+Double_t AliHMPIDParam::Sigma2(Double_t trkTheta,Double_t trkPhi,Double_t ckovTh, Double_t ckovPh)
+{
+// Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
+// created by a given MIP. Fromulae according to CERN-EP-2000-058
+// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
+// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
+// MIP beta
+// Returns: absolute error on Cerenkov angle, [radians]
+
+ TVector3 v(-999,-999,-999);
+ Double_t trkBeta = 1./(TMath::Cos(ckovTh)*GetRefIdx());
+
+ if(trkBeta > 1) trkBeta = 1; //protection against bad measured thetaCer
+ if(trkBeta < 0) trkBeta = 0.0001; //
+
+ v.SetX(SigLoc (trkTheta,trkPhi,ckovTh,ckovPh,trkBeta));
+ v.SetY(SigGeom(trkTheta,trkPhi,ckovTh,ckovPh,trkBeta));
+ v.SetZ(SigCrom(trkTheta,trkPhi,ckovTh,ckovPh,trkBeta));
+
+ return v.Mag2();
+}
+//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Double_t AliHMPIDParam::SigLoc(Double_t trkTheta,Double_t trkPhi,Double_t thetaC, Double_t phiC,Double_t betaM)
+{
+// Analitical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
+// created by a given MIP. Fromulae according to CERN-EP-2000-058
+// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
+// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
+// MIP beta
+// Returns: absolute error on Cerenkov angle, [radians]
+
+ Double_t phiDelta = phiC - trkPhi;
+
+ Double_t sint = TMath::Sin(trkTheta);
+ Double_t cost = TMath::Cos(trkTheta);
+ Double_t sinf = TMath::Sin(trkPhi);
+ Double_t cosf = TMath::Cos(trkPhi);
+ Double_t sinfd = TMath::Sin(phiDelta);
+ Double_t cosfd = TMath::Cos(phiDelta);
+ Double_t tantheta = TMath::Tan(thetaC);
+
+ Double_t alpha =cost-tantheta*cosfd*sint; // formula (11)
+ Double_t k = 1.-GetRefIdx()*GetRefIdx()+alpha*alpha/(betaM*betaM); // formula (after 8 in the text)
+ if (k<0) return 1e10;
+ Double_t mu =sint*sinf+tantheta*(cost*cosfd*sinf+sinfd*cosf); // formula (10)
+ Double_t e =sint*cosf+tantheta*(cost*cosfd*cosf-sinfd*sinf); // formula (9)
+
+ Double_t kk = betaM*TMath::Sqrt(k)/(GapThick()*alpha); // formula (6) and (7)
+ Double_t dtdxc = kk*(k*(cosfd*cosf-cost*sinfd*sinf)-(alpha*mu/(betaM*betaM))*sint*sinfd); // formula (6)
+ Double_t dtdyc = kk*(k*(cosfd*sinf+cost*sinfd*cosf)+(alpha* e/(betaM*betaM))*sint*sinfd); // formula (7) pag.4
+
+ Double_t errX = 0.2,errY=0.25; //end of page 7
+ return TMath::Sqrt(errX*errX*dtdxc*dtdxc + errY*errY*dtdyc*dtdyc);
+}
+//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Double_t AliHMPIDParam::SigCrom(Double_t trkTheta,Double_t trkPhi,Double_t thetaC, Double_t phiC,Double_t betaM)
+{
+// Analitical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
+// created by a given MIP. Fromulae according to CERN-EP-2000-058
+// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
+// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
+// MIP beta
+// Returns: absolute error on Cerenkov angle, [radians]
+
+ Double_t phiDelta = phiC - trkPhi;
+
+ Double_t sint = TMath::Sin(trkTheta);
+ Double_t cost = TMath::Cos(trkTheta);
+ Double_t cosfd = TMath::Cos(phiDelta);
+ Double_t tantheta = TMath::Tan(thetaC);
+
+ Double_t alpha =cost-tantheta*cosfd*sint; // formula (11)
+ Double_t dtdn = cost*GetRefIdx()*betaM*betaM/(alpha*tantheta); // formula (12)
+
+// Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
+ Double_t f = 0.0172*(7.75-5.635)/TMath::Sqrt(24.);
+
+ return f*dtdn;
+}//SigCrom()
+//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+Double_t AliHMPIDParam::SigGeom(Double_t trkTheta,Double_t trkPhi,Double_t thetaC, Double_t phiC,Double_t betaM)
+{
+// Analitical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
+// created by a given MIP. Formulae according to CERN-EP-2000-058
+// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
+// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
+// MIP beta
+// Returns: absolute error on Cerenkov angle, [radians]
+
+ Double_t phiDelta = phiC - trkPhi;
+
+ Double_t sint = TMath::Sin(trkTheta);
+ Double_t cost = TMath::Cos(trkTheta);
+ Double_t sinf = TMath::Sin(trkPhi);
+ Double_t cosfd = TMath::Cos(phiDelta);
+ Double_t costheta = TMath::Cos(thetaC);
+ Double_t tantheta = TMath::Tan(thetaC);
+
+ Double_t alpha =cost-tantheta*cosfd*sint; // formula (11)
+
+ Double_t k = 1.-GetRefIdx()*GetRefIdx()+alpha*alpha/(betaM*betaM); // formula (after 8 in the text)
+ if (k<0) return 1e10;
+
+ Double_t eTr = 0.5*RadThick()*betaM*TMath::Sqrt(k)/(GapThick()*alpha); // formula (14)
+ Double_t lambda = 1.-sint*sint*sinf*sinf; // formula (15)
+
+ Double_t c1 = 1./(1.+ eTr*k/(alpha*alpha*costheta*costheta)); // formula (13.a)
+ Double_t c2 = betaM*TMath::Power(k,1.5)*tantheta*lambda/(GapThick()*alpha*alpha); // formula (13.b)
+ Double_t c3 = (1.+eTr*k*betaM*betaM)/((1+eTr)*alpha*alpha); // formula (13.c)
+ Double_t c4 = TMath::Sqrt(k)*tantheta*(1-lambda)/(GapThick()*betaM); // formula (13.d)
+ Double_t dtdT = c1 * (c2+c3*c4);
+ Double_t trErr = RadThick()/(TMath::Sqrt(12.)*cost);
+
+ return trErr*dtdT;
+}//SigGeom()
+//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++