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

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

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

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

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

ALICE HLT algorithms for TPC tracking Low multiplicity (up to dN/dy~2000-3000): 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: 1000-2000s for central PbPb event Fast ‘counting’ Hough Transform approach 13-17 Feb 2006 Track Reconstruction Algorithms for the ALICE HLT

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

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

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

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

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

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

Track Reconstruction Algorithms for the ALICE HLT Inner Tracking System Silicon Pixel Detectors (2D) 80+160 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

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

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

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

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

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

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

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

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