CandidateMatchHelpers: Try to transform the cluster calo position vector wrt to (0,0,0) to a position vector wrt to track perigee position

Mentioning @amorley as this tries to tackle of the issues he brough up.

The issue is that for large track r/d0 or z0 one needs to approximate "transform" the position of the cluster from something wrt to (0,0,0) to something wrt track perigee position (x0,y0,z0) before performing the quick and dirty candidate match.

Reconstruction/egamma/egammaAlgs/src/egammaSelectedTrackCopy.cxx

@@ -192,14 +192,17 @@ bool egammaSelectedTrackCopy::Select(const EventContext& ctx,
 {
 
   ATH_MSG_DEBUG("egammaSelectedTrackCopy::Select()" );
-  if (cluster == 0 || track == 0) return false;
+  if (cluster == nullptr || track == nullptr) return false;
   const Trk::Perigee& candidatePerigee = track->perigeeParameters();
 
   //Get Perigee Parameters
   const double  trkPhi = candidatePerigee.parameters()[Trk::phi];
   const double  trkEta = candidatePerigee.eta();
-  const double  r_first=candidatePerigee.position().perp();
-  const double  z_first=candidatePerigee.position().z();
+  const double  z_perigee=candidatePerigee.position().z();
+  const double  r_perigee=candidatePerigee.position().perp();
+  const Amg::Vector3D PerigeeXYZPosition(candidatePerigee.position().x(),
+                                         candidatePerigee.position().y(),
+                                         z_perigee);
 
   //Get Cluster parameters
   const double clusterEta=cluster->etaBE(2);
@@ -215,42 +218,59 @@ bool egammaSelectedTrackCopy::Select(const EventContext& ctx,
     return false;
   }
 
-  //Calculate corrrected eta and Phi
-  const double etaclus_corrected = CandidateMatchHelpers::CorrectedEta(clusterEta,z_first,isEndCap);
-  const double phiRot = CandidateMatchHelpers::PhiROT(Et,trkEta, track->charge(),r_first ,isEndCap)  ;
-  const double phiRotTrack = CandidateMatchHelpers::PhiROT(track->pt(),trkEta, track->charge(),r_first ,isEndCap)  ;
-  //Calcualate deltaPhis 
-  const double deltaPhiStd = P4Helpers::deltaPhi(cluster->phiBE(2), trkPhi);
-  const double trkPhiCorr = P4Helpers::deltaPhi(trkPhi, phiRot);
-  const double deltaPhi2 = P4Helpers::deltaPhi(cluster->phiBE(2), trkPhiCorr);
+  //Calculate the eta/phi of the cluster as would be seen from the perigee position of the Track
+  const Amg::Vector3D XYZClusterWrtTrackPerigee = CandidateMatchHelpers::approxXYZwrtPoint(*cluster,
+                                                                                           PerigeeXYZPosition,
+                                                                                           isEndCap);
+  //Calculate the possible rotation of the track 
+  //Once assuming the cluster Et being the better estimate (e.g big brem)
+  const double phiRotRescaled = CandidateMatchHelpers::PhiROT(Et,trkEta, 
+                                                              track->charge(),
+                                                              r_perigee,
+                                                              isEndCap)  ;
+  //And also assuming the track Pt being correct 
+  const double phiRotTrack = CandidateMatchHelpers::PhiROT(track->pt(),
+                                                           trkEta, 
+                                                           track->charge(),
+                                                           r_perigee,
+                                                           isEndCap)  ;
+  //
+  const double clusterPhiCorrected=XYZClusterWrtTrackPerigee.phi();   
+  //deltaPhi between the track and the cluster 
+  const double deltaPhiStd = P4Helpers::deltaPhi(clusterPhiCorrected, trkPhi);
+  //deltaPhi between the track and the cluster accounting for rotation assuming cluster Et is a better estimator
+  const double trkPhiRescaled= P4Helpers::deltaPhi(trkPhi, phiRotRescaled);
+  const double deltaPhiRescaled = P4Helpers::deltaPhi(clusterPhiCorrected, trkPhiRescaled);
+  //deltaPhi between the track and the cluster accounting for rotation
   const double trkPhiCorrTrack = P4Helpers::deltaPhi(trkPhi, phiRotTrack);
-  const double deltaPhi2Track = P4Helpers::deltaPhi(cluster->phiBE(2), trkPhiCorrTrack);
-
+  const double deltaPhiTrack = P4Helpers::deltaPhi(clusterPhiCorrected, trkPhiCorrTrack);
   /* 
    * First we will see if it fails the quick match 
    * Then if it passed it will get 2 chances to be selected
    * One if it matches from last measurement
    * The second if it matched from Perigee rescales
    */
-
   //Broad phi check
-  if ( (fabs(deltaPhi2) > 2*m_broadDeltaPhi) 
-       && (fabs(deltaPhi2Track) > 2.*m_broadDeltaPhi) 
+  if ((fabs(deltaPhiRescaled) > 2*m_broadDeltaPhi) 
+       && (fabs(deltaPhiTrack) > 2.*m_broadDeltaPhi) 
        && (fabs(deltaPhiStd) > 2*m_broadDeltaPhi)){
-    ATH_MSG_DEBUG("FAILS broad window phi match (track phi, phirotCluster , phiRotTrack ,cluster phi): ( " 
-                  << trkPhi << ", " << phiRot<< ", "<<phiRotTrack<< ", " << cluster->phiBE(2) << ")" );
+    ATH_MSG_DEBUG("FAILS broad window phi match (track phi, phirotCluster , phiRotTrack , "
+                  <<"cluster phi corrected, cluster phi): ( " 
+                  << trkPhi << ", " << phiRotRescaled<< ", "<<phiRotTrack<< ", " 
+                  <<clusterPhiCorrected<<  ", " <<cluster->phi() <<")" );
     return false;
   }
   //if TRT we can stop here , we can not check much in eta really.
   if(trkTRT){
     return true;
   }
+  const double clusterEtaCorrected=XYZClusterWrtTrackPerigee.eta();
 
-  //eta check
-  if (fabs(cluster->etaBE(2) - trkEta) > 2*m_broadDeltaEta && 
-      fabs( etaclus_corrected- trkEta) > 2.*m_broadDeltaEta){
+  //Broad eta check
+  if (fabs(cluster->eta() - trkEta) > 2*m_broadDeltaEta && 
+      fabs(clusterEtaCorrected- trkEta) > 2.*m_broadDeltaEta){
     ATH_MSG_DEBUG("FAILS broad window eta match (track eta, cluster eta, cluster eta corrected): ( " 
-                  << trkEta << ", " << cluster->etaBE(2) <<", "<<etaclus_corrected<<")" );
+                  << trkEta << ", " << cluster->etaBE(2) <<", "<<clusterEtaCorrected<<" )");
     return false;
   }