PPR meeting - January 23, 2003 Andrea Dainese 1 TPC tracking parameterization: a useful tool for simulation studies with large statistics Motivation Implementation of the tool Results Howto

PPR meeting - January 23, 2003 Andrea Dainese 2 Motivation Starting point: background simulation for hadronic charm studies Used also for B  e ± +X and for Hyperons ( ,  ) These simulation studies: need for a large number of BKG events (~10 4 ) performances determined mainly by ITS (d 0 measurement) BKG event size (galice.root): 20 MB (only ITS) 1.3 GB (ITS+TPC, incl. digits) impossible to include complete TPC simulation

PPR meeting - January 23, 2003 Andrea Dainese 3 Use Kalman filter in ITS w/o simulating the TPC ? Kalman filter reconstruction chain (V2): TPC reconstruction ITS reconstruction After TPC rec. all the information from the TPC is “summarized” at a certain reference place (R ~ 85 cm) in the object AliTPCtrack This object is the input for the Kalman filter in the ITS The idea is: parameterize the AliTPCtrack starting from the GEANT information at the beginning of the TPC proceed with standard V2 Kalman filter in the ITS

PPR meeting - January 23, 2003 Andrea Dainese 4 Strategy: how to “build” AliTPCtracks First hit in TPC “knows” the track momentum in that point build “true” AliTPCtrack at reference plane Need to: keep into account TPC tracking efficiency assign a covariance matrix to the track smear track parameters according to Kalman covariance matrix assing a value of dE/dx to the track (important, because dE/dx in the TPC is used by the ITS tracker to make a mass hypothesis) Strategy: efficiencies and dE/dx have been parameterized covariance matrix is too “delicate” to be parameterized (many correlations should be accounted for) covariance matrix will be “picked up” from a Database of real matrices given by the Kalman filter for various particle types and kinematic conditions

PPR meeting - January 23, 2003 Andrea Dainese 5 Implementation of the tool First implementation: Pb-Pb with dN ch /dy = 6000, B = 0.4 T Generated many (~300) Pb-Pb events + injected tracks at fixed p T and PDG: , K, e bins in p T = 0.2  20 GeV/c Reconstruction V2 in the TPC Get true AliTPCtracks using TPC first hit Study efficiency (Kalman/TPCparam) VS kine, PDG Study covariance matrix: check how it describes the residuals on track parameters study its momentum dependence (“regularization”) create a “Database” of matrices in bins of p T and  (separated for pions, kaons and electrons)

PPR meeting - January 23, 2003 Andrea Dainese 6 Efficiency for parameterization Efficiency: # tracks found by Kalman / # number of tracks fulfilling acceptance requirements (roughly |  |<0.9 && 1 st hit in TPC) SELECTION according to these efficiencies track-density as given by Kalman in TPC

PPR meeting - January 23, 2003 Andrea Dainese 7 A general look at the covariance matrix Y Z  tan k Y Z  tan k Bending plane Beam direction

PPR meeting - January 23, 2003 Andrea Dainese 8 Pulls:  P i /  C ii If covariance matrix describes correctly the resolutions on track parameters, the distributions of the pulls should be normal  = 1.7  = 1.0  = 1.4  = 1.3

PPR meeting - January 23, 2003 Andrea Dainese 9 Smearing of track parameters Pulls analysis shows that covariance matrix C underestimates Kalman resolution on track parameters Cannot use covariance matrix directly to smear parameters Smearing is done with C’ matrix: C’ = S C S S is diagonal with S ii =  (Pulls i ) Pulls sigmas have been calculated in kinematical bins, separately for pions, kaons and electrons

PPR meeting - January 23, 2003 Andrea Dainese 10 Momentum dependence of the covariance matrix Covariance matrix elements account for measurement error and error due to multiple scattering: As a first approximation: ~ constant depends on the track momentum (e.g. for the track curvature k: ) In general one can parameterize these dependencies: flat versus p Get “regularized” matrix safer to create a DB with bins in p T

PPR meeting - January 23, 2003 Andrea Dainese 11 Parameterization of dE/dx in the TPC protons kaons electrons pions

PPR meeting - January 23, 2003 Andrea Dainese 12 Summary of the procedure 1. Build track from 1 st hit (or AliTrackReference) in the TPC 2. Apply selection for TPC efficiency 3. Assign a value of dE/dx to the track 4. Pick “regularized” covariance matrix from the Database, according to track PDG and kinematics 5. Deregularize matrix using track momentum 6. Assign this matrix to the track 7. “Stretch” covariance matrix using the pulls 8. Use stretched matrix to smear the track parameters

PPR meeting - January 23, 2003 Andrea Dainese 13 Results: resolution on track parameters in TPC-ITS

PPR meeting - January 23, 2003 Andrea Dainese 14 Results: fraction of TPC tracks prolonged tracks in the ITS

PPR meeting - January 23, 2003 Andrea Dainese 15 How to use the parameterization Tool provided for 5.5 TeV and 14 TeV (B=0.4 T) Generated events must have TPC 1 st hits (or AliTrackReferences, recently introduced): include TPC (iTPC=1) tell GEANT to stop transport at R = 90 cm (gAlice->TrackingLimits(rmax,zmax);) Reconstruction via macro AliBarrelRec_TPCparam.C which uses class AliTPCtrackerParam Gain in CPU time and disk space is of a factor ~ 40

PPR meeting - January 23, 2003 Andrea Dainese 16 Time for an update 1 year old, the databases should be updated Include improvements from new TPC tracking Include TRD tracking (improvement in momentum resolution) Idea for later upgrade: include (combined) PID probabilities (weights) from TRD, TPC dE/dx and TOF (maybe with a couple of possibilities for TOF and TRD PID strategies) fully parameterize response of TPC, TRD, TOF