Tracking in High Density Environment

Jouri BELIKOV (CERN)Peter HRISTOV (CERN)Marian IVANOV (CERN)Karel SAFARIK (CERN)

Outlook

The ALICE detector description ALICE Transition Radiation Detector (TRD)

Working principle Local reconstruction TRD tracking algorithm

Results

The ALICE Experiment

ITSLow pt trackingVertexing

ITSLow pt trackingVertexing

TPCTracking, dEdxTPCTracking, dEdx

TRDElectron ID, TrackingTRDElectron ID, Tracking

TOFPIDTOFPID

HMPIDPID (RICH) @ high pt

HMPIDPID (RICH) @ high pt

PHOS,0 PHOS,0 MUON

-pairs MUON -pairs

PMD multiplicityPMD multiplicity

The TRD Characteristics

• 18 super modules• 6 radial layers• 5 longitudinal stacks 540 chambers 750m2 active area 28m3 of gas

Each chamber:≈ 1.45 x 1.20m2

≈ 12cm thick (incl. Radiators and electronics)

in total 1.18 million read out channels

Working Principle of the TRD• Drift chambers with FADC readout at 10MHz combined with a fiber/

foam sandwich radiator in front.

• Transition Radiation (TR) photons (< 30keV, only for electrons) are absorbed by high-Z gas mixture (Xe,Co2) large clusters

• For each time bin (X direction) the position of the cluster along the pad rows (Y direction) is reconstructed:

•Lookup table (amplitudes of the maximum and the two neighbors) used instead of COG to minimize non-linearity's

Fast calculation, better precision than a Mathieson fit.

• The track parameters are obtained from a straight line fit.

Local Reconstruction

Precision of Local Reconstruction Y-Position resolution is determined

by the S/N ratio and by the incident angle Resolution is not proportional to

the cluster’s RMS Better estimate of uncertainty

during tracking – knowing incident angle

Uncertainty in x-coordinate (time) Width of time response function (local

– on cluster level) Unisochronity effect and non-

homogeneity of drift velocity (global shift of tracklet)

Signal shaping (software tail cancellation) before local reconstruction Reduction of the uncertainty in x Local

m

m

x

noise

xnoisey

2000~

200~

)(tan 222

Signal processing Unisochronity

m

m

x

PRF

xPRFys

2000~

2000~

)(tan 222

Resolution Cluster RMS

Combined Tracking

Combining tracking - Iterative process

Forward propagation towards to the vertex –TPC-ITS

Back propagation –ITS-TPC-TRD-TOF Refit inward TOF-TRD-TPC-ITS

Continuous seeding and track segment finding in all detectors

TRD

TPC

ITS

TOF

TRD tracking Back propagation to TOF – all

clusters are considered Refit inward

Starts from the last chamber before crossing the frame or from the last “gold tracklet”

TRD Tracking: Challenge

1) High density environment ~ about 1.5 clusters in track road

2) Significant material budget in the TRD volume1) Fraction of tracks is absorbed ~ 35%2) Mean energy losses ~15 % of energy

Absorption points

Fraction of non absorbed tracks

Material budget

Energy Losses in the TRD

Left side – relative energy loss in TRD detector Integrated over all tracks reached TOF - Hijing events

Right side – precision of dEdx correction

Energy Losses: Correction TGeoManager used to get information necessary for energy loss

calculation and multiple scattering Local information: density, radiation length, Z, A defined in each point Mean query time ~ 15 s Mean number of queries

~15 – between 2 ITS layer ~15 – between 2 TRD layers

Two options considered 1. Propagate track up to material boundary defined by modeler – get

local material parameters Time consuming - too many propagations and updates of the track

2. Calculate mean parameters between start and end point <density>, <density*Z/A>, <radiation length> Faster (only one propagation), reusable in case of parallel hypothesis

TRD Tracking TRD tracking in high density environment

1)Non combinatorial Kalman filter (tracks from TPC):120 propagation layers in 6 planes

2)Riemann sphere fit for TRD standalone tracking and seeding

3)Cluster association replaced with tracklet search in each plane

1) High flux ~ 1.5 clusters in the road defined by cluster and track positions uncertainty

2) Chi2 minimization for full tracklet not for separate clusters3) Several hypothesis investigated

Tracklet: set of clusters belonging to the same track in one chamber

Tracklet Search: Principles

R-phi resolution on the level of 0.04 cm Track extrapolation has ~ 2 times worse resolution than the tracklet resolution

Z - rectangular distribution given by length of pads (+-5 cm) Probability to cross the pad-row on the level of 15 % - (3.6cm*tan10cm) Track can cross the pad-row once at maximum

Clusters in road - R – phi projection Clusters in road - Z projection

Tracklet Search Combinatorial algorithm too expensive

Case of 2 tracks in road – 1 million combinations Reduction – restricting number of row-crossing points (1

maximum) Iterative algorithm:

1 approximation - closest clusters to the track taken Resolve trivial z swapped clusters

{ Tracklet position, angle and their uncertainty

calculated Weighted mean position calculated (tracklet+ track) Chi2 calculation for tracklet Closest clusters to the weighted mean taken

} Projection algorithm

Loop over possible change of z direction {

Calculates residuals Find sub-sample (number of time bins in

plane) of clusters with minimal chi^2 distance to the weighted mean (track + tracklet)

Simple sort used – N problem }

Projection

Clusters: Error Parameterizationwithin the Tracklet Fluctuation of cluster’s position

Estimated as RMS of tracklet - cluster residuals N - number of clusters in the tracklet dy – cluster residual from a straight line fit

Uncertainty corresponding to collective shifts of tracklet added to all clusters

Correction for unisochronity and width of the Time Response Function

Systematic shift – multiplication factor N Additional penalty factor for mean number of

clusters per layer and number of pad-rows changes

N

iiy dy

N22 )(

1

Nxy *))(tan( 222

Performance: Transverse Momentum Resolution

Low density environment ITS +TPC – without TRD detector Old TRD tracking – error parameterization based

only on cluster shape New TRD tracking – cluster error parameterization

with angular dependence (without unisochronity correction)

New TRD tracking (cor) – chamber calibrated (with unisochronitiy correction)

High density environment (dNch/dy~5000) ITS +TPC – without TRD detector New TRD tracking with unisochronity

correction

Conclusion TRD detector was originally developed for

electron identification It is also very useful for reconstruction:

Excellent space resolution for high momentum track (small incident angle) significant improvement in the momentum resolution

Works in high density environment The most significant improvement is due to the

correct error parameterization