tracking in high density environment jourijouri belikov (cern) peter hristov (cern) marian ivanov...
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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
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