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c04e3238 | 1 | /************************************************************************** |
2 | * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * | |
3 | * * | |
4 | * Author: The ALICE Off-line Project. * | |
5 | * Contributors are mentioned in the code where appropriate. * | |
6 | * * | |
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 | **************************************************************************/ | |
15 | ||
16 | /* $Id$ */ | |
17 | ||
56316147 | 18 | //----------------------------------------------------------------------------- |
19 | // Class AliMUONTrackExtrap | |
20 | // ------------------------ | |
21 | // Tools for track extrapolation in ALICE dimuon spectrometer | |
22 | // Author: Philippe Pillot | |
23 | //----------------------------------------------------------------------------- | |
c04e3238 | 24 | |
c04e3238 | 25 | #include "AliMUONTrackExtrap.h" |
26 | #include "AliMUONTrackParam.h" | |
27 | #include "AliMUONConstants.h" | |
0e894e58 | 28 | #include "AliMUONReconstructor.h" |
8cde4af5 | 29 | |
ecdf58c4 | 30 | #include "AliMagF.h" |
31 | #include "AliExternalTrackParam.h" | |
8cde4af5 | 32 | |
f7a1cc68 | 33 | #include <TGeoGlobalMagField.h> |
8cde4af5 | 34 | #include <TGeoManager.h> |
f7a1cc68 | 35 | #include <TMath.h> |
ecdf58c4 | 36 | #include <TDatabasePDG.h> |
c04e3238 | 37 | |
ea94c18b | 38 | #include <Riostream.h> |
39 | ||
78649106 | 40 | /// \cond CLASSIMP |
c04e3238 | 41 | ClassImp(AliMUONTrackExtrap) // Class implementation in ROOT context |
78649106 | 42 | /// \endcond |
c04e3238 | 43 | |
9f093251 | 44 | const Double_t AliMUONTrackExtrap::fgkSimpleBPosition = 0.5 * (AliMUONConstants::CoilZ() + AliMUONConstants::YokeZ()); |
45 | const Double_t AliMUONTrackExtrap::fgkSimpleBLength = 0.5 * (AliMUONConstants::CoilL() + AliMUONConstants::YokeL()); | |
46 | Double_t AliMUONTrackExtrap::fgSimpleBValue = 0.; | |
47 | Bool_t AliMUONTrackExtrap::fgFieldON = kFALSE; | |
4284483e | 48 | const Bool_t AliMUONTrackExtrap::fgkUseHelix = kFALSE; |
208f139e | 49 | const Int_t AliMUONTrackExtrap::fgkMaxStepNumber = 5000; |
4284483e | 50 | const Double_t AliMUONTrackExtrap::fgkHelixStepLength = 6.; |
51 | const Double_t AliMUONTrackExtrap::fgkRungeKuttaMaxResidue = 0.002; | |
208f139e | 52 | |
9f093251 | 53 | //__________________________________________________________________________ |
f7a1cc68 | 54 | void AliMUONTrackExtrap::SetField() |
9f093251 | 55 | { |
cddcc1f3 | 56 | /// set field on/off flag; |
57 | /// set field at the centre of the dipole | |
f7a1cc68 | 58 | const Double_t x[3] = {50.,50.,fgkSimpleBPosition}; |
59 | Double_t b[3] = {0.,0.,0.}; | |
60 | TGeoGlobalMagField::Instance()->Field(x,b); | |
61 | fgSimpleBValue = b[0]; | |
62 | fgFieldON = fgSimpleBValue ? kTRUE : kFALSE; | |
9f093251 | 63 | |
64 | } | |
65 | ||
690d2205 | 66 | //__________________________________________________________________________ |
208f139e | 67 | Double_t AliMUONTrackExtrap::GetImpactParamFromBendingMomentum(Double_t bendingMomentum) |
68 | { | |
69 | /// Returns impact parameter at vertex in bending plane (cm), | |
70 | /// from the signed bending momentum "BendingMomentum" in bending plane (GeV/c), | |
71 | /// using simple values for dipole magnetic field. | |
72 | /// The sign of "BendingMomentum" is the sign of the charge. | |
73 | ||
74 | if (bendingMomentum == 0.) return 1.e10; | |
75 | ||
6b191dea | 76 | const Double_t kCorrectionFactor = 1.1; // impact parameter is 10% underestimated |
9f093251 | 77 | |
78 | return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / bendingMomentum); | |
208f139e | 79 | } |
80 | ||
690d2205 | 81 | //__________________________________________________________________________ |
9bdbee64 | 82 | Double_t |
83 | AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(Double_t impactParam) | |
208f139e | 84 | { |
85 | /// Returns signed bending momentum in bending plane (GeV/c), | |
86 | /// the sign being the sign of the charge for particles moving forward in Z, | |
87 | /// from the impact parameter "ImpactParam" at vertex in bending plane (cm), | |
88 | /// using simple values for dipole magnetic field. | |
89 | ||
90 | if (impactParam == 0.) return 1.e10; | |
91 | ||
9f093251 | 92 | const Double_t kCorrectionFactor = 1.1; // bending momentum is 10% underestimated |
93 | ||
9bdbee64 | 94 | if (fgFieldON) |
95 | { | |
96 | return kCorrectionFactor * (-0.0003 * fgSimpleBValue * fgkSimpleBLength * fgkSimpleBPosition / impactParam); | |
97 | } | |
98 | else | |
99 | { | |
100 | return AliMUONConstants::GetMostProbBendingMomentum(); | |
101 | } | |
019df241 | 102 | } |
103 | ||
690d2205 | 104 | //__________________________________________________________________________ |
3fe6651e | 105 | void AliMUONTrackExtrap::LinearExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd) |
019df241 | 106 | { |
3fe6651e | 107 | /// Track parameters linearly extrapolated to the plane at "zEnd". |
019df241 | 108 | /// On return, results from the extrapolation are updated in trackParam. |
109 | ||
110 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z | |
111 | ||
112 | // Compute track parameters | |
113 | Double_t dZ = zEnd - trackParam->GetZ(); | |
114 | trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ); | |
115 | trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ); | |
116 | trackParam->SetZ(zEnd); | |
3fe6651e | 117 | } |
118 | ||
119 | //__________________________________________________________________________ | |
120 | void AliMUONTrackExtrap::LinearExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator) | |
121 | { | |
122 | /// Track parameters and their covariances linearly extrapolated to the plane at "zEnd". | |
123 | /// On return, results from the extrapolation are updated in trackParam. | |
019df241 | 124 | |
3fe6651e | 125 | if (trackParam->GetZ() == zEnd) return; // nothing to be done if same z |
126 | ||
127 | // No need to propagate the covariance matrix if it does not exist | |
128 | if (!trackParam->CovariancesExist()) { | |
129 | cout<<"W-AliMUONTrackExtrap::LinearExtrapToZCov: Covariance matrix does not exist"<<endl; | |
130 | // Extrapolate linearly track parameters to "zEnd" | |
131 | LinearExtrapToZ(trackParam,zEnd); | |
132 | return; | |
019df241 | 133 | } |
134 | ||
3fe6651e | 135 | // Compute track parameters |
136 | Double_t dZ = zEnd - trackParam->GetZ(); | |
137 | trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + trackParam->GetNonBendingSlope() * dZ); | |
138 | trackParam->SetBendingCoor(trackParam->GetBendingCoor() + trackParam->GetBendingSlope() * dZ); | |
139 | trackParam->SetZ(zEnd); | |
140 | ||
141 | // Calculate the jacobian related to the track parameters linear extrapolation to "zEnd" | |
142 | TMatrixD jacob(5,5); | |
143 | jacob.UnitMatrix(); | |
144 | jacob(0,1) = dZ; | |
145 | jacob(2,3) = dZ; | |
146 | ||
147 | // Extrapolate track parameter covariances to "zEnd" | |
148 | TMatrixD tmp(trackParam->GetCovariances(),TMatrixD::kMultTranspose,jacob); | |
149 | TMatrixD tmp2(jacob,TMatrixD::kMult,tmp); | |
150 | trackParam->SetCovariances(tmp2); | |
151 | ||
152 | // Update the propagator if required | |
153 | if (updatePropagator) trackParam->UpdatePropagator(jacob); | |
208f139e | 154 | } |
c04e3238 | 155 | |
690d2205 | 156 | //__________________________________________________________________________ |
4ea3f013 | 157 | Bool_t AliMUONTrackExtrap::ExtrapToZ(AliMUONTrackParam* trackParam, Double_t zEnd) |
c04e3238 | 158 | { |
4284483e | 159 | /// Interface to track parameter extrapolation to the plane at "Z" using Helix or Rungekutta algorithm. |
160 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. | |
4ea3f013 | 161 | if (!fgFieldON) { |
162 | AliMUONTrackExtrap::LinearExtrapToZ(trackParam,zEnd); | |
163 | return kTRUE; | |
164 | } | |
165 | else if (fgkUseHelix) return AliMUONTrackExtrap::ExtrapToZHelix(trackParam,zEnd); | |
166 | else return AliMUONTrackExtrap::ExtrapToZRungekutta(trackParam,zEnd); | |
4284483e | 167 | } |
168 | ||
690d2205 | 169 | //__________________________________________________________________________ |
4ea3f013 | 170 | Bool_t AliMUONTrackExtrap::ExtrapToZHelix(AliMUONTrackParam* trackParam, Double_t zEnd) |
4284483e | 171 | { |
172 | /// Track parameter extrapolation to the plane at "Z" using Helix algorithm. | |
c04e3238 | 173 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. |
4ea3f013 | 174 | if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z |
c04e3238 | 175 | Double_t forwardBackward; // +1 if forward, -1 if backward |
176 | if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 | |
177 | else forwardBackward = -1.0; | |
dade8580 | 178 | Double_t v3[7], v3New[7]; // 7 in parameter ???? |
179 | Int_t i3, stepNumber; | |
c04e3238 | 180 | // For safety: return kTRUE or kFALSE ???? |
181 | // Parameter vector for calling EXTRAP_ONESTEP | |
4284483e | 182 | ConvertTrackParamForExtrap(trackParam, forwardBackward, v3); |
c04e3238 | 183 | // sign of charge (sign of fInverseBendingMomentum if forward motion) |
184 | // must be changed if backward extrapolation | |
208f139e | 185 | Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); |
c04e3238 | 186 | // Extrapolation loop |
187 | stepNumber = 0; | |
208f139e | 188 | while (((-forwardBackward * (v3[2] - zEnd)) <= 0.0) && (stepNumber < fgkMaxStepNumber)) { // spectro. z<0 |
c04e3238 | 189 | stepNumber++; |
4284483e | 190 | ExtrapOneStepHelix(chargeExtrap, fgkHelixStepLength, v3, v3New); |
dade8580 | 191 | if ((-forwardBackward * (v3New[2] - zEnd)) > 0.0) break; // one is beyond Z spectro. z<0 |
690d2205 | 192 | // better use TArray ???? |
208f139e | 193 | for (i3 = 0; i3 < 7; i3++) {v3[i3] = v3New[i3];} |
c04e3238 | 194 | } |
208f139e | 195 | // check fgkMaxStepNumber ???? |
c04e3238 | 196 | // Interpolation back to exact Z (2nd order) |
197 | // should be in function ???? using TArray ???? | |
dade8580 | 198 | Double_t dZ12 = v3New[2] - v3[2]; // 1->2 |
c04e3238 | 199 | if (TMath::Abs(dZ12) > 0) { |
dade8580 | 200 | Double_t dZ1i = zEnd - v3[2]; // 1-i |
201 | Double_t dZi2 = v3New[2] - zEnd; // i->2 | |
202 | Double_t xPrime = (v3New[0] - v3[0]) / dZ12; | |
203 | Double_t xSecond = ((v3New[3] / v3New[5]) - (v3[3] / v3[5])) / dZ12; | |
204 | Double_t yPrime = (v3New[1] - v3[1]) / dZ12; | |
205 | Double_t ySecond = ((v3New[4] / v3New[5]) - (v3[4] / v3[5])) / dZ12; | |
206 | v3[0] = v3[0] + xPrime * dZ1i - 0.5 * xSecond * dZ1i * dZi2; // X | |
207 | v3[1] = v3[1] + yPrime * dZ1i - 0.5 * ySecond * dZ1i * dZi2; // Y | |
208 | v3[2] = zEnd; // Z | |
c04e3238 | 209 | Double_t xPrimeI = xPrime - 0.5 * xSecond * (dZi2 - dZ1i); |
210 | Double_t yPrimeI = yPrime - 0.5 * ySecond * (dZi2 - dZ1i); | |
211 | // (PX, PY, PZ)/PTOT assuming forward motion | |
208f139e | 212 | v3[5] = 1.0 / TMath::Sqrt(1.0 + xPrimeI * xPrimeI + yPrimeI * yPrimeI); // PZ/PTOT |
dade8580 | 213 | v3[3] = xPrimeI * v3[5]; // PX/PTOT |
214 | v3[4] = yPrimeI * v3[5]; // PY/PTOT | |
c04e3238 | 215 | } else { |
4284483e | 216 | cout<<"W-AliMUONTrackExtrap::ExtrapToZHelix: Extrap. to Z not reached, Z = "<<zEnd<<endl; |
c04e3238 | 217 | } |
4284483e | 218 | // Recover track parameters (charge back for forward motion) |
dade8580 | 219 | RecoverTrackParam(v3, chargeExtrap * forwardBackward, trackParam); |
4ea3f013 | 220 | return kTRUE; |
c04e3238 | 221 | } |
222 | ||
690d2205 | 223 | //__________________________________________________________________________ |
4ea3f013 | 224 | Bool_t AliMUONTrackExtrap::ExtrapToZRungekutta(AliMUONTrackParam* trackParam, Double_t zEnd) |
4284483e | 225 | { |
226 | /// Track parameter extrapolation to the plane at "Z" using Rungekutta algorithm. | |
227 | /// On return, the track parameters resulting from the extrapolation are updated in trackParam. | |
4ea3f013 | 228 | if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same Z |
4284483e | 229 | Double_t forwardBackward; // +1 if forward, -1 if backward |
230 | if (zEnd < trackParam->GetZ()) forwardBackward = 1.0; // spectro. z<0 | |
231 | else forwardBackward = -1.0; | |
232 | // sign of charge (sign of fInverseBendingMomentum if forward motion) | |
233 | // must be changed if backward extrapolation | |
234 | Double_t chargeExtrap = forwardBackward * TMath::Sign(Double_t(1.0), trackParam->GetInverseBendingMomentum()); | |
235 | Double_t v3[7], v3New[7]; | |
236 | Double_t dZ, step; | |
237 | Int_t stepNumber = 0; | |
238 | ||
4ea3f013 | 239 | // Extrapolation loop (until within tolerance or the track turn around) |
4284483e | 240 | Double_t residue = zEnd - trackParam->GetZ(); |
4ea3f013 | 241 | Bool_t uturn = kFALSE; |
242 | Bool_t tooManyStep = kFALSE; | |
4284483e | 243 | while (TMath::Abs(residue) > fgkRungeKuttaMaxResidue && stepNumber <= fgkMaxStepNumber) { |
4ea3f013 | 244 | |
4284483e | 245 | dZ = zEnd - trackParam->GetZ(); |
246 | // step lenght assuming linear trajectory | |
247 | step = dZ * TMath::Sqrt(1.0 + trackParam->GetBendingSlope()*trackParam->GetBendingSlope() + | |
690d2205 | 248 | trackParam->GetNonBendingSlope()*trackParam->GetNonBendingSlope()); |
4284483e | 249 | ConvertTrackParamForExtrap(trackParam, forwardBackward, v3); |
4ea3f013 | 250 | |
4284483e | 251 | do { // reduce step lenght while zEnd oversteped |
252 | if (stepNumber > fgkMaxStepNumber) { | |
253 | cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: Too many trials: "<<stepNumber<<endl; | |
4ea3f013 | 254 | tooManyStep = kTRUE; |
4284483e | 255 | break; |
256 | } | |
257 | stepNumber ++; | |
258 | step = TMath::Abs(step); | |
259 | AliMUONTrackExtrap::ExtrapOneStepRungekutta(chargeExtrap,step,v3,v3New); | |
260 | residue = zEnd - v3New[2]; | |
261 | step *= dZ/(v3New[2]-trackParam->GetZ()); | |
262 | } while (residue*dZ < 0 && TMath::Abs(residue) > fgkRungeKuttaMaxResidue); | |
4ea3f013 | 263 | |
264 | if (v3New[5]*v3[5] < 0) { // the track turned around | |
265 | cout<<"W-AliMUONTrackExtrap::ExtrapToZRungekutta: The track turned around"<<endl; | |
266 | uturn = kTRUE; | |
267 | break; | |
268 | } else RecoverTrackParam(v3New, chargeExtrap * forwardBackward, trackParam); | |
269 | ||
4284483e | 270 | } |
271 | ||
272 | // terminate the extropolation with a straight line up to the exact "zEnd" value | |
4ea3f013 | 273 | if (uturn) { |
274 | ||
275 | // track ends +-100 meters away in the bending direction | |
276 | dZ = zEnd - v3[2]; | |
277 | Double_t bendingSlope = TMath::Sign(1.e4,-fgSimpleBValue*trackParam->GetInverseBendingMomentum()) / dZ; | |
278 | Double_t pZ = TMath::Abs(1. / trackParam->GetInverseBendingMomentum()) / TMath::Sqrt(1.0 + bendingSlope * bendingSlope); | |
279 | Double_t nonBendingSlope = TMath::Sign(TMath::Abs(v3[3]) * v3[6] / pZ, trackParam->GetNonBendingSlope()); | |
280 | trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + dZ * nonBendingSlope); | |
281 | trackParam->SetNonBendingSlope(nonBendingSlope); | |
282 | trackParam->SetBendingCoor(trackParam->GetBendingCoor() + dZ * bendingSlope); | |
283 | trackParam->SetBendingSlope(bendingSlope); | |
284 | trackParam->SetZ(zEnd); | |
285 | ||
286 | return kFALSE; | |
287 | ||
288 | } else { | |
289 | ||
290 | // track extrapolated normally | |
291 | trackParam->SetNonBendingCoor(trackParam->GetNonBendingCoor() + residue * trackParam->GetNonBendingSlope()); | |
292 | trackParam->SetBendingCoor(trackParam->GetBendingCoor() + residue * trackParam->GetBendingSlope()); | |
293 | trackParam->SetZ(zEnd); | |
294 | ||
295 | return !tooManyStep; | |
296 | ||
297 | } | |
298 | ||
4284483e | 299 | } |
300 | ||
690d2205 | 301 | //__________________________________________________________________________ |
4284483e | 302 | void AliMUONTrackExtrap::ConvertTrackParamForExtrap(AliMUONTrackParam* trackParam, Double_t forwardBackward, Double_t *v3) |
c04e3238 | 303 | { |
dade8580 | 304 | /// Set vector of Geant3 parameters pointed to by "v3" from track parameters in trackParam. |
c04e3238 | 305 | /// Since AliMUONTrackParam is only geometry, one uses "forwardBackward" |
306 | /// to know whether the particle is going forward (+1) or backward (-1). | |
dade8580 | 307 | v3[0] = trackParam->GetNonBendingCoor(); // X |
308 | v3[1] = trackParam->GetBendingCoor(); // Y | |
309 | v3[2] = trackParam->GetZ(); // Z | |
c04e3238 | 310 | Double_t pYZ = TMath::Abs(1.0 / trackParam->GetInverseBendingMomentum()); |
311 | Double_t pZ = pYZ / TMath::Sqrt(1.0 + trackParam->GetBendingSlope() * trackParam->GetBendingSlope()); | |
dade8580 | 312 | v3[6] = TMath::Sqrt(pYZ * pYZ + pZ * pZ * trackParam->GetNonBendingSlope() * trackParam->GetNonBendingSlope()); // PTOT |
313 | v3[5] = -forwardBackward * pZ / v3[6]; // PZ/PTOT spectro. z<0 | |
314 | v3[3] = trackParam->GetNonBendingSlope() * v3[5]; // PX/PTOT | |
315 | v3[4] = trackParam->GetBendingSlope() * v3[5]; // PY/PTOT | |
c04e3238 | 316 | } |
317 | ||
690d2205 | 318 | //__________________________________________________________________________ |
dade8580 | 319 | void AliMUONTrackExtrap::RecoverTrackParam(Double_t *v3, Double_t charge, AliMUONTrackParam* trackParam) |
c04e3238 | 320 | { |
dade8580 | 321 | /// Set track parameters in trackParam from Geant3 parameters pointed to by "v3", |
c04e3238 | 322 | /// assumed to be calculated for forward motion in Z. |
323 | /// "InverseBendingMomentum" is signed with "charge". | |
dade8580 | 324 | trackParam->SetNonBendingCoor(v3[0]); // X |
325 | trackParam->SetBendingCoor(v3[1]); // Y | |
326 | trackParam->SetZ(v3[2]); // Z | |
60e55aee | 327 | Double_t pYZ = v3[6] * TMath::Sqrt((1.-v3[3])*(1.+v3[3])); |
c04e3238 | 328 | trackParam->SetInverseBendingMomentum(charge/pYZ); |
dade8580 | 329 | trackParam->SetBendingSlope(v3[4]/v3[5]); |
330 | trackParam->SetNonBendingSlope(v3[3]/v3[5]); | |
208f139e | 331 | } |
332 | ||
690d2205 | 333 | //__________________________________________________________________________ |
4ea3f013 | 334 | Bool_t AliMUONTrackExtrap::ExtrapToZCov(AliMUONTrackParam* trackParam, Double_t zEnd, Bool_t updatePropagator) |
208f139e | 335 | { |
336 | /// Track parameters and their covariances extrapolated to the plane at "zEnd". | |
337 | /// On return, results from the extrapolation are updated in trackParam. | |
338 | ||
4ea3f013 | 339 | if (trackParam->GetZ() == zEnd) return kTRUE; // nothing to be done if same z |
208f139e | 340 | |
9f093251 | 341 | if (!fgFieldON) { // linear extrapolation if no magnetic field |
3fe6651e | 342 | AliMUONTrackExtrap::LinearExtrapToZCov(trackParam,zEnd,updatePropagator); |
4ea3f013 | 343 | return kTRUE; |
9f093251 | 344 | } |
345 | ||
ea94c18b | 346 | // No need to propagate the covariance matrix if it does not exist |
347 | if (!trackParam->CovariancesExist()) { | |
348 | cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Covariance matrix does not exist"<<endl; | |
349 | // Extrapolate track parameters to "zEnd" | |
4ea3f013 | 350 | return ExtrapToZ(trackParam,zEnd); |
ea94c18b | 351 | } |
352 | ||
208f139e | 353 | // Save the actual track parameters |
354 | AliMUONTrackParam trackParamSave(*trackParam); | |
ea94c18b | 355 | TMatrixD paramSave(trackParamSave.GetParameters()); |
356 | Double_t zBegin = trackParamSave.GetZ(); | |
357 | ||
358 | // Get reference to the parameter covariance matrix | |
359 | const TMatrixD& kParamCov = trackParam->GetCovariances(); | |
9bf6860b | 360 | |
208f139e | 361 | // Extrapolate track parameters to "zEnd" |
4ea3f013 | 362 | // Do not update the covariance matrix if the extrapolation failed |
363 | if (!ExtrapToZ(trackParam,zEnd)) return kFALSE; | |
208f139e | 364 | |
ea94c18b | 365 | // Get reference to the extrapolated parameters |
366 | const TMatrixD& extrapParam = trackParam->GetParameters(); | |
208f139e | 367 | |
368 | // Calculate the jacobian related to the track parameters extrapolation to "zEnd" | |
4ea3f013 | 369 | Bool_t extrapStatus = kTRUE; |
208f139e | 370 | TMatrixD jacob(5,5); |
ea94c18b | 371 | jacob.Zero(); |
372 | TMatrixD dParam(5,1); | |
6b191dea | 373 | Double_t direction[5] = {-1.,-1.,1.,1.,-1.}; |
208f139e | 374 | for (Int_t i=0; i<5; i++) { |
375 | // Skip jacobian calculation for parameters with no associated error | |
18abc511 | 376 | if (kParamCov(i,i) <= 0.) continue; |
ea94c18b | 377 | |
208f139e | 378 | // Small variation of parameter i only |
379 | for (Int_t j=0; j<5; j++) { | |
380 | if (j==i) { | |
ea94c18b | 381 | dParam(j,0) = TMath::Sqrt(kParamCov(i,i)); |
6b191dea | 382 | dParam(j,0) *= TMath::Sign(1.,direction[j]*paramSave(j,0)); // variation always in the same direction |
ea94c18b | 383 | } else dParam(j,0) = 0.; |
208f139e | 384 | } |
ea94c18b | 385 | |
208f139e | 386 | // Set new parameters |
ea94c18b | 387 | trackParamSave.SetParameters(paramSave); |
388 | trackParamSave.AddParameters(dParam); | |
389 | trackParamSave.SetZ(zBegin); | |
390 | ||
208f139e | 391 | // Extrapolate new track parameters to "zEnd" |
4ea3f013 | 392 | if (!ExtrapToZ(&trackParamSave,zEnd)) { |
393 | cout<<"W-AliMUONTrackExtrap::ExtrapToZCov: Bad covariance matrix"<<endl; | |
394 | extrapStatus = kFALSE; | |
395 | } | |
ea94c18b | 396 | |
208f139e | 397 | // Calculate the jacobian |
ea94c18b | 398 | TMatrixD jacobji(trackParamSave.GetParameters(),TMatrixD::kMinus,extrapParam); |
399 | jacobji *= 1. / dParam(i,0); | |
400 | jacob.SetSub(0,i,jacobji); | |
208f139e | 401 | } |
402 | ||
403 | // Extrapolate track parameter covariances to "zEnd" | |
ea94c18b | 404 | TMatrixD tmp(kParamCov,TMatrixD::kMultTranspose,jacob); |
405 | TMatrixD tmp2(jacob,TMatrixD::kMult,tmp); | |
406 | trackParam->SetCovariances(tmp2); | |
407 | ||
408 | // Update the propagator if required | |
409 | if (updatePropagator) trackParam->UpdatePropagator(jacob); | |
4ea3f013 | 410 | |
411 | return extrapStatus; | |
208f139e | 412 | } |
413 | ||
690d2205 | 414 | //__________________________________________________________________________ |
37a615ac | 415 | void AliMUONTrackExtrap::AddMCSEffectInAbsorber(AliMUONTrackParam* param, Double_t signedPathLength, Double_t f0, Double_t f1, Double_t f2) |
8cde4af5 | 416 | { |
417 | /// Add to the track parameter covariances the effects of multiple Coulomb scattering | |
37a615ac | 418 | /// signedPathLength must have the sign of (zOut - zIn) where all other parameters are assumed to be given at zOut. |
8cde4af5 | 419 | |
420 | // absorber related covariance parameters | |
421 | Double_t bendingSlope = param->GetBendingSlope(); | |
422 | Double_t nonBendingSlope = param->GetNonBendingSlope(); | |
423 | Double_t inverseBendingMomentum = param->GetInverseBendingMomentum(); | |
424 | Double_t alpha2 = 0.0136 * 0.0136 * inverseBendingMomentum * inverseBendingMomentum * (1.0 + bendingSlope * bendingSlope) / | |
690d2205 | 425 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); // velocity = 1 |
37a615ac | 426 | Double_t pathLength = TMath::Abs(signedPathLength); |
8cde4af5 | 427 | Double_t varCoor = alpha2 * (pathLength * pathLength * f0 - 2. * pathLength * f1 + f2); |
37a615ac | 428 | Double_t covCorrSlope = TMath::Sign(1.,signedPathLength) * alpha2 * (pathLength * f0 - f1); |
8cde4af5 | 429 | Double_t varSlop = alpha2 * f0; |
430 | ||
690d2205 | 431 | // Set MCS covariance matrix |
ea94c18b | 432 | TMatrixD newParamCov(param->GetCovariances()); |
8cde4af5 | 433 | // Non bending plane |
ea94c18b | 434 | newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope; |
435 | newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop; | |
8cde4af5 | 436 | // Bending plane |
ea94c18b | 437 | newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope; |
438 | newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop; | |
c24543a2 | 439 | |
440 | // Set momentum related covariances if B!=0 | |
441 | if (fgFieldON) { | |
442 | // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY | |
443 | Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
444 | Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope / | |
445 | (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
446 | // Inverse bending momentum (due to dependences with bending and non bending slopes) | |
447 | newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope; | |
448 | newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop; | |
449 | newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope; | |
450 | newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop; | |
451 | newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop; | |
452 | } | |
ea94c18b | 453 | |
454 | // Set new covariances | |
455 | param->SetCovariances(newParamCov); | |
690d2205 | 456 | } |
457 | ||
458 | //__________________________________________________________________________ | |
459 | void AliMUONTrackExtrap::CorrectMCSEffectInAbsorber(AliMUONTrackParam* param, | |
460 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
461 | Double_t errXVtx, Double_t errYVtx, | |
462 | Double_t absZBeg, Double_t pathLength, Double_t f0, Double_t f1, Double_t f2) | |
463 | { | |
464 | /// Correct parameters and corresponding covariances using Branson correction | |
465 | /// - input param are parameters and covariances at the end of absorber | |
466 | /// - output param are parameters and covariances at vertex | |
467 | /// Absorber correction parameters are supposed to be calculated at the current track z-position | |
468 | ||
469 | // Position of the Branson plane (spectro. (z<0)) | |
470 | Double_t zB = (f1>0.) ? absZBeg - f2/f1 : 0.; | |
471 | ||
37a615ac | 472 | // Add MCS effects to current parameter covariances (spectro. (z<0)) |
473 | AddMCSEffectInAbsorber(param, -pathLength, f0, f1, f2); | |
690d2205 | 474 | |
475 | // Get track parameters and covariances in the Branson plane corrected for magnetic field effect | |
476 | ExtrapToZCov(param,zVtx); | |
3fe6651e | 477 | LinearExtrapToZCov(param,zB); |
690d2205 | 478 | |
479 | // compute track parameters at vertex | |
480 | TMatrixD newParam(5,1); | |
481 | newParam(0,0) = xVtx; | |
482 | newParam(1,0) = (param->GetNonBendingCoor() - xVtx) / (zB - zVtx); | |
483 | newParam(2,0) = yVtx; | |
484 | newParam(3,0) = (param->GetBendingCoor() - yVtx) / (zB - zVtx); | |
485 | newParam(4,0) = param->GetCharge() / param->P() * | |
486 | TMath::Sqrt(1.0 + newParam(1,0)*newParam(1,0) + newParam(3,0)*newParam(3,0)) / | |
487 | TMath::Sqrt(1.0 + newParam(3,0)*newParam(3,0)); | |
488 | ||
489 | // Get covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system | |
490 | TMatrixD paramCovP(param->GetCovariances()); | |
491 | Cov2CovP(param->GetParameters(),paramCovP); | |
492 | ||
493 | // Get the covariance matrix in the (XVtx, X, YVtx, Y, q*PTot) coordinate system | |
494 | TMatrixD paramCovVtx(5,5); | |
495 | paramCovVtx.Zero(); | |
496 | paramCovVtx(0,0) = errXVtx * errXVtx; | |
497 | paramCovVtx(1,1) = paramCovP(0,0); | |
498 | paramCovVtx(2,2) = errYVtx * errYVtx; | |
499 | paramCovVtx(3,3) = paramCovP(2,2); | |
500 | paramCovVtx(4,4) = paramCovP(4,4); | |
501 | paramCovVtx(1,3) = paramCovP(0,2); | |
502 | paramCovVtx(3,1) = paramCovP(2,0); | |
503 | paramCovVtx(1,4) = paramCovP(0,4); | |
504 | paramCovVtx(4,1) = paramCovP(4,0); | |
505 | paramCovVtx(3,4) = paramCovP(2,4); | |
506 | paramCovVtx(4,3) = paramCovP(4,2); | |
507 | ||
508 | // Jacobian of the transformation (XVtx, X, YVtx, Y, q*PTot) -> (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) | |
509 | TMatrixD jacob(5,5); | |
510 | jacob.UnitMatrix(); | |
511 | jacob(1,0) = - 1. / (zB - zVtx); | |
512 | jacob(1,1) = 1. / (zB - zVtx); | |
513 | jacob(3,2) = - 1. / (zB - zVtx); | |
514 | jacob(3,3) = 1. / (zB - zVtx); | |
8cde4af5 | 515 | |
690d2205 | 516 | // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q*PTotVtx) coordinate system |
517 | TMatrixD tmp(paramCovVtx,TMatrixD::kMultTranspose,jacob); | |
518 | TMatrixD newParamCov(jacob,TMatrixD::kMult,tmp); | |
519 | ||
520 | // Compute covariances at vertex in the (XVtx, SlopeXVtx, YVtx, SlopeYVtx, q/PyzVtx) coordinate system | |
521 | CovP2Cov(newParam,newParamCov); | |
522 | ||
523 | // Set parameters and covariances at vertex | |
524 | param->SetParameters(newParam); | |
525 | param->SetZ(zVtx); | |
526 | param->SetCovariances(newParamCov); | |
8cde4af5 | 527 | } |
528 | ||
690d2205 | 529 | //__________________________________________________________________________ |
530 | void AliMUONTrackExtrap::CorrectELossEffectInAbsorber(AliMUONTrackParam* param, Double_t eLoss, Double_t sigmaELoss2) | |
531 | { | |
532 | /// Correct parameters for energy loss and add energy loss fluctuation effect to covariances | |
533 | ||
534 | // Get parameter covariances in (X, SlopeX, Y, SlopeY, q*PTot) coordinate system | |
535 | TMatrixD newParamCov(param->GetCovariances()); | |
536 | Cov2CovP(param->GetParameters(),newParamCov); | |
537 | ||
690d2205 | 538 | // Compute new parameters corrected for energy loss |
ecdf58c4 | 539 | Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV |
540 | Double_t p = param->P(); | |
541 | Double_t e = TMath::Sqrt(p*p + muMass*muMass); | |
542 | Double_t eCorr = e + eLoss; | |
543 | Double_t pCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass); | |
690d2205 | 544 | Double_t nonBendingSlope = param->GetNonBendingSlope(); |
545 | Double_t bendingSlope = param->GetBendingSlope(); | |
ecdf58c4 | 546 | param->SetInverseBendingMomentum(param->GetCharge() / pCorr * |
690d2205 | 547 | TMath::Sqrt(1.0 + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope) / |
548 | TMath::Sqrt(1.0 + bendingSlope*bendingSlope)); | |
549 | ||
ecdf58c4 | 550 | // Add effects of energy loss fluctuation to covariances |
551 | newParamCov(4,4) += eCorr * eCorr / pCorr / pCorr * sigmaELoss2; | |
552 | ||
690d2205 | 553 | // Get new parameter covariances in (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system |
554 | CovP2Cov(param->GetParameters(),newParamCov); | |
555 | ||
556 | // Set new parameter covariances | |
557 | param->SetCovariances(newParamCov); | |
558 | } | |
559 | ||
560 | //__________________________________________________________________________ | |
18abc511 | 561 | Bool_t AliMUONTrackExtrap::GetAbsorberCorrectionParam(Double_t trackXYZIn[3], Double_t trackXYZOut[3], Double_t pTotal, |
562 | Double_t &pathLength, Double_t &f0, Double_t &f1, Double_t &f2, | |
563 | Double_t &meanRho, Double_t &totalELoss, Double_t &sigmaELoss2) | |
8cde4af5 | 564 | { |
565 | /// Parameters used to correct for Multiple Coulomb Scattering and energy loss in absorber | |
690d2205 | 566 | /// Calculated assuming a linear propagation from trackXYZIn to trackXYZOut (order is important) |
8cde4af5 | 567 | // pathLength: path length between trackXYZIn and trackXYZOut (cm) |
568 | // f0: 0th moment of z calculated with the inverse radiation-length distribution | |
569 | // f1: 1st moment of z calculated with the inverse radiation-length distribution | |
570 | // f2: 2nd moment of z calculated with the inverse radiation-length distribution | |
571 | // meanRho: average density of crossed material (g/cm3) | |
84f061ef | 572 | // totalELoss: total energy loss in absorber |
8cde4af5 | 573 | |
574 | // Reset absorber's parameters | |
575 | pathLength = 0.; | |
576 | f0 = 0.; | |
577 | f1 = 0.; | |
578 | f2 = 0.; | |
579 | meanRho = 0.; | |
84f061ef | 580 | totalELoss = 0.; |
690d2205 | 581 | sigmaELoss2 = 0.; |
8cde4af5 | 582 | |
583 | // Check whether the geometry is available | |
584 | if (!gGeoManager) { | |
585 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: no TGeo"<<endl; | |
18abc511 | 586 | return kFALSE; |
8cde4af5 | 587 | } |
588 | ||
589 | // Initialize starting point and direction | |
590 | pathLength = TMath::Sqrt((trackXYZOut[0] - trackXYZIn[0])*(trackXYZOut[0] - trackXYZIn[0])+ | |
591 | (trackXYZOut[1] - trackXYZIn[1])*(trackXYZOut[1] - trackXYZIn[1])+ | |
592 | (trackXYZOut[2] - trackXYZIn[2])*(trackXYZOut[2] - trackXYZIn[2])); | |
18abc511 | 593 | if (pathLength < TGeoShape::Tolerance()) return kFALSE; |
8cde4af5 | 594 | Double_t b[3]; |
595 | b[0] = (trackXYZOut[0] - trackXYZIn[0]) / pathLength; | |
596 | b[1] = (trackXYZOut[1] - trackXYZIn[1]) / pathLength; | |
597 | b[2] = (trackXYZOut[2] - trackXYZIn[2]) / pathLength; | |
598 | TGeoNode *currentnode = gGeoManager->InitTrack(trackXYZIn, b); | |
599 | if (!currentnode) { | |
600 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: start point out of geometry"<<endl; | |
18abc511 | 601 | return kFALSE; |
8cde4af5 | 602 | } |
603 | ||
604 | // loop over absorber slices and calculate absorber's parameters | |
605 | Double_t rho = 0.; // material density (g/cm3) | |
606 | Double_t x0 = 0.; // radiation-length (cm-1) | |
84f061ef | 607 | Double_t atomicA = 0.; // A of material |
608 | Double_t atomicZ = 0.; // Z of material | |
fa5e35be | 609 | Double_t atomicZoverA = 0.; // Z/A of material |
8cde4af5 | 610 | Double_t localPathLength = 0; |
611 | Double_t remainingPathLength = pathLength; | |
612 | Double_t zB = trackXYZIn[2]; | |
613 | Double_t zE, dzB, dzE; | |
614 | do { | |
615 | // Get material properties | |
616 | TGeoMaterial *material = currentnode->GetVolume()->GetMedium()->GetMaterial(); | |
617 | rho = material->GetDensity(); | |
618 | x0 = material->GetRadLen(); | |
84f061ef | 619 | atomicA = material->GetA(); |
620 | atomicZ = material->GetZ(); | |
fa5e35be | 621 | if(material->IsMixture()){ |
622 | TGeoMixture * mixture = (TGeoMixture*)material; | |
623 | atomicZoverA = 0.; | |
624 | Double_t sum = 0.; | |
625 | for (Int_t iel=0;iel<mixture->GetNelements();iel++){ | |
626 | sum += mixture->GetWmixt()[iel]; | |
627 | atomicZoverA += mixture->GetZmixt()[iel]*mixture->GetWmixt()[iel]/mixture->GetAmixt()[iel]; | |
628 | } | |
629 | atomicZoverA/=sum; | |
630 | } | |
631 | else atomicZoverA = atomicZ/atomicA; | |
8cde4af5 | 632 | |
633 | // Get path length within this material | |
634 | gGeoManager->FindNextBoundary(remainingPathLength); | |
635 | localPathLength = gGeoManager->GetStep() + 1.e-6; | |
636 | // Check if boundary within remaining path length. If so, make sure to cross the boundary to prepare the next step | |
637 | if (localPathLength >= remainingPathLength) localPathLength = remainingPathLength; | |
638 | else { | |
639 | currentnode = gGeoManager->Step(); | |
640 | if (!currentnode) { | |
641 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl; | |
18abc511 | 642 | f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.; |
643 | return kFALSE; | |
8cde4af5 | 644 | } |
645 | if (!gGeoManager->IsEntering()) { | |
646 | // make another small step to try to enter in new absorber slice | |
647 | gGeoManager->SetStep(0.001); | |
648 | currentnode = gGeoManager->Step(); | |
649 | if (!gGeoManager->IsEntering() || !currentnode) { | |
650 | cout<<"E-AliMUONTrackExtrap::GetAbsorberCorrectionParam: navigation failed"<<endl; | |
18abc511 | 651 | f0 = f1 = f2 = meanRho = totalELoss = sigmaELoss2 = 0.; |
652 | return kFALSE; | |
8cde4af5 | 653 | } |
654 | localPathLength += 0.001; | |
655 | } | |
656 | } | |
657 | ||
658 | // calculate absorber's parameters | |
659 | zE = b[2] * localPathLength + zB; | |
660 | dzB = zB - trackXYZIn[2]; | |
661 | dzE = zE - trackXYZIn[2]; | |
662 | f0 += localPathLength / x0; | |
663 | f1 += (dzE*dzE - dzB*dzB) / b[2] / b[2] / x0 / 2.; | |
664 | f2 += (dzE*dzE*dzE - dzB*dzB*dzB) / b[2] / b[2] / b[2] / x0 / 3.; | |
665 | meanRho += localPathLength * rho; | |
fa5e35be | 666 | totalELoss += BetheBloch(pTotal, localPathLength, rho, atomicZ, atomicZoverA); |
667 | sigmaELoss2 += EnergyLossFluctuation2(pTotal, localPathLength, rho, atomicZoverA); | |
8cde4af5 | 668 | |
669 | // prepare next step | |
670 | zB = zE; | |
671 | remainingPathLength -= localPathLength; | |
672 | } while (remainingPathLength > TGeoShape::Tolerance()); | |
673 | ||
674 | meanRho /= pathLength; | |
18abc511 | 675 | |
676 | return kTRUE; | |
8cde4af5 | 677 | } |
678 | ||
690d2205 | 679 | //__________________________________________________________________________ |
ea94c18b | 680 | Double_t AliMUONTrackExtrap::GetMCSAngle2(const AliMUONTrackParam& param, Double_t dZ, Double_t x0) |
681 | { | |
682 | /// Return the angular dispersion square due to multiple Coulomb scattering | |
683 | /// through a material of thickness "dZ" and of radiation length "x0" | |
684 | /// assuming linear propagation and using the small angle approximation. | |
685 | ||
686 | Double_t bendingSlope = param.GetBendingSlope(); | |
687 | Double_t nonBendingSlope = param.GetNonBendingSlope(); | |
688 | Double_t inverseTotalMomentum2 = param.GetInverseBendingMomentum() * param.GetInverseBendingMomentum() * | |
690d2205 | 689 | (1.0 + bendingSlope * bendingSlope) / |
690 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); | |
ea94c18b | 691 | // Path length in the material |
692 | Double_t pathLength = TMath::Abs(dZ) * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope); | |
693 | // relativistic velocity | |
694 | Double_t velo = 1.; | |
695 | // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory | |
696 | Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLength/x0)); | |
697 | ||
698 | return theta02 * theta02 * inverseTotalMomentum2 * pathLength / x0; | |
699 | } | |
700 | ||
690d2205 | 701 | //__________________________________________________________________________ |
8cde4af5 | 702 | void AliMUONTrackExtrap::AddMCSEffect(AliMUONTrackParam *param, Double_t dZ, Double_t x0) |
208f139e | 703 | { |
704 | /// Add to the track parameter covariances the effects of multiple Coulomb scattering | |
37a615ac | 705 | /// through a material of thickness "Abs(dZ)" and of radiation length "x0" |
208f139e | 706 | /// assuming linear propagation and using the small angle approximation. |
37a615ac | 707 | /// dZ = zOut - zIn (sign is important) and "param" is assumed to be given zOut. |
708 | /// If x0 <= 0., assume dZ = pathLength/x0 and consider the material thickness as negligible. | |
208f139e | 709 | |
710 | Double_t bendingSlope = param->GetBendingSlope(); | |
711 | Double_t nonBendingSlope = param->GetNonBendingSlope(); | |
690d2205 | 712 | Double_t inverseBendingMomentum = param->GetInverseBendingMomentum(); |
713 | Double_t inverseTotalMomentum2 = inverseBendingMomentum * inverseBendingMomentum * | |
714 | (1.0 + bendingSlope * bendingSlope) / | |
715 | (1.0 + bendingSlope *bendingSlope + nonBendingSlope * nonBendingSlope); | |
208f139e | 716 | // Path length in the material |
37a615ac | 717 | Double_t signedPathLength = dZ * TMath::Sqrt(1.0 + bendingSlope*bendingSlope + nonBendingSlope*nonBendingSlope); |
718 | Double_t pathLengthOverX0 = (x0 > 0.) ? TMath::Abs(signedPathLength) / x0 : TMath::Abs(signedPathLength); | |
208f139e | 719 | // relativistic velocity |
720 | Double_t velo = 1.; | |
721 | // Angular dispersion square of the track (variance) in a plane perpendicular to the trajectory | |
37a615ac | 722 | Double_t theta02 = 0.0136 / velo * (1 + 0.038 * TMath::Log(pathLengthOverX0)); |
723 | theta02 *= theta02 * inverseTotalMomentum2 * pathLengthOverX0; | |
208f139e | 724 | |
37a615ac | 725 | Double_t varCoor = (x0 > 0.) ? signedPathLength * signedPathLength * theta02 / 3. : 0.; |
208f139e | 726 | Double_t varSlop = theta02; |
37a615ac | 727 | Double_t covCorrSlope = (x0 > 0.) ? signedPathLength * theta02 / 2. : 0.; |
ea94c18b | 728 | |
690d2205 | 729 | // Set MCS covariance matrix |
ea94c18b | 730 | TMatrixD newParamCov(param->GetCovariances()); |
208f139e | 731 | // Non bending plane |
ea94c18b | 732 | newParamCov(0,0) += varCoor; newParamCov(0,1) += covCorrSlope; |
733 | newParamCov(1,0) += covCorrSlope; newParamCov(1,1) += varSlop; | |
208f139e | 734 | // Bending plane |
ea94c18b | 735 | newParamCov(2,2) += varCoor; newParamCov(2,3) += covCorrSlope; |
736 | newParamCov(3,2) += covCorrSlope; newParamCov(3,3) += varSlop; | |
c24543a2 | 737 | |
738 | // Set momentum related covariances if B!=0 | |
739 | if (fgFieldON) { | |
740 | // compute derivative d(q/Pxy) / dSlopeX and d(q/Pxy) / dSlopeY | |
741 | Double_t dqPxydSlopeX = inverseBendingMomentum * nonBendingSlope / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
742 | Double_t dqPxydSlopeY = - inverseBendingMomentum * nonBendingSlope*nonBendingSlope * bendingSlope / | |
743 | (1. + bendingSlope*bendingSlope) / (1. + nonBendingSlope*nonBendingSlope + bendingSlope*bendingSlope); | |
744 | // Inverse bending momentum (due to dependences with bending and non bending slopes) | |
745 | newParamCov(4,0) += dqPxydSlopeX * covCorrSlope; newParamCov(0,4) += dqPxydSlopeX * covCorrSlope; | |
746 | newParamCov(4,1) += dqPxydSlopeX * varSlop; newParamCov(1,4) += dqPxydSlopeX * varSlop; | |
747 | newParamCov(4,2) += dqPxydSlopeY * covCorrSlope; newParamCov(2,4) += dqPxydSlopeY * covCorrSlope; | |
748 | newParamCov(4,3) += dqPxydSlopeY * varSlop; newParamCov(3,4) += dqPxydSlopeY * varSlop; | |
749 | newParamCov(4,4) += (dqPxydSlopeX*dqPxydSlopeX + dqPxydSlopeY*dqPxydSlopeY) * varSlop; | |
750 | } | |
208f139e | 751 | |
ea94c18b | 752 | // Set new covariances |
753 | param->SetCovariances(newParamCov); | |
c04e3238 | 754 | } |
755 | ||
690d2205 | 756 | //__________________________________________________________________________ |
757 | void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, | |
758 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
759 | Double_t errXVtx, Double_t errYVtx, | |
760 | Bool_t correctForMCS, Bool_t correctForEnergyLoss) | |
c04e3238 | 761 | { |
690d2205 | 762 | /// Main method for extrapolation to the vertex: |
763 | /// Returns the track parameters and covariances resulting from the extrapolation of the current trackParam | |
764 | /// Changes parameters and covariances according to multiple scattering and energy loss corrections: | |
765 | /// if correctForMCS=kTRUE: compute parameters using Branson correction and add correction resolution to covariances | |
766 | /// if correctForMCS=kFALSE: add parameter dispersion due to MCS in parameter covariances | |
767 | /// if correctForEnergyLoss=kTRUE: correct parameters for energy loss and add energy loss fluctuation to covariances | |
768 | /// if correctForEnergyLoss=kFALSE: do nothing about energy loss | |
c04e3238 | 769 | |
8cde4af5 | 770 | if (trackParam->GetZ() == zVtx) return; // nothing to be done if already at vertex |
c04e3238 | 771 | |
8cde4af5 | 772 | if (trackParam->GetZ() > zVtx) { // spectro. (z<0) |
690d2205 | 773 | cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() |
774 | <<") upstream the vertex (zVtx = "<<zVtx<<")"<<endl; | |
fac70e25 | 775 | return; |
776 | } | |
777 | ||
8cde4af5 | 778 | // Check the vertex position relatively to the absorber |
ea94c18b | 779 | if (zVtx < AliMUONConstants::AbsZBeg() && zVtx > AliMUONConstants::AbsZEnd()) { // spectro. (z<0) |
8cde4af5 | 780 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx |
690d2205 | 781 | <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl; |
ea94c18b | 782 | } else if (zVtx < AliMUONConstants::AbsZEnd() ) { // spectro. (z<0) |
8cde4af5 | 783 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Ending Z ("<<zVtx |
690d2205 | 784 | <<") downstream the front absorber (zAbsorberEnd = "<<AliMUONConstants::AbsZEnd()<<")"<<endl; |
785 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx); | |
786 | else ExtrapToZ(trackParam,zVtx); | |
8cde4af5 | 787 | return; |
788 | } | |
789 | ||
790 | // Check the track position relatively to the absorber and extrapolate track parameters to the end of the absorber if needed | |
ea94c18b | 791 | if (trackParam->GetZ() > AliMUONConstants::AbsZBeg()) { // spectro. (z<0) |
8cde4af5 | 792 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() |
690d2205 | 793 | <<") upstream the front absorber (zAbsorberBegin = "<<AliMUONConstants::AbsZBeg()<<")"<<endl; |
794 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx); | |
795 | else ExtrapToZ(trackParam,zVtx); | |
8cde4af5 | 796 | return; |
ea94c18b | 797 | } else if (trackParam->GetZ() > AliMUONConstants::AbsZEnd()) { // spectro. (z<0) |
8cde4af5 | 798 | cout<<"W-AliMUONTrackExtrap::ExtrapToVertex: Starting Z ("<<trackParam->GetZ() |
690d2205 | 799 | <<") inside the front absorber ("<<AliMUONConstants::AbsZBeg()<<","<<AliMUONConstants::AbsZEnd()<<")"<<endl; |
c04e3238 | 800 | } else { |
690d2205 | 801 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,AliMUONConstants::AbsZEnd()); |
802 | else ExtrapToZ(trackParam,AliMUONConstants::AbsZEnd()); | |
c04e3238 | 803 | } |
c04e3238 | 804 | |
690d2205 | 805 | // Get absorber correction parameters assuming linear propagation in absorber |
8cde4af5 | 806 | Double_t trackXYZOut[3]; |
807 | trackXYZOut[0] = trackParam->GetNonBendingCoor(); | |
808 | trackXYZOut[1] = trackParam->GetBendingCoor(); | |
809 | trackXYZOut[2] = trackParam->GetZ(); | |
810 | Double_t trackXYZIn[3]; | |
690d2205 | 811 | if (correctForMCS) { // assume linear propagation until the vertex |
812 | trackXYZIn[2] = TMath::Min(zVtx, AliMUONConstants::AbsZBeg()); // spectro. (z<0) | |
813 | trackXYZIn[0] = trackXYZOut[0] + (xVtx - trackXYZOut[0]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]); | |
814 | trackXYZIn[1] = trackXYZOut[1] + (yVtx - trackXYZOut[1]) / (zVtx - trackXYZOut[2]) * (trackXYZIn[2] - trackXYZOut[2]); | |
815 | } else { | |
816 | AliMUONTrackParam trackParamIn(*trackParam); | |
817 | ExtrapToZ(&trackParamIn, TMath::Min(zVtx, AliMUONConstants::AbsZBeg())); | |
818 | trackXYZIn[0] = trackParamIn.GetNonBendingCoor(); | |
819 | trackXYZIn[1] = trackParamIn.GetBendingCoor(); | |
820 | trackXYZIn[2] = trackParamIn.GetZ(); | |
821 | } | |
84f061ef | 822 | Double_t pTot = trackParam->P(); |
ecdf58c4 | 823 | Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2; |
824 | if (!GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2)) { | |
18abc511 | 825 | cout<<"E-AliMUONTrackExtrap::ExtrapToVertex: Unable to take into account the absorber effects"<<endl; |
826 | if (trackParam->CovariancesExist()) ExtrapToZCov(trackParam,zVtx); | |
827 | else ExtrapToZ(trackParam,zVtx); | |
828 | return; | |
829 | } | |
8cde4af5 | 830 | |
690d2205 | 831 | // Compute track parameters and covariances at vertex according to correctForMCS and correctForEnergyLoss flags |
832 | if (correctForMCS) { | |
fac70e25 | 833 | |
690d2205 | 834 | if (correctForEnergyLoss) { |
835 | ||
836 | // Correct for multiple scattering and energy loss | |
ecdf58c4 | 837 | CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2); |
690d2205 | 838 | CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, |
839 | trackXYZIn[2], pathLength, f0, f1, f2); | |
ecdf58c4 | 840 | CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2); |
690d2205 | 841 | |
842 | } else { | |
843 | ||
844 | // Correct for multiple scattering | |
845 | CorrectMCSEffectInAbsorber(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, | |
846 | trackXYZIn[2], pathLength, f0, f1, f2); | |
847 | } | |
fac70e25 | 848 | |
fac70e25 | 849 | } else { |
690d2205 | 850 | |
851 | if (correctForEnergyLoss) { | |
852 | ||
18abc511 | 853 | // Correct for energy loss add multiple scattering dispersion in covariance matrix |
ecdf58c4 | 854 | CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2); |
37a615ac | 855 | AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0)) |
690d2205 | 856 | ExtrapToZCov(trackParam, trackXYZIn[2]); |
ecdf58c4 | 857 | CorrectELossEffectInAbsorber(trackParam, 0.5*totalELoss, 0.5*sigmaELoss2); |
690d2205 | 858 | ExtrapToZCov(trackParam, zVtx); |
859 | ||
860 | } else { | |
861 | ||
18abc511 | 862 | // add multiple scattering dispersion in covariance matrix |
37a615ac | 863 | AddMCSEffectInAbsorber(trackParam, -pathLength, f0, f1, f2); // (spectro. (z<0)) |
690d2205 | 864 | ExtrapToZCov(trackParam, zVtx); |
865 | ||
866 | } | |
867 | ||
fac70e25 | 868 | } |
8cde4af5 | 869 | |
fac70e25 | 870 | } |
871 | ||
690d2205 | 872 | //__________________________________________________________________________ |
873 | void AliMUONTrackExtrap::ExtrapToVertex(AliMUONTrackParam* trackParam, | |
874 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
875 | Double_t errXVtx, Double_t errYVtx) | |
876 | { | |
877 | /// Extrapolate track parameters to vertex, corrected for multiple scattering and energy loss effects | |
878 | /// Add branson correction resolution and energy loss fluctuation to parameter covariances | |
879 | ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kTRUE); | |
880 | } | |
881 | ||
882 | //__________________________________________________________________________ | |
883 | void AliMUONTrackExtrap::ExtrapToVertexWithoutELoss(AliMUONTrackParam* trackParam, | |
884 | Double_t xVtx, Double_t yVtx, Double_t zVtx, | |
885 | Double_t errXVtx, Double_t errYVtx) | |
886 | { | |
887 | /// Extrapolate track parameters to vertex, corrected for multiple scattering effects only | |
888 | /// Add branson correction resolution to parameter covariances | |
889 | ExtrapToVertex(trackParam, xVtx, yVtx, zVtx, errXVtx, errYVtx, kTRUE, kFALSE); | |
890 | } | |
891 | ||
892 | //__________________________________________________________________________ | |
893 | void AliMUONTrackExtrap::ExtrapToVertexWithoutBranson(AliMUONTrackParam* trackParam, Double_t zVtx) | |
894 | { | |
895 | /// Extrapolate track parameters to vertex, corrected for energy loss effects only | |
896 | /// Add dispersion due to multiple scattering and energy loss fluctuation to parameter covariances | |
897 | ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kTRUE); | |
898 | } | |
899 | ||
900 | //__________________________________________________________________________ | |
901 | void AliMUONTrackExtrap::ExtrapToVertexUncorrected(AliMUONTrackParam* trackParam, Double_t zVtx) | |
902 | { | |
903 | /// Extrapolate track parameters to vertex without multiple scattering and energy loss corrections | |
904 | /// Add dispersion due to multiple scattering to parameter covariances | |
905 | ExtrapToVertex(trackParam, 0., 0., zVtx, 0., 0., kFALSE, kFALSE); | |
906 | } | |
907 | ||
908 | //__________________________________________________________________________ | |
fac70e25 | 909 | Double_t AliMUONTrackExtrap::TotalMomentumEnergyLoss(AliMUONTrackParam* trackParam, Double_t xVtx, Double_t yVtx, Double_t zVtx) |
910 | { | |
911 | /// Calculate the total momentum energy loss in-between the track position and the vertex assuming a linear propagation | |
912 | ||
913 | if (trackParam->GetZ() == zVtx) return 0.; // nothing to be done if already at vertex | |
8cde4af5 | 914 | |
fac70e25 | 915 | // Check whether the geometry is available |
916 | if (!gGeoManager) { | |
917 | cout<<"E-AliMUONTrackExtrap::TotalMomentumEnergyLoss: no TGeo"<<endl; | |
918 | return 0.; | |
919 | } | |
920 | ||
921 | // Get encountered material correction parameters assuming linear propagation from vertex to the track position | |
922 | Double_t trackXYZOut[3]; | |
923 | trackXYZOut[0] = trackParam->GetNonBendingCoor(); | |
924 | trackXYZOut[1] = trackParam->GetBendingCoor(); | |
925 | trackXYZOut[2] = trackParam->GetZ(); | |
926 | Double_t trackXYZIn[3]; | |
927 | trackXYZIn[0] = xVtx; | |
928 | trackXYZIn[1] = yVtx; | |
929 | trackXYZIn[2] = zVtx; | |
84f061ef | 930 | Double_t pTot = trackParam->P(); |
18abc511 | 931 | Double_t pathLength, f0, f1, f2, meanRho, totalELoss, sigmaELoss2; |
690d2205 | 932 | GetAbsorberCorrectionParam(trackXYZIn,trackXYZOut,pTot,pathLength,f0,f1,f2,meanRho,totalELoss,sigmaELoss2); |
fac70e25 | 933 | |
ecdf58c4 | 934 | // total momentum corrected for energy loss |
935 | Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV | |
936 | Double_t e = TMath::Sqrt(pTot*pTot + muMass*muMass); | |
937 | Double_t eCorr = e + totalELoss; | |
938 | Double_t pTotCorr = TMath::Sqrt(eCorr*eCorr - muMass*muMass); | |
939 | ||
940 | return pTotCorr - pTot; | |
c04e3238 | 941 | } |
942 | ||
690d2205 | 943 | //__________________________________________________________________________ |
fa5e35be | 944 | Double_t AliMUONTrackExtrap::BetheBloch(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZ, Double_t atomicZoverA) |
c04e3238 | 945 | { |
84f061ef | 946 | /// Returns the mean total momentum energy loss of muon with total momentum='pTotal' |
947 | /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ' | |
ecdf58c4 | 948 | Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV |
84f061ef | 949 | |
ecdf58c4 | 950 | // mean exitation energy (GeV) |
951 | Double_t i; | |
952 | if (atomicZ < 13) i = (12. * atomicZ + 7.) * 1.e-9; | |
953 | else i = (9.76 * atomicZ + 58.8 * TMath::Power(atomicZ,-0.19)) * 1.e-9; | |
690d2205 | 954 | |
fa5e35be | 955 | return pathLength * rho * AliExternalTrackParam::BetheBlochGeant(pTotal/muMass, rho, 0.20, 3.00, i, atomicZoverA); |
c04e3238 | 956 | } |
957 | ||
690d2205 | 958 | //__________________________________________________________________________ |
fa5e35be | 959 | Double_t AliMUONTrackExtrap::EnergyLossFluctuation2(Double_t pTotal, Double_t pathLength, Double_t rho, Double_t atomicZoverA) |
690d2205 | 960 | { |
961 | /// Returns the total momentum energy loss fluctuation of muon with total momentum='pTotal' | |
962 | /// in the absorber layer of lenght='pathLength', density='rho', A='atomicA' and Z='atomicZ' | |
ecdf58c4 | 963 | Double_t muMass = TDatabasePDG::Instance()->GetParticle("mu-")->Mass(); // GeV |
690d2205 | 964 | //Double_t eMass = 0.510998918e-3; // GeV |
965 | Double_t k = 0.307075e-3; // GeV.g^-1.cm^2 | |
966 | Double_t p2=pTotal*pTotal; | |
967 | Double_t beta2=p2/(p2 + muMass*muMass); | |
968 | ||
fa5e35be | 969 | Double_t fwhm = 2. * k * rho * pathLength * atomicZoverA / beta2; // FWHM of the energy loss Landau distribution |
690d2205 | 970 | Double_t sigma2 = fwhm * fwhm / (8.*log(2.)); // gaussian: fwmh = 2 * srqt(2*ln(2)) * sigma (i.e. fwmh = 2.35 * sigma) |
971 | ||
972 | //sigma2 = k * rho * pathLength * atomicZ / atomicA * eMass; // sigma2 of the energy loss gaussian distribution | |
973 | ||
974 | return sigma2; | |
975 | } | |
976 | ||
977 | //__________________________________________________________________________ | |
978 | void AliMUONTrackExtrap::Cov2CovP(const TMatrixD ¶m, TMatrixD &cov) | |
979 | { | |
980 | /// change coordinate system: (X, SlopeX, Y, SlopeY, q/Pyz) -> (X, SlopeX, Y, SlopeY, q*PTot) | |
981 | /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system | |
982 | ||
983 | // charge * total momentum | |
984 | Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) / | |
985 | TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0); | |
986 | ||
987 | // Jacobian of the opposite transformation | |
988 | TMatrixD jacob(5,5); | |
989 | jacob.UnitMatrix(); | |
990 | jacob(4,1) = qPTot * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
991 | jacob(4,3) = - qPTot * param(1,0) * param(1,0) * param(3,0) / | |
992 | (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
993 | jacob(4,4) = - qPTot / param(4,0); | |
994 | ||
995 | // compute covariances in new coordinate system | |
996 | TMatrixD tmp(cov,TMatrixD::kMultTranspose,jacob); | |
997 | cov.Mult(jacob,tmp); | |
998 | } | |
999 | ||
1000 | //__________________________________________________________________________ | |
1001 | void AliMUONTrackExtrap::CovP2Cov(const TMatrixD ¶m, TMatrixD &covP) | |
1002 | { | |
1003 | /// change coordinate system: (X, SlopeX, Y, SlopeY, q*PTot) -> (X, SlopeX, Y, SlopeY, q/Pyz) | |
1004 | /// parameters (param) are given in the (X, SlopeX, Y, SlopeY, q/Pyz) coordinate system | |
1005 | ||
1006 | // charge * total momentum | |
1007 | Double_t qPTot = TMath::Sqrt(1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)) / | |
1008 | TMath::Sqrt(1. + param(3,0)*param(3,0)) / param(4,0); | |
1009 | ||
1010 | // Jacobian of the transformation | |
1011 | TMatrixD jacob(5,5); | |
1012 | jacob.UnitMatrix(); | |
1013 | jacob(4,1) = param(4,0) * param(1,0) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
1014 | jacob(4,3) = - param(4,0) * param(1,0) * param(1,0) * param(3,0) / | |
1015 | (1. + param(3,0)*param(3,0)) / (1. + param(1,0)*param(1,0) + param(3,0)*param(3,0)); | |
1016 | jacob(4,4) = - param(4,0) / qPTot; | |
1017 | ||
1018 | // compute covariances in new coordinate system | |
1019 | TMatrixD tmp(covP,TMatrixD::kMultTranspose,jacob); | |
1020 | covP.Mult(jacob,tmp); | |
1021 | } | |
1022 | ||
c04e3238 | 1023 | //__________________________________________________________________________ |
1024 | void AliMUONTrackExtrap::ExtrapOneStepHelix(Double_t charge, Double_t step, Double_t *vect, Double_t *vout) | |
1025 | { | |
71a2d3aa | 1026 | /// <pre> |
c04e3238 | 1027 | /// ****************************************************************** |
1028 | /// * * | |
1029 | /// * Performs the tracking of one step in a magnetic field * | |
1030 | /// * The trajectory is assumed to be a helix in a constant field * | |
1031 | /// * taken at the mid point of the step. * | |
1032 | /// * Parameters: * | |
1033 | /// * input * | |
1034 | /// * STEP =arc length of the step asked * | |
1035 | /// * VECT =input vector (position,direction cos and momentum) * | |
1036 | /// * CHARGE= electric charge of the particle * | |
1037 | /// * output * | |
1038 | /// * VOUT = same as VECT after completion of the step * | |
1039 | /// * * | |
2060b217 | 1040 | /// * ==>Called by : USER, GUSWIM * |
c04e3238 | 1041 | /// * Author m.hansroul ********* * |
1042 | /// * modified s.egli, s.v.levonian * | |
1043 | /// * modified v.perevoztchikov | |
1044 | /// * * | |
1045 | /// ****************************************************************** | |
71a2d3aa | 1046 | /// </pre> |
c04e3238 | 1047 | |
1048 | // modif: everything in double precision | |
1049 | ||
1050 | Double_t xyz[3], h[4], hxp[3]; | |
1051 | Double_t h2xy, hp, rho, tet; | |
1052 | Double_t sint, sintt, tsint, cos1t; | |
1053 | Double_t f1, f2, f3, f4, f5, f6; | |
1054 | ||
1055 | const Int_t kix = 0; | |
1056 | const Int_t kiy = 1; | |
1057 | const Int_t kiz = 2; | |
1058 | const Int_t kipx = 3; | |
1059 | const Int_t kipy = 4; | |
1060 | const Int_t kipz = 5; | |
1061 | const Int_t kipp = 6; | |
1062 | ||
1063 | const Double_t kec = 2.9979251e-4; | |
1064 | // | |
1065 | // ------------------------------------------------------------------ | |
1066 | // | |
1067 | // units are kgauss,centimeters,gev/c | |
1068 | // | |
1069 | vout[kipp] = vect[kipp]; | |
1070 | if (TMath::Abs(charge) < 0.00001) { | |
1071 | for (Int_t i = 0; i < 3; i++) { | |
1072 | vout[i] = vect[i] + step * vect[i+3]; | |
1073 | vout[i+3] = vect[i+3]; | |
1074 | } | |
1075 | return; | |
1076 | } | |
1077 | xyz[0] = vect[kix] + 0.5 * step * vect[kipx]; | |
1078 | xyz[1] = vect[kiy] + 0.5 * step * vect[kipy]; | |
1079 | xyz[2] = vect[kiz] + 0.5 * step * vect[kipz]; | |
1080 | ||
1081 | //cmodif: call gufld (xyz, h) changed into: | |
f7a1cc68 | 1082 | TGeoGlobalMagField::Instance()->Field(xyz,h); |
c04e3238 | 1083 | |
1084 | h2xy = h[0]*h[0] + h[1]*h[1]; | |
1085 | h[3] = h[2]*h[2]+ h2xy; | |
1086 | if (h[3] < 1.e-12) { | |
1087 | for (Int_t i = 0; i < 3; i++) { | |
1088 | vout[i] = vect[i] + step * vect[i+3]; | |
1089 | vout[i+3] = vect[i+3]; | |
1090 | } | |
1091 | return; | |
1092 | } | |
1093 | if (h2xy < 1.e-12*h[3]) { | |
1094 | ExtrapOneStepHelix3(charge*h[2], step, vect, vout); | |
1095 | return; | |
1096 | } | |
1097 | h[3] = TMath::Sqrt(h[3]); | |
1098 | h[0] /= h[3]; | |
1099 | h[1] /= h[3]; | |
1100 | h[2] /= h[3]; | |
1101 | h[3] *= kec; | |
1102 | ||
1103 | hxp[0] = h[1]*vect[kipz] - h[2]*vect[kipy]; | |
1104 | hxp[1] = h[2]*vect[kipx] - h[0]*vect[kipz]; | |
1105 | hxp[2] = h[0]*vect[kipy] - h[1]*vect[kipx]; | |
1106 | ||
1107 | hp = h[0]*vect[kipx] + h[1]*vect[kipy] + h[2]*vect[kipz]; | |
1108 | ||
1109 | rho = -charge*h[3]/vect[kipp]; | |
1110 | tet = rho * step; | |
1111 | ||
1112 | if (TMath::Abs(tet) > 0.15) { | |
1113 | sint = TMath::Sin(tet); | |
1114 | sintt = (sint/tet); | |
1115 | tsint = (tet-sint)/tet; | |
1116 | cos1t = 2.*(TMath::Sin(0.5*tet))*(TMath::Sin(0.5*tet))/tet; | |
1117 | } else { | |
1118 | tsint = tet*tet/36.; | |
1119 | sintt = (1. - tsint); | |
1120 | sint = tet*sintt; | |
1121 | cos1t = 0.5*tet; | |
1122 | } | |
1123 | ||
1124 | f1 = step * sintt; | |
1125 | f2 = step * cos1t; | |
1126 | f3 = step * tsint * hp; | |
1127 | f4 = -tet*cos1t; | |
1128 | f5 = sint; | |
1129 | f6 = tet * cos1t * hp; | |
1130 | ||
1131 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0] + f3*h[0]; | |
1132 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1] + f3*h[1]; | |
1133 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f2*hxp[2] + f3*h[2]; | |
1134 | ||
1135 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0] + f6*h[0]; | |
1136 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1] + f6*h[1]; | |
1137 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f5*hxp[2] + f6*h[2]; | |
1138 | ||
1139 | return; | |
1140 | } | |
1141 | ||
1142 | //__________________________________________________________________________ | |
1143 | void AliMUONTrackExtrap::ExtrapOneStepHelix3(Double_t field, Double_t step, Double_t *vect, Double_t *vout) | |
1144 | { | |
71a2d3aa | 1145 | /// <pre> |
c04e3238 | 1146 | /// ****************************************************************** |
1147 | /// * * | |
1148 | /// * Tracking routine in a constant field oriented * | |
1149 | /// * along axis 3 * | |
1150 | /// * Tracking is performed with a conventional * | |
1151 | /// * helix step method * | |
1152 | /// * * | |
2060b217 | 1153 | /// * ==>Called by : USER, GUSWIM * |
c04e3238 | 1154 | /// * Authors R.Brun, M.Hansroul ********* * |
1155 | /// * Rewritten V.Perevoztchikov | |
1156 | /// * * | |
1157 | /// ****************************************************************** | |
71a2d3aa | 1158 | /// </pre> |
c04e3238 | 1159 | |
1160 | Double_t hxp[3]; | |
1161 | Double_t h4, hp, rho, tet; | |
1162 | Double_t sint, sintt, tsint, cos1t; | |
1163 | Double_t f1, f2, f3, f4, f5, f6; | |
1164 | ||
1165 | const Int_t kix = 0; | |
1166 | const Int_t kiy = 1; | |
1167 | const Int_t kiz = 2; | |
1168 | const Int_t kipx = 3; | |
1169 | const Int_t kipy = 4; | |
1170 | const Int_t kipz = 5; | |
1171 | const Int_t kipp = 6; | |
1172 | ||
1173 | const Double_t kec = 2.9979251e-4; | |
1174 | ||
1175 | // | |
1176 | // ------------------------------------------------------------------ | |
1177 | // | |
1178 | // units are kgauss,centimeters,gev/c | |
1179 | // | |
1180 | vout[kipp] = vect[kipp]; | |
1181 | h4 = field * kec; | |
1182 | ||
1183 | hxp[0] = - vect[kipy]; | |
1184 | hxp[1] = + vect[kipx]; | |
1185 | ||
1186 | hp = vect[kipz]; | |
1187 | ||
1188 | rho = -h4/vect[kipp]; | |
1189 | tet = rho * step; | |
1190 | if (TMath::Abs(tet) > 0.15) { | |
1191 | sint = TMath::Sin(tet); | |
1192 | sintt = (sint/tet); | |
1193 | tsint = (tet-sint)/tet; | |
1194 | cos1t = 2.* TMath::Sin(0.5*tet) * TMath::Sin(0.5*tet)/tet; | |
1195 | } else { | |
1196 | tsint = tet*tet/36.; | |
1197 | sintt = (1. - tsint); | |
1198 | sint = tet*sintt; | |
1199 | cos1t = 0.5*tet; | |
1200 | } | |
1201 | ||
1202 | f1 = step * sintt; | |
1203 | f2 = step * cos1t; | |
1204 | f3 = step * tsint * hp; | |
1205 | f4 = -tet*cos1t; | |
1206 | f5 = sint; | |
1207 | f6 = tet * cos1t * hp; | |
1208 | ||
1209 | vout[kix] = vect[kix] + f1*vect[kipx] + f2*hxp[0]; | |
1210 | vout[kiy] = vect[kiy] + f1*vect[kipy] + f2*hxp[1]; | |
1211 | vout[kiz] = vect[kiz] + f1*vect[kipz] + f3; | |
1212 | ||
1213 | vout[kipx] = vect[kipx] + f4*vect[kipx] + f5*hxp[0]; | |
1214 | vout[kipy] = vect[kipy] + f4*vect[kipy] + f5*hxp[1]; | |
1215 | vout[kipz] = vect[kipz] + f4*vect[kipz] + f6; | |
1216 | ||
1217 | return; | |
1218 | } | |
8cde4af5 | 1219 | |
c04e3238 | 1220 | //__________________________________________________________________________ |
1221 | void AliMUONTrackExtrap::ExtrapOneStepRungekutta(Double_t charge, Double_t step, Double_t* vect, Double_t* vout) | |
1222 | { | |
71a2d3aa | 1223 | /// <pre> |
c04e3238 | 1224 | /// ****************************************************************** |
1225 | /// * * | |
1226 | /// * Runge-Kutta method for tracking a particle through a magnetic * | |
1227 | /// * field. Uses Nystroem algorithm (See Handbook Nat. Bur. of * | |
1228 | /// * Standards, procedure 25.5.20) * | |
1229 | /// * * | |
1230 | /// * Input parameters * | |
1231 | /// * CHARGE Particle charge * | |
1232 | /// * STEP Step size * | |
1233 | /// * VECT Initial co-ords,direction cosines,momentum * | |
1234 | /// * Output parameters * | |
1235 | /// * VOUT Output co-ords,direction cosines,momentum * | |
1236 | /// * User routine called * | |
1237 | /// * CALL GUFLD(X,F) * | |
1238 | /// * * | |
2060b217 | 1239 | /// * ==>Called by : USER, GUSWIM * |
c04e3238 | 1240 | /// * Authors R.Brun, M.Hansroul ********* * |
1241 | /// * V.Perevoztchikov (CUT STEP implementation) * | |
1242 | /// * * | |
1243 | /// * * | |
1244 | /// ****************************************************************** | |
71a2d3aa | 1245 | /// </pre> |
c04e3238 | 1246 | |
1247 | Double_t h2, h4, f[4]; | |
1248 | Double_t xyzt[3], a, b, c, ph,ph2; | |
1249 | Double_t secxs[4],secys[4],seczs[4],hxp[3]; | |
1250 | Double_t g1, g2, g3, g4, g5, g6, ang2, dxt, dyt, dzt; | |
1251 | Double_t est, at, bt, ct, cba; | |
1252 | Double_t f1, f2, f3, f4, rho, tet, hnorm, hp, rho1, sint, cost; | |
1253 | ||
1254 | Double_t x; | |
1255 | Double_t y; | |
1256 | Double_t z; | |
1257 | ||
1258 | Double_t xt; | |
1259 | Double_t yt; | |
1260 | Double_t zt; | |
1261 | ||
1262 | Double_t maxit = 1992; | |
1263 | Double_t maxcut = 11; | |
1264 | ||
1265 | const Double_t kdlt = 1e-4; | |
1266 | const Double_t kdlt32 = kdlt/32.; | |
1267 | const Double_t kthird = 1./3.; | |
1268 | const Double_t khalf = 0.5; | |
1269 | const Double_t kec = 2.9979251e-4; | |
1270 | ||
1271 | const Double_t kpisqua = 9.86960440109; | |
1272 | const Int_t kix = 0; | |
1273 | const Int_t kiy = 1; | |
1274 | const Int_t kiz = 2; | |
1275 | const Int_t kipx = 3; | |
1276 | const Int_t kipy = 4; | |
1277 | const Int_t kipz = 5; | |
1278 | ||
1279 | // *. | |
1280 | // *. ------------------------------------------------------------------ | |
1281 | // *. | |
1282 | // * this constant is for units cm,gev/c and kgauss | |
1283 | // * | |
1284 | Int_t iter = 0; | |
1285 | Int_t ncut = 0; | |
1286 | for(Int_t j = 0; j < 7; j++) | |
1287 | vout[j] = vect[j]; | |
1288 | ||
1289 | Double_t pinv = kec * charge / vect[6]; | |
1290 | Double_t tl = 0.; | |
1291 | Double_t h = step; | |
1292 | Double_t rest; | |
1293 | ||
1294 | ||
1295 | do { | |
1296 | rest = step - tl; | |
1297 | if (TMath::Abs(h) > TMath::Abs(rest)) h = rest; | |
1298 | //cmodif: call gufld(vout,f) changed into: | |
f7a1cc68 | 1299 | TGeoGlobalMagField::Instance()->Field(vout,f); |
c04e3238 | 1300 | |
1301 | // * | |
1302 | // * start of integration | |
1303 | // * | |
1304 | x = vout[0]; | |
1305 | y = vout[1]; | |
1306 | z = vout[2]; | |
1307 | a = vout[3]; | |
1308 | b = vout[4]; | |
1309 | c = vout[5]; | |
1310 | ||
1311 | h2 = khalf * h; | |
1312 | h4 = khalf * h2; | |
1313 | ph = pinv * h; | |
1314 | ph2 = khalf * ph; | |
1315 | secxs[0] = (b * f[2] - c * f[1]) * ph2; | |
1316 | secys[0] = (c * f[0] - a * f[2]) * ph2; | |
1317 | seczs[0] = (a * f[1] - b * f[0]) * ph2; | |
1318 | ang2 = (secxs[0]*secxs[0] + secys[0]*secys[0] + seczs[0]*seczs[0]); | |
1319 | if (ang2 > kpisqua) break; | |
1320 | ||
1321 | dxt = h2 * a + h4 * secxs[0]; | |
1322 | dyt = h2 * b + h4 * secys[0]; | |
1323 | dzt = h2 * c + h4 * seczs[0]; | |
1324 | xt = x + dxt; | |
1325 | yt = y + dyt; | |
1326 | zt = z + dzt; | |
1327 | // * | |
1328 | // * second intermediate point | |
1329 | // * | |
1330 | ||
1331 | est = TMath::Abs(dxt) + TMath::Abs(dyt) + TMath::Abs(dzt); | |
1332 | if (est > h) { | |
1333 | if (ncut++ > maxcut) break; | |
1334 | h *= khalf; | |
1335 | continue; | |
1336 | } | |
1337 | ||
1338 | xyzt[0] = xt; | |
1339 | xyzt[1] = yt; | |
1340 | xyzt[2] = zt; | |
1341 | ||
1342 | //cmodif: call gufld(xyzt,f) changed into: | |
f7a1cc68 | 1343 | TGeoGlobalMagField::Instance()->Field(xyzt,f); |
c04e3238 | 1344 | |
1345 | at = a + secxs[0]; | |
1346 | bt = b + secys[0]; | |
1347 | ct = c + seczs[0]; | |
1348 | ||
1349 | secxs[1] = (bt * f[2] - ct * f[1]) * ph2; | |
1350 | secys[1] = (ct * f[0] - at * f[2]) * ph2; | |
1351 | seczs[1] = (at * f[1] - bt * f[0]) * ph2; | |
1352 | at = a + secxs[1]; | |
1353 | bt = b + secys[1]; | |
1354 | ct = c + seczs[1]; | |
1355 | secxs[2] = (bt * f[2] - ct * f[1]) * ph2; | |
1356 | secys[2] = (ct * f[0] - at * f[2]) * ph2; | |
1357 | seczs[2] = (at * f[1] - bt * f[0]) * ph2; | |
1358 | dxt = h * (a + secxs[2]); | |
1359 | dyt = h * (b + secys[2]); | |
1360 | dzt = h * (c + seczs[2]); | |
1361 | xt = x + dxt; | |
1362 | yt = y + dyt; | |
1363 | zt = z + dzt; | |
1364 | at = a + 2.*secxs[2]; | |
1365 | bt = b + 2.*secys[2]; | |
1366 | ct = c + 2.*seczs[2]; | |
1367 | ||
1368 | est = TMath::Abs(dxt)+TMath::Abs(dyt)+TMath::Abs(dzt); | |
1369 | if (est > 2.*TMath::Abs(h)) { | |
1370 | if (ncut++ > maxcut) break; | |
1371 | h *= khalf; | |
1372 | continue; | |
1373 | } | |
1374 | ||
1375 | xyzt[0] = xt; | |
1376 | xyzt[1] = yt; | |
1377 | xyzt[2] = zt; | |
1378 | ||
1379 | //cmodif: call gufld(xyzt,f) changed into: | |
f7a1cc68 | 1380 | TGeoGlobalMagField::Instance()->Field(xyzt,f); |
c04e3238 | 1381 | |
1382 | z = z + (c + (seczs[0] + seczs[1] + seczs[2]) * kthird) * h; | |
1383 | y = y + (b + (secys[0] + secys[1] + secys[2]) * kthird) * h; | |
1384 | x = x + (a + (secxs[0] + secxs[1] + secxs[2]) * kthird) * h; | |
1385 | ||
1386 | secxs[3] = (bt*f[2] - ct*f[1])* ph2; | |
1387 | secys[3] = (ct*f[0] - at*f[2])* ph2; | |
1388 | seczs[3] = (at*f[1] - bt*f[0])* ph2; | |
1389 | a = a+(secxs[0]+secxs[3]+2. * (secxs[1]+secxs[2])) * kthird; | |
1390 | b = b+(secys[0]+secys[3]+2. * (secys[1]+secys[2])) * kthird; | |
1391 | c = c+(seczs[0]+seczs[3]+2. * (seczs[1]+seczs[2])) * kthird; | |
1392 | ||
1393 | est = TMath::Abs(secxs[0]+secxs[3] - (secxs[1]+secxs[2])) | |
1394 | + TMath::Abs(secys[0]+secys[3] - (secys[1]+secys[2])) | |
1395 | + TMath::Abs(seczs[0]+seczs[3] - (seczs[1]+seczs[2])); | |
1396 | ||
1397 | if (est > kdlt && TMath::Abs(h) > 1.e-4) { | |
1398 | if (ncut++ > maxcut) break; | |
1399 | h *= khalf; | |
1400 | continue; | |
1401 | } | |
1402 | ||
1403 | ncut = 0; | |
1404 | // * if too many iterations, go to helix | |
1405 | if (iter++ > maxit) break; | |
1406 | ||
1407 | tl += h; | |
1408 | if (est < kdlt32) | |
1409 | h *= 2.; | |
1410 | cba = 1./ TMath::Sqrt(a*a + b*b + c*c); | |
1411 | vout[0] = x; | |
1412 | vout[1] = y; | |
1413 | vout[2] = z; | |
1414 | vout[3] = cba*a; | |
1415 | vout[4] = cba*b; | |
1416 | vout[5] = cba*c; | |
1417 | rest = step - tl; | |
1418 | if (step < 0.) rest = -rest; | |
1419 | if (rest < 1.e-5*TMath::Abs(step)) return; | |
1420 | ||
1421 | } while(1); | |
1422 | ||
1423 | // angle too big, use helix | |
1424 | ||
1425 | f1 = f[0]; | |
1426 | f2 = f[1]; | |
1427 | f3 = f[2]; | |
1428 | f4 = TMath::Sqrt(f1*f1+f2*f2+f3*f3); | |
1429 | rho = -f4*pinv; | |
1430 | tet = rho * step; | |
1431 | ||
1432 | hnorm = 1./f4; | |
1433 | f1 = f1*hnorm; | |
1434 | f2 = f2*hnorm; | |
1435 | f3 = f3*hnorm; | |
1436 | ||
1437 | hxp[0] = f2*vect[kipz] - f3*vect[kipy]; | |
1438 | hxp[1] = f3*vect[kipx] - f1*vect[kipz]; | |
1439 | hxp[2] = f1*vect[kipy] - f2*vect[kipx]; | |
1440 | ||
1441 | hp = f1*vect[kipx] + f2*vect[kipy] + f3*vect[kipz]; | |
1442 | ||
1443 | rho1 = 1./rho; | |
1444 | sint = TMath::Sin(tet); | |
1445 | cost = 2.*TMath::Sin(khalf*tet)*TMath::Sin(khalf*tet); | |
1446 | ||
1447 | g1 = sint*rho1; | |
1448 | g2 = cost*rho1; | |
1449 | g3 = (tet-sint) * hp*rho1; | |
1450 | g4 = -cost; | |
1451 | g5 = sint; | |
1452 | g6 = cost * hp; | |
1453 | ||
1454 | vout[kix] = vect[kix] + g1*vect[kipx] + g2*hxp[0] + g3*f1; | |
1455 | vout[kiy] = vect[kiy] + g1*vect[kipy] + g2*hxp[1] + g3*f2; | |
1456 | vout[kiz] = vect[kiz] + g1*vect[kipz] + g2*hxp[2] + g3*f3; | |
1457 | ||
1458 | vout[kipx] = vect[kipx] + g4*vect[kipx] + g5*hxp[0] + g6*f1; | |
1459 | vout[kipy] = vect[kipy] + g4*vect[kipy] + g5*hxp[1] + g6*f2; | |
1460 | vout[kipz] = vect[kipz] + g4*vect[kipz] + g5*hxp[2] + g6*f3; | |
1461 | ||
1462 | return; | |
1463 | } | |
8cde4af5 | 1464 |