TPC parallel tracking and
Particle Identification
03.03.03
Marian Ivanov
Alice TPC
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Time Projection chamber – main
tracking device of the Alice central
barrel
Main tasks
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Track finding
Momentum measurements
Particle identification by dE/dx
Alice TPC
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Geometrical features:
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Drift region:
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Cylindrical vessel
Length = 250+250 cm
Rin/Rout ~87/252 cm
Readout chambers
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2×18 sectors (72 chambers)
Sector opening angle 20 degrees
Pad shapes 7.5x4, 10x6 and 15x6
mm ~ 0.5 million pads
Time sampling ~ 445 time bins
per pad ~220 million samples per
event
TPC simulations
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Physical processes:
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Relevant GEANT processes
Diffusion
Gas gain fluctuation
ExB effect
Responses in time and pad direction (2D)
noise
TPC tracking
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First TPC tracking 1997
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Iouri Belikov, Boris Batyunya, Karel Safarik
Based on Kalman filtering approach
“offline” tracking
Parallel development
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Bergen group
Hough transform – global approach
“online” tracking – only “almost” primary particles
New tracking
Maximal Information principle
Use everything what you can ==> You get the best
Why?
You can't use more
Problem – too many degrees of freedom (~220 million 10
bits samples
Compromise – looking for orthogonal parameters
Parallel Kalman Filter tracking approach chosen
To allow to use optimal combination of local and
global information about track's and clusters
Global tracking approach (Hough transform)
considered only as seeding for track candidates
New cluster finder
Cluster finder looks for local maxima in two
dimensional time x pad-row plane
Neighbourhood - matrix 5x5 with maxima at
central bin
5x5 is bigger then typical size of cluster
Standard centre of gravity and RMS used to
characterize cluster
Problem
Systematic error due to the threshold effect
New cluster finder
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Parameterization of the cluster shape
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Depend on the track parameters
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Z position – gives the diffusion component
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Θ angle – gives the z angular component
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Known during clustering
Known during clustering for primary particles
φ angle – depend on the pad row radius and particle
momentum
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Known only during tracking
Conservative approach – supposing 0 degree – good for
high pt tracks
New cluster finder
“RMS” fitting of the cluster
Virtual charge added
signal below threshold replaced by expected value
according gauss interpolation
if bigger replaced with amplitude equal to threshold
Signal shape (RMS) used for later error estimation
- and as a criteria for cluster unfolding
Gives comparable results with Gaussian fit of
the cluster, but is much faster
RMS versus fitting
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left side: reconstructed RMS to fitted sigma ratio
right side: ratio as function of the expected cluster
RMS
Cluster unfolding
If one of the RMS's – in time or pad direction
is bigger then critical RMS - unfolding
Fast spline method for unfolding
Charge conservation
Small systematic effect
Supposing the same signal shape – equivalent to
the same track angles – if not fulfilled – tracks
diverge very rapidly
Spline unfolding
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Amplitude in bin 4
corresponding to cluster
on left side
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Right side
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Amplitude in 5 and
derivation in five 0
Amplitude in 2 and 3
taken
C1_4 calculated
symmetric C2_4
calculated
C1_4 =
C1_4*C4/(C1_4+C2_4)
Spline unfolding (standalone
simulator)
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Dependence of the
reconstructed
cluster position as
function of the
distance to the next
cluster
RMS of clusters –
0.75
Cluster characteristic
fY,fZ
centre of gravity
fSigmaY, fSigmaZ
shape of the cluster
in case of overlapped clusters – characterize cluster
background
fMax, fQ
Signal at the maximum – respectively total charge in
cluster
fCType
Cluster type - characterize overlap factor
Cluster error estimation
Errors estimated only during tracking
Using
cluster shape information
cluster amplitude
type of the cluster – is gold-plated or overlapped
track angles and position
is shared info (not yet implemented)
Error parameterization
Different for different pad geometries
Cluster error estimation
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Previous parameterization used for
“gold-plated” clusters
Overlapped clusters
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Additional correction as function of the
distortion from expected size
Edge clusters taken separately
Error parameterization principle
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Make Gaussian pulls with unite sigma
Seeding with vertex constrain
Seeding 2 times
1 seeding - 90 % of tracks are
found
2 seeding - 6.7 % additional
found
Problems
N2 problem (2 minutes of CPU)
Vertex constrain suppress
secondaries
Solution ?
Seeding using polynomial fit
without any assumption on
vertex position
Seeding without vertex constrain
Simple track follower
Algorithm
Seeding between pad-row i1 and i2 – start in the
middle pad-row
Take cluster at middle pad-row
Find 2 nearest up and down – make linear fit
Find prolongation
Take next 2 nearest - update fit - prolongation
....
After 7 cluster - make polynomial fit ...
continue
Tracking
2 seedings with constrain + few seedings
without at different radii (necessary for kinks)
Tracking - parallel
Find for each track the prolongation to the next
pad-row
Estimate the errors
Update track according current cluster parameters
Track several track hypothesis in parallel
Allow cluster sharing between different tracks
Removing track hypothesis
Remove-Overlap – called 3 times
After seeding (threshold =50 %)
After tracking outer sectors (threshold =50 %)
After tracking inner sector (threshold =50 %)
Effect (full event)
New tracker - 3 fakes
Old tracker - 7 fakes
dEdx
Truncated mean – 60 %
Currently signals at cluster maximum
Shared clusters not used at all
Correction function for cluster shape
Function of ratio of measured cluster shape
to expected cluster shape
Comparison of new tracking and
old tracking
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Full event dN/dy compared – Hijing
parameterization
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efficiency comparison for primaries
dEdx comparison for primaries
efficiency comparison for primaries
+secondary crossing full TPC
dEdx comparison for primaries +secondary
crossing full TPC
Particle identification using TPC
dE/dx
dE/dx measurement in TPC (in combination
with TRD and ITS) can be used for PID
Next slides
First systematic study of using new TPC tracking
and dE/dx information for PID determination (lowmomentum region) (Boris Batiounia)
dE/dx as function of momentum
dE/dx spectra for fixed momentum
PID efficiency and contamination (old and new
tracking
dEdx as function of the momenta
TPC PID separation (primaries)
Efficiency as function of pt
Efficiency as function of pt
Efficiency as function of pt
Efficiency as function of pt
Pt resolution as function of pt
Pt resolution as function of pt
Pt resolution as function of pt
Pt resolution as function of pt
Efficiency (for kinks)
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Left – primaries decaying at radius r
Right - secondary created at radius r
Kink and secondary vertex finder
Track candidates - seeded in several positions within
chamber
'easy' to implement using current new tracking
Algorithm
Combinatorial search – closest point between two tracks
investigated
Cluster density criteria before and after kink respectively
(V0 used to determine the criteria for hypothesis removal)
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Status
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First attempts – systematic study of efficiency and
contamination still to be done
Conclusion
New tracking developed
Efficiency improvement (for primaries more 96%,
before ~90%)
Momentum resolution improvement
20% - pt
Angular resolution improvement
30 % - φ
7%-θ
dE/dx resolution – 6.8 % full event (8.7 % before)
Seeding for secondary added
Outlook
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Current approach - as a first iteration
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Clustering without tracks information
Tracking several hypothesis
Second iteration – unfolding of cluster using
overlapped tracks information
TPC data lossy compression
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requirement – conserve cluster shape
first optimistic results – additional compression
factor 60 %