1. Track Reconstruction Algorithms for the ALICE High-Level Trigger
ALICE HLT team:
T.Alt, C.Loizides, G.Overbekk, M.Richter, D.Rohrich, A.Vestbo, T.Vik
and
ALICE Core Offline group:
C.Cheshkov, J.Belikov, P.Hristov & M.Ivanov
13-17 Feb 2006
CHEP’2006

2. Track Reconstruction Algorithms for the ALICE HLT
Outline
Introduction
ALICE High Level Trigger (HLT)
Physics cases
Tracking algorithms for ALICE TPC
Fast Hough Transform tracking for TPC
Tracking for ALICE ITS
Example of triggers
D0K trigger
High-Pt jet trigger
Conclusions
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

3. ALICE High Level Trigger
Data rate from central PbPb collisions (dN/dy~ ):
200Hz*(30Mb-60Mb)=6-12Gb/s
Max mass storage bandwidth ~1.2Gb/s
The goal of HLT is to reduce the data rate without biasing important physics information:
Event triggering
“Regions of Interest”
Advanced data compression
Detectors
DAQ
HLT
Mass Storage
1.2GB/s
12GB/s
Requirements:
Fast and robust online reconstruction
Sufficient tracking efficiency and resolution
Fast analysis of important physics observables
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

4. ALICE HLT - Physics Cases
Large computer cluster (about 400 nodes)
Off-the-shell PCs connected with high-bandwidth network
Fault-tolerant publisher/subscriber principle
FPGA co-processors for local pattern recognition
“Barrel” HLT Physics cases:
Jets
Aim: trigger for high-Et jets
Requires: TPC tracking (+ITS)
Open charm
Aim: trigger for D0K
Requires: TPC and ITS tracking
Charmonium spectroscopy
Aim: trigger for dielectrons
Requires: TPC and TRD tracking, TRD electron PID
Pile-up removal in p-p
Aim: reduce the size of TPC raw data by filtering out background events
Requires: TPC tracking
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

5. Track Reconstruction Algorithms for the ALICE HLT
ALICE TPC
Acceptance ||<0.9
18 trapezoidal sectors
72 Cathode pad readout chambers
159 rows
~5.6x105 pads E E
84 cm
250 cm
B=0.5T
500 cm
Only primary tracks with Pt>1GeV/c are shown
Readout chambers
~15-30% occupancy
~50 million ADC amplitudes
~3 million clusters
~10000 tracks in acceptance
~50 Mbytes compressed data
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

6. ALICE HLT algorithms for TPC tracking
Low multiplicity (up to dN/dy~ ):
Cluster finder + track follower (in Conformal Mapping space)
~13s for dN/dy=4000 (including 4s for cluster finder)
Cluster finder implemented on FPGA
High multiplicity (up to dN/dy~8000):
Standard ‘grayscale’ Hough Transform
Satisfactory tracking efficiency
But…
High fake track rate
Resolution affected by the high multiplicity environment
Poor time performance: s for central PbPb event
Fast ‘counting’ Hough Transform approach
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

7. Hough Transform TPC tracking
Highly parallelizable – FPGA implementation
Computing time - massive random memory access
Efficiency and resolution limitations – parameter space binning
Image space – TPC sector
Tracking algorithm:
Consider only primary tracks
Neglect energy losses and multiple scattering
 track model: helix crossing the origin
Split TPC data in bins of pseudo-rapidity
 3D2D Hough Transform
Parameter space – histogram with tracks helix parameters
Space-points transformed into curves corresponding to all possible track helices they can belong to
Parameter space peaks are found and tracks are reconstructed
Parameter space
Track curvature
Emission angle
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

8. Hough Transform TPC tracking
TPC sector
‘Grayscale’ HT:
Parameter space bins incremented by raw ADC counts (accumulate charge along particle trajectory)
Peaks: charge>threshold
‘Counting’ HT:
Parameter space bins incremented by distance to last filled pad-row (count the # of ‘gaps’ along particle trajectory)
Peaks: #gaps<threshold
Powerful identification of good track candidates
100% intrinsic TPC efficiency  Good tracks have ‘almost’ no gaps
Unbiased extraction of track parameters
Background does not affect the parameter space peaks
Large room for speeding up
Perform HT for “cluster” edges and fill the entire “cluster” at once
Early fake tracks removal by accumulated # of gaps
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

9. Parameter Space Definition
TPC sector layout
Conformal Mapping space
(x,y)  =x/(x2+y2) , =y/(x2+y2)
Define two curves =const. (circles)
Tracks are represented by two points on these curves 1 and 2
Space-points are transformed into straight lines in parameter space
 Linear Hough transform
 curves chosen at middle and outer sector edge
 Min correlation between variables
 Powerful seeding of track candidates (by ordered processing of pad-rows )
Conformal space
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

10. Hough transform tracking
Other performance improvements:
Reduced parameter space size - 2 bytes/bin
Extensive usage of LUTs
Dynamic pointers between neighbor track candidates
fast “jumping” during the parameter space filling
Fast parameterized calculation of pseudo-rapidity index
Example of tracking in one TPC sector:
Track candidates are identified by a simple peak finder
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

11. Track Reconstruction Algorithms for the ALICE HLT
Tracking Performance
Efficiency
Resolution
Tracking efficiency  95%
No dependence on multiplicity
Sources of inefficiencies:
-binning
Overlaps in parameter space
Mult.scat. + energy losses
Pt resolution dominated by param. space bin size:
(1/Pt)~bin size  Pt/Pt=(Ahough*Pt + Bmult.scat)
No dependence on multiplicity
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

12. Overall computing time for Hough Transform tracking
For comparison: Computing time ~ time needed just to unpack Huffman encoded TPC data
Only ~5% of the time is outside param. space filling
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

13. Track Reconstruction Algorithms for the ALICE HLT
Inner Tracking System
Silicon Pixel Detectors (2D)
ladders
~107 channels
Silicon Drift Detectors (2D)
14+24 ladders
~1.4x105 channels
Silicon Strip Detectors (1D)
34+38 ladders
~2.5x106 channels
R=43.6 cm
Vertex reconstruction (primary, secondary) resolution <100 μm
L=97.6 cm
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

14. Track Reconstruction Algorithms for the ALICE HLT
ITS tracking for HLT
Offline ITS clusterer
Optimized for time performance offline Z vertex finder:
Based on SPD clusters only
Simple histogramming method
Simplified and optimized for time performance offline tracking algorithm:
No cluster error parametrization
Reduced tree of hypothesis in combinatorial Kalman filter
(Silicon Drift Layers not used)
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

15. ITS tracking performance
Efficiency
Impact param resolution
dN/dy=4000
Impact parameter resolution dominated by SPD (~ off-line resolution)
For 1 GeV/c track:
60 microns (trans) and 160 microns (long)
Quite satisfactory overall efficiency
ITS tracking almost completely removes “ghost” Hough tracks
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

16. Track Reconstruction Algorithms for the ALICE HLT
HLT ITS Timings
dN/dy=2000
dN/dy=4000
dN/dy=6000
dN/dy=8000
Clusterer
1.29(0.53)s
1.46(0.61)s
1.66(0.70)s
1.83(0.79)s
Vertexer
0.04s
0.075s
0.125s
0.180s
Tracking
0.33(0.26)s
0.87(0.54)s
1.56(0.90)s
2.41(1.38)s
The numbers in brackets are without using the 2 SDD layers
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

17. Track Reconstruction Algorithms for the ALICE HLT
D0->K trigger
Invariant mass resolution ~35 MeV/c2 (about 2x-3x offline one)
Efficiency and selectivity of the trigger is under investigation
The expected rejection factor is ~10-30
M=(355)MeV/c2
Time performance (starting from reconstructed tracks):
dN/dy=2000
dN/dy=4000
dN/dy=6000
dN/dy=8000
10ms
30ms
90ms
160ms
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

18. High-Pt Jet Trigger (PhD Thesis, C.Loizides)
Reconstructed jet energy (fraction)
Jet energy resolution
Ideal case
Tracking
The losses due to HLT tracking are negligible compared to fluctuations in “missing” neutral part of the jets and “background” in PbPb
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

19. Track Reconstruction Algorithms for the ALICE HLT
Conclusions
Fast Hough-Transform TPC Tracking:
Very good efficiency (stable up to dN/dy~8000)
Pt resolution worsens linearly with Pt
~5s comp. time for central PbPb event with dN/dy~4000
~8 Mbytes/s processing rate (compressed data)
~0.15 s/ADC count (hit)
FPGA implementation is under development - would allow to diminish the computing time to hundreds of milliseconds
ITS Tracking:
Hough Transform tracks are efficiently propagated to ITS
Fast and efficient ITS cluster finder, vertex and tracking
Track parameters resolution is greatly improved (excellent impact parameter resolution)
High-Pt jet and open charm triggers look very promising
Further development of the HLT algorithms and functionality is underway
 Be ready for first LHC beams in 2007 !
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

20. Track Reconstruction Algorithms for the ALICE HLT
SPARES
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT

21. Track Reconstruction Algorithms for the ALICE HLT
Tracking Performance
The presented tracking performance obtained with the following Hough space parameters:
Binning: 80(1)x120(2)x100()
~2x pad size in  direction
Range: tracking with minimum Pt = 0.5GeV/c
Chosen Hough space is a compromise between tracking efficiency, resolution and required computing time
Resolution ~ bin size
Comp. time ~ 1/bin size
Comp. time ~ 1/Ptmin
13-17 Feb 2006
Track Reconstruction Algorithms for the ALICE HLT