Track Reconstruction Algorithms for the ALICE HighLevel Trigger

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 13 -17 Feb 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 – D 0 K trigger – High-Pt jet trigger Conclusions 13 -17 Feb 2006 Track Reconstruction Algorithms for the ALICE HLT 2

ALICE High Level Trigger Data rate from central Pb. Pb collisions (d. N/dy~2000 -4000): 200 Hz*(30 Mb-60 Mb)=6 -12 Gb/s Max mass storage bandwidth ~1. 2 Gb/s Detectors 12 GB/s DAQ HLT 1. 2 GB/s Mass Storage The goal of HLT is to reduce the data rate without biasing important physics information: – Event triggering – “Regions of Interest” – Advanced data compression 13 -17 Feb 2006 Requirements: Fast and robust online reconstruction ― Sufficient tracking efficiency and resolution ― Fast analysis of important physics observables ― Track Reconstruction Algorithms for the ALICE HLT 3

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 D 0 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 4

ALICE TPC E 84 E cm . B=0 250 cm 5 T 500 cm Acceptance | |<0. 9 18 trapezoidal sectors 72 Cathode pad readout chambers 159 rows ~5. 6 x 105 pads Only primary tracks with Pt>1 Ge. V/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 5

ALICE HLT algorithms for TPC tracking Low multiplicity (up to d. N/dy~2000 -3000): – Cluster finder + track follower (in Conformal Mapping space) – ~13 s for d. N/dy=4000 (including 4 s for cluster finder) – Cluster finder implemented on FPGA High multiplicity (up to d. N/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 -2000 s for central Pb. Pb event Fast ‘counting’ Hough Transform approach 13 -17 Feb 2006 Track Reconstruction Algorithms for the ALICE HLT 6

Hough Transform TPC tracking Hough Transform: Highly parallelizable – FPGA implementation Computing time - massive random memory access Efficiency and resolution limitations – parameter space binning Tracking algorithm: Image space – TPC sector – Consider only primary tracks – Neglect energy losses and multiple scattering track model: helix crossing the origin – Split TPC data in bins of pseudo-rapidity 3 D 2 D Hough Transform 13 -17 Feb 2006 Track curvature – 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 Reconstruction Algorithms for the ALICE HLT Emission angle 7

Hough Transform TPC tracking TPC sector ‘Grayscale’ HT: ‘Counting’ HT: – Parameter space bins incremented by raw ADC counts (accumulate charge along particle trajectory) – Peaks: charge>threshold – 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 8

Parameter Space Definition Conformal Mapping space TPC sector layout (x, y) =x/(x 2+y 2) , =y/(x 2+y 2) 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 Conformal space curves chosen at middle and outer sector edge Min correlation between variables Powerful seeding of track candidates (by ordered processing of pad-rows ) 13 -17 Feb 2006 Track Reconstruction Algorithms for the ALICE HLT 9

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 10

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

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 12

Inner Tracking System • Silicon Pixel Detectors (2 D) • 80+160 ladders • ~107 channels • Silicon Drift Detectors (2 D) • 14+24 ladders • ~1. 4 x 105 channels • Silicon Strip Detectors (1 D) • 34+38 ladders • ~2. 5 x 106 channels R=43. 6 cm 6 . 97 L= 13 -17 Feb 2006 cm Vertex reconstruction (primary, secondary) resolution <100 μm Track Reconstruction Algorithms for the ALICE HLT 13

ITS tracking for HLT Offline ITS clusterer Optimized for time performance offline Z vertex finder: – Based on SPD clusters only – Simple histogramming method ITS Clusterer Clusters ITS Vertexer 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 Hough Transform Tracker Hough Tracks ITS Tracker 14

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

HLT ITS Timings d. N/dy=2000 d. N/dy=4000 d. N/dy=6000 d. N/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. 04 s 0. 075 s 0. 125 s 0. 180 s 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 16

D 0 ->K trigger Invariant mass resolution ~35 Me. V/c 2 (about 2 x-3 x offline one) Efficiency and selectivity of the trigger is under investigation The expected rejection factor is ~10 -30 M=(35 5)Me. V/c 2 Time performance (starting from reconstructed tracks): d. N/dy=2000 d. N/dy=4000 d. N/dy=6000 d. N/dy=8000 10 ms 30 ms 90 ms 160 ms 13 -17 Feb 2006 Track Reconstruction Algorithms for the ALICE HLT 17

High-Pt Jet Trigger (Ph. D 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 Pb. Pb 13 -17 Feb 2006 Track Reconstruction Algorithms for the ALICE HLT 18

Conclusions Fast Hough-Transform TPC Tracking: – – – Very good efficiency (stable up to d. N/dy~8000) Pt resolution worsens linearly with Pt ~5 s comp. time for central Pb. Pb event with d. N/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 19

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

Tracking Performance The presented tracking performance obtained with the following Hough space parameters: – Binning: 80( 1)x 120( 2)x 100( ) ~2 x pad size in direction – Range: tracking with minimum Pt = 0. 5 Ge. V/c Chosen Hough space is a compromise between tracking efficiency, resolution and required computing time – Resolution ~ bin size – Comp. time ~ 1/Ptmin 13 -17 Feb 2006 Track Reconstruction Algorithms for the ALICE HLT 21