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 (~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” AliTPCtracksFirst hit in TPC “knows” the track momentum in that point

build “true” AliTPCtrack at reference planeNeed to:

keep into account TPC tracking efficiencyassign a covariance matrix to the tracksmear track parameters according to Kalman covariance matrixassing 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 parameterizedcovariance 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:

, 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

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: Pi /Cii

If covariance matrix describes correctly the resolutions on track parameters, the distributions of the pulls should be normal

= 1.7

= 1.0

= 1.4 = 1.4

= 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 Sii = (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

222scattermeas

2meas2scatter

22 /1 pscatter

Bscattermeas pAA /

2

PPR meeting - January 23, 2003 Andrea Dainese 11

Parameterization of dE/dx in the TPC

protonskaonselectronspions

PPR meeting - January 23, 2003 Andrea Dainese 12

Summary of the procedure

1. Build track from 1st 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 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