HMPID/AliHMPIDRecon.cxx

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  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 #include <AliESDtrack.h>   //CkovAngle()
  30
  31 const Double_t AliHMPIDRecon::fgkRadThick=1.5;
  32 const Double_t AliHMPIDRecon::fgkWinThick=0.5;
  33 const Double_t AliHMPIDRecon::fgkGapThick=8.0;
  34 const Double_t AliHMPIDRecon::fgkWinIdx  =1.5787;
  35 const Double_t AliHMPIDRecon::fgkGapIdx  =1.0005;
  36
  37
  38 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  39 AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
  40   fRadNmean(1.292),
  41   fPhotCnt(-1),
  42   fCkovSigma2(0),
  43   fIsWEIGHT(kFALSE),
  44   fDTheta(0.001),
  45   fWindowWidth(0.045),
  46   fTrkDir(TVector3(0,0,1)),fTrkPos(TVector2(30,40))
  47 {
  48 // main ctor
  49   for (Int_t i=0; i<3000; i++) {
  50     fPhotFlag[i] =  0;
  51     fPhotCkov[i] = -1;
  52     fPhotPhi [i] = -1;
  53     fPhotWei [i] =  0;
  54   }
  55 }
  56 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  57 void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
  58 {
  59 // Pattern recognition method based on Hough transform
  60 // Arguments:   pTrk     - track for which Ckov angle is to be found
  61 //              pCluLst  - list of clusters for this chamber
  62 //   Returns:            - track ckov angle, [rad],
  63
  64   if(pCluLst->GetEntries()>200) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
  65   else                          fIsWEIGHT = kFALSE;
  66
  67   // Photon Flag:  Flag = 0 initial set; Flag = 1 good candidate (charge compatible with photon); Flag = 2 photon used for the ring;
  68   Float_t xPc,yPc,th,ph;      pTrk->GetHMPIDtrk(xPc,yPc,th,ph);  SetTrack(xPc,yPc,th,ph); //initialize this track
  69   fRadNmean=nmean;
  70
  71
  72
  73   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
  74   fPhotCnt=0;
  75   for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
  76     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster
  77     chId=pClu->Ch();
  78     if(pClu->Q()>100){                                                                        //charge compartible with MIP clusters
  79       Float_t dX=xPc-pClu->X(),dY=yPc-pClu->Y(),d =TMath::Sqrt(dX*dX+dY*dY);                  //distance between current cluster and intersection point
  80       if( d < dMin) {mipId=iClu; dMin=d;mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();}//current cluster is closer, overwrite data for min cluster
  81     }else{                                                                                    //charge compartible with photon cluster
  82       fPhotCkov[fPhotCnt]=FindPhotCkov(pClu->X(),pClu->Y());                                  //find ckov angle for this  photon candidate
  83       fPhotCnt++;         //increment counter of photon candidates
  84     }
  85   }//clusters loop
  86   Int_t iNacc=FlagPhot(HoughResponse());                                   //flag photons according to individual theta ckov with respect to most probable
  87
  88                  pTrk->SetHMPIDmip      (mipX,mipY,mipQ,iNacc);                 //store mip info
  89
  90   if(mipId==-1) {pTrk->SetHMPIDsignal   (kMipQdcCut);  return;}                 //no clusters with QDC more the threshold at all
  91   if(dMin>1)    {pTrk->SetHMPIDsignal   (kMipDistCut); return;}                 //closest cluster with enough charge is still too far from intersection
  92                  pTrk->SetHMPIDcluIdx(chId,mipId);
  93   if(iNacc<1)    pTrk->SetHMPIDsignal(kNoPhotAccept);                         //no photon candidates is accepted
  94   else           pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries()));   //find best Theta ckov for ring i.e. track
  95
  96                  pTrk->SetHMPIDchi2(fCkovSigma2);                              //error squared
  97
  98 }//ThetaCerenkov()
  99 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 100 Double_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY)
 101 {
 102 // Finds Cerenkov angle  for this photon candidate
 103 // Arguments: cluX,cluY - position of cadidate's cluster
 104 //   Returns: Cerenkov angle
 105
 106   TVector2 pos(cluX,cluY); Double_t cluR=(pos-fTrkPos).Mod();  Double_t phi=FindPhotPhi(cluX,cluY);
 107   Double_t ckov1=0,ckov2=0.75;
 108   const Double_t kTol=0.05;
 109   Int_t iIterCnt = 0;
 110   while(1){
 111     if(iIterCnt>=50) return -1;
 112     Double_t ckov=0.5*(ckov1+ckov2);
 113     Double_t dist=cluR-TracePhot(ckov,phi,pos); iIterCnt++;   //get distance between trial point and cluster position
 114     if     (dist> kTol) ckov1=ckov;                           //cluster @ larger ckov
 115     else if(dist<-kTol) ckov2=ckov;                           //cluster @ smaller ckov
 116     else                return ckov;                          //precision achived
 117   }
 118 }//FindPhotTheta()
 119 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 120 Double_t AliHMPIDRecon::FindPhotPhi(Double_t cluX,Double_t cluY)
 121 {
 122 // Finds phi angle og photon candidate by considering the cluster's position  of this candudate w.r.t track position
 123
 124   Double_t emiss=0;
 125   return fPhotPhi[fPhotCnt]=TMath::ATan2(cluY-fTrkPos.Y()-emiss*TMath::Tan(fTrkDir.Theta())*TMath::Sin(fTrkDir.Phi()),
 126                                          cluX-fTrkPos.X()-emiss*TMath::Tan(fTrkDir.Theta())*TMath::Cos(fTrkDir.Phi()));
 127 }
 128 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 129 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
 130 {
 131 // Find area inside the cerenkov ring which lays inside PCs
 132 // Arguments: ckovThe - cernkov
 133 //   Returns: area of the ring in cm^2 for given theta ckov
 134
 135
 136   TVector2 pos1,pos2;
 137
 138   const Int_t kN=100;
 139   Double_t area=0;
 140   for(Int_t i=0;i<kN;i++){
 141     TracePhot(ckovAng,Double_t(TMath::TwoPi()*i    /kN),pos1);//trace this photon
 142     TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN),pos2);//trace this photon
 143     area+=(pos1-fTrkPos)*(pos2-fTrkPos);
 144
 145   }
 146   return area;
 147 }//FindRingArea()
 148 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 149 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
 150 {
 151 // 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
 152 // collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
 153 // Arguments: iNclus- total number of clusters in chamber for background estimation
 154 //    Return: best estimation of track Theta ckov
 155
 156   Double_t wei = 0.;
 157   Double_t weightThetaCerenkov = 0.;
 158
 159   Double_t ckovMin=9999.,ckovMax=0.;
 160   Double_t sigma2 = 0;   //to collect error squared for this ring
 161
 162   for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
 163     if(fPhotFlag[i] == 2){
 164       if(fPhotCkov[i]<=0) continue;//?????????????????Flag photos = 2 may imply CkovEta = 0??????????????
 165       if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i];  //find max and min Theta ckov from all candidates within probable window
 166       if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
 167       weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];   wei += fPhotWei[i];                 //collect weight as sum of all candidate weghts
 168
 169       sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
 170     }
 171   }//candidates loop
 172
 173   if(sigma2>0) fCkovSigma2=1./sigma2;
 174   else         fCkovSigma2=1e10;
 175
 176   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
 177   return weightThetaCerenkov;
 178 }//FindCkovRing()
 179 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 180 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
 181 {
 182 // Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by  HoughResponse()
 183 // Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
 184 //   Returns: number of photon candidates happened to be inside the window
 185
 186
 187   Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0  and thetaCkovHough
 188
 189   Double_t tmin = (Double_t)(steps - 1)*fDTheta;
 190   Double_t tmax = (Double_t)(steps)*fDTheta;
 191   Double_t tavg = 0.5*(tmin+tmax);
 192
 193   tmin = tavg - 0.5*fWindowWidth;  tmax = tavg + 0.5*fWindowWidth;
 194
 195   Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
 196   for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
 197     if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax)    {
 198       fPhotFlag[i]=2;
 199       iInsideCnt++;
 200     }
 201   }
 202   return iInsideCnt;
 203 }//FlagPhot()
 204 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 205 Double_t AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi,TVector2 &pos)const
 206 {
 207 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
 208 // Arguments: ckovThe,ckovPhi- photon ckov angles, [rad]  (warning: not photon theta and phi)
 209 //   Returns: distance between photon point on PC and track projection
 210   TRotation mtheta;   mtheta.RotateY(fTrkDir.Theta());
 211   TRotation mphi;       mphi.RotateZ(fTrkDir.Phi());
 212   TRotation mrot=mphi*mtheta;
 213
 214   TVector3  posCkov(fTrkPos.X(),fTrkPos.Y(),-0.5*fgkRadThick-fgkWinThick-fgkGapThick);   //RAD: photon position is track position @ middle of RAD
 215   TVector3  dirCkov;   dirCkov.SetMagThetaPhi(1,ckovThe,ckovPhi);                        //initially photon is directed according to requested ckov angle
 216                                                dirCkov=mrot*dirCkov;                     //now we know photon direction in LORS
 217                        dirCkov.SetPhi(ckovPhi);
 218   if(dirCkov.Theta() > TMath::ASin(1./fRadNmean)) return -999;//total refraction on WIN-GAP boundary
 219
 220   Propagate(dirCkov,posCkov,-fgkWinThick-fgkGapThick); //go to RAD-WIN boundary  remeber that z=0 is PC plane
 221   Refract  (dirCkov,         fRadNmean,fgkWinIdx    ); //RAD-WIN refraction
 222   Propagate(dirCkov,posCkov,-fgkGapThick           );  //go to WIN-GAP boundary
 223   Refract  (dirCkov,         fgkWinIdx,fgkGapIdx    ); //WIN-GAP refraction
 224   Propagate(dirCkov,posCkov,0                     );   //go to PC
 225
 226   pos.Set(posCkov.X(),posCkov.Y());
 227   return (pos-fTrkPos).Mod();
 228 }//TracePhoton()
 229 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 230 void AliHMPIDRecon::Propagate(const TVector3 &dir,TVector3 &pos,Double_t z)const
 231 {
 232 // Finds an intersection point between a line and XY plane shifted along Z.
 233 // Arguments:  dir,pos   - vector along the line and any point of the line
 234 //             z         - z coordinate of plain
 235 //   Returns:  none
 236 //   On exit:  pos is the position if this intesection if any
 237   static TVector3 nrm(0,0,1);
 238          TVector3 pnt(0,0,z);
 239
 240   TVector3 diff=pnt-pos;
 241   Double_t sint=(nrm*diff)/(nrm*dir);
 242   pos+=sint*dir;
 243 }//Propagate()
 244 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 245 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
 246 {
 247 // Refract direction vector according to Snell law
 248 // Arguments:
 249 //            n1 - ref idx of first substance
 250 //            n2 - ref idx of second substance
 251 //   Returns: none
 252 //   On exit: dir is new direction
 253   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
 254   if(sinref>1.)    dir.SetXYZ(-999,-999,-999);
 255   else             dir.SetTheta(TMath::ASin(sinref));
 256 }//Refract()
 257 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 258 Double_t AliHMPIDRecon::HoughResponse()
 259 {
 260 //
 261 //
 262 //
 263   Double_t kThetaMax=0.75;
 264   Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
 265   TH1D *phots   = new TH1D("Rphot"  ,"phots"         ,nChannels,0,kThetaMax);
 266   TH1D *photsw  = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
 267   TH1D *resultw = new TH1D("resultw","resultw"       ,nChannels,0,kThetaMax);
 268   Int_t nBin = (Int_t)(kThetaMax/fDTheta);
 269   Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
 270
 271   for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
 272     Double_t angle = fPhotCkov[i];  if(angle<0||angle>kThetaMax) continue;
 273     phots->Fill(angle);
 274     Int_t bin = (Int_t)(0.5+angle/(fDTheta));
 275     Double_t weight=1.;
 276     if(fIsWEIGHT){
 277       Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta;  Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
 278       Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
 279       if(diffArea>0) weight = 1./diffArea;
 280     }
 281     photsw->Fill(angle,weight);
 282     fPhotWei[i]=weight;
 283   }//photon candidates loop
 284
 285   for (Int_t i=1; i<=nBin;i++){
 286     Int_t bin1= i-nCorrBand;
 287     Int_t bin2= i+nCorrBand;
 288     if(bin1<1) bin1=1;
 289     if(bin2>nBin)bin2=nBin;
 290     Double_t sumPhots=phots->Integral(bin1,bin2);
 291     if(sumPhots<3) continue;                            // if less then 3 photons don't trust to this ring
 292     Double_t sumPhotsw=photsw->Integral(bin1,bin2);
 293     resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
 294   }
 295 // evaluate the "BEST" theta ckov as the maximum value of histogramm
 296   Double_t *pVec = resultw->GetArray();
 297   Int_t locMax = TMath::LocMax(nBin,pVec);
 298   phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
 299
 300   return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
 301 }//HoughResponse()
 302 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 303 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
 304 {
 305 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
 306 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 307 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 308 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 309 //            MIP beta
 310 //   Returns: absolute error on Cerenkov angle, [radians]
 311
 312   TVector3 v(-999,-999,-999);
 313   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
 314
 315   v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
 316   v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
 317   v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
 318
 319   return v.Mag2();
 320 }
 321 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 322 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
 323 {
 324 // Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
 325 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 326 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 327 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 328 //            MIP beta
 329 //   Returns: absolute error on Cerenkov angle, [radians]
 330   Double_t phiDelta = phiC - fTrkDir.Phi();
 331
 332   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 333   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 334   if (k<0) return 1e10;
 335
 336   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()));
 337   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()));
 338
 339   Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
 340   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));
 341   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));
 342
 343   return  TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
 344 }
 345 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 346 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 347 {
 348 // Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
 349 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 350 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 351 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 352 //            MIP beta
 353 //   Returns: absolute error on Cerenkov angle, [radians]
 354   Double_t phiDelta = phiC - fTrkDir.Phi();
 355   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 356
 357   Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fRadNmean*betaM*betaM/(alpha*TMath::Tan(thetaC));
 358
 359   Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
 360
 361   return f*dtdn;
 362 }//SigCrom()
 363 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 364 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 365 {
 366 // Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
 367 // created by a given MIP. Formulae according to CERN-EP-2000-058
 368 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 369 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 370 //            MIP beta
 371 //   Returns: absolute error on Cerenkov angle, [radians]
 372
 373   Double_t phiDelta = phiC - fTrkDir.Phi();
 374   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 375
 376   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 377   if (k<0) return 1e10;
 378
 379   Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
 380   Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
 381
 382   Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
 383   Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
 384   Double_t ii = 1.+eTr*betaM*i;
 385
 386   Double_t err = c * (i/(alpha*alpha*8) +  ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
 387   Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
 388
 389   return trErr*err;
 390 }//SigGeom()
 391 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++