TPC tracking parameterization: a useful tool for simulation studies with large statistics

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 (~104) • performances determined mainly by ITS (d0 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 dNch/dy = 6000, B = 0.4 T • Generated many (~300) Pb-Pb events + injected tracks at fixed pT and PDG: • p, K, e • bins in pT = 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 pT 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 && 1st hit in TPC) • SELECTION according to these efficiencies track-density as given by Kalman in TPC PPR meeting - January 23, 2003 Andrea Dainese

7. Y Zgtan l k Y Z g tan l k A general look at the covariance matrix + + Bending plane Beam direction - + + - + + PPR meeting - January 23, 2003 Andrea Dainese

8. Pulls: DPi /Cii • If covariance matrix describes correctly the resolutions on track parameters, the distributions of the pulls should be normal s = 1.7 s = 1.4 s = 1.4 s = 1.0 s = 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 Sii = s(Pullsi) • 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 pT PPR meeting - January 23, 2003 Andrea Dainese

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

12. Summary of the procedure • Build track from 1st hit (or AliTrackReference) in the TPC • Apply selection for TPC efficiency • Assign a value of dE/dx to the track • Pick “regularized” covariance matrix from the Database, according to track PDG and kinematics • Deregularize matrix using track momentum • Assign this matrix to the track • “Stretch” covariance matrix using the pulls • 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 Pb-Pb @ 5.5 TeV and pp @ 14 TeV(B=0.4 T) • Generated events must have TPC 1st 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 PPR meeting - January 23, 2003 Andrea Dainese