Track Reconstruction Algorithms for the ALICE High-Level Trigger

Track Reconstruction AlgorithmsTrack Reconstruction Algorithmsfor the ALICE High-Level Triggerfor the ALICE High-Level Trigger

ALICE HLT team:ALICE HLT team:T.Alt, C.Loizides, G.Overbekk, M.Richter, D.Rohrich, A.Vestbo, T.VikT.Alt, C.Loizides, G.Overbekk, M.Richter, D.Rohrich, A.Vestbo, T.Vik

andandALICE Core Offline group:ALICE Core Offline group:

C.Cheshkov, J.Belikov, P.Hristov & M.IvanovC.Cheshkov, J.Belikov, P.Hristov & M.Ivanov13-17 Feb 200613-17 Feb 2006

CHEP’2006CHEP’2006

13-17 Feb 200613-17 Feb 2006 Track Reconstruction Algorithms for the ALTrack Reconstruction Algorithms for the ALICE HLTICE HLT

22

OutlineOutline

IntroductionIntroduction– ALICE High Level Trigger (HLT)ALICE High Level Trigger (HLT)– Physics casesPhysics cases

Tracking algorithms for ALICE TPCTracking algorithms for ALICE TPC

Fast Hough Transform tracking for TPCFast Hough Transform tracking for TPC

Tracking for ALICE ITSTracking for ALICE ITS

Example of triggersExample of triggers– DD00KK trigger trigger– High-Pt jet triggerHigh-Pt jet trigger

ConclusionsConclusions


33

ALICE High Level TriggerALICE High Level Trigger

Data rate from central PbPb Data rate from central PbPb collisions (dN/dy~2000-4000):collisions (dN/dy~2000-4000):

200Hz*(30Mb-60Mb)=200Hz*(30Mb-60Mb)=6-12Gb/s6-12Gb/s

Max mass storage bandwidth Max mass storage bandwidth ~1.2Gb/s~1.2Gb/s

The goal of HLT is to reduce the The goal of HLT is to reduce the data rate without biasing data rate without biasing important physics information:important physics information:– Event triggeringEvent triggering– ““Regions of Interest”Regions of Interest”– Advanced data compressionAdvanced data compression

Requirements:Requirements:― Fast and robust online Fast and robust online reconstructionreconstruction― Sufficient tracking Sufficient tracking efficiency and resolutionefficiency and resolution― Fast analysis of important Fast analysis of important physics observablesphysics observables

Detectors

DAQ HLT

Detectors

DAQ HLT

Mass Storage

1.2GB/s1.2GB/s

12GB/s12GB/s

Detectors

DAQ HLT

Detectors

DAQ HLT

Mass Storage

1.2GB/s1.2GB/s

12GB/s12GB/s


44

ALICE HLT - Physics CasesALICE HLT - Physics Cases

Large computer cluster (about 400 nodes)Large computer cluster (about 400 nodes)– Off-the-shell PCs connected with high-bandwidth networkOff-the-shell PCs connected with high-bandwidth network– Fault-tolerant publisher/subscriber principleFault-tolerant publisher/subscriber principle– FPGA co-processors for local pattern recognitionFPGA co-processors for local pattern recognition

““Barrel” HLT Physics cases:Barrel” HLT Physics cases:– JetsJets

Aim: trigger for high-Et jetsAim: trigger for high-Et jetsRequires: TPC tracking (+ITS)Requires: TPC tracking (+ITS)

– Open charmOpen charmAim: trigger for D0Aim: trigger for D0KKRequires: TPC and ITS trackingRequires: TPC and ITS tracking

– Charmonium spectroscopyCharmonium spectroscopyAim: trigger for dielectronsAim: trigger for dielectronsRequires: TPC and TRD tracking, TRD electron PIDRequires: TPC and TRD tracking, TRD electron PID

– Pile-up removal in p-pPile-up removal in p-pAim: reduce the size of TPC raw data by filtering out Aim: reduce the size of TPC raw data by filtering out background eventsbackground eventsRequires: TPC trackingRequires: TPC tracking


55

ALICE TPCALICE TPCAcceptance |Acceptance ||<0.9|<0.918 trapezoidal sectors18 trapezoidal sectors72 Cathode pad readout 72 Cathode pad readout chamberschambers159 rows159 rows~5.6x10~5.6x1055 pads pads

EE

B=0.5T

Readout chambers

84 cm

250 cm

500 cm Only primary tracks with Pt>1GeV/c are shown

~15-30% occupancy

~50 million ADC amplitudes

~3 million clusters

~10000 tracks in acceptance

~50 Mbytes compressed data


66

ALICE HLT algorithms for TPC trackingALICE HLT algorithms for TPC tracking

Low multiplicity (up to dN/dy~2000-3000):Low multiplicity (up to dN/dy~2000-3000):– Cluster finder + track follower (in Conformal Mapping Cluster finder + track follower (in Conformal Mapping

space)space)– ~13s for dN/dy=4000 (including 4s for cluster finder)~13s for dN/dy=4000 (including 4s for cluster finder)– Cluster finder implemented on FPGACluster finder implemented on FPGA

High multiplicity (up to dN/dy~8000):High multiplicity (up to dN/dy~8000):– Standard ‘grayscale’ Hough TransformStandard ‘grayscale’ Hough Transform– Satisfactory tracking efficiencySatisfactory tracking efficiency– But…But…

High fake track rateHigh fake track rateResolution affected by the high multiplicity Resolution affected by the high multiplicity environmentenvironmentPoor time performance: 1000-2000s for central PbPb Poor time performance: 1000-2000s for central PbPb eventevent

Fast ‘counting’ Hough Transform approachFast ‘counting’ Hough Transform approach


77

Hough Transform TPC trackingHough Transform TPC trackingHough Transform:Hough Transform:

Highly parallelizable – FPGA implementationHighly parallelizable – FPGA implementationComputing time - massive random memory accessComputing time - massive random memory accessEfficiency and resolution limitations – parameter space binningEfficiency and resolution limitations – parameter space binning

Tracking algorithm:Tracking algorithm:– Consider only primary tracksConsider only primary tracks– Neglect energy losses and multiple Neglect energy losses and multiple

scatteringscattering track model: helix crossing the origintrack model: helix crossing the origin

– Split TPC data in bins of pseudo-rapiditySplit TPC data in bins of pseudo-rapidity 3D3D2D Hough Transform2D Hough Transform

– Parameter space – histogram with tracks Parameter space – histogram with tracks helix parametershelix parameters

– Space-points transformed into curves Space-points transformed into curves corresponding to all possible track corresponding to all possible track helices they can belong tohelices they can belong to

– Parameter space peaks are found and Parameter space peaks are found and tracks are reconstructedtracks are reconstructed

Tra

ck c

urv

atu

re

Emission angle

Image space – TPC sector

Parameter space


88

Hough Transform TPC trackingHough Transform TPC tracking

‘‘Grayscale’ HT:Grayscale’ HT:– Parameter space bins Parameter space bins

incremented by raw ADC incremented by raw ADC counts counts (accumulate charge (accumulate charge along particle trajectory)along particle trajectory)

– Peaks: charge>thresholdPeaks: charge>threshold

‘‘Counting’ HT:Counting’ HT:– Parameter space bins incremented Parameter space bins incremented

by distance to last filled pad-row by distance to last filled pad-row (count the # of ‘gaps’ along particle (count the # of ‘gaps’ along particle trajectory)trajectory)

– Peaks: #gaps<thresholdPeaks: #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

TPC sector


99

Parameter Space DefinitionParameter Space Definition

Conformal Mapping spaceConformal Mapping space

(x,y) (x,y) =x/(x=x/(x22+y+y22) , ) , =y/(x=y/(x22+y+y22))

Define two curves Define two curves =const. (circles)=const. (circles)

Tracks are represented by two Tracks are represented by two points on these curves points on these curves 11 and and 22

Space-points are transformed into Space-points are transformed into straight lines in parameter spacestraight lines in parameter space Linear Hough transformLinear Hough transform

curves chosen at middle and outer curves chosen at middle and outer sector edgesector edge Min correlation between variablesMin correlation between variables Powerful seeding of track Powerful seeding of track candidates (by ordered processing candidates (by ordered processing of pad-rows )of pad-rows )

TPC sector layout

Conformal space


1010

Hough transform trackingHough transform trackingOther performance improvements:Other performance improvements:– Reduced parameter space size - 2 bytes/binReduced parameter space size - 2 bytes/bin– Extensive usage of LUTsExtensive usage of LUTs– Dynamic pointers between neighbor track candidatesDynamic pointers between neighbor track candidates

fast “jumping” during the parameter space fillingfast “jumping” during the parameter space filling– Fast parameterized calculation of pseudo-rapidity indexFast parameterized calculation of pseudo-rapidity index

Example of tracking in one TPC sector:Example of tracking in one TPC sector:– Track candidates are identified by a simple peak finderTrack candidates are identified by a simple peak finder


1111

Tracking PerformanceTracking Performance

Tracking efficiency Tracking efficiency 95% 95%– No dependence on multiplicityNo dependence on multiplicity

Sources of inefficiencies:Sources of inefficiencies: -binning-binning– Overlaps in parameter spaceOverlaps in parameter space– Mult.scat. + energy lossesMult.scat. + energy losses

Pt resolution dominated by Pt resolution dominated by param. space bin size:param. space bin size:

(1/Pt)~bin size (1/Pt)~bin size Pt/Pt=(APt/Pt=(Ahoughhough*Pt + B*Pt + Bmult.scatmult.scat))

No dependence on multiplicityNo dependence on multiplicity

Efficiency Resolution


1212

2.2

3.9

5.8

8.2

2.8

4.8

7.1

9.3

3.5

5.8

8.7

11.8

0 2 4 6 8 10 12 14

dN/dy=2000

dN/dy=4000

dN/dy=6000

dN/dy=8000

Computing time, s

AMD Opteron 246 Intel Itanium II Intel Pentium 4

• For comparison: Computing time ~ time needed just to For comparison: Computing time ~ time needed just to unpack Huffman encoded TPC dataunpack Huffman encoded TPC data

• Only ~5% of the time is outside param. space fillingOnly ~5% of the time is outside param. space filling

Overall computing time for Hough Overall computing time for Hough Transform trackingTransform tracking


1313

Inner Tracking SystemInner Tracking System• Silicon Pixel Detectors (2D)Silicon Pixel Detectors (2D)

• 80+160 ladders

• ~107 channels

• Silicon Drift Detectors (2D)Silicon Drift Detectors (2D)

• 14+24 ladders

• ~1.4x105 channels

• Silicon Strip Detectors (1D)Silicon Strip Detectors (1D)

• 34+38 ladders

• ~2.5x106 channels

R=43.6 cm

Vertex Vertex reconstruction reconstruction (primary, secondary) (primary, secondary) resolution <100 resolution <100 μμmm

L=97.6

cm


1414

ITS tracking for HLTITS tracking for HLT

Offline ITS clustererOffline ITS clusterer

Optimized for time Optimized for time performance offline Z vertex performance offline Z vertex finder:finder:– Based on SPD clusters onlyBased on SPD clusters only– Simple histogramming methodSimple histogramming method

Simplified and optimized for Simplified and optimized for time performance offline time performance offline tracking algorithm:tracking algorithm:– No cluster error parametrizationNo cluster error parametrization– Reduced tree of hypothesis in Reduced tree of hypothesis in

combinatorial Kalman filtercombinatorial Kalman filter– (Silicon Drift Layers not used)(Silicon Drift Layers not used)

Clusters

ITS Vertexer

Hough TransformTracker

Hough Tracks

ITS Tracker

ITS Clusterer


1515

ITS tracking performanceITS tracking performance

Quite satisfactory overall Quite satisfactory overall efficiencyefficiency

ITS tracking almost ITS tracking almost completely removes completely removes “ghost” Hough tracks“ghost” Hough tracks

Efficiency

Impact parameter resolution Impact parameter resolution dominated by SPD (~ off-dominated by SPD (~ off-line resolution)line resolution)For 1 GeV/c track:For 1 GeV/c track:60 microns (trans) and 160 60 microns (trans) and 160 microns (long)microns (long)

Impact param resolution dN/dy=4000


1616

HLT ITS TimingsHLT ITS Timings

The numbers in brackets are without using the 2 SDD layersThe numbers in brackets are without using the 2 SDD layers

dN/dy=2000dN/dy=2000 dN/dy=4000dN/dy=4000 dN/dy=6000dN/dy=6000 dN/dy=8000dN/dy=8000

ClustererClusterer 1.29(0.53)s1.29(0.53)s 1.46(0.61)s1.46(0.61)s 1.66(0.70)s1.66(0.70)s 1.83(0.79)s1.83(0.79)s

VertexerVertexer 0.04s0.04s 0.075s0.075s 0.125s0.125s 0.180s0.180s

TrackingTracking 0.33(0.26)s0.33(0.26)s 0.87(0.54)s0.87(0.54)s 1.56(0.90)s1.56(0.90)s 2.41(1.38)s2.41(1.38)s


1717

D0->KD0->K trigger trigger

Invariant mass resolution ~35 MeV/cInvariant mass resolution ~35 MeV/c2 2 (about 2x-3x offline one)(about 2x-3x offline one)Efficiency and selectivity of the trigger is under investigationEfficiency and selectivity of the trigger is under investigationThe expected rejection factor is ~10-30The expected rejection factor is ~10-30

M=(355)MeV/c2

dN/dy=2000dN/dy=2000 dN/dy=4000dN/dy=4000 dN/dy=6000dN/dy=6000 dN/dy=8000dN/dy=8000

10ms10ms 30ms30ms 90ms90ms 160ms160ms

Time performance (starting from reconstructed tracks):Time performance (starting from reconstructed tracks):


1818

High-Pt Jet Trigger (PhD Thesis, C.Loizides)High-Pt Jet Trigger (PhD Thesis, C.Loizides)

The losses due to HLT tracking are negligible compared to fluctuations The losses due to HLT tracking are negligible compared to fluctuations in “missing” neutral part of the jets and “background” in PbPbin “missing” neutral part of the jets and “background” in PbPb

Reconstructed jet energy (fraction) Jet energy resolution

Ideal case

Tracking


1919

ConclusionsConclusionsFast Hough-Transform TPC Tracking:Fast Hough-Transform TPC Tracking:– Very good efficiency (stable up to dN/dy~8000)Very good efficiency (stable up to dN/dy~8000)– Pt resolution worsens linearly with PtPt resolution worsens linearly with Pt– ~5s comp. time for central PbPb event with dN/dy~4000~5s comp. time for central PbPb event with dN/dy~4000

~8 Mbytes/s processing rate (compressed data)~8 Mbytes/s processing rate (compressed data)~0.15 ~0.15 s/ADC count (hit)s/ADC count (hit)

– FPGA implementation is under development - would allow to FPGA implementation is under development - would allow to diminish the computing time to hundreds of millisecondsdiminish the computing time to hundreds of milliseconds

ITS Tracking:ITS Tracking:– Hough Transform tracks are efficiently propagated to ITSHough Transform tracks are efficiently propagated to ITS– Fast and efficient ITS cluster finder, vertex and trackingFast and efficient ITS cluster finder, vertex and tracking– Track parameters resolution is greatly improved (excellent impact Track parameters resolution is greatly improved (excellent impact

parameter resolution)parameter resolution)

High-Pt jet and open charm triggers look very promisingHigh-Pt jet and open charm triggers look very promising

Further development of the HLT algorithms and functionality Further development of the HLT algorithms and functionality is underwayis underway

Be ready for first LHC beams in 2007 !Be ready for first LHC beams in 2007 !


2020

SPARESSPARES


2121

Tracking PerformanceTracking Performance

The presented tracking performance obtained The presented tracking performance obtained with the following Hough space parameters:with the following Hough space parameters:– Binning: 80(Binning: 80(1)x120(1)x120(2)x100(2)x100() )

~2x pad size in ~2x pad size in direction direction– Range: tracking with minimum Pt = 0.5GeV/cRange: tracking with minimum Pt = 0.5GeV/c

Chosen Hough space is a compromise between Chosen Hough space is a compromise between tracking efficiency, resolution and required tracking efficiency, resolution and required computing timecomputing time– Resolution ~ bin sizeResolution ~ bin size– Comp. time ~ 1/bin sizeComp. time ~ 1/bin size– Comp. time ~ 1/PtComp. time ~ 1/Ptminmin

Documents

Track Reconstruction Algorithms for the ALICE High-Level Trigger