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 "AliMUONTrackParam.h"
31 #include "AliMUONConstants.h"
32 #include "AliESDMuonTrack.h"
35 #include "AliTracker.h"
37 ClassImp(AliMUONTrackParam) // Class implementation in ROOT context
39 //_________________________________________________________________________
40 AliMUONTrackParam::AliMUONTrackParam()
42 fInverseBendingMomentum(0.),
50 // get field from outside
51 fkField = AliTracker::GetFieldMap();
52 if (!fkField) AliFatal("No field available");
55 //_________________________________________________________________________
57 AliMUONTrackParam::operator=(const AliMUONTrackParam& theMUONTrackParam)
60 if (this == &theMUONTrackParam)
63 // base class assignement
64 TObject::operator=(theMUONTrackParam);
66 fInverseBendingMomentum = theMUONTrackParam.fInverseBendingMomentum;
67 fBendingSlope = theMUONTrackParam.fBendingSlope;
68 fNonBendingSlope = theMUONTrackParam.fNonBendingSlope;
69 fZ = theMUONTrackParam.fZ;
70 fBendingCoor = theMUONTrackParam.fBendingCoor;
71 fNonBendingCoor = theMUONTrackParam.fNonBendingCoor;
75 //_________________________________________________________________________
76 AliMUONTrackParam::AliMUONTrackParam(const AliMUONTrackParam& theMUONTrackParam)
77 : TObject(theMUONTrackParam),
78 fInverseBendingMomentum(theMUONTrackParam.fInverseBendingMomentum),
79 fBendingSlope(theMUONTrackParam.fBendingSlope),
80 fNonBendingSlope(theMUONTrackParam.fNonBendingSlope),
81 fZ(theMUONTrackParam.fZ),
82 fBendingCoor(theMUONTrackParam.fBendingCoor),
83 fNonBendingCoor(theMUONTrackParam.fNonBendingCoor)
89 //_________________________________________________________________________
90 void AliMUONTrackParam::GetParamFrom(const AliESDMuonTrack& esdMuonTrack)
92 // assigned value form ESD track.
93 fInverseBendingMomentum = esdMuonTrack.GetInverseBendingMomentum();
94 fBendingSlope = TMath::Tan(esdMuonTrack.GetThetaY());
95 fNonBendingSlope = TMath::Tan(esdMuonTrack.GetThetaX());
96 fZ = esdMuonTrack.GetZ();
97 fBendingCoor = esdMuonTrack.GetBendingCoor();
98 fNonBendingCoor = esdMuonTrack.GetNonBendingCoor();
101 //_________________________________________________________________________
102 void AliMUONTrackParam::SetParamFor(AliESDMuonTrack& esdMuonTrack)
104 // assigned value form ESD track.
105 esdMuonTrack.SetInverseBendingMomentum(fInverseBendingMomentum);
106 esdMuonTrack.SetThetaX(TMath::ATan(fNonBendingSlope));
107 esdMuonTrack.SetThetaY(TMath::ATan(fBendingSlope));
108 esdMuonTrack.SetZ(fZ);
109 esdMuonTrack.SetBendingCoor(fBendingCoor);
110 esdMuonTrack.SetNonBendingCoor(fNonBendingCoor);
113 //__________________________________________________________________________
114 void AliMUONTrackParam::ExtrapToZ(Double_t Z)
116 // Track parameter extrapolation to the plane at "Z".
117 // On return, the track parameters resulting from the extrapolation
118 // replace the current track parameters.
119 if (this->fZ == Z) return; // nothing to be done if same Z
120 Double_t forwardBackward; // +1 if forward, -1 if backward
121 if (Z < this->fZ) forwardBackward = 1.0; // spectro. z<0
122 else forwardBackward = -1.0;
123 Double_t vGeant3[7], vGeant3New[7]; // 7 in parameter ????
124 Int_t iGeant3, stepNumber;
125 Int_t maxStepNumber = 5000; // in parameter ????
126 // For safety: return kTRUE or kFALSE ????
127 // Parameter vector for calling EXTRAP_ONESTEP
128 SetGeant3Parameters(vGeant3, forwardBackward);
129 // sign of charge (sign of fInverseBendingMomentum if forward motion)
130 // must be changed if backward extrapolation
131 Double_t chargeExtrap = forwardBackward *
132 TMath::Sign(Double_t(1.0), this->fInverseBendingMomentum);
133 Double_t stepLength = 6.0; // in parameter ????
134 // Extrapolation loop
136 while (((-forwardBackward * (vGeant3[2] - Z)) <= 0.0) && // spectro. z<0
137 (stepNumber < maxStepNumber)) {
139 // Option for switching between helix and Runge-Kutta ????
140 //ExtrapOneStepRungekutta(chargeExtrap, stepLength, vGeant3, vGeant3New);
141 ExtrapOneStepHelix(chargeExtrap, stepLength, vGeant3, vGeant3New);
142 if ((-forwardBackward * (vGeant3New[2] - Z)) > 0.0) break; // one is beyond Z spectro. z<0
143 // better use TArray ????
144 for (iGeant3 = 0; iGeant3 < 7; iGeant3++)
145 {vGeant3[iGeant3] = vGeant3New[iGeant3];}
147 // check maxStepNumber ????
148 // Interpolation back to exact Z (2nd order)
149 // should be in function ???? using TArray ????
150 Double_t dZ12 = vGeant3New[2] - vGeant3[2]; // 1->2
151 if (TMath::Abs(dZ12) > 0) {
152 Double_t dZ1i = Z - vGeant3[2]; // 1-i
153 Double_t dZi2 = vGeant3New[2] - Z; // i->2
154 Double_t xPrime = (vGeant3New[0] - vGeant3[0]) / dZ12;
156 ((vGeant3New[3] / vGeant3New[5]) - (vGeant3[3] / vGeant3[5])) / dZ12;
157 Double_t yPrime = (vGeant3New[1] - vGeant3[1]) / dZ12;
159 ((vGeant3New[4] / vGeant3New[5]) - (vGeant3[4] / vGeant3[5])) / dZ12;
160 vGeant3[0] = vGeant3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
161 vGeant3[1] = vGeant3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
163 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
164 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
165 // (PX, PY, PZ)/PTOT assuming forward motion
167 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
168 vGeant3[3] = xPrimeI * vGeant3[5]; // PX/PTOT
169 vGeant3[4] = yPrimeI * vGeant3[5]; // PY/PTOT
171 AliWarning(Form("Extrap. to Z not reached, Z = %f",Z));
173 // Track parameters from Geant3 parameters,
174 // with charge back for forward motion
175 GetFromGeant3Parameters(vGeant3, chargeExtrap * forwardBackward);
178 //__________________________________________________________________________
179 void AliMUONTrackParam::SetGeant3Parameters(Double_t *VGeant3, Double_t ForwardBackward)
181 // Set vector of Geant3 parameters pointed to by "VGeant3"
182 // from track parameters in current AliMUONTrackParam.
183 // Since AliMUONTrackParam is only geometry, one uses "ForwardBackward"
184 // to know whether the particle is going forward (+1) or backward (-1).
185 VGeant3[0] = this->fNonBendingCoor; // X
186 VGeant3[1] = this->fBendingCoor; // Y
187 VGeant3[2] = this->fZ; // Z
188 Double_t pYZ = TMath::Abs(1.0 / this->fInverseBendingMomentum);
190 pYZ / TMath::Sqrt(1.0 + this->fBendingSlope * this->fBendingSlope);
192 TMath::Sqrt(pYZ * pYZ +
193 pZ * pZ * this->fNonBendingSlope * this->fNonBendingSlope); // PTOT
194 VGeant3[5] = -ForwardBackward * pZ / VGeant3[6]; // PZ/PTOT spectro. z<0
195 VGeant3[3] = this->fNonBendingSlope * VGeant3[5]; // PX/PTOT
196 VGeant3[4] = this->fBendingSlope * VGeant3[5]; // PY/PTOT
199 //__________________________________________________________________________
200 void AliMUONTrackParam::GetFromGeant3Parameters(Double_t *VGeant3, Double_t Charge)
202 // Get track parameters in current AliMUONTrackParam
203 // from Geant3 parameters pointed to by "VGeant3",
204 // assumed to be calculated for forward motion in Z.
205 // "InverseBendingMomentum" is signed with "Charge".
206 this->fNonBendingCoor = VGeant3[0]; // X
207 this->fBendingCoor = VGeant3[1]; // Y
208 this->fZ = VGeant3[2]; // Z
209 Double_t pYZ = VGeant3[6] * TMath::Sqrt(1.0 - VGeant3[3] * VGeant3[3]);
210 this->fInverseBendingMomentum = Charge / pYZ;
211 this->fBendingSlope = VGeant3[4] / VGeant3[5];
212 this->fNonBendingSlope = VGeant3[3] / VGeant3[5];
215 //__________________________________________________________________________
216 void AliMUONTrackParam::ExtrapToStation(Int_t Station, AliMUONTrackParam *TrackParam)
218 // Track parameters extrapolated from current track parameters ("this")
219 // to both chambers of the station(0..) "Station"
220 // are returned in the array (dimension 2) of track parameters
221 // pointed to by "TrackParam" (index 0 and 1 for first and second chambers).
222 Double_t extZ[2], z1, z2;
223 Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
224 // range of Station to be checked ????
225 z1 = AliMUONConstants::DefaultChamberZ(2 * Station);
226 z2 = AliMUONConstants::DefaultChamberZ(2 * Station + 1);
227 // First and second Z to extrapolate at
228 if ((z1 > this->fZ) && (z2 > this->fZ)) {i1 = 0; i2 = 1;}
229 else if ((z1 < this->fZ) && (z2 < this->fZ)) {i1 = 1; i2 = 0;}
231 AliError(Form("Starting Z (%f) in between z1 (%f) and z2 (%f) of station(0..)%d",this->fZ,z1,z2,Station));
232 // cout << "ERROR in AliMUONTrackParam::CreateExtrapSegmentInStation" << endl;
233 // cout << "Starting Z (" << this->fZ << ") in between z1 (" << z1 <<
234 // ") and z2 (" << z2 << ") of station(0..) " << Station << endl;
238 // copy of track parameters
239 TrackParam[i1] = *this;
240 // first extrapolation
241 (&(TrackParam[i1]))->ExtrapToZ(extZ[0]);
242 TrackParam[i2] = TrackParam[i1];
243 // second extrapolation
244 (&(TrackParam[i2]))->ExtrapToZ(extZ[1]);
248 //__________________________________________________________________________
249 void AliMUONTrackParam::ExtrapToVertex(Double_t xVtx, Double_t yVtx, Double_t zVtx)
251 // Extrapolation to the vertex.
252 // Returns the track parameters resulting from the extrapolation,
253 // in the current TrackParam.
254 // Changes parameters according to Branson correction through the absorber
256 Double_t zAbsorber = -503.0; // to be coherent with the Geant absorber geometry !!!!
258 // Extrapolates track parameters upstream to the "Z" end of the front absorber
259 ExtrapToZ(zAbsorber); // !!!
260 // Makes Branson correction (multiple scattering + energy loss)
261 BransonCorrection(xVtx,yVtx,zVtx);
262 // Makes a simple magnetic field correction through the absorber
263 FieldCorrection(zAbsorber);
267 // Keep this version for future developments
268 //__________________________________________________________________________
269 // void AliMUONTrackParam::BransonCorrection()
271 // // Branson correction of track parameters
272 // // the entry parameters have to be calculated at the end of the absorber
273 // Double_t zEndAbsorber, zBP, xBP, yBP;
274 // Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
276 // // Would it be possible to calculate all that from Geant configuration ????
277 // // and to get the Branson parameters from a function in ABSO module ????
278 // // with an eventual contribution from other detectors like START ????
279 // // Radiation lengths outer part theta > 3 degres
280 // static Double_t x01[9] = { 18.8, // C (cm)
281 // 10.397, // Concrete (cm)
282 // 0.56, // Plomb (cm)
283 // 47.26, // Polyethylene (cm)
284 // 0.56, // Plomb (cm)
285 // 47.26, // Polyethylene (cm)
286 // 0.56, // Plomb (cm)
287 // 47.26, // Polyethylene (cm)
288 // 0.56 }; // Plomb (cm)
289 // // inner part theta < 3 degres
290 // static Double_t x02[3] = { 18.8, // C (cm)
291 // 10.397, // Concrete (cm)
293 // // z positions of the materials inside the absober outer part theta > 3 degres
294 // static Double_t z1[10] = { 90, 315, 467, 472, 477, 482, 487, 492, 497, 502 };
295 // // inner part theta < 3 degres
296 // static Double_t z2[4] = { 90, 315, 467, 503 };
297 // static Bool_t first = kTRUE;
298 // static Double_t zBP1, zBP2, rLimit;
299 // // Calculates z positions of the Branson's planes: zBP1 for outer part and zBP2 for inner part (only at the first call)
302 // Double_t aNBP = 0.0;
303 // Double_t aDBP = 0.0;
306 // for (iBound = 0; iBound < 9; iBound++) {
308 // (z1[iBound+1] * z1[iBound+1] * z1[iBound+1] -
309 // z1[iBound] * z1[iBound] * z1[iBound] ) / x01[iBound];
311 // (z1[iBound+1] * z1[iBound+1] - z1[iBound] * z1[iBound] ) / x01[iBound];
313 // zBP1 = (2.0 * aNBP) / (3.0 * aDBP);
316 // for (iBound = 0; iBound < 3; iBound++) {
318 // (z2[iBound+1] * z2[iBound+1] * z2[iBound+1] -
319 // z2[iBound] * z2[iBound ] * z2[iBound] ) / x02[iBound];
321 // (z2[iBound+1] * z2[iBound+1] - z2[iBound] * z2[iBound]) / x02[iBound];
323 // zBP2 = (2.0 * aNBP) / (3.0 * aDBP);
324 // rLimit = z2[3] * TMath::Tan(3.0 * (TMath::Pi()) / 180.);
327 // pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
329 // if (fInverseBendingMomentum < 0) sign = -1;
330 // pZ = pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope));
331 // pX = pZ * fNonBendingSlope;
332 // pY = pZ * fBendingSlope;
333 // pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
334 // xEndAbsorber = fNonBendingCoor;
335 // yEndAbsorber = fBendingCoor;
336 // radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
338 // if (radiusEndAbsorber2 > rLimit*rLimit) {
339 // zEndAbsorber = z1[9];
342 // zEndAbsorber = z2[3];
346 // xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
347 // yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
349 // // new parameters after Branson and energy loss corrections
350 // pZ = pTotal * zBP / TMath::Sqrt(xBP * xBP + yBP * yBP + zBP * zBP);
351 // pX = pZ * xBP / zBP;
352 // pY = pZ * yBP / zBP;
353 // fBendingSlope = pY / pZ;
354 // fNonBendingSlope = pX / pZ;
356 // pT = TMath::Sqrt(pX * pX + pY * pY);
357 // theta = TMath::ATan2(pT, pZ);
359 // TotalMomentumEnergyLoss(rLimit, pTotal, theta, xEndAbsorber, yEndAbsorber);
361 // fInverseBendingMomentum = (sign / pTotal) *
363 // fBendingSlope * fBendingSlope +
364 // fNonBendingSlope * fNonBendingSlope) /
365 // TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope);
367 // // vertex position at (0,0,0)
368 // // should be taken from vertex measurement ???
369 // fBendingCoor = 0.0;
370 // fNonBendingCoor = 0;
374 void AliMUONTrackParam::BransonCorrection(Double_t xVtx,Double_t yVtx,Double_t zVtx)
376 // Branson correction of track parameters
377 // the entry parameters have to be calculated at the end of the absorber
378 // simplified version: the z positions of Branson's planes are no longer calculated
379 // but are given as inputs. One can use the macros MUONTestAbso.C and DrawTestAbso.C
380 // to test this correction.
381 // Would it be possible to calculate all that from Geant configuration ????
382 // and to get the Branson parameters from a function in ABSO module ????
383 // with an eventual contribution from other detectors like START ????
384 //change to take into account the vertex postition (real, reconstruct,....)
386 Double_t zBP, xBP, yBP;
387 Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
389 static Bool_t first = kTRUE;
390 static Double_t zBP1, zBP2, rLimit, thetaLimit, zEndAbsorber;
391 // zBP1 for outer part and zBP2 for inner part (only at the first call)
395 zEndAbsorber = -503; // spectro (z<0)
396 thetaLimit = 3.0 * (TMath::Pi()) / 180.;
397 rLimit = TMath::Abs(zEndAbsorber) * TMath::Tan(thetaLimit);
398 zBP1 = -450; // values close to those calculated with EvalAbso.C
402 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
404 if (fInverseBendingMomentum < 0) sign = -1;
408 pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
409 xEndAbsorber = fNonBendingCoor;
410 yEndAbsorber = fBendingCoor;
411 radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
413 if (radiusEndAbsorber2 > rLimit*rLimit) {
419 xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
420 yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
422 // new parameters after Branson and energy loss corrections
423 // Float_t zSmear = zBP - gRandom->Gaus(0.,2.); // !!! possible smearing of Z vertex position
425 Float_t zSmear = zBP ;
427 pZ = pTotal * (zSmear-zVtx) / TMath::Sqrt((xBP-xVtx) * (xBP-xVtx) + (yBP-yVtx) * (yBP-yVtx) +( zSmear-zVtx) * (zSmear-zVtx) );
428 pX = pZ * (xBP - xVtx)/ (zSmear-zVtx);
429 pY = pZ * (yBP - yVtx) / (zSmear-zVtx);
430 fBendingSlope = pY / pZ;
431 fNonBendingSlope = pX / pZ;
434 pT = TMath::Sqrt(pX * pX + pY * pY);
435 theta = TMath::ATan2(pT, TMath::Abs(pZ));
436 pTotal = TotalMomentumEnergyLoss(thetaLimit, pTotal, theta);
438 fInverseBendingMomentum = (sign / pTotal) *
440 fBendingSlope * fBendingSlope +
441 fNonBendingSlope * fNonBendingSlope) /
442 TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope);
444 // vertex position at (0,0,0)
445 // should be taken from vertex measurement ???
448 fNonBendingCoor = yVtx;
453 //__________________________________________________________________________
454 Double_t AliMUONTrackParam::TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta)
456 // Returns the total momentum corrected from energy loss in the front absorber
457 // One can use the macros MUONTestAbso.C and DrawTestAbso.C
458 // to test this correction.
459 // Momentum energy loss behaviour evaluated with the simulation of single muons (april 2002)
460 Double_t deltaP, pTotalCorrected;
462 // Parametrization to be redone according to change of absorber material ????
463 // See remark in function BransonCorrection !!!!
464 // The name is not so good, and there are many arguments !!!!
465 if (theta < thetaLimit ) {
467 deltaP = 2.5938 + 0.0570 * pTotal - 0.001151 * pTotal * pTotal;
469 deltaP = 3.0714 + 0.011767 *pTotal;
471 deltaP *= 0.75; // AZ
474 deltaP = 2.1207 + 0.05478 * pTotal - 0.00145079 * pTotal * pTotal;
476 deltaP = 2.6069 + 0.0051705 * pTotal;
480 pTotalCorrected = pTotal + deltaP / TMath::Cos(theta);
481 return pTotalCorrected;
484 //__________________________________________________________________________
485 void AliMUONTrackParam::FieldCorrection(Double_t Z)
488 // Correction of the effect of the magnetic field in the absorber
489 // Assume a constant field along Z axis.
493 Double_t pYZ,pX,pY,pZ,pT;
494 Double_t pXNew,pYNew;
497 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
498 c = TMath::Sign(1.0,fInverseBendingMomentum); // particle charge
503 pT = TMath::Sqrt(pX*pX+pY*pY);
505 if (TMath::Abs(pZ) <= 0) return;
507 x[0] = x[2]*fNonBendingSlope;
508 x[1] = x[2]*fBendingSlope;
510 // Take magn. field value at position x.
511 fkField->Field(x, b);
514 // Transverse momentum rotation
515 // Parameterized with the study of DeltaPhi = phiReco - phiGen as a function of pZ.
516 Double_t phiShift = c*0.436*0.0003*bZ*Z/pZ;
517 // Rotate momentum around Z axis.
518 pXNew = pX*TMath::Cos(phiShift) - pY*TMath::Sin(phiShift);
519 pYNew = pX*TMath::Sin(phiShift) + pY*TMath::Cos(phiShift);
521 fBendingSlope = pYNew / pZ;
522 fNonBendingSlope = pXNew / pZ;
524 fInverseBendingMomentum = c / TMath::Sqrt(pYNew*pYNew+pZ*pZ);
527 //__________________________________________________________________________
528 Double_t AliMUONTrackParam::Px() const
530 // return px from track paramaters
531 Double_t pYZ, pZ, pX;
533 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
534 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
535 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
536 pX = pZ * fNonBendingSlope;
539 //__________________________________________________________________________
540 Double_t AliMUONTrackParam::Py() const
542 // return px from track paramaters
543 Double_t pYZ, pZ, pY;
545 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
546 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
547 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
548 pY = pZ * fBendingSlope;
551 //__________________________________________________________________________
552 Double_t AliMUONTrackParam::Pz() const
554 // return px from track paramaters
557 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
558 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
559 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
562 //__________________________________________________________________________
563 Double_t AliMUONTrackParam::P() const
565 // return p from track paramaters
568 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
569 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
570 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
572 TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope + fNonBendingSlope * fNonBendingSlope);
576 //__________________________________________________________________________
577 void AliMUONTrackParam::ExtrapOneStepHelix(Double_t charge, Double_t step,
578 Double_t *vect, Double_t *vout) const
580 // ******************************************************************
582 // * Performs the tracking of one step in a magnetic field *
583 // * The trajectory is assumed to be a helix in a constant field *
584 // * taken at the mid point of the step. *
587 // * STEP =arc length of the step asked *
588 // * VECT =input vector (position,direction cos and momentum) *
589 // * CHARGE= electric charge of the particle *
591 // * VOUT = same as VECT after completion of the step *
593 // * ==>Called by : <USER>, GUSWIM *
594 // * Author m.hansroul ********* *
595 // * modified s.egli, s.v.levonian *
596 // * modified v.perevoztchikov
598 // ******************************************************************
601 // modif: everything in double precision
603 Double_t xyz[3], h[4], hxp[3];
604 Double_t h2xy, hp, rho, tet;
605 Double_t sint, sintt, tsint, cos1t;
606 Double_t f1, f2, f3, f4, f5, f6;
611 const Int_t kipx = 3;
612 const Int_t kipy = 4;
613 const Int_t kipz = 5;
614 const Int_t kipp = 6;
616 const Double_t kec = 2.9979251e-4;
618 // ------------------------------------------------------------------
620 // units are kgauss,centimeters,gev/c
622 vout[kipp] = vect[kipp];
623 if (TMath::Abs(charge) < 0.00001) {
624 for (Int_t i = 0; i < 3; i++) {
625 vout[i] = vect[i] + step * vect[i+3];
626 vout[i+3] = vect[i+3];
630 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
631 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
632 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
634 //cmodif: call gufld (xyz, h) changed into:
637 h2xy = h[0]*h[0] + h[1]*h[1];
638 h[3] = h[2]*h[2]+ h2xy;
640 for (Int_t i = 0; i < 3; i++) {
641 vout[i] = vect[i] + step * vect[i+3];
642 vout[i+3] = vect[i+3];
646 if (h2xy < 1.e-12*h[3]) {
647 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
650 h[3] = TMath::Sqrt(h[3]);
656 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
657 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
658 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
660 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
662 rho = -charge*h[3]/vect[kipp];
665 if (TMath::Abs(tet) > 0.15) {
666 sint = TMath::Sin(tet);
668 tsint = (tet-sint)/tet;
669 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
672 sintt = (1. - tsint);
679 f3 = step * tsint * hp;
682 f6 = tet * cos1t * hp;
684 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
685 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
686 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
688 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
689 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
690 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
695 //__________________________________________________________________________
696 void AliMUONTrackParam::ExtrapOneStepHelix3(Double_t field, Double_t step,
697 Double_t *vect, Double_t *vout) const
700 // ******************************************************************
702 // * Tracking routine in a constant field oriented *
704 // * Tracking is performed with a conventional *
705 // * helix step method *
707 // * ==>Called by : <USER>, GUSWIM *
708 // * Authors R.Brun, M.Hansroul ********* *
709 // * Rewritten V.Perevoztchikov
711 // ******************************************************************
715 Double_t h4, hp, rho, tet;
716 Double_t sint, sintt, tsint, cos1t;
717 Double_t f1, f2, f3, f4, f5, f6;
722 const Int_t kipx = 3;
723 const Int_t kipy = 4;
724 const Int_t kipz = 5;
725 const Int_t kipp = 6;
727 const Double_t kec = 2.9979251e-4;
730 // ------------------------------------------------------------------
732 // units are kgauss,centimeters,gev/c
734 vout[kipp] = vect[kipp];
737 hxp[0] = - vect[kipy];
738 hxp[1] = + vect[kipx];
742 rho = -h4/vect[kipp];
744 if (TMath::Abs(tet) > 0.15) {
745 sint = TMath::Sin(tet);
747 tsint = (tet-sint)/tet;
748 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
751 sintt = (1. - tsint);
758 f3 = step * tsint * hp;
761 f6 = tet * cos1t * hp;
763 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
764 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
765 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
767 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
768 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
769 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
773 //__________________________________________________________________________
774 void AliMUONTrackParam::ExtrapOneStepRungekutta(Double_t charge, Double_t step,
775 Double_t* vect, Double_t* vout) const
778 // ******************************************************************
780 // * Runge-Kutta method for tracking a particle through a magnetic *
781 // * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
782 // * Standards, procedure 25.5.20) *
784 // * Input parameters *
785 // * CHARGE Particle charge *
786 // * STEP Step size *
787 // * VECT Initial co-ords,direction cosines,momentum *
788 // * Output parameters *
789 // * VOUT Output co-ords,direction cosines,momentum *
790 // * User routine called *
791 // * CALL GUFLD(X,F) *
793 // * ==>Called by : <USER>, GUSWIM *
794 // * Authors R.Brun, M.Hansroul ********* *
795 // * V.Perevoztchikov (CUT STEP implementation) *
798 // ******************************************************************
801 Double_t h2, h4, f[4];
802 Double_t xyzt[3], a, b, c, ph,ph2;
803 Double_t secxs[4],secys[4],seczs[4],hxp[3];
804 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
805 Double_t est, at, bt, ct, cba;
806 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
816 Double_t maxit = 1992;
817 Double_t maxcut = 11;
819 const Double_t kdlt = 1e-4;
820 const Double_t kdlt32 = kdlt/32.;
821 const Double_t kthird = 1./3.;
822 const Double_t khalf = 0.5;
823 const Double_t kec = 2.9979251e-4;
825 const Double_t kpisqua = 9.86960440109;
829 const Int_t kipx = 3;
830 const Int_t kipy = 4;
831 const Int_t kipz = 5;
834 // *. ------------------------------------------------------------------
836 // * this constant is for units cm,gev/c and kgauss
840 for(Int_t j = 0; j < 7; j++)
843 Double_t pinv = kec * charge / vect[6];
851 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
852 //cmodif: call gufld(vout,f) changed into:
857 // * start of integration
870 secxs[0] = (b * f[2] - c * f[1]) * ph2;
871 secys[0] = (c * f[0] - a * f[2]) * ph2;
872 seczs[0] = (a * f[1] - b * f[0]) * ph2;
873 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
874 if (ang2 > kpisqua) break;
876 dxt = h2 * a + h4 * secxs[0];
877 dyt = h2 * b + h4 * secys[0];
878 dzt = h2 * c + h4 * seczs[0];
883 // * second intermediate point
886 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
888 if (ncut++ > maxcut) break;
897 //cmodif: call gufld(xyzt,f) changed into:
904 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
905 secys[1] = (ct * f[0] - at * f[2]) * ph2;
906 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
910 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
911 secys[2] = (ct * f[0] - at * f[2]) * ph2;
912 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
913 dxt = h * (a + secxs[2]);
914 dyt = h * (b + secys[2]);
915 dzt = h * (c + seczs[2]);
919 at = a + 2.*secxs[2];
920 bt = b + 2.*secys[2];
921 ct = c + 2.*seczs[2];
923 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
924 if (est > 2.*TMath::Abs(h)) {
925 if (ncut++ > maxcut) break;
934 //cmodif: call gufld(xyzt,f) changed into:
937 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
938 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
939 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
941 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
942 secys[3] = (ct*f[0] - at*f[2])* ph2;
943 seczs[3] = (at*f[1] - bt*f[0])* ph2;
944 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
945 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
946 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
948 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
949 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
950 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
952 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
953 if (ncut++ > maxcut) break;
959 // * if too many iterations, go to helix
960 if (iter++ > maxit) break;
965 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
973 if (step < 0.) rest = -rest;
974 if (rest < 1.e-5*TMath::Abs(step)) return;
978 // angle too big, use helix
983 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
992 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
993 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
994 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
996 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
999 sint = TMath::Sin(tet);
1000 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
1004 g3 = (tet-sint) * hp*rho1;
1009 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
1010 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
1011 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
1013 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
1014 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
1015 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
1019 //___________________________________________________________
1020 void AliMUONTrackParam::GetField(Double_t *Position, Double_t *Field) const
1022 // interface for arguments in double precision (Why ? ChF)
1026 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
1028 fkField->Field(x, b);
1029 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];
1033 //_____________________________________________-
1034 void AliMUONTrackParam::Print(Option_t* opt) const
1037 // Printing TrackParam information
1038 // "full" option for printing all the information about the TrackParam
1043 if ( sopt.Contains("FULL") ) {
1044 cout << "<AliMUONTrackParam> Bending P=" << setw(5) << setprecision(3) << 1./GetInverseBendingMomentum() <<
1045 ", NonBendSlope=" << setw(5) << setprecision(3) << GetNonBendingSlope()*180./TMath::Pi() <<
1046 ", BendSlope=" << setw(5) << setprecision(3) << GetBendingSlope()*180./TMath::Pi() <<
1047 ", (x,y,z)_IP=(" << setw(5) << setprecision(3) << GetNonBendingCoor() <<
1048 "," << setw(5) << setprecision(3) << GetBendingCoor() <<
1049 "," << setw(5) << setprecision(3) << GetZ() <<
1050 ") cm, (px,py,pz)=(" << setw(5) << setprecision(3) << Px() <<
1051 "," << setw(5) << setprecision(3) << Py() <<
1052 "," << setw(5) << setprecision(3) << Pz() << ") GeV/c" << endl;
1055 cout << "<AliMUONTrackParam>" << endl;