1. Tracking in High Density Environment
Jouri BELIKOV (CERN) Peter HRISTOV (CERN) Marian IVANOV (CERN) Karel SAFARIK (CERN)

2. Outlook The ALICE detector description
ALICE Transition Radiation Detector (TRD)
Working principle
Local reconstruction
TRD tracking algorithm
Results
Lead not only as shielding…

3. The ALICE Experiment HMPID TOF TRD PMD TPC PHOS MUON ITS
PID high pt
TOF
PID
TRD
Electron ID, Tracking
PMD
g multiplicity
TPC
Tracking, dEdx
MUON
m-pairs
PHOS
g,p0
ITS
Low pt tracking
Vertexing

4. 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

5. 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

6. Local Reconstruction
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.

7. 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
Resolution
Cluster RMS
Signal processing
Unisochronity

8. Combined Tracking TRD tracking Combining tracking - Iterative process
TPC
ITS
TOF
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 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”

9. TRD Tracking: Challenge
High density environment ~ about 1.5 clusters in track road
Significant material budget in the TRD volume
Fraction of tracks is absorbed ~ 35%
Mean energy losses ~15 % of energy
Material budget
Absorption points
Fraction of non absorbed tracks

10. 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

11. 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 ms
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

12. TRD Tracking TRD tracking in high density environment
Non combinatorial Kalman filter (tracks from TPC):
120 propagation layers in 6 planes
Riemann sphere fit for TRD standalone tracking and seeding
Cluster association replaced with tracklet search in each plane
High flux ~ 1.5 clusters in the road defined by cluster and track positions uncertainty
Chi2 minimization for full tracklet not for separate clusters
Several hypothesis investigated
Tracklet: set of clusters belonging to the same track in one chamber

13. Tracklet Search: Principles
Clusters in road - R – phi projection
Clusters in road - Z projection
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*tan(q)/10cm)
Track can cross the pad-row once at maximum

14. Tracklet Search Projection 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

15. Clusters: Error Parameterization within 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

16. 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

17. 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