STEER/STEERBase/AliHMPIDPIDResponse.cxx

   1 /**************************************************************************
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   3  *                                                                        *
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  15
  16 //***********************************************************
  17 // Class AliHMPIDPIDResponse
  18 //
  19 // HMPID class to perfom particle identification
  20 //
  21 // Author: G. Volpe, giacomo.volpe@cern.ch
  22 //***********************************************************
  23
  24
  25 #include "AliHMPIDPIDResponse.h"  //class header
  26 #include "AliPID.h"               //FindPid()
  27 #include "AliVTrack.h"            //FindPid()
  28 #include "AliLog.h"               //general
  29 #include <TRandom.h>              //Resolution()
  30 #include <TVector2.h>             //Resolution()
  31 #include <TRotation.h>
  32 #include <TF1.h>
  33 #include <TGeoManager.h>          //Instance()
  34 #include <TGeoMatrix.h>           //Instance()
  35 #include <TGeoPhysicalNode.h>     //ctor
  36 #include <TGeoBBox.h>
  37 #include <TObjArray.h>
  38
  39 Float_t AliHMPIDPIDResponse::fgkMinPcX[]={0.,0.,0.,0.,0.,0.};
  40 Float_t AliHMPIDPIDResponse::fgkMaxPcX[]={0.,0.,0.,0.,0.,0.};
  41 Float_t AliHMPIDPIDResponse::fgkMinPcY[]={0.,0.,0.,0.,0.,0.};
  42 Float_t AliHMPIDPIDResponse::fgkMaxPcY[]={0.,0.,0.,0.,0.,0.};
  43
  44 Float_t AliHMPIDPIDResponse::fgCellX=0.;
  45 Float_t AliHMPIDPIDResponse::fgCellY=0.;
  46
  47 Float_t AliHMPIDPIDResponse::fgPcX=0;
  48 Float_t AliHMPIDPIDResponse::fgPcY=0;
  49
  50 Float_t AliHMPIDPIDResponse::fgAllX=0;
  51 Float_t AliHMPIDPIDResponse::fgAllY=0;
  52
  53 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  54 AliHMPIDPIDResponse::AliHMPIDPIDResponse():
  55   TNamed("HMPIDPIDResponseRec","HMPIDPIDResponsePid"),
  56   fRefIdx(1.28947),
  57   fTrkDir(0,0,1),
  58   fTrkPos(30,40),
  59   fRefIndexArray(0x0)
  60 {
  61   //
  62   // ctor
  63   //
  64
  65   Float_t dead=2.6;// cm of the dead zones between PCs-> See 2CRC2099P1
  66
  67   fgCellX=0.8; fgCellY=0.84;
  68
  69   fgPcX  = 80.*fgCellX;      fgPcY = 48.*fgCellY;
  70   fgAllX = 2.*fgPcX+dead;
  71   fgAllY = 3.*fgPcY+2.*dead;
  72
  73   fgkMinPcX[1]=fgPcX+dead; fgkMinPcX[3]=fgkMinPcX[1];  fgkMinPcX[5]=fgkMinPcX[3];
  74   fgkMaxPcX[0]=fgPcX;      fgkMaxPcX[2]=fgkMaxPcX[0];  fgkMaxPcX[4]=fgkMaxPcX[2];
  75   fgkMaxPcX[1]=fgAllX;     fgkMaxPcX[3]=fgkMaxPcX[1];  fgkMaxPcX[5]=fgkMaxPcX[3];
  76
  77   fgkMinPcY[2]=fgPcY+dead;       fgkMinPcY[3]=fgkMinPcY[2];
  78   fgkMinPcY[4]=2.*fgPcY+2.*dead; fgkMinPcY[5]=fgkMinPcY[4];
  79   fgkMaxPcY[0]=fgPcY;            fgkMaxPcY[1]=fgkMaxPcY[0];
  80   fgkMaxPcY[2]=2.*fgPcY+dead;    fgkMaxPcY[3]=fgkMaxPcY[2];
  81   fgkMaxPcY[4]=fgAllY;           fgkMaxPcY[5]=fgkMaxPcY[4];
  82
  83   for(Int_t i=kMinCh;i<=kMaxCh;i++)
  84     if(gGeoManager && gGeoManager->IsClosed()) {
  85       TGeoPNEntry* pne = gGeoManager->GetAlignableEntry(Form("/HMPID/Chamber%i",i));
  86       if (!pne) {
  87         AliErrorClass(Form("The symbolic volume %s does not correspond to any physical entry!",Form("HMPID_%i",i)));
  88         fM[i]=new TGeoHMatrix;
  89         IdealPosition(i,fM[i]);
  90       } else {
  91         TGeoPhysicalNode *pnode = pne->GetPhysicalNode();
  92         if(pnode) fM[i]=new TGeoHMatrix(*(pnode->GetMatrix()));
  93         else {
  94           fM[i]=new TGeoHMatrix;
  95           IdealPosition(i,fM[i]);
  96         }
  97       }
  98     } else{
  99       fM[i]=new TGeoHMatrix;
 100       IdealPosition(i,fM[i]);
 101     }
 102
 103 }//ctor
 104 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 105 AliHMPIDPIDResponse::AliHMPIDPIDResponse(const AliHMPIDPIDResponse& c):
 106   TNamed(c),
 107   fRefIdx(c.fRefIdx),
 108   fTrkDir(c.fTrkDir),
 109   fTrkPos(c.fTrkPos),
 110   fRefIndexArray(c.fRefIndexArray)
 111  {
 112    //
 113    // copy ctor
 114    //
 115
 116    for(Int_t i=0; i<6; i++) {
 117
 118       fgkMinPcX[i] = c.fgkMinPcX[i];
 119       fgkMinPcY[i] = c.fgkMinPcY[i];
 120       fgkMaxPcX[i] = c.fgkMaxPcX[i];
 121       fgkMaxPcY[i] = c.fgkMaxPcY[i];
 122      }
 123
 124    for(Int_t i=0; i<7; i++) fM[i] = c.fM[i];
 125  }
 126 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 127 AliHMPIDPIDResponse& AliHMPIDPIDResponse::operator=(const AliHMPIDPIDResponse& c) {
 128
 129    //
 130    // assignment operator
 131    //
 132   if(this!=&c){
 133      TNamed::operator=(c);
 134      fgCellX = c.fgCellX;
 135      fgCellY = c.fgCellY;
 136      fgPcX   = c.fgPcX;
 137      fgPcY   = c.fgPcY;
 138      fgAllX  = c.fgAllX;
 139      fgAllY  = c.fgAllY;
 140      fRefIdx = c.fRefIdx;
 141      fTrkDir = c.fTrkDir;
 142      fTrkPos = c.fTrkPos;
 143      fRefIndexArray = c.fRefIndexArray;
 144      for(Int_t i=0; i<6; i++) {
 145       fgkMinPcX[i] = c.fgkMinPcX[i];
 146       fgkMinPcY[i] = c.fgkMinPcY[i];
 147       fgkMaxPcX[i] = c.fgkMaxPcX[i];
 148       fgkMaxPcY[i] = c.fgkMaxPcY[i];
 149      }
 150      for(Int_t i=0; i<7; i++) fM[i] = c.fM[i];
 151     }
 152
 153   return *this;
 154 }
 155 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 156 void AliHMPIDPIDResponse::IdealPosition(Int_t iCh, TGeoHMatrix *pMatrix) {
 157
 158 // Construct ideal position matrix for a given chamber
 159 // Arguments: iCh- chamber ID; pMatrix- pointer to precreated unity matrix where to store the results
 160 // Returns: none
 161
 162   const Double_t kAngHor=19.5;        //  horizontal angle between chambers  19.5 grad
 163   const Double_t kAngVer=20;          //  vertical angle between chambers    20   grad
 164   const Double_t kAngCom=30;          //  common HMPID rotation with respect to x axis  30   grad
 165   const Double_t kTrans[3]={490,0,0}; //  center of the chamber is on window-gap surface
 166   pMatrix->RotateY(90);               //  rotate around y since initial position is in XY plane -> now in YZ plane
 167   pMatrix->SetTranslation(kTrans);    //  now plane in YZ is shifted along x
 168   switch(iCh){
 169     case 0:                pMatrix->RotateY(kAngHor);  pMatrix->RotateZ(-kAngVer);  break; //right and down
 170     case 1:                                            pMatrix->RotateZ(-kAngVer);  break; //down
 171     case 2:                pMatrix->RotateY(kAngHor);                               break; //right
 172     case 3:                                                                         break; //no rotation
 173     case 4:                pMatrix->RotateY(-kAngHor);                              break; //left
 174     case 5:                                            pMatrix->RotateZ(kAngVer);   break; //up
 175     case 6:                pMatrix->RotateY(-kAngHor); pMatrix->RotateZ(kAngVer);   break; //left and up
 176   }
 177   pMatrix->RotateZ(kAngCom);     //apply common rotation  in XY plane
 178
 179 }
 180 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 181 Double_t AliHMPIDPIDResponse::GetExpectedSignal(const AliVTrack *vTrk, AliPID::EParticleType specie) const {
 182
 183   // expected Cherenkov angle calculation
 184
 185   const Double_t nmean = GetNMean(vTrk);
 186   return ExpectedSignal(vTrk,nmean,specie);
 187 }
 188 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 189 Double_t AliHMPIDPIDResponse::GetExpectedSigma(const AliVTrack *vTrk, AliPID::EParticleType specie) const {
 190
 191   // expected resolution calculation
 192
 193   const Double_t nmean = GetNMean(vTrk);
 194   return ExpectedSigma(vTrk,nmean,specie);
 195 }
 196 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 197 Double_t AliHMPIDPIDResponse::ExpectedSignal(const AliVTrack *vTrk, Double_t nmean, AliPID::EParticleType specie) const {
 198
 199   // expected Cherenkov angle calculation
 200
 201   Double_t thetaTheor = -999.;
 202
 203   Double_t p[3] = {0}, mom = 0;
 204   if(vTrk->GetOuterHmpPxPyPz(p))  mom = TMath::Sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]);  // Momentum of the charged particle
 205   else return thetaTheor;
 206
 207   const Double_t mass = AliPID::ParticleMass(specie);
 208   const Double_t cosTheta = TMath::Sqrt(mass*mass+mom*mom)/(nmean*mom);
 209
 210   if(cosTheta>1) return thetaTheor;
 211
 212   else thetaTheor = TMath::ACos(cosTheta);
 213
 214   return thetaTheor;                                                                                          //  evaluate the theor. Theta Cherenkov
 215 }
 216 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 217 Double_t AliHMPIDPIDResponse::ExpectedSigma(const AliVTrack *vTrk, Double_t nmean, AliPID::EParticleType specie) const {
 218
 219   // expected resolution calculation
 220
 221   Float_t x=0., y=0.;
 222   Int_t q=0, nph=0;
 223   Float_t xPc=0.,yPc=0.,thRa=0.,phRa=0.;
 224
 225   vTrk->GetHMPIDmip(x,y,q,nph);
 226   vTrk->GetHMPIDtrk(xPc,yPc,thRa,phRa);
 227
 228   const Double_t xRa = xPc - (RadThick()+WinThick()+GapThick())*TMath::Cos(phRa)*TMath::Tan(thRa);  //just linear extrapolation back to RAD
 229   const Double_t yRa = yPc - (RadThick()+WinThick()+GapThick())*TMath::Sin(phRa)*TMath::Tan(thRa);  //just linear extrapolation back to RAD
 230
 231   const Double_t thetaCerTh = ExpectedSignal(vTrk,nmean,specie);
 232   const Double_t occupancy  = vTrk->GetHMPIDoccupancy();
 233   const Double_t thetaMax   = TMath::ACos(1./nmean);
 234   const Int_t    nPhotsTh   = (Int_t)(12.*TMath::Sin(thetaCerTh)*TMath::Sin(thetaCerTh)/(TMath::Sin(thetaMax)*TMath::Sin(thetaMax))+0.01);
 235
 236   Double_t sigmatot = 0;
 237   Int_t nTrks = 20;
 238   for(Int_t iTrk=0;iTrk<nTrks;iTrk++) {
 239     Double_t invSigma = 0;
 240     Int_t nPhotsAcc = 0;
 241
 242     Int_t nPhots = 0;
 243     if(nph<nPhotsTh+TMath::Sqrt(nPhotsTh) && nph>nPhotsTh-TMath::Sqrt(nPhotsTh)) nPhots = nph;
 244     else nPhots = gRandom->Poisson(nPhotsTh);
 245
 246     for(Int_t j=0;j<nPhots;j++){
 247       Double_t phi = gRandom->Rndm()*TMath::TwoPi();
 248       TVector2 pos; pos = TracePhot(xRa,yRa,thRa,phRa,thetaCerTh,phi);
 249       if(!IsInside(pos.X(),pos.Y())) continue;
 250       if(IsInDead(pos.X(),pos.Y()))  continue;
 251       Double_t sigma2 = Sigma2(thRa,thRa,thetaCerTh,phi); //photon candidate sigma^2
 252
 253       if(sigma2!=0) {
 254         invSigma += 1./sigma2;
 255         nPhotsAcc++;
 256       }
 257     }
 258     if(invSigma!=0) sigmatot += 1./TMath::Sqrt(invSigma);
 259   }
 260
 261   return (sigmatot/nTrks)*SigmaCorrFact(specie,occupancy);
 262 }
 263 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 264 Double_t AliHMPIDPIDResponse::GetNumberOfSigmas(const AliVTrack *vTrk, AliPID::EParticleType specie) const {
 265
 266   // Number of sigmas calculation
 267
 268   Double_t nSigmas = -999.;
 269
 270   if(vTrk->GetHMPIDsignal()<0.) return nSigmas;
 271
 272   const Double_t nmean = GetNMean(vTrk);
 273
 274   const Double_t expSigma = ExpectedSigma(vTrk, nmean, specie);
 275
 276   if(expSigma > 0.) nSigmas = (vTrk->GetHMPIDsignal() - ExpectedSignal(vTrk,nmean,specie))/expSigma;
 277
 278   return nSigmas;
 279
 280 }
 281 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 282 void AliHMPIDPIDResponse::GetProbability(const AliVTrack *vTrk,Int_t nSpecies,Double_t *prob) const {
 283
 284 // Calculates probability to be a electron-muon-pion-kaon-proton with the "amplitude" method
 285 // from the given Cerenkov angle and momentum assuming no initial particle composition
 286
 287   const Double_t thetaCerExp = vTrk->GetHMPIDsignal();
 288
 289   const Double_t nmean = GetNMean(vTrk);
 290
 291   if(thetaCerExp<=0){                                                                                     // HMPID does not find anything reasonable for this track, assign 0.2 for all species
 292     for(Int_t iPart=0;iPart<nSpecies;iPart++) prob[iPart]=1.0/(Float_t)nSpecies;
 293     return;
 294   }
 295
 296   Double_t p[3] = {0,0,0};
 297
 298   if(!(vTrk->GetOuterHmpPxPyPz(p))) for(Int_t iPart=0;iPart<nSpecies;iPart++) prob[iPart]=1.0/(Float_t)nSpecies;
 299
 300   Double_t hTot=0;                                                                                        // Initialize the total height of the amplitude method
 301   Double_t *h = new Double_t [nSpecies];                                                                  // number of charged particles to be considered
 302
 303   Bool_t desert = kTRUE;                                                                                  // Flag to evaluate if ThetaC is far ("desert") from the given Gaussians
 304
 305   for(Int_t iPart=0;iPart<nSpecies;iPart++){                                                              // for each particle
 306
 307
 308     h[iPart] = 0;                                                                                         // reset the height
 309     Double_t thetaCerTh = ExpectedSignal(vTrk,nmean,(AliPID::EParticleType)iPart);                        // theoretical Theta Cherenkov
 310     if(thetaCerTh>900.) continue;                                                                         // no light emitted, zero height
 311     Double_t sigmaRing = ExpectedSigma(vTrk,nmean,(AliPID::EParticleType)iPart);
 312
 313     if(sigmaRing==0) continue;
 314
 315     if(TMath::Abs(thetaCerExp-thetaCerTh)<4*sigmaRing) desert = kFALSE;
 316     h[iPart] =TMath::Gaus(thetaCerTh,thetaCerExp,sigmaRing,kTRUE);
 317     hTot    +=h[iPart];                                                                                   // total height of all theoretical heights for normalization
 318
 319   }//species loop
 320
 321   for(Int_t iPart=0;iPart<nSpecies;iPart++) {                                                             // species loop to assign probabilities
 322
 323     if(!desert) prob[iPart]=h[iPart]/hTot;
 324     else        prob[iPart]=1.0/(Float_t)nSpecies;                                                        // all theoretical values are far away from experemental one
 325
 326   }
 327
 328   delete [] h;
 329 }
 330 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 331 Double_t AliHMPIDPIDResponse::GetSignalDelta(const AliVTrack *vTrk, AliPID::EParticleType specie, Bool_t ratio/*=kFALSE*/) const {
 332
 333   //
 334   // calculation of Experimental Cherenkov angle - Theoretical Cherenkov angle
 335   //
 336   const Double_t signal    = vTrk->GetHMPIDsignal();
 337   const Double_t expSignal = GetExpectedSignal(vTrk,specie);
 338
 339   Double_t delta = -9999.;
 340   if (!ratio) delta=signal-expSignal;
 341   else if (expSignal>1.e-20) delta=signal/expSignal;
 342
 343   return delta;
 344 }
 345 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 346 TVector2 AliHMPIDPIDResponse::TracePhot(Double_t xRa, Double_t yRa, Double_t thRa, Double_t phRa, Double_t ckovThe,Double_t ckovPhi) const {
 347
 348 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
 349 // Returns: distance between photon point on PC and track projection
 350
 351   Double_t theta=0.,phi=0.;
 352   TVector3  dirTRS,dirLORS;
 353   dirTRS.SetMagThetaPhi(1,ckovThe,ckovPhi);                     //photon in TRS
 354   Trs2Lors(thRa,phRa,dirTRS,theta,phi);
 355   dirLORS.SetMagThetaPhi(1,theta,phi);                          //photon in LORS
 356   return TraceForward(xRa,yRa,dirLORS);                                 //now foward tracing
 357 }//TracePhot()
 358 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 359 TVector2 AliHMPIDPIDResponse::TraceForward(Double_t xRa, Double_t yRa, TVector3 dirCkov) const {
 360
 361 // Trace forward a photon from (x,y) up to PC
 362 // Returns: pos of traced photon at PC
 363
 364   TVector2 pos(-999,-999);
 365   Double_t thetaCer = dirCkov.Theta();
 366   if(thetaCer > TMath::ASin(1./GetRefIdx())) return pos;          //total refraction on WIN-GAP boundary
 367   Double_t zRad= -0.5*RadThick()-0.5*WinThick();          //z position of middle of RAD
 368   TVector3  posCkov(xRa,yRa,zRad);                        //RAD: photon position is track position @ middle of RAD
 369   Propagate(dirCkov,posCkov,           -0.5*WinThick());          //go to RAD-WIN boundary
 370   Refract  (dirCkov,         GetRefIdx(),WinIdx());       //RAD-WIN refraction
 371   Propagate(dirCkov,posCkov,            0.5*WinThick());          //go to WIN-GAP boundary
 372   Refract  (dirCkov,         WinIdx(),GapIdx());          //WIN-GAP refraction
 373   Propagate(dirCkov,posCkov,0.5*WinThick()+GapThick());   //go to PC
 374   pos.Set(posCkov.X(),posCkov.Y());
 375   return pos;
 376 }//TraceForward()
 377 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 378 void AliHMPIDPIDResponse::Propagate(const TVector3 dir,TVector3 &pos,Double_t z) const {
 379
 380 // Finds an intersection point between a line and XY plane shifted along Z.
 381 // Arguments:  dir,pos   - vector along the line and any point of the line
 382 //             z         - z coordinate of plain
 383 // Returns:  none
 384 // On exit:  pos is the position if this intesection if any
 385
 386   static TVector3 nrm(0,0,1);
 387          TVector3 pnt(0,0,z);
 388
 389   TVector3 diff=pnt-pos;
 390   Double_t sint=(nrm*diff)/(nrm*dir);
 391   pos+=sint*dir;
 392 }//Propagate()
 393 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 394 void AliHMPIDPIDResponse::Refract(TVector3 &dir,Double_t n1,Double_t n2) const {
 395
 396 // Refract direction vector according to Snell law
 397 // Arguments:
 398 //            n1 - ref idx of first substance
 399 //            n2 - ref idx of second substance
 400 //   Returns: none
 401 //   On exit: dir is new direction
 402
 403   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
 404   if(TMath::Abs(sinref)>1.) dir.SetXYZ(-999,-999,-999);
 405   else             dir.SetTheta(TMath::ASin(sinref));
 406 }//Refract()
 407 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 408 void AliHMPIDPIDResponse::Trs2Lors(Double_t thRa, Double_t phRa, TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer) const {
 409
 410   // Theta Cerenkov reconstruction
 411   // Returns: thetaCer of photon in LORS
 412   //          phiCer of photon in LORS
 413
 414   TRotation mtheta;   mtheta.RotateY(thRa);
 415   TRotation mphi;       mphi.RotateZ(phRa);
 416   TRotation mrot=mphi*mtheta;
 417   TVector3 dirCkovLORS;
 418   dirCkovLORS=mrot*dirCkov;
 419   phiCer  = dirCkovLORS.Phi();                                          //actual value of the phi of the photon
 420   thetaCer= dirCkovLORS.Theta();                                        //actual value of thetaCerenkov of the photon
 421 }
 422 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 423 Bool_t AliHMPIDPIDResponse::IsInDead(Float_t x,Float_t y)  {
 424
 425 // Check is the current point is outside of sensitive area or in dead zones
 426 // Arguments: x,y -position
 427 // Returns: 1 if not in sensitive zone
 428
 429   for(Int_t iPc=0;iPc<6;iPc++)
 430     if(x>=fgkMinPcX[iPc] && x<=fgkMaxPcX[iPc] && y>=fgkMinPcY[iPc] && y<=fgkMaxPcY [iPc]) return kFALSE; //in current pc
 431
 432   return kTRUE;
 433 }
 434 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 435 Double_t AliHMPIDPIDResponse::Sigma2(Double_t trkTheta,Double_t trkPhi,Double_t ckovTh, Double_t ckovPh) const {
 436
 437 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
 438 // created by a given MIP. Formules according to CERN-EP-2000-058
 439 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 440 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 441 //            MIP beta
 442 // Returns: absolute error on Cerenkov angle, [radians]
 443
 444   TVector3 v(-999,-999,-999);
 445   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*GetRefIdx());
 446
 447   if(trkBeta > 1) trkBeta = 1;                 //protection against bad measured thetaCer
 448   if(trkBeta < 0) trkBeta = 0.0001;            //
 449
 450   v.SetX(SigLoc (trkTheta,trkPhi,ckovTh,ckovPh,trkBeta));
 451   v.SetY(SigGeom(trkTheta,trkPhi,ckovTh,ckovPh,trkBeta));
 452   v.SetZ(SigCrom(trkTheta,ckovTh,ckovPh,trkBeta));
 453
 454   return v.Mag2();
 455 }
 456 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 457 Double_t AliHMPIDPIDResponse::SigLoc(Double_t trkTheta,Double_t trkPhi,Double_t thetaC, Double_t phiC,Double_t betaM) const {
 458
 459 // Analitical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
 460 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 461 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 462 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 463 //            MIP beta
 464 // Returns: absolute error on Cerenkov angle, [radians]
 465
 466   Double_t phiDelta = phiC;
 467
 468   Double_t sint     = TMath::Sin(trkTheta);
 469   Double_t cost     = TMath::Cos(trkTheta);
 470   Double_t sinf     = TMath::Sin(trkPhi);
 471   Double_t cosf     = TMath::Cos(trkPhi);
 472   Double_t sinfd    = TMath::Sin(phiDelta);
 473   Double_t cosfd    = TMath::Cos(phiDelta);
 474   Double_t tantheta = TMath::Tan(thetaC);
 475
 476   Double_t alpha =cost-tantheta*cosfd*sint;                                                    // formula (11)
 477   Double_t k = 1.-GetRefIdx()*GetRefIdx()+alpha*alpha/(betaM*betaM);                           // formula (after 8 in the text)
 478   if (k<0) return 1e10;
 479   Double_t mu =sint*sinf+tantheta*(cost*cosfd*sinf+sinfd*cosf);                                // formula (10)
 480   Double_t e  =sint*cosf+tantheta*(cost*cosfd*cosf-sinfd*sinf);                                // formula (9)
 481
 482   Double_t kk = betaM*TMath::Sqrt(k)/(GapThick()*alpha);                                       // formula (6) and (7)
 483   Double_t dtdxc = kk*(k*(cosfd*cosf-cost*sinfd*sinf)-(alpha*mu/(betaM*betaM))*sint*sinfd);    // formula (6)
 484   Double_t dtdyc = kk*(k*(cosfd*sinf+cost*sinfd*cosf)+(alpha* e/(betaM*betaM))*sint*sinfd);    // formula (7)            pag.4
 485
 486   Double_t errX = 0.2,errY=0.25;                                                                //end of page 7
 487   return  TMath::Sqrt(errX*errX*dtdxc*dtdxc + errY*errY*dtdyc*dtdyc);
 488 }
 489 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 490 Double_t AliHMPIDPIDResponse::SigCrom(Double_t trkTheta,Double_t thetaC, Double_t phiC,Double_t betaM) const {
 491
 492 // Analitical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
 493 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 494 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 495 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 496 //            MIP beta
 497 //   Returns: absolute error on Cerenkov angle, [radians]
 498
 499   Double_t phiDelta = phiC;
 500
 501   Double_t sint     = TMath::Sin(trkTheta);
 502   Double_t cost     = TMath::Cos(trkTheta);
 503   Double_t cosfd    = TMath::Cos(phiDelta);
 504   Double_t tantheta = TMath::Tan(thetaC);
 505
 506   Double_t alpha =cost-tantheta*cosfd*sint;                                         // formula (11)
 507   Double_t dtdn = cost*GetRefIdx()*betaM*betaM/(alpha*tantheta);                    // formula (12)
 508
 509   Double_t f = 0.0172*(7.75-5.635)/TMath::Sqrt(24.);
 510
 511   return f*dtdn;
 512 }//SigCrom()
 513 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 514 Double_t AliHMPIDPIDResponse::SigGeom(Double_t trkTheta,Double_t trkPhi,Double_t thetaC, Double_t phiC,Double_t betaM) const {
 515
 516 // Analitical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
 517 // created by a given MIP. Formulae according to CERN-EP-2000-058
 518 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 519 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 520 //            MIP beta
 521 //   Returns: absolute error on Cerenkov angle, [radians]
 522
 523   Double_t phiDelta = phiC;
 524
 525   Double_t sint     = TMath::Sin(trkTheta);
 526   Double_t cost     = TMath::Cos(trkTheta);
 527   Double_t sinf     = TMath::Sin(trkPhi);
 528   Double_t cosfd    = TMath::Cos(phiDelta);
 529   Double_t costheta = TMath::Cos(thetaC);
 530   Double_t tantheta = TMath::Tan(thetaC);
 531
 532   Double_t alpha =cost-tantheta*cosfd*sint;                                                // formula (11)
 533
 534   Double_t k = 1.-GetRefIdx()*GetRefIdx()+alpha*alpha/(betaM*betaM);                       // formula (after 8 in the text)
 535   if (k<0) return 1e10;
 536
 537   Double_t eTr = 0.5*RadThick()*betaM*TMath::Sqrt(k)/(GapThick()*alpha);                    // formula (14)
 538   Double_t lambda = (1.-sint*sinf)*(1.+sint*sinf);                                          // formula (15)
 539
 540   Double_t c1 = 1./(1.+ eTr*k/(alpha*alpha*costheta*costheta));                             // formula (13.a)
 541   Double_t c2 = betaM*TMath::Power(k,1.5)*tantheta*lambda/(GapThick()*alpha*alpha);         // formula (13.b)
 542   Double_t c3 = (1.+eTr*k*betaM*betaM)/((1+eTr)*alpha*alpha);                               // formula (13.c)
 543   Double_t c4 = TMath::Sqrt(k)*tantheta*(1-lambda)/(GapThick()*betaM);                      // formula (13.d)
 544   Double_t dtdT = c1 * (c2+c3*c4);
 545   Double_t trErr = RadThick()/(TMath::Sqrt(12.)*cost);
 546
 547   return trErr*dtdT;
 548 }//SigGeom()
 549 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 550 Double_t AliHMPIDPIDResponse::GetNMean(const AliVTrack *vTrk) const {
 551
 552   //
 553   // mean refractive index calculation
 554   //
 555   Double_t nmean = -999.;
 556
 557   Float_t xPc=0.,yPc=0.,thRa=0.,phRa=0.;
 558   vTrk->GetHMPIDtrk(xPc,yPc,thRa,phRa);
 559
 560   const Int_t ch = vTrk->GetHMPIDcluIdx()/1000000;
 561
 562   const Double_t yRa = yPc - (RadThick()+WinThick()+GapThick())*TMath::Sin(phRa)*TMath::Tan(thRa);  //just linear extrapolation back to RAD
 563
 564   TF1 *RefIndex=0x0;
 565
 566   if(GetRefIndexArray()) RefIndex = (TF1*)(GetRefIndexArray()->At(ch));
 567   else return nmean;
 568
 569   if(RefIndex) nmean = RefIndex->Eval(yRa);
 570   else return nmean;
 571
 572   return nmean;
 573 }
 574 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 575 Double_t AliHMPIDPIDResponse::SigmaCorrFact  (Int_t iPart, Double_t occupancy) {
 576
 577 // calculation of sigma correction factor
 578
 579   Double_t corr = 1.0;
 580
 581   switch(iPart) {
 582     case 0: corr = 0.115*occupancy + 1.166; break;
 583     case 1: corr = 0.115*occupancy + 1.166; break;
 584     case 2: corr = 0.115*occupancy + 1.166; break;
 585     case 3: corr = 0.065*occupancy + 1.137; break;
 586     case 4: corr = 0.048*occupancy + 1.202; break;
 587   }
 588  return corr;
 589 }
 590