Removing include AliRun.h (not needed)
[u/mrichter/AliRoot.git] / HMPID / AliHMPIDRecon.cxx
CommitLineData
d3da6dc4 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//////////////////////////////////////////////////////////////////////////
17// //
18// AliHMPIDRecon //
19// //
20// HMPID class to perfom pattern recognition based on Hough transfrom //
21// for single chamber //
22//////////////////////////////////////////////////////////////////////////
23
24#include "AliHMPIDRecon.h" //class header
25#include "AliHMPIDCluster.h" //CkovAngle()
26#include <TRotation.h> //TracePhoton()
27#include <TH1D.h> //HoughResponse()
28#include <TClonesArray.h> //CkovAngle()
29
30#include <TTree.h> //Display()
31#include <TFile.h> //Display()
32#include <AliESD.h> //Display()
33#include <TPolyMarker.h> //Display()
34#include <TLatex.h> //Display()
35#include <TCanvas.h> //Display()
36
37
38const Double_t AliHMPIDRecon::fgkRadThick=1.5;
39const Double_t AliHMPIDRecon::fgkWinThick=0.5;
40const Double_t AliHMPIDRecon::fgkGapThick=8.0;
41const Double_t AliHMPIDRecon::fgkRadIdx =1.292;
42const Double_t AliHMPIDRecon::fgkWinIdx =1.5787;
43const Double_t AliHMPIDRecon::fgkGapIdx =1.0005;
44
45
46//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
47AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
48 fPhotCnt(-1),
49 fCkovSigma2(0),
50 fIsWEIGHT(kFALSE),
51 fDTheta(0.001),
52 fWindowWidth(0.045),
53 fTrkDir(TVector3(0,0,1)),fTrkPos(TVector2(30,40))
54{
55// main ctor
56 for (Int_t i=0; i<3000; i++) {
57 fPhotFlag[i] = 0;
58 fPhotCkov[i] = -1;
59 fPhotPhi [i] = -1;
60 fPhotWei [i] = 0;
61 }
62}
63//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
64Double_t AliHMPIDRecon::CkovAngle(TClonesArray *pCluLst,Int_t &iNaccepted)
65{
66// Pattern recognition method based on Hough transform
67// Arguments: pCluLst - list of clusters for this chamber
68// Returns: - track ckov angle, [rad],
69
70 if(pCluLst->GetEntries()>200) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
71 else fIsWEIGHT = kFALSE;
72
73 // Photon Flag: Flag = 0 initial set; Flag = 1 good candidate (charge compatible with photon); Flag = 2 photon used for the ring;
74
75 fPhotCnt=0;
76 for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
77 AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu); //get pointer to current cluster
78 if(pClu->Q()>100) continue; //avoid MIP clusters from bkg
79
80 fPhotCkov[fPhotCnt]=FindPhotCkov(pClu->X(),pClu->Y()); //find ckov angle for this photon candidate
81 fPhotCnt++; //increment counter of photon candidates
82 }//clusters loop
83
84 iNaccepted=FlagPhot(HoughResponse()); //flag photons according to individual theta ckov with respect to most probable track theta ckov
85 if(iNaccepted<1) return -11;
86 else return FindRingCkov(pCluLst->GetEntries()); //find best Theta ckov for ring i.e. track
87}//ThetaCerenkov()
88//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
89Double_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY)
90{
91// Finds Cerenkov angle for this photon candidate
92// Arguments: cluX,cluY - position of cadidate's cluster
93// Returns: Cerenkov angle
94
95 TVector2 pos(cluX,cluY); Double_t cluR=(pos-fTrkPos).Mod(); Double_t phi=FindPhotPhi(cluX,cluY);
d3da6dc4 96 Double_t ckov1=0,ckov2=0.75;
97 const Double_t kTol=0.05;
98 Int_t iIterCnt = 0;
99 while(1){
100 if(iIterCnt>=50) return -1;
101 Double_t ckov=0.5*(ckov1+ckov2);
102 Double_t dist=cluR-TracePhot(ckov,phi,pos); iIterCnt++; //get distance between trial point and cluster position
d3da6dc4 103 if (dist> kTol) ckov1=ckov; //cluster @ larger ckov
104 else if(dist<-kTol) ckov2=ckov; //cluster @ smaller ckov
105 else return ckov; //precision achived
106 }
107}//FindPhotTheta()
108//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
109Double_t AliHMPIDRecon::FindPhotPhi(Double_t cluX,Double_t cluY)
110{
111// Finds phi angle og photon candidate by considering the cluster's position of this candudate w.r.t track position
112
113 Double_t emiss=0;
114 return fPhotPhi[fPhotCnt]=TMath::ATan2(cluY-fTrkPos.Y()-emiss*TMath::Tan(fTrkDir.Theta())*TMath::Sin(fTrkDir.Phi()),
115 cluX-fTrkPos.X()-emiss*TMath::Tan(fTrkDir.Theta())*TMath::Cos(fTrkDir.Phi()));
116}
117//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
118Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
119{
120// Find area inside the cerenkov ring which lays inside PCs
121// Arguments: ckovThe - cernkov
122// Returns: area of the ring in cm^2 for given theta ckov
123
124
125 TVector2 pos1,pos2;
126
127 const Int_t kN=100;
128 Double_t area=0;
129 for(Int_t i=0;i<kN;i++){
130 TracePhot(ckovAng,Double_t(TMath::TwoPi()*i /kN),pos1);//trace this photon
131 TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN),pos2);//trace this photon
132 area+=(pos1-fTrkPos)*(pos2-fTrkPos);
133
134 }
135 return area;
136}//FindRingArea()
137//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
138Double_t AliHMPIDRecon::FindRingCkov(Int_t)
139{
140// Loops on all Ckov candidates and estimates the best Theta Ckov for a ring formed by those candidates. Also estimates an error for that Theat Ckov
141// collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
142// Arguments: iNclus- total number of clusters in chamber for background estimation
143// Return: best estimation of track Theta ckov
144
145 Double_t wei = 0.;
146 Double_t weightThetaCerenkov = 0.;
147
148 Double_t ckovMin=9999.,ckovMax=0.;
149 Double_t sigma2 = 0; //to collect error squared for this ring
150
151 for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
152 if(fPhotFlag[i] == 2){
3c6274c1 153 if(fPhotCkov[i]<=0) continue;//?????????????????Flag photos = 2 may imply CkovEta = 0??????????????
d3da6dc4 154 if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i]; //find max and min Theta ckov from all candidates within probable window
155 if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
156 weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i]; wei += fPhotWei[i]; //collect weight as sum of all candidate weghts
157
d3da6dc4 158 sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
159 }
160 }//candidates loop
161
162 if(sigma2>0) fCkovSigma2=1./sigma2;
163 else fCkovSigma2=1e10;
164
d3da6dc4 165 if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
166 return weightThetaCerenkov;
167}//FindCkovRing()
168//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
169Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
170{
171// Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by HoughResponse()
172// Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
173// Returns: number of photon candidates happened to be inside the window
174
175
176 Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0 and thetaCkovHough
177
178 Double_t tmin = (Double_t)(steps - 1)*fDTheta;
179 Double_t tmax = (Double_t)(steps)*fDTheta;
180 Double_t tavg = 0.5*(tmin+tmax);
181
182 tmin = tavg - 0.5*fWindowWidth; tmax = tavg + 0.5*fWindowWidth;
183
184 Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
185 for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
186 if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax) {
187 fPhotFlag[i]=2;
188 iInsideCnt++;
189 }
190 }
191 return iInsideCnt;
192}//FlagPhot()
193//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
194Double_t AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi,TVector2 &pos)const
195{
196// Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
197// Arguments: ckovThe,ckovPhi- photon ckov angles, [rad] (warning: not photon theta and phi)
198// Returns: distance between photon point on PC and track projection
199 TRotation mtheta; mtheta.RotateY(fTrkDir.Theta());
200 TRotation mphi; mphi.RotateZ(fTrkDir.Phi());
201 TRotation mrot=mphi*mtheta;
202
203 TVector3 posCkov(fTrkPos.X(),fTrkPos.Y(),-0.5*fgkRadThick-fgkWinThick-fgkGapThick); //RAD: photon position is track position @ middle of RAD
204 TVector3 dirCkov; dirCkov.SetMagThetaPhi(1,ckovThe,ckovPhi); //initially photon is directed according to requested ckov angle
205 dirCkov=mrot*dirCkov; //now we know photon direction in LORS
206 dirCkov.SetPhi(ckovPhi);
207 if(dirCkov.Theta() > TMath::ASin(1./fgkRadIdx)) return -999;//total refraction on WIN-GAP boundary
208
209 Propagate(dirCkov,posCkov,-fgkWinThick-fgkGapThick); //go to RAD-WIN boundary remeber that z=0 is PC plane
210 Refract (dirCkov, fgkRadIdx,fgkWinIdx ); //RAD-WIN refraction
211 Propagate(dirCkov,posCkov,-fgkGapThick ); //go to WIN-GAP boundary
212 Refract (dirCkov, fgkWinIdx,fgkGapIdx ); //WIN-GAP refraction
213 Propagate(dirCkov,posCkov,0 ); //go to PC
214
215 pos.Set(posCkov.X(),posCkov.Y());
216 return (pos-fTrkPos).Mod();
217}//TracePhoton()
218//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
219void AliHMPIDRecon::Propagate(const TVector3 &dir,TVector3 &pos,Double_t z)const
220{
221// Finds an intersection point between a line and XY plane shifted along Z.
222// Arguments: dir,pos - vector along the line and any point of the line
223// z - z coordinate of plain
224// Returns: none
225// On exit: pos is the position if this intesection if any
226 static TVector3 nrm(0,0,1);
227 TVector3 pnt(0,0,z);
228
229 TVector3 diff=pnt-pos;
230 Double_t sint=(nrm*diff)/(nrm*dir);
231 pos+=sint*dir;
232}//Propagate()
233//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
234void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
235{
236// Refract direction vector according to Snell law
237// Arguments:
238// n1 - ref idx of first substance
239// n2 - ref idx of second substance
240// Returns: none
241// On exit: dir is new direction
242 Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
243 if(sinref>1.) dir.SetXYZ(-999,-999,-999);
244 else dir.SetTheta(TMath::ASin(sinref));
245}//Refract()
246//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
247Double_t AliHMPIDRecon::HoughResponse()
248{
249//
250//
251//
252 Double_t kThetaMax=0.75;
253 Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
254 TH1D *phots = new TH1D("Rphot" ,"phots" ,nChannels,0,kThetaMax);
255 TH1D *photsw = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
256 TH1D *resultw = new TH1D("resultw","resultw" ,nChannels,0,kThetaMax);
257 Int_t nBin = (Int_t)(kThetaMax/fDTheta);
258 Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
259
260 for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
261 Double_t angle = fPhotCkov[i]; if(angle<0||angle>kThetaMax) continue;
262 phots->Fill(angle);
263 Int_t bin = (Int_t)(0.5+angle/(fDTheta));
264 Double_t weight=1.;
265 if(fIsWEIGHT){
266 Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta; Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
267 Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
268 if(diffArea>0) weight = 1./diffArea;
269 }
270 photsw->Fill(angle,weight);
271 fPhotWei[i]=weight;
272 }//photon candidates loop
273
274 for (Int_t i=1; i<=nBin;i++){
275 Int_t bin1= i-nCorrBand;
276 Int_t bin2= i+nCorrBand;
277 if(bin1<1) bin1=1;
278 if(bin2>nBin)bin2=nBin;
279 Double_t sumPhots=phots->Integral(bin1,bin2);
280 if(sumPhots<3) continue; // if less then 3 photons don't trust to this ring
281 Double_t sumPhotsw=photsw->Integral(bin1,bin2);
282 resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
283 }
284// evaluate the "BEST" theta ckov as the maximum value of histogramm
285 Double_t *pVec = resultw->GetArray();
286 Int_t locMax = TMath::LocMax(nBin,pVec);
287 phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
288
289 return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
290}//HoughResponse()
291//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
292Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
293{
294// Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
295// created by a given MIP. Fromulae according to CERN-EP-2000-058
296// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
297// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
298// MIP beta
299// Returns: absolute error on Cerenkov angle, [radians]
300
301 TVector3 v(-999,-999,-999);
302 Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fgkRadIdx);
303
304 v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
305 v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
306 v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
307
308 return v.Mag2();
309}
310//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
311Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
312{
313// Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
314// created by a given MIP. Fromulae according to CERN-EP-2000-058
315// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
316// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
317// MIP beta
318// Returns: absolute error on Cerenkov angle, [radians]
319 Double_t phiDelta = phiC - fTrkDir.Phi();
320
321 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
322 Double_t k = 1.-fgkRadIdx*fgkRadIdx+alpha*alpha/(betaM*betaM);
323 if (k<0) return 1e10;
324
325 Double_t mu =TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()));
326 Double_t e =TMath::Sin(fTrkDir.Theta())*TMath::Cos(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()));
327
328 Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
329 Double_t dtdxc = kk*(k*(TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()))-(alpha*mu/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
330 Double_t dtdyc = kk*(k*(TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()))+(alpha* e/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
331
332 return TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
333}
334//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
335Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
336{
337// Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
338// created by a given MIP. Fromulae according to CERN-EP-2000-058
339// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
340// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
341// MIP beta
342// Returns: absolute error on Cerenkov angle, [radians]
343 Double_t phiDelta = phiC - fTrkDir.Phi();
344 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
345
346 Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fgkRadIdx*betaM*betaM/(alpha*TMath::Tan(thetaC));
347
348 Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
349
350 return f*dtdn;
351}//SigCrom()
352//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
353Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
354{
355// Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
356// created by a given MIP. Formulae according to CERN-EP-2000-058
357// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
358// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
359// MIP beta
360// Returns: absolute error on Cerenkov angle, [radians]
361
362 Double_t phiDelta = phiC - fTrkDir.Phi();
363 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
364
365 Double_t k = 1.-fgkRadIdx*fgkRadIdx+alpha*alpha/(betaM*betaM);
366 if (k<0) return 1e10;
367
368 Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
369 Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
370
371 Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
372 Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
373 Double_t ii = 1.+eTr*betaM*i;
374
375 Double_t err = c * (i/(alpha*alpha*8) + ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
376 Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
377
378 return trErr*err;
379}//SigGeom()
380//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++