  seczs[1] = (at * f[1] - bt * f[0]) * ph2;
1362  at = a + secxs[1];
1363  bt = b + secys[1];
1364  ct = c + seczs[1];
1365  secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
1366  secys[2] = (ct * f[0] - at * f[2]) * ph2;
1367  seczs[2] = (at * f[1] - bt * f[0]) * ph2;
1368  dxt = h * (a + secxs[2]);
1369  dyt = h * (b + secys[2]);
1370  dzt = h * (c + seczs[2]);
1371  xt = x + dxt;
1372  yt = y + dyt;
1373  zt = z + dzt;
1374  at = a + 2.*secxs[2];
1375  bt = b + 2.*secys[2];
1376  ct = c + 2.*seczs[2];
1377 
1378  est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
1379  if (est > 2.*TMath::Abs(h)) {
1380  if (ncut++ > maxcut) break;
1381  h *= khalf;
1382  continue;
1383  }
1384 
1385  xyzt[0] = xt;
1386  xyzt[1] = yt;
1387  xyzt[2] = zt;
1388 
1389  //cmodif: call gufld(xyzt,f) changed into:
1390  TGeoGlobalMagField::Instance()->Field(xyzt,f);
1391 
1392  z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
1393  y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
1394  x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
1395 
1396  secxs[3] = (bt*f[2] - ct*f[1])* ph2;
1397  secys[3] = (ct*f[0] - at*f[2])* ph2;
1398  seczs[3] = (at*f[1] - bt*f[0])* ph2;
1399  a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
1400  b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
1401  c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
1402 
1403  est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
1404  + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
1405  + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
1406 
1407  if (est > kdlt && TMath::Abs(h) > 1.e-4) {
1408  if (ncut++ > maxcut) break;
1409  h *= khalf;
1410  continue;
1411  }
1412 
1413  ncut = 0;
1414  // * if too many iterations, go to helix
1415  if (iter++ > maxit) break;
1416 
1417  tl += h;
1418  if (est < kdlt32)
1419  h *= 2.;
1420  cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
1421  vout[0] = x;
1422  vout[1] = y;
1423  vout[2] = z;
1424  vout[3] = cba*a;
1425  vout[4] = cba*b;
1426  vout[5] = cba*c;
1427  rest = step - tl;
1428  if (step < 0.) rest = -rest;
1429  if (rest < 1.e-5*TMath::Abs(step)) return kTRUE;
1430 
1431  } while(1);
1432 
1433  // angle too big, use helix
1434  cout<<"W-AliMUONTrackExtrap::ExtrapOneStepRungekutta: Ruge-Kutta failed: switch to helix"<<endl;
1435 
1436  f1 = f[0];
1437  f2 = f[1];
1438  f3 = f[2];
1439  f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
1440  if (f4 < 1.e-10) {
1441  cout<<"E-AliMUONTrackExtrap::ExtrapOneStepRungekutta: magnetic field at (";
1442  cout<<xyzt[0]<<", "<<xyzt[1]<<", "<<xyzt[2]<<") = "<<f4<<": giving up"<<endl;
1443  return kFALSE;
1444  }
1445  rho = -f4*pinv;
1446  tet = rho * step;
1447 
1448  hnorm = 1./f4;
1449  f1 = f1*hnorm;
1450  f2 = f2*hnorm;
1451  f3 = f3*hnorm;
1452 
1453  hxp[0] = f2*vect[kipz] - f3*vect[kipy];
1454  hxp[1] = f3*vect[kipx] - f1*vect[kipz];
1455  hxp[2] = f1*vect[kipy] - f2*vect[kipx];
1456 
1457  hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
1458 
1459  rho1 = 1./rho;
1460  sint = TMath::Sin(tet);
1461  cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1462 
1463  g1 = sint*rho1;
1464  g2 = cost*rho1;
1465  g3 = (tet-sint) * hp*rho1;
1466  g4 = -cost;
1467  g5 = sint;
1468  g6 = cost * hp;
1469 
1470  vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1471  vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1472  vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1473 
1474  vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1475  vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1476  vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1477 
1478  return kTRUE;
1479 }
1480 
static const Double_t fgkRungeKuttaMaxResidue
! Maximal distance (in Z) to destination to stop the track extrapolation (used in Runge-Kutta) ...
static Double_t AbsZEnd()
Return z-position of absorber end.
static const Double_t fgkHelixStepLength
! Step lenght for track extrapolation (used in Helix)
static Bool_t ExtrapToZHelix(AliMUONTrackParam *trackParam, Double_t Z)
static void ExtrapToVertex(AliMUONTrackParam *trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx, Double_t errXVtx, Double_t errYVtx)
static void 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)
static Bool_t ExtrapOneStepRungekutta(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
Double_t GetBendingCoor() const
return bending coordinate (cm)
static const Double_t fgkSimpleBPosition
! position of the dipole
const TMatrixD & GetParameters() const
return track parameters
void dZ()
Definition: CalibAlign.C:517
static Bool_t ExtrapToZRungekutta(AliMUONTrackParam *trackParam, Double_t Z)
static void CorrectELossEffectInAbsorber(AliMUONTrackParam *param, Double_t eLoss, Double_t sigmaELoss2)
static const Bool_t fgkUseHelix
! Tell whether to use Helix or not (default is Runge-Kutta)
static Double_t BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA)
TFile f("CalibObjects.root")
Bool_t CovariancesExist() const
return kTRUE if the covariance matrix exist, kFALSE if not
static Double_t TotalMomentumEnergyLoss(AliMUONTrackParam *trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx)
static Bool_t fgFieldON
! kTRUE if the field is switched ON
Double_t GetZ() const
return Z coordinate (cm)
static void ExtrapToVertexUncorrected(AliMUONTrackParam *trackParam, Double_t zVtx)
Track parameters in ALICE dimuon spectrometer.
static void AddMCSEffectInAbsorber(AliMUONTrackParam *trackParam, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2)
void SetNonBendingCoor(Double_t nonBendingCoor)
set non bending coordinate (cm)
static Bool_t ExtrapToZ(AliMUONTrackParam *trackParam, Double_t zEnd)
void AddParameters(const TMatrixD &parameters)
add track parameters
Double_t GetInverseBendingMomentum() const
return inverse bending momentum (GeV/c ** -1) times the charge (assumed forward motion) ...
static Bool_t 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)
static const Double_t fgkSimpleBLength
! length of the dipole
ClassImp(TPCGenInfo)
Definition: AliTPCCmpNG.C:254
void sum()
static Double_t fgSimpleBValue
! magnetic field value at the centre
Double_t GetBendingSlope() const
return bending slope (cm ** -1)
void SetBendingSlope(Double_t bendingSlope)
set bending slope (cm ** -1)
static Double_t GetMostProbBendingMomentum()
Return the most probable bending momentum (GeV/c) (used when B = 0)
static const Int_t fgkMaxStepNumber
! Maximum number of steps for track extrapolation
static Bool_t ExtrapToZCov(AliMUONTrackParam *trackParam, Double_t zEnd, Bool_t updatePropagator=kFALSE)
static void LinearExtrapToZCov(AliMUONTrackParam *trackParam, Double_t zEnd, Bool_t updatePropagator=kFALSE)
Double_t GetCharge() const
return the charge (assumed forward motion)
static void LinearExtrapToZ(AliMUONTrackParam *trackParam, Double_t zEnd)
static void ConvertTrackParamForExtrap(AliMUONTrackParam *trackParam, Double_t forwardBackward, Double_t *v3)
static void Cov2CovP(const TMatrixD &param, TMatrixD &cov)
MUON global constants.
static void AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0)
Double_t P() const
void SetNonBendingSlope(Double_t nonBendingSlope)
set non bending slope (cm ** -1)
static Double_t GetImpactParamFromBendingMomentum(Double_t bendingMomentum)
static Double_t GetMCSAngle2(const AliMUONTrackParam &param, Double_t dZ, Double_t x0)
void SetParameters(const TMatrixD &parameters)
set track parameters
static void RecoverTrackParam(Double_t *v3, Double_t Charge, AliMUONTrackParam *trackParam)
void SetInverseBendingMomentum(Double_t inverseBendingMomentum)
set inverse bending momentum (GeV/c ** -1) times the charge (assumed forward motion) ...
static void ExtrapToVertexWithoutBranson(AliMUONTrackParam *trackParam, Double_t zVtx)
void SetBendingCoor(Double_t bendingCoor)
set bending coordinate (cm)
Double_t GetNonBendingCoor() const
return non bending coordinate (cm)
static void ExtrapOneStepHelix(Double_t charge, Double_t step, const Double_t *vect, Double_t *vout)
static Double_t EnergyLossFluctuation(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA)
static void ExtrapOneStepHelix3(Double_t field, Double_t step, const Double_t *vect, Double_t *vout)
void UpdatePropagator(const TMatrixD &propagator)
static void CovP2Cov(const TMatrixD &param, TMatrixD &cov)
void SetCovariances(const TMatrixD &covariances)
static void ExtrapToVertexWithoutELoss(AliMUONTrackParam *trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx, Double_t errXVtx, Double_t errYVtx)
void SetZ(Double_t z)
set Z coordinate (cm)
const TMatrixD & GetCovariances() const
static Double_t GetBendingMomentumFromImpactParam(Double_t impactParam)
Track parameters in ALICE dimuon spectrometer.
static Double_t AbsZBeg()
Return z-position of absorber begining.
Double_t GetNonBendingSlope() const
return non bending slope (cm ** -1)