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"
36 ClassImp(AliMUONTrackParam) // Class implementation in ROOT context
38 //_________________________________________________________________________
39 AliMUONTrackParam::AliMUONTrackParam()
44 fInverseBendingMomentum = 0;
52 //_________________________________________________________________________
54 AliMUONTrackParam::operator=(const AliMUONTrackParam& theMUONTrackParam)
57 if (this == &theMUONTrackParam)
60 // base class assignement
61 TObject::operator=(theMUONTrackParam);
63 fInverseBendingMomentum = theMUONTrackParam.fInverseBendingMomentum;
64 fBendingSlope = theMUONTrackParam.fBendingSlope;
65 fNonBendingSlope = theMUONTrackParam.fNonBendingSlope;
66 fZ = theMUONTrackParam.fZ;
67 fBendingCoor = theMUONTrackParam.fBendingCoor;
68 fNonBendingCoor = theMUONTrackParam.fNonBendingCoor;
72 //_________________________________________________________________________
73 AliMUONTrackParam::AliMUONTrackParam(const AliMUONTrackParam& theMUONTrackParam)
74 : TObject(theMUONTrackParam)
77 fInverseBendingMomentum = theMUONTrackParam.fInverseBendingMomentum;
78 fBendingSlope = theMUONTrackParam.fBendingSlope;
79 fNonBendingSlope = theMUONTrackParam.fNonBendingSlope;
80 fZ = theMUONTrackParam.fZ;
81 fBendingCoor = theMUONTrackParam.fBendingCoor;
82 fNonBendingCoor = theMUONTrackParam.fNonBendingCoor;
85 //__________________________________________________________________________
86 void AliMUONTrackParam::ExtrapToZ(Double_t Z)
88 // Track parameter extrapolation to the plane at "Z".
89 // On return, the track parameters resulting from the extrapolation
90 // replace the current track parameters.
91 if (this->fZ == Z) return; // nothing to be done if same Z
92 Double_t forwardBackward; // +1 if forward, -1 if backward
93 if (Z < this->fZ) forwardBackward = 1.0; // spectro. z<0
94 else forwardBackward = -1.0;
95 Double_t vGeant3[7], vGeant3New[7]; // 7 in parameter ????
96 Int_t iGeant3, stepNumber;
97 Int_t maxStepNumber = 5000; // in parameter ????
98 // For safety: return kTRUE or kFALSE ????
99 // Parameter vector for calling EXTRAP_ONESTEP
100 SetGeant3Parameters(vGeant3, forwardBackward);
101 // sign of charge (sign of fInverseBendingMomentum if forward motion)
102 // must be changed if backward extrapolation
103 Double_t chargeExtrap = forwardBackward *
104 TMath::Sign(Double_t(1.0), this->fInverseBendingMomentum);
105 Double_t stepLength = 6.0; // in parameter ????
106 // Extrapolation loop
108 while (((-forwardBackward * (vGeant3[2] - Z)) <= 0.0) && // spectro. z<0
109 (stepNumber < maxStepNumber)) {
111 // Option for switching between helix and Runge-Kutta ????
112 //ExtrapOneStepRungekutta(chargeExtrap, stepLength, vGeant3, vGeant3New);
113 ExtrapOneStepHelix(chargeExtrap, stepLength, vGeant3, vGeant3New);
114 if ((-forwardBackward * (vGeant3New[2] - Z)) > 0.0) break; // one is beyond Z spectro. z<0
115 // better use TArray ????
116 for (iGeant3 = 0; iGeant3 < 7; iGeant3++)
117 {vGeant3[iGeant3] = vGeant3New[iGeant3];}
119 // check maxStepNumber ????
120 // Interpolation back to exact Z (2nd order)
121 // should be in function ???? using TArray ????
122 Double_t dZ12 = vGeant3New[2] - vGeant3[2]; // 1->2
123 if (TMath::Abs(dZ12) > 0) {
124 Double_t dZ1i = Z - vGeant3[2]; // 1-i
125 Double_t dZi2 = vGeant3New[2] - Z; // i->2
126 Double_t xPrime = (vGeant3New[0] - vGeant3[0]) / dZ12;
128 ((vGeant3New[3] / vGeant3New[5]) - (vGeant3[3] / vGeant3[5])) / dZ12;
129 Double_t yPrime = (vGeant3New[1] - vGeant3[1]) / dZ12;
131 ((vGeant3New[4] / vGeant3New[5]) - (vGeant3[4] / vGeant3[5])) / dZ12;
132 vGeant3[0] = vGeant3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X
133 vGeant3[1] = vGeant3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y
135 Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i);
136 Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i);
137 // (PX, PY, PZ)/PTOT assuming forward motion
139 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT
140 vGeant3[3] = xPrimeI * vGeant3[5]; // PX/PTOT
141 vGeant3[4] = yPrimeI * vGeant3[5]; // PY/PTOT
143 AliWarning(Form("Extrap. to Z not reached, Z = %f",Z));
145 // Track parameters from Geant3 parameters,
146 // with charge back for forward motion
147 GetFromGeant3Parameters(vGeant3, chargeExtrap * forwardBackward);
150 //__________________________________________________________________________
151 void AliMUONTrackParam::SetGeant3Parameters(Double_t *VGeant3, Double_t ForwardBackward)
153 // Set vector of Geant3 parameters pointed to by "VGeant3"
154 // from track parameters in current AliMUONTrackParam.
155 // Since AliMUONTrackParam is only geometry, one uses "ForwardBackward"
156 // to know whether the particle is going forward (+1) or backward (-1).
157 VGeant3[0] = this->fNonBendingCoor; // X
158 VGeant3[1] = this->fBendingCoor; // Y
159 VGeant3[2] = this->fZ; // Z
160 Double_t pYZ = TMath::Abs(1.0 / this->fInverseBendingMomentum);
162 pYZ / TMath::Sqrt(1.0 + this->fBendingSlope * this->fBendingSlope);
164 TMath::Sqrt(pYZ * pYZ +
165 pZ * pZ * this->fNonBendingSlope * this->fNonBendingSlope); // PTOT
166 VGeant3[5] = -ForwardBackward * pZ / VGeant3[6]; // PZ/PTOT spectro. z<0
167 VGeant3[3] = this->fNonBendingSlope * VGeant3[5]; // PX/PTOT
168 VGeant3[4] = this->fBendingSlope * VGeant3[5]; // PY/PTOT
171 //__________________________________________________________________________
172 void AliMUONTrackParam::GetFromGeant3Parameters(Double_t *VGeant3, Double_t Charge)
174 // Get track parameters in current AliMUONTrackParam
175 // from Geant3 parameters pointed to by "VGeant3",
176 // assumed to be calculated for forward motion in Z.
177 // "InverseBendingMomentum" is signed with "Charge".
178 this->fNonBendingCoor = VGeant3[0]; // X
179 this->fBendingCoor = VGeant3[1]; // Y
180 this->fZ = VGeant3[2]; // Z
181 Double_t pYZ = VGeant3[6] * TMath::Sqrt(1.0 - VGeant3[3] * VGeant3[3]);
182 this->fInverseBendingMomentum = Charge / pYZ;
183 this->fBendingSlope = VGeant3[4] / VGeant3[5];
184 this->fNonBendingSlope = VGeant3[3] / VGeant3[5];
187 //__________________________________________________________________________
188 void AliMUONTrackParam::ExtrapToStation(Int_t Station, AliMUONTrackParam *TrackParam)
190 // Track parameters extrapolated from current track parameters ("this")
191 // to both chambers of the station(0..) "Station"
192 // are returned in the array (dimension 2) of track parameters
193 // pointed to by "TrackParam" (index 0 and 1 for first and second chambers).
194 Double_t extZ[2], z1, z2;
195 Int_t i1 = -1, i2 = -1; // = -1 to avoid compilation warnings
196 // range of Station to be checked ????
197 z1 = AliMUONConstants::DefaultChamberZ(2 * Station);
198 z2 = AliMUONConstants::DefaultChamberZ(2 * Station + 1);
199 // First and second Z to extrapolate at
200 if ((z1 > this->fZ) && (z2 > this->fZ)) {i1 = 0; i2 = 1;}
201 else if ((z1 < this->fZ) && (z2 < this->fZ)) {i1 = 1; i2 = 0;}
203 AliError(Form("Starting Z (%f) in between z1 (%f) and z2 (%f) of station(0..)%d",this->fZ,z1,z2,Station));
204 // cout << "ERROR in AliMUONTrackParam::CreateExtrapSegmentInStation" << endl;
205 // cout << "Starting Z (" << this->fZ << ") in between z1 (" << z1 <<
206 // ") and z2 (" << z2 << ") of station(0..) " << Station << endl;
210 // copy of track parameters
211 TrackParam[i1] = *this;
212 // first extrapolation
213 (&(TrackParam[i1]))->ExtrapToZ(extZ[0]);
214 TrackParam[i2] = TrackParam[i1];
215 // second extrapolation
216 (&(TrackParam[i2]))->ExtrapToZ(extZ[1]);
220 //__________________________________________________________________________
221 void AliMUONTrackParam::ExtrapToVertex(Double_t xVtx, Double_t yVtx, Double_t zVtx)
223 // Extrapolation to the vertex.
224 // Returns the track parameters resulting from the extrapolation,
225 // in the current TrackParam.
226 // Changes parameters according to Branson correction through the absorber
228 Double_t zAbsorber = -503.0; // to be coherent with the Geant absorber geometry !!!!
230 // Extrapolates track parameters upstream to the "Z" end of the front absorber
231 ExtrapToZ(zAbsorber); // !!!
232 // Makes Branson correction (multiple scattering + energy loss)
233 BransonCorrection(xVtx,yVtx,zVtx);
234 // Makes a simple magnetic field correction through the absorber
235 FieldCorrection(zAbsorber);
239 // Keep this version for future developments
240 //__________________________________________________________________________
241 // void AliMUONTrackParam::BransonCorrection()
243 // // Branson correction of track parameters
244 // // the entry parameters have to be calculated at the end of the absorber
245 // Double_t zEndAbsorber, zBP, xBP, yBP;
246 // Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
248 // // Would it be possible to calculate all that from Geant configuration ????
249 // // and to get the Branson parameters from a function in ABSO module ????
250 // // with an eventual contribution from other detectors like START ????
251 // // Radiation lengths outer part theta > 3 degres
252 // static Double_t x01[9] = { 18.8, // C (cm)
253 // 10.397, // Concrete (cm)
254 // 0.56, // Plomb (cm)
255 // 47.26, // Polyethylene (cm)
256 // 0.56, // Plomb (cm)
257 // 47.26, // Polyethylene (cm)
258 // 0.56, // Plomb (cm)
259 // 47.26, // Polyethylene (cm)
260 // 0.56 }; // Plomb (cm)
261 // // inner part theta < 3 degres
262 // static Double_t x02[3] = { 18.8, // C (cm)
263 // 10.397, // Concrete (cm)
265 // // z positions of the materials inside the absober outer part theta > 3 degres
266 // static Double_t z1[10] = { 90, 315, 467, 472, 477, 482, 487, 492, 497, 502 };
267 // // inner part theta < 3 degres
268 // static Double_t z2[4] = { 90, 315, 467, 503 };
269 // static Bool_t first = kTRUE;
270 // static Double_t zBP1, zBP2, rLimit;
271 // // Calculates z positions of the Branson's planes: zBP1 for outer part and zBP2 for inner part (only at the first call)
274 // Double_t aNBP = 0.0;
275 // Double_t aDBP = 0.0;
278 // for (iBound = 0; iBound < 9; iBound++) {
280 // (z1[iBound+1] * z1[iBound+1] * z1[iBound+1] -
281 // z1[iBound] * z1[iBound] * z1[iBound] ) / x01[iBound];
283 // (z1[iBound+1] * z1[iBound+1] - z1[iBound] * z1[iBound] ) / x01[iBound];
285 // zBP1 = (2.0 * aNBP) / (3.0 * aDBP);
288 // for (iBound = 0; iBound < 3; iBound++) {
290 // (z2[iBound+1] * z2[iBound+1] * z2[iBound+1] -
291 // z2[iBound] * z2[iBound ] * z2[iBound] ) / x02[iBound];
293 // (z2[iBound+1] * z2[iBound+1] - z2[iBound] * z2[iBound]) / x02[iBound];
295 // zBP2 = (2.0 * aNBP) / (3.0 * aDBP);
296 // rLimit = z2[3] * TMath::Tan(3.0 * (TMath::Pi()) / 180.);
299 // pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
301 // if (fInverseBendingMomentum < 0) sign = -1;
302 // pZ = pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope));
303 // pX = pZ * fNonBendingSlope;
304 // pY = pZ * fBendingSlope;
305 // pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
306 // xEndAbsorber = fNonBendingCoor;
307 // yEndAbsorber = fBendingCoor;
308 // radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
310 // if (radiusEndAbsorber2 > rLimit*rLimit) {
311 // zEndAbsorber = z1[9];
314 // zEndAbsorber = z2[3];
318 // xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
319 // yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
321 // // new parameters after Branson and energy loss corrections
322 // pZ = pTotal * zBP / TMath::Sqrt(xBP * xBP + yBP * yBP + zBP * zBP);
323 // pX = pZ * xBP / zBP;
324 // pY = pZ * yBP / zBP;
325 // fBendingSlope = pY / pZ;
326 // fNonBendingSlope = pX / pZ;
328 // pT = TMath::Sqrt(pX * pX + pY * pY);
329 // theta = TMath::ATan2(pT, pZ);
331 // TotalMomentumEnergyLoss(rLimit, pTotal, theta, xEndAbsorber, yEndAbsorber);
333 // fInverseBendingMomentum = (sign / pTotal) *
335 // fBendingSlope * fBendingSlope +
336 // fNonBendingSlope * fNonBendingSlope) /
337 // TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope);
339 // // vertex position at (0,0,0)
340 // // should be taken from vertex measurement ???
341 // fBendingCoor = 0.0;
342 // fNonBendingCoor = 0;
346 void AliMUONTrackParam::BransonCorrection(Double_t xVtx,Double_t yVtx,Double_t zVtx)
348 // Branson correction of track parameters
349 // the entry parameters have to be calculated at the end of the absorber
350 // simplified version: the z positions of Branson's planes are no longer calculated
351 // but are given as inputs. One can use the macros MUONTestAbso.C and DrawTestAbso.C
352 // to test this correction.
353 // Would it be possible to calculate all that from Geant configuration ????
354 // and to get the Branson parameters from a function in ABSO module ????
355 // with an eventual contribution from other detectors like START ????
356 //change to take into account the vertex postition (real, reconstruct,....)
358 Double_t zBP, xBP, yBP;
359 Double_t pYZ, pX, pY, pZ, pTotal, xEndAbsorber, yEndAbsorber, radiusEndAbsorber2, pT, theta;
361 static Bool_t first = kTRUE;
362 static Double_t zBP1, zBP2, rLimit, thetaLimit, zEndAbsorber;
363 // zBP1 for outer part and zBP2 for inner part (only at the first call)
367 zEndAbsorber = -503; // spectro (z<0)
368 thetaLimit = 3.0 * (TMath::Pi()) / 180.;
369 rLimit = TMath::Abs(zEndAbsorber) * TMath::Tan(thetaLimit);
370 zBP1 = -450; // values close to those calculated with EvalAbso.C
374 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
376 if (fInverseBendingMomentum < 0) sign = -1;
380 pTotal = TMath::Sqrt(pYZ *pYZ + pX * pX);
381 xEndAbsorber = fNonBendingCoor;
382 yEndAbsorber = fBendingCoor;
383 radiusEndAbsorber2 = xEndAbsorber * xEndAbsorber + yEndAbsorber * yEndAbsorber;
385 if (radiusEndAbsorber2 > rLimit*rLimit) {
391 xBP = xEndAbsorber - (pX / pZ) * (zEndAbsorber - zBP);
392 yBP = yEndAbsorber - (pY / pZ) * (zEndAbsorber - zBP);
394 // new parameters after Branson and energy loss corrections
395 // Float_t zSmear = zBP - gRandom->Gaus(0.,2.); // !!! possible smearing of Z vertex position
397 Float_t zSmear = zBP ;
399 pZ = pTotal * (zSmear-zVtx) / TMath::Sqrt((xBP-xVtx) * (xBP-xVtx) + (yBP-yVtx) * (yBP-yVtx) +( zSmear-zVtx) * (zSmear-zVtx) );
400 pX = pZ * (xBP - xVtx)/ (zSmear-zVtx);
401 pY = pZ * (yBP - yVtx) / (zSmear-zVtx);
402 fBendingSlope = pY / pZ;
403 fNonBendingSlope = pX / pZ;
406 pT = TMath::Sqrt(pX * pX + pY * pY);
407 theta = TMath::ATan2(pT, TMath::Abs(pZ));
408 pTotal = TotalMomentumEnergyLoss(thetaLimit, pTotal, theta);
410 fInverseBendingMomentum = (sign / pTotal) *
412 fBendingSlope * fBendingSlope +
413 fNonBendingSlope * fNonBendingSlope) /
414 TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope);
416 // vertex position at (0,0,0)
417 // should be taken from vertex measurement ???
420 fNonBendingCoor = yVtx;
425 //__________________________________________________________________________
426 Double_t AliMUONTrackParam::TotalMomentumEnergyLoss(Double_t thetaLimit, Double_t pTotal, Double_t theta)
428 // Returns the total momentum corrected from energy loss in the front absorber
429 // One can use the macros MUONTestAbso.C and DrawTestAbso.C
430 // to test this correction.
431 // Momentum energy loss behaviour evaluated with the simulation of single muons (april 2002)
432 Double_t deltaP, pTotalCorrected;
434 // Parametrization to be redone according to change of absorber material ????
435 // See remark in function BransonCorrection !!!!
436 // The name is not so good, and there are many arguments !!!!
437 if (theta < thetaLimit ) {
439 deltaP = 2.5938 + 0.0570 * pTotal - 0.001151 * pTotal * pTotal;
441 deltaP = 3.0714 + 0.011767 *pTotal;
443 deltaP *= 0.75; // AZ
446 deltaP = 2.1207 + 0.05478 * pTotal - 0.00145079 * pTotal * pTotal;
448 deltaP = 2.6069 + 0.0051705 * pTotal;
452 pTotalCorrected = pTotal + deltaP / TMath::Cos(theta);
453 return pTotalCorrected;
456 //__________________________________________________________________________
457 void AliMUONTrackParam::FieldCorrection(Double_t Z)
460 // Correction of the effect of the magnetic field in the absorber
461 // Assume a constant field along Z axis.
465 Double_t pYZ,pX,pY,pZ,pT;
466 Double_t pXNew,pYNew;
469 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
470 c = TMath::Sign(1.0,fInverseBendingMomentum); // particle charge
475 pT = TMath::Sqrt(pX*pX+pY*pY);
477 if (TMath::Abs(pZ) <= 0) return;
479 x[0] = x[2]*fNonBendingSlope;
480 x[1] = x[2]*fBendingSlope;
482 // Take magn. field value at position x.
483 gAlice->Field()->Field(x, b);
486 // Transverse momentum rotation
487 // Parameterized with the study of DeltaPhi = phiReco - phiGen as a function of pZ.
488 Double_t phiShift = c*0.436*0.0003*bZ*Z/pZ;
489 // Rotate momentum around Z axis.
490 pXNew = pX*TMath::Cos(phiShift) - pY*TMath::Sin(phiShift);
491 pYNew = pX*TMath::Sin(phiShift) + pY*TMath::Cos(phiShift);
493 fBendingSlope = pYNew / pZ;
494 fNonBendingSlope = pXNew / pZ;
496 fInverseBendingMomentum = c / TMath::Sqrt(pYNew*pYNew+pZ*pZ);
499 //__________________________________________________________________________
500 Double_t AliMUONTrackParam::Px()
502 // return px from track paramaters
503 Double_t pYZ, pZ, pX;
505 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
506 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
507 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
508 pX = pZ * fNonBendingSlope;
511 //__________________________________________________________________________
512 Double_t AliMUONTrackParam::Py()
514 // return px from track paramaters
515 Double_t pYZ, pZ, pY;
517 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
518 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
519 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
520 pY = pZ * fBendingSlope;
523 //__________________________________________________________________________
524 Double_t AliMUONTrackParam::Pz()
526 // return px from track paramaters
529 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
530 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
531 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
534 //__________________________________________________________________________
535 Double_t AliMUONTrackParam::P()
537 // return p from track paramaters
540 if ( TMath::Abs(fInverseBendingMomentum) > 0 )
541 pYZ = TMath::Abs(1.0 / fInverseBendingMomentum);
542 pZ = -pYZ / (TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope)); // spectro. (z<0)
544 TMath::Sqrt(1.0 + fBendingSlope * fBendingSlope + fNonBendingSlope * fNonBendingSlope);
548 //__________________________________________________________________________
549 void AliMUONTrackParam::ExtrapOneStepHelix(Double_t charge, Double_t step,
550 Double_t *vect, Double_t *vout) const
552 // ******************************************************************
554 // * Performs the tracking of one step in a magnetic field *
555 // * The trajectory is assumed to be a helix in a constant field *
556 // * taken at the mid point of the step. *
559 // * STEP =arc length of the step asked *
560 // * VECT =input vector (position,direction cos and momentum) *
561 // * CHARGE= electric charge of the particle *
563 // * VOUT = same as VECT after completion of the step *
565 // * ==>Called by : <USER>, GUSWIM *
566 // * Author m.hansroul ********* *
567 // * modified s.egli, s.v.levonian *
568 // * modified v.perevoztchikov
570 // ******************************************************************
573 // modif: everything in double precision
575 Double_t xyz[3], h[4], hxp[3];
576 Double_t h2xy, hp, rho, tet;
577 Double_t sint, sintt, tsint, cos1t;
578 Double_t f1, f2, f3, f4, f5, f6;
583 const Int_t kipx = 3;
584 const Int_t kipy = 4;
585 const Int_t kipz = 5;
586 const Int_t kipp = 6;
588 const Double_t kec = 2.9979251e-4;
590 // ------------------------------------------------------------------
592 // units are kgauss,centimeters,gev/c
594 vout[kipp] = vect[kipp];
595 if (TMath::Abs(charge) < 0.00001) {
596 for (Int_t i = 0; i < 3; i++) {
597 vout[i] = vect[i] + step * vect[i+3];
598 vout[i+3] = vect[i+3];
602 xyz[0] = vect[kix] + 0.5 * step * vect[kipx];
603 xyz[1] = vect[kiy] + 0.5 * step * vect[kipy];
604 xyz[2] = vect[kiz] + 0.5 * step * vect[kipz];
606 //cmodif: call gufld (xyz, h) changed into:
609 h2xy = h[0]*h[0] + h[1]*h[1];
610 h[3] = h[2]*h[2]+ h2xy;
612 for (Int_t i = 0; i < 3; i++) {
613 vout[i] = vect[i] + step * vect[i+3];
614 vout[i+3] = vect[i+3];
618 if (h2xy < 1.e-12*h[3]) {
619 ExtrapOneStepHelix3(charge*h[2], step, vect, vout);
622 h[3] = TMath::Sqrt(h[3]);
628 hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy];
629 hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz];
630 hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx];
632 hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz];
634 rho = -charge*h[3]/vect[kipp];
637 if (TMath::Abs(tet) > 0.15) {
638 sint = TMath::Sin(tet);
640 tsint = (tet-sint)/tet;
641 cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet;
644 sintt = (1. - tsint);
651 f3 = step * tsint * hp;
654 f6 = tet * cos1t * hp;
656 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0];
657 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1];
658 vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2];
660 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0];
661 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1];
662 vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2];
667 //__________________________________________________________________________
668 void AliMUONTrackParam::ExtrapOneStepHelix3(Double_t field, Double_t step,
669 Double_t *vect, Double_t *vout) const
672 // ******************************************************************
674 // * Tracking routine in a constant field oriented *
676 // * Tracking is performed with a conventional *
677 // * helix step method *
679 // * ==>Called by : <USER>, GUSWIM *
680 // * Authors R.Brun, M.Hansroul ********* *
681 // * Rewritten V.Perevoztchikov
683 // ******************************************************************
687 Double_t h4, hp, rho, tet;
688 Double_t sint, sintt, tsint, cos1t;
689 Double_t f1, f2, f3, f4, f5, f6;
694 const Int_t kipx = 3;
695 const Int_t kipy = 4;
696 const Int_t kipz = 5;
697 const Int_t kipp = 6;
699 const Double_t kec = 2.9979251e-4;
702 // ------------------------------------------------------------------
704 // units are kgauss,centimeters,gev/c
706 vout[kipp] = vect[kipp];
709 hxp[0] = - vect[kipy];
710 hxp[1] = + vect[kipx];
714 rho = -h4/vect[kipp];
716 if (TMath::Abs(tet) > 0.15) {
717 sint = TMath::Sin(tet);
719 tsint = (tet-sint)/tet;
720 cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet;
723 sintt = (1. - tsint);
730 f3 = step * tsint * hp;
733 f6 = tet * cos1t * hp;
735 vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0];
736 vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1];
737 vout[kiz] = vect[kiz] + f1*vect[kipz] + f3;
739 vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0];
740 vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1];
741 vout[kipz] = vect[kipz] + f4*vect[kipz] + f6;
745 //__________________________________________________________________________
746 void AliMUONTrackParam::ExtrapOneStepRungekutta(Double_t charge, Double_t step,
747 Double_t* vect, Double_t* vout) const
750 // ******************************************************************
752 // * Runge-Kutta method for tracking a particle through a magnetic *
753 // * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of *
754 // * Standards, procedure 25.5.20) *
756 // * Input parameters *
757 // * CHARGE Particle charge *
758 // * STEP Step size *
759 // * VECT Initial co-ords,direction cosines,momentum *
760 // * Output parameters *
761 // * VOUT Output co-ords,direction cosines,momentum *
762 // * User routine called *
763 // * CALL GUFLD(X,F) *
765 // * ==>Called by : <USER>, GUSWIM *
766 // * Authors R.Brun, M.Hansroul ********* *
767 // * V.Perevoztchikov (CUT STEP implementation) *
770 // ******************************************************************
773 Double_t h2, h4, f[4];
774 Double_t xyzt[3], a, b, c, ph,ph2;
775 Double_t secxs[4],secys[4],seczs[4],hxp[3];
776 Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt;
777 Double_t est, at, bt, ct, cba;
778 Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost;
788 Double_t maxit = 1992;
789 Double_t maxcut = 11;
791 const Double_t kdlt = 1e-4;
792 const Double_t kdlt32 = kdlt/32.;
793 const Double_t kthird = 1./3.;
794 const Double_t khalf = 0.5;
795 const Double_t kec = 2.9979251e-4;
797 const Double_t kpisqua = 9.86960440109;
801 const Int_t kipx = 3;
802 const Int_t kipy = 4;
803 const Int_t kipz = 5;
806 // *. ------------------------------------------------------------------
808 // * this constant is for units cm,gev/c and kgauss
812 for(Int_t j = 0; j < 7; j++)
815 Double_t pinv = kec * charge / vect[6];
823 if (TMath::Abs(h) > TMath::Abs(rest)) h = rest;
824 //cmodif: call gufld(vout,f) changed into:
829 // * start of integration
842 secxs[0] = (b * f[2] - c * f[1]) * ph2;
843 secys[0] = (c * f[0] - a * f[2]) * ph2;
844 seczs[0] = (a * f[1] - b * f[0]) * ph2;
845 ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]);
846 if (ang2 > kpisqua) break;
848 dxt = h2 * a + h4 * secxs[0];
849 dyt = h2 * b + h4 * secys[0];
850 dzt = h2 * c + h4 * seczs[0];
855 // * second intermediate point
858 est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt);
860 if (ncut++ > maxcut) break;
869 //cmodif: call gufld(xyzt,f) changed into:
876 secxs[1] = (bt * f[2] - ct * f[1]) * ph2;
877 secys[1] = (ct * f[0] - at * f[2]) * ph2;
878 seczs[1] = (at * f[1] - bt * f[0]) * ph2;
882 secxs[2] = (bt * f[2] - ct * f[1]) * ph2;
883 secys[2] = (ct * f[0] - at * f[2]) * ph2;
884 seczs[2] = (at * f[1] - bt * f[0]) * ph2;
885 dxt = h * (a + secxs[2]);
886 dyt = h * (b + secys[2]);
887 dzt = h * (c + seczs[2]);
891 at = a + 2.*secxs[2];
892 bt = b + 2.*secys[2];
893 ct = c + 2.*seczs[2];
895 est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt);
896 if (est > 2.*TMath::Abs(h)) {
897 if (ncut++ > maxcut) break;
906 //cmodif: call gufld(xyzt,f) changed into:
909 z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h;
910 y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h;
911 x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h;
913 secxs[3] = (bt*f[2] - ct*f[1])* ph2;
914 secys[3] = (ct*f[0] - at*f[2])* ph2;
915 seczs[3] = (at*f[1] - bt*f[0])* ph2;
916 a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird;
917 b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird;
918 c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird;
920 est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2]))
921 + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2]))
922 + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2]));
924 if (est > kdlt && TMath::Abs(h) > 1.e-4) {
925 if (ncut++ > maxcut) break;
931 // * if too many iterations, go to helix
932 if (iter++ > maxit) break;
937 cba = 1./ TMath::Sqrt(a*a + b*b + c*c);
945 if (step < 0.) rest = -rest;
946 if (rest < 1.e-5*TMath::Abs(step)) return;
950 // angle too big, use helix
955 f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3);
964 hxp[0] = f2*vect[kipz] - f3*vect[kipy];
965 hxp[1] = f3*vect[kipx] - f1*vect[kipz];
966 hxp[2] = f1*vect[kipy] - f2*vect[kipx];
968 hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz];
971 sint = TMath::Sin(tet);
972 cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet);
976 g3 = (tet-sint) * hp*rho1;
981 vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1;
982 vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2;
983 vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3;
985 vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1;
986 vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2;
987 vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3;
991 //___________________________________________________________
992 void AliMUONTrackParam::GetField(Double_t *Position, Double_t *Field) const
994 // interface to "gAlice->Field()->Field" for arguments in double precision
998 x[0] = Position[0]; x[1] = Position[1]; x[2] = Position[2];
1000 gAlice->Field()->Field(x, b);
1001 Field[0] = b[0]; Field[1] = b[1]; Field[2] = b[2];