1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
18 ///////////////////////////////////////////////////
26 ///////////////////////////////////////////////////
28 #include <Riostream.h>
30 #include "AliCallf77.h"
32 #include "AliMUONTrackParam.h"
33 #include "AliMUONChamber.h"
38 ClassImp(AliMUONTrackParam) // Class implementation in ROOT context
40 // A few calls in Fortran or from Fortran (extrap.F).
41 // Needed, instead of calls to Geant subroutines,
42 // because double precision is necessary for track fit converging with Minuit.
43 // The "extrap" functions should be translated into C++ ????
45 # define extrap_onestep_helix extrap_onestep_helix_
46 # define extrap_onestep_helix3 extrap_onestep_helix3_
47 # define extrap_onestep_rungekutta extrap_onestep_rungekutta_
48 # define gufld_double gufld_double_
50 # define extrap_onestep_helix EXTRAP_ONESTEP_HELIX
51 # define extrap_onestep_helix3 EXTRAP_ONESTEP_HELIX3
52 # define extrap_onestep_rungekutta EXTRAP_ONESTEP_RUNGEKUTTA
53 # define gufld_double GUFLD_DOUBLE
57 void type_of_call extrap_onestep_helix
58 (Double_t &Charge, Double_t &StepLength, Double_t *VGeant3, Double_t *VGeant3New);
60 void type_of_call extrap_onestep_helix3
61 (Double_t &Field, Double_t &StepLength, Double_t *VGeant3, Double_t *VGeant3New);
63 void type_of_call extrap_onestep_rungekutta
64 (Double_t &Charge, Double_t &StepLength, Double_t *VGeant3, Double_t *VGeant3New);
66 void type_of_call gufld_double(Double_t *Position, Double_t *Field) {
67 // interface to "gAlice->Field()->Field" for arguments in double precision
69 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
70 gAlice->Field()->Field(x, b);
71 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
75 //_________________________________________________________________________
76 AliMUONTrackParam::AliMUONTrackParam()
81 fInverseBendingMomentum = 0;
89 //_________________________________________________________________________
91 AliMUONTrackParam::operator=(const AliMUONTrackParam& theMUONTrackParam)
93 if (this == &theMUONTrackParam)
96 // base class assignement
97 TObject::operator=(theMUONTrackParam);
99 fInverseBendingMomentum = theMUONTrackParam.fInverseBendingMomentum;
100 fBendingSlope = theMUONTrackParam.fBendingSlope;
101 fNonBendingSlope = theMUONTrackParam.fNonBendingSlope;
102 fZ = theMUONTrackParam.fZ;
103 fBendingCoor = theMUONTrackParam.fBendingCoor;
104 fNonBendingCoor = theMUONTrackParam.fNonBendingCoor;
108 //_________________________________________________________________________
109 AliMUONTrackParam::AliMUONTrackParam(const AliMUONTrackParam& theMUONTrackParam)
110 : TObject(theMUONTrackParam)
112 fInverseBendingMomentum = theMUONTrackParam.fInverseBendingMomentum;
113 fBendingSlope = theMUONTrackParam.fBendingSlope;
114 fNonBendingSlope = theMUONTrackParam.fNonBendingSlope;
115 fZ = theMUONTrackParam.fZ;
116 fBendingCoor = theMUONTrackParam.fBendingCoor;
117 fNonBendingCoor = theMUONTrackParam.fNonBendingCoor;
120 //__________________________________________________________________________
121 void AliMUONTrackParam::ExtrapToZ(Double_t Z)
123 // Track parameter extrapolation to the plane at "Z".
124 // On return, the track parameters resulting from the extrapolation
125 // replace the current track parameters.
126 if (this->fZ == Z) return; // nothing to be done if same Z
127 Double_t forwardBackward; // +1 if forward, -1 if backward
128 if (Z < this->fZ) forwardBackward = 1.0; // spectro. z<0
129 else forwardBackward = -1.0;
130 Double_t vGeant3[7], vGeant3New[7]; // 7 in parameter ????
131 Int_t iGeant3, stepNumber;
132 Int_t maxStepNumber = 5000; // in parameter ????
133 // For safety: return kTRUE or kFALSE ????
134 // Parameter vector for calling EXTRAP_ONESTEP
135 SetGeant3Parameters(vGeant3, forwardBackward);
136 // sign of charge (sign of fInverseBendingMomentum if forward motion)
137 // must be changed if backward extrapolation
138 Double_t chargeExtrap = forwardBackward *
139 TMath::Sign(Double_t(1.0), this->fInverseBendingMomentum);
140 Double_t stepLength = 6.0; // in parameter ????
141 // Extrapolation loop
143 while (((-forwardBackward * (vGeant3[2] - Z)) <= 0.0) && // spectro. z<0
144 (stepNumber < maxStepNumber)) {
146 // Option for switching between helix and Runge-Kutta ????
147 // extrap_onestep_rungekutta(chargeExtrap, stepLength, vGeant3, vGeant3New);
148 extrap_onestep_helix(chargeExtrap, stepLength, vGeant3, vGeant3New);
149 if ((-forwardBackward * (vGeant3New[2] - Z)) > 0.0) break; // one is beyond Z spectro. z<0
150 // better use TArray ????
151 for (iGeant3 = 0; iGeant3 < 7; iGeant3++)
152 {vGeant3[iGeant3] = vGeant3New[iGeant3];}
154 // check maxStepNumber ????
155 // Interpolation back to exact Z (2nd order)
156 // should be in function ???? using TArray ????
157 Double_t dZ12 = vGeant3New[2] - vGeant3[2]; // 1->2
158 Double_t dZ1i = Z - vGeant3[2]; // 1-i
159 Double_t dZi2 = vGeant3New[2] - Z; // i->2
160 Double_t xPrime = (vGeant3New[0] - vGeant3[0]) / dZ12;
162 ((vGeant3New[3] / vGeant3New[5]) - (vGeant3[3] / vGeant3[5])) / dZ12;
163 Double_t yPrime = (vGeant3New[1] - vGeant3[1]) / dZ12;
165 ((vGeant3New[4] / vGeant3New[5]) - (vGeant3[4] / vGeant3[5])) / dZ12;
166 vGeant3[0] = vGeant3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
167 vGeant3[1] = vGeant3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
169 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
170 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
171 // (PX, PY, PZ)/PTOT assuming forward motion
173 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
174 vGeant3[3] = xPrimeI * vGeant3[5]; // PX/PTOT
175 vGeant3[4] = yPrimeI * vGeant3[5]; // PY/PTOT
176 // Track parameters from Geant3 parameters,
177 // with charge back for forward motion
178 GetFromGeant3Parameters(vGeant3, chargeExtrap * forwardBackward);
181 //__________________________________________________________________________
182 void AliMUONTrackParam::SetGeant3Parameters(Double_t *VGeant3, Double_t ForwardBackward)
184 // Set vector of Geant3 parameters pointed to by "VGeant3"
185 // from track parameters in current AliMUONTrackParam.
186 // Since AliMUONTrackParam is only geometry, one uses "ForwardBackward"
187 // to know whether the particle is going forward (+1) or backward (-1).
188 VGeant3[0] = this->fNonBendingCoor; // X
189 VGeant3[1] = this->fBendingCoor; // Y
190 VGeant3[2] = this->fZ; // Z
191 Double_t pYZ = TMath::Abs(1.0 / this->fInverseBendingMomentum);
193 pYZ / TMath::Sqrt(1.0 + this->fBendingSlope * this->fBendingSlope);
195 TMath::Sqrt(pYZ * pYZ +
196 pZ * pZ * this->fNonBendingSlope * this->fNonBendingSlope); // PTOT
197 VGeant3[5] = -ForwardBackward * pZ / VGeant3[6]; // PZ/PTOT spectro. z<0
198 VGeant3[3] = this->fNonBendingSlope * VGeant3[5]; // PX/PTOT
199 VGeant3[4] = this->fBendingSlope * VGeant3[5]; // PY/PTOT
202 //__________________________________________________________________________
203 void AliMUONTrackParam::GetFromGeant3Parameters(Double_t *VGeant3, Double_t Charge)
205 // Get track parameters in current AliMUONTrackParam
206 // from Geant3 parameters pointed to by "VGeant3",
207 // assumed to be calculated for forward motion in Z.
208 // "InverseBendingMomentum" is signed with "Charge".
209 this->fNonBendingCoor = VGeant3[0]; // X
210 this->fBendingCoor = VGeant3[1]; // Y
211 this->fZ = VGeant3[2]; // Z
212 Double_t pYZ = VGeant3[6] * TMath::Sqrt(1.0 - VGeant3[3] * VGeant3[3]);
213 this->fInverseBendingMomentum = Charge / pYZ;
214 this->fBendingSlope = VGeant3[4] / VGeant3[5];
215 this->fNonBendingSlope = VGeant3[3] / VGeant3[5];
218 //__________________________________________________________________________
219 void AliMUONTrackParam::ExtrapToStation(Int_t Station, AliMUONTrackParam *TrackParam)
221 // Track parameters extrapolated from current track parameters ("this")
222 // to both chambers of the station(0..) "Station"
223 // are returned in the array (dimension 2) of track parameters
224 // pointed to by "TrackParam" (index 0 and 1 for first and second chambers).
225 Double_t extZ[2], z1, z2;
226 Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
227 AliMUON *pMUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
228 // range of Station to be checked ????
229 z1 = (&(pMUON->Chamber(2 * Station)))->Z(); // Z of first chamber
230 z2 = (&(pMUON->Chamber(2 * Station + 1)))->Z(); // Z of second chamber
231 // First and second Z to extrapolate at
232 if ((z1 > this->fZ) && (z2 > this->fZ)) {i1 = 0; i2 = 1;}
233 else if ((z1 < this->fZ) && (z2 < this->fZ)) {i1 = 1; i2 = 0;}
235 AliError(Form("Starting Z (%f) in between z1 (%f) and z2 (%f) of station(0..)%d",this->fZ,z1,z2,Station));
236 // cout << "ERROR in AliMUONTrackParam::CreateExtrapSegmentInStation" << endl;
237 // cout << "Starting Z (" << this->fZ << ") in between z1 (" << z1 <<
238 // ") and z2 (" << z2 << ") of station(0..) " << Station << endl;
242 // copy of track parameters
243 TrackParam[i1] = *this;
244 // first extrapolation
245 (&(TrackParam[i1]))->ExtrapToZ(extZ[0]);
246 TrackParam[i2] = TrackParam[i1];
247 // second extrapolation
248 (&(TrackParam[i2]))->ExtrapToZ(extZ[1]);
252 //__________________________________________________________________________
253 void AliMUONTrackParam::ExtrapToVertex()
255 // Extrapolation to the vertex.
256 // Returns the track parameters resulting from the extrapolation,
257 // in the current TrackParam.
258 // Changes parameters according to Branson correction through the absorber
260 Double_t zAbsorber = -503.0; // to be coherent with the Geant absorber geometry !!!!
262 // Extrapolates track parameters upstream to the "Z" end of the front absorber
263 ExtrapToZ(zAbsorber); // !!!
264 // Makes Branson correction (multiple scattering + energy loss)
266 // Makes a simple magnetic field correction through the absorber
267 FieldCorrection(zAbsorber);
271 // Keep this version for future developments
272 //__________________________________________________________________________
273 // void AliMUONTrackParam::BransonCorrection()
275 // // Branson correction of track parameters
276 // // the entry parameters have to be calculated at the end of the absorber
277 // Double_t zEndAbsorber, zBP, xBP, yBP;
278 // Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
280 // // Would it be possible to calculate all that from Geant configuration ????
281 // // and to get the Branson parameters from a function in ABSO module ????
282 // // with an eventual contribution from other detectors like START ????
283 // // Radiation lengths outer part theta > 3 degres
284 // static Double_t x01[9] = { 18.8, // C (cm)
285 // 10.397, // Concrete (cm)
286 // 0.56, // Plomb (cm)
287 // 47.26, // Polyethylene (cm)
288 // 0.56, // Plomb (cm)
289 // 47.26, // Polyethylene (cm)
290 // 0.56, // Plomb (cm)
291 // 47.26, // Polyethylene (cm)
292 // 0.56 }; // Plomb (cm)
293 // // inner part theta < 3 degres
294 // static Double_t x02[3] = { 18.8, // C (cm)
295 // 10.397, // Concrete (cm)
297 // // z positions of the materials inside the absober outer part theta > 3 degres
298 // static Double_t z1[10] = { 90, 315, 467, 472, 477, 482, 487, 492, 497, 502 };
299 // // inner part theta < 3 degres
300 // static Double_t z2[4] = { 90, 315, 467, 503 };
301 // static Bool_t first = kTRUE;
302 // static Double_t zBP1, zBP2, rLimit;
303 // // Calculates z positions of the Branson's planes: zBP1 for outer part and zBP2 for inner part (only at the first call)
306 // Double_t aNBP = 0.0;
307 // Double_t aDBP = 0.0;
310 // for (iBound = 0; iBound < 9; iBound++) {
312 // (z1[iBound+1] * z1[iBound+1] * z1[iBound+1] -
313 // z1[iBound] * z1[iBound] * z1[iBound] ) / x01[iBound];
315 // (z1[iBound+1] * z1[iBound+1] - z1[iBound] * z1[iBound] ) / x01[iBound];
317 // zBP1 = (2.0 * aNBP) / (3.0 * aDBP);
320 // for (iBound = 0; iBound < 3; iBound++) {
322 // (z2[iBound+1] * z2[iBound+1] * z2[iBound+1] -
323 // z2[iBound] * z2[iBound ] * z2[iBound] ) / x02[iBound];
325 // (z2[iBound+1] * z2[iBound+1] - z2[iBound] * z2[iBound]) / x02[iBound];
327 // zBP2 = (2.0 * aNBP) / (3.0 * aDBP);
328 // rLimit = z2[3] * TMath::Tan(3.0 * (TMath::Pi()) / 180.);
331 // pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
333 // if (fInverseBendingMomentum < 0) sign = -1;
334 // pZ = pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope));
335 // pX = pZ * fNonBendingSlope;
336 // pY = pZ * fBendingSlope;
337 // pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
338 // xEndAbsorber = fNonBendingCoor;
339 // yEndAbsorber = fBendingCoor;
340 // radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
342 // if (radiusEndAbsorber2 > rLimit*rLimit) {
343 // zEndAbsorber = z1[9];
346 // zEndAbsorber = z2[3];
350 // xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
351 // yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
353 // // new parameters after Branson and energy loss corrections
354 // pZ = pTotal * zBP / TMath::Sqrt(xBP * xBP + yBP * yBP + zBP * zBP);
355 // pX = pZ * xBP / zBP;
356 // pY = pZ * yBP / zBP;
357 // fBendingSlope = pY / pZ;
358 // fNonBendingSlope = pX / pZ;
360 // pT = TMath::Sqrt(pX * pX + pY * pY);
361 // theta = TMath::ATan2(pT, pZ);
363 // TotalMomentumEnergyLoss(rLimit, pTotal, theta, xEndAbsorber, yEndAbsorber);
365 // fInverseBendingMomentum = (sign / pTotal) *
367 // fBendingSlope * fBendingSlope +
368 // fNonBendingSlope * fNonBendingSlope) /
369 // TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope);
371 // // vertex position at (0,0,0)
372 // // should be taken from vertex measurement ???
373 // fBendingCoor = 0.0;
374 // fNonBendingCoor = 0;
378 void AliMUONTrackParam::BransonCorrection()
380 // Branson correction of track parameters
381 // the entry parameters have to be calculated at the end of the absorber
382 // simplified version: the z positions of Branson's planes are no longer calculated
383 // but are given as inputs. One can use the macros MUONTestAbso.C and DrawTestAbso.C
384 // to test this correction.
385 // Would it be possible to calculate all that from Geant configuration ????
386 // and to get the Branson parameters from a function in ABSO module ????
387 // with an eventual contribution from other detectors like START ????
388 Double_t zBP, xBP, yBP;
389 Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
391 static Bool_t first = kTRUE;
392 static Double_t zBP1, zBP2, rLimit, thetaLimit, zEndAbsorber;
393 // zBP1 for outer part and zBP2 for inner part (only at the first call)
397 zEndAbsorber = -503; // spectro (z<0)
398 thetaLimit = 3.0 * (TMath::Pi()) / 180.;
399 rLimit = TMath::Abs(zEndAbsorber) * TMath::Tan(thetaLimit);
400 zBP1 = -450; // values close to those calculated with EvalAbso.C
404 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
406 if (fInverseBendingMomentum < 0) sign = -1;
407 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro (z<0)
408 pX = pZ * fNonBendingSlope;
409 pY = pZ * fBendingSlope;
410 pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
411 xEndAbsorber = fNonBendingCoor;
412 yEndAbsorber = fBendingCoor;
413 radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
415 if (radiusEndAbsorber2 > rLimit*rLimit) {
421 xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
422 yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
424 // new parameters after Branson and energy loss corrections
425 // Float_t zSmear = zBP - gRandom->Gaus(0.,2.); // !!! possible smearing of Z vertex position
426 Float_t zSmear = zBP;
428 pZ = pTotal * zSmear / TMath::Sqrt(xBP * xBP + yBP * yBP + zSmear * zSmear);
429 pX = pZ * xBP / zSmear;
430 pY = pZ * yBP / zSmear;
431 fBendingSlope = pY / pZ;
432 fNonBendingSlope = pX / pZ;
435 pT = TMath::Sqrt(pX * pX + pY * pY);
436 theta = TMath::ATan2(pT, TMath::Abs(pZ));
437 pTotal = TotalMomentumEnergyLoss(thetaLimit, pTotal, theta);
439 fInverseBendingMomentum = (sign / pTotal) *
441 fBendingSlope * fBendingSlope +
442 fNonBendingSlope * fNonBendingSlope) /
443 TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope);
445 // vertex position at (0,0,0)
446 // should be taken from vertex measurement ???
452 //__________________________________________________________________________
453 Double_t AliMUONTrackParam::TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta)
455 // Returns the total momentum corrected from energy loss in the front absorber
456 // One can use the macros MUONTestAbso.C and DrawTestAbso.C
457 // to test this correction.
458 // Momentum energy loss behaviour evaluated with the simulation of single muons (april 2002)
459 Double_t deltaP, pTotalCorrected;
461 // Parametrization to be redone according to change of absorber material ????
462 // See remark in function BransonCorrection !!!!
463 // The name is not so good, and there are many arguments !!!!
464 if (theta < thetaLimit ) {
466 deltaP = 2.5938 + 0.0570 * pTotal - 0.001151 * pTotal * pTotal;
468 deltaP = 3.0714 + 0.011767 *pTotal;
472 deltaP = 2.1207 + 0.05478 * pTotal - 0.00145079 * pTotal * pTotal;
474 deltaP = 2.6069 + 0.0051705 * pTotal;
477 pTotalCorrected = pTotal + deltaP / TMath::Cos(theta);
478 return pTotalCorrected;
481 //__________________________________________________________________________
482 void AliMUONTrackParam::FieldCorrection(Double_t Z)
485 // Correction of the effect of the magnetic field in the absorber
486 // Assume a constant field along Z axis.
490 Double_t pYZ,pX,pY,pZ,pT;
491 Double_t pXNew,pYNew;
494 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
495 c = TMath::Sign(1.0,fInverseBendingMomentum); // particle charge
497 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
498 pX = pZ * fNonBendingSlope;
499 pY = pZ * fBendingSlope;
500 pT = TMath::Sqrt(pX*pX+pY*pY);
502 if (TMath::Abs(pZ) <= 0) return;
504 x[0] = x[2]*fNonBendingSlope;
505 x[1] = x[2]*fBendingSlope;
507 // Take magn. field value at position x.
508 gAlice->Field()->Field(x, b);
511 // Transverse momentum rotation
512 // Parameterized with the study of DeltaPhi = phiReco - phiGen as a function of pZ.
513 Double_t phiShift = c*0.436*0.0003*bZ*Z/pZ;
514 // Rotate momentum around Z axis.
515 pXNew = pX*TMath::Cos(phiShift) - pY*TMath::Sin(phiShift);
516 pYNew = pX*TMath::Sin(phiShift) + pY*TMath::Cos(phiShift);
518 fBendingSlope = pYNew / pZ;
519 fNonBendingSlope = pXNew / pZ;
521 fInverseBendingMomentum = c / TMath::Sqrt(pYNew*pYNew+pZ*pZ);