track reconstruction in the lhc experiments

Track Track reconstruction in reconstruction in

the LHC the LHC experimentsexperiments

1st LHC Detector Alignment Workshop, 1st LHC Detector Alignment Workshop, CERN, September 5. 2006CERN, September 5. 2006

Are StrandlieAre Strandlie

Gjøvik University College, Norway andGjøvik University College, Norway andUniversity of Oslo, NorwayUniversity of Oslo, Norway

A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006

This talk will be an overview of the This talk will be an overview of the track track reconstruction strategies and reconstruction strategies and algorithmsalgorithms in the four LHC experiments in the four LHC experiments will not be able to cover all relevant material will not be able to cover all relevant material

in 30 minutesin 30 minutes e.g. effects of misalignment treated in other talkse.g. effects of misalignment treated in other talks

have therefore chosen to emphasizehave therefore chosen to emphasize algorithms rather than software technicalitiesalgorithms rather than software technicalities main/inner tracking systems and track main/inner tracking systems and track

reconstruction starting from prepared raw datareconstruction starting from prepared raw data


OutlineOutline

IntroductionIntroduction Overall comparison of tracking Overall comparison of tracking

strategiesstrategies similaritiessimilarities differencesdifferences

Specific strategies for each experimentSpecific strategies for each experiment Examples of (relatively) recent Examples of (relatively) recent

developmentsdevelopments ConclusionsConclusions


IntroductionIntroduction Track reconstruction is traditionally divided into two separate Track reconstruction is traditionally divided into two separate

subtasks:subtasks: track findingtrack finding track fittingtrack fitting

Track finding:Track finding: division of set of measurements in a tracking detector into division of set of measurements in a tracking detector into

subsetssubsets each subset contains measurements believed to originate each subset contains measurements believed to originate

from the same particlefrom the same particle Track fitting:Track fitting:

starts out with the measurements inside one subset as starts out with the measurements inside one subset as provided by the track finderprovided by the track finder

aims to optimally estimate a set of track parameters from the aims to optimally estimate a set of track parameters from the information from the measurements information from the measurements

evaluates the quality and final acceptance of the track evaluates the quality and final acceptance of the track candidatecandidate


IntroductionIntroductionTracking detector

with cylindrical layers

Input to track findingis all or parts of

the measurementsin the detector at a

given instance

A successful track finderidentifies a set of potential

tracks as indicated in the figure

Measurements along these tracks are given to the track

fitter for parameter estimation and final validation of track

candidate


IntroductionIntroduction

After the track fit one usually forgets aboutthe measurements and

only cares about a compact representation

of the tracks


Overall strategiesOverall strategies

All experiments have implemented All experiments have implemented several tracking strategiesseveral tracking strategies seems to be consensus that there is seems to be consensus that there is no no

single algorithm optimal for all use single algorithm optimal for all use casescases

typically one default approach as well typically one default approach as well as various alternative approaches, e. g.as various alternative approaches, e. g. second-pass track findingsecond-pass track finding track fitting in dense jetstrack fitting in dense jets special treatment of electronsspecial treatment of electrons



Overall decomposition in all Overall decomposition in all experiments:experiments: Seed generationSeed generation Local track finding (trajectory building) Local track finding (trajectory building)

starting from seedstarting from seed Track fittingTrack fitting Post-processingPost-processing

refitting, ambiguity resolution etc.refitting, ambiguity resolution etc.


Overall strategiesOverall strategies Seed generationSeed generation

seed: typically a few measurements (and seed: typically a few measurements (and sometimes a vertex constraint) plus initial track sometimes a vertex constraint) plus initial track parametersparameters

ALICE: outer part of TPCALICE: outer part of TPC alternative starting in ITS (close to beam)alternative starting in ITS (close to beam)

ATLAS: inner part of Inner DetectorATLAS: inner part of Inner Detector alternative starting in TRTalternative starting in TRT

CMS: inner part of TrackerCMS: inner part of Tracker recent alternative using measurements also at the recent alternative using measurements also at the

outsideoutside LHCb: seeds in VELO (close to beam)LHCb: seeds in VELO (close to beam)

alternative starting in T stations further outalternative starting in T stations further out


Overall strategiesOverall strategies Local track finding starting from seedLocal track finding starting from seed

global approaches more or less absent, except e. global approaches more or less absent, except e. g.g.

ALICE: ALICE: Hough transform in slices of TPCHough transform in slices of TPC Hopfield neural network in stand-alone track finding in ITSHopfield neural network in stand-alone track finding in ITS

ATLAS: ATLAS: Hough transform in TRTHough transform in TRT

CMS: CMS: Hopfield net tried out and abandoned several years agoHopfield net tried out and abandoned several years ago

none of the above are defaultnone of the above are default common denominator: common denominator: combinatorial Kalman combinatorial Kalman

filter (CKF)filter (CKF) all experiments except LHCb for default track findingall experiments except LHCb for default track finding LHCb: histogram of distances from measurements to LHCb: histogram of distances from measurements to

parameterized trajectoryparameterized trajectory


Overall strategiesOverall strategies Kalman filter:Kalman filter:

recursive least-squares recursive least-squares estimator, mathematically estimator, mathematically equivalent to global least-equivalent to global least-squares fitsquares fit

alternating between alternating between propagation and update stepspropagation and update steps

several advantages as several advantages as compared to global least-compared to global least-squares approachsquares approach

introduced by P. Billoir in 1984 introduced by P. Billoir in 1984 (without realizing it was a (without realizing it was a Kalman filter) and R. Kalman filter) and R. FrFrühwirth in 1987 (realizing it ühwirth in 1987 (realizing it was a Kalman filter , was a Kalman filter , introducing the Kalman introducing the Kalman smoother)smoother)

first implementation in first implementation in DELPHI experiment at LEP at DELPHI experiment at LEP at CERNCERN


Overall strategiesOverall strategies Due to recursive nature Due to recursive nature

Kalman filter well suited Kalman filter well suited for combined track for combined track finding and fittingfinding and fitting

CKF most popular CKF most popular approach (due to Rainer approach (due to Rainer Mankel, NIM A 395 Mankel, NIM A 395 (1997)):(1997)): build up tree of track build up tree of track

candidates starting from candidates starting from seedseed

various quality criteria used various quality criteria used to cut branches during to cut branches during recursive procedurerecursive procedure

keep best candidate in the keep best candidate in the endend


Overall strategiesOverall strategies Track fittingTrack fitting

Kalman filter most common track fitting Kalman filter most common track fitting algorithm in all LHC experimentsalgorithm in all LHC experiments

global fit still used as alternative in ATLAS global fit still used as alternative in ATLAS Inner Detector and as default in ATLAS muon Inner Detector and as default in ATLAS muon systemsystem

generalizations of Kalman filter also used in generalizations of Kalman filter also used in ATLAS and CMSATLAS and CMS

Deterministic Annealing Filter (DAF)Deterministic Annealing Filter (DAF) high-luminosity TRT track fitting in ATLAShigh-luminosity TRT track fitting in ATLAS track fitting in dense jets in CMStrack fitting in dense jets in CMS

Gaussian-sum filter (GSF)Gaussian-sum filter (GSF) electron track fitting in both experimentselectron track fitting in both experiments



Post-processing:Post-processing: CMS: removing track candidates which CMS: removing track candidates which

have too many measurements in commonhave too many measurements in common trajectory cleaningtrajectory cleaning

ATLAS: outlier rejection at various stagesATLAS: outlier rejection at various stages ALICE+LHCb: second-pass track findingALICE+LHCb: second-pass track finding refittingrefitting


Muon trackingMuon tracking In general more material, less well-behaved In general more material, less well-behaved

magnetic fields and longer propagation magnetic fields and longer propagation distances than in main tracking systemsdistances than in main tracking systems need of dedicated propagatorsneed of dedicated propagators potential code re-use if propagator potential code re-use if propagator

implementations are hidden behind abstract implementations are hidden behind abstract interfaceinterface

ALICE+CMS: combinatorial Kalman filterALICE+CMS: combinatorial Kalman filter ATLAS: local track finding in regions of ATLAS: local track finding in regions of

interest, matching track segments, global interest, matching track segments, global track fittrack fit

LHCb: local track finding, momentum LHCb: local track finding, momentum estimated by vertex constraint and measured estimated by vertex constraint and measured kink through magnetic fieldkink through magnetic field


SoftwareSoftware Main programming language: C++Main programming language: C++

some (very few) pieces of residual F77some (very few) pieces of residual F77 important part of ATLAS muon reconstruction in important part of ATLAS muon reconstruction in

F90F90 Trend: decomposition of code into Trend: decomposition of code into

components with implementation details components with implementation details hidden behind abstract interfaceshidden behind abstract interfaces different reconstruction algorithms put basic different reconstruction algorithms put basic

components together in different wayscomponents together in different ways ATLAS+CMS: code sharing muon/inner tracking ATLAS+CMS: code sharing muon/inner tracking

systemssystems in general the experiments are moving away from in general the experiments are moving away from

monolithic packagesmonolithic packages

ALICEALICE


ALICE ALICE detectordetector

ssSolenoid magnet B<0.5 T TPC (the largest ever…):

88 m3 , 510 cm length, 250 cm radius Ne (90%) + CO2 (10%)88 μs drift time160 pad rows570312 pads - channelsmain tracking device, dE/dx

22 * 1.8 units of pseudo-rapidity * 1.8 units of pseudo-rapidity

ITS6 Layers, 3 technologies

Material budget < 1% of X0 per layer! Silicon Pixels vertices resolution in xy (0.2 m2, 9.8 Mchannels) Silicon Drift resolution in z(1.3 m2, 133 kchannels) Double-sided Strip connection w/TPC(4.9 m2, 2.6 Mchannels)

Central tracking system:• Inner Tracking System • Time Projection Chamber


ALICE ALICE detectordetector

ss

Central tracking system:•Transition Radiation Detector• Time Of Flight

22 * 1.8 units of pseudo-rapidity * 1.8 units of pseudo-rapidity

TRD6 layers for:• electron/pion separation at pt>1 GeV•tracking complement •high pt trigger

Multigap Resistive Plate Multigap Resistive Plate ChambersChambers5 years R&D, and5 years R&D, and < 100 ps < 100 ps pions, kaons, protons separation electrons/pions at low pt


Tracking strategy – Tracking strategy – Primary tracksPrimary tracks

Iterative processIterative process Forward Forward

propagation propagation towards to the towards to the vertex –TPC-ITSvertex –TPC-ITS

Back propagation –Back propagation –ITS-TPC-TRD-TOFITS-TPC-TRD-TOF

Refit inward TOF-Refit inward TOF-TRD-TPC-ITSTRD-TPC-ITS

Continuous Continuous seeding –track seeding –track segment finding in segment finding in all detectorsall detectors

TRD

TPC

ITS

TOF

Marian IvanovMarian Ivanov


Tracking efficiencyTracking efficiency

TPC

all detectors

For realistic particle densitiesdN/dy = 2000 – 4000

combined efficiency well above 90%and fake track probability below 5%

Challenge in high-particle density environment

ATLASATLAS


The ATLAS DetectorThe ATLAS Detector

Weight: 7000 t

44 m

22

m


ATLAS Inner DetectorATLAS Inner Detector


Wolfgang LiebigWolfgang Liebig

CMSCMS


Thomas SpeerThomas Speer

LHCbLHCb


Matt NeedhamMatt Needham

Tracking beyond Tracking beyond the Kalman filterthe Kalman filter

Deterministic Annealing Deterministic Annealing FilterFilter

Gaussian-sum filterGaussian-sum filter

ATLAS + CMSATLAS + CMS


Sebastian FleischmannSebastian Fleischmann


ATLAS: resolution as function of noiseATLAS: resolution as function of noise

fast simulationfast simulation

preliminarypreliminary


CMS: tracks in high-pt CMS: tracks in high-pt b-jetsb-jets

Matthias WinklerMatthias Winkler


ElectronsElectronsElectrons lose energy mostly by Bremsstrahlung

z

final Energyinitial Energy

t

XX

0

amount of material

f(z) ln z t

ln(2) 1

tln(2)

Bethe-Heitler Distribution PDF

Tom AtkinsonTom Atkinson


Gaussian-Sum FilterGaussian-Sum Filter GSF resembles GSF resembles

several Kalman filters several Kalman filters running in parallelrunning in parallel

Different components Different components correspond to various correspond to various degrees of hardness degrees of hardness of bremsstrahlung of bremsstrahlung radiationradiation

Measurements used Measurements used to a posteriori to a posteriori determine which determine which component is correctcomponent is correct


Momentum residualsMomentum residuals

ATLAATLASS

CMSCMS


Effective 1

resolution vs. true

momentum

Effective 2

resolution vs. true

momentum

ATLASATLAS

CMSCMS

Effective 1 and

2 resolution vs. true

momentum


J/J/ reconstruction reconstruction

mJ/ = 3096.9GeV

Full width = 91.0KeV

Invariant mass from GSFInvariant mass from KF

Reconstructed invariant mass e+e-

m02=E2-

p

2Invariant mass:

ATLASATLAS


ConclusionsConclusions I have given an overview of current I have given an overview of current

tracking strategies in the LHC experimentstracking strategies in the LHC experiments transverse viewtransverse view longitudinal viewlongitudinal view

Many commonalities but also differencesMany commonalities but also differences detectors are differentdetectors are different manpower situation is differentmanpower situation is different

Significant changes since beginning of LEP Significant changes since beginning of LEP era:era: early LEP: dominated by global least-squares early LEP: dominated by global least-squares

techniques, Kalman filter was new and exotictechniques, Kalman filter was new and exotic early LHC: dominated by Kalman filter, some early LHC: dominated by Kalman filter, some

new developments are starting to appear in new developments are starting to appear in ATLAS and CMSATLAS and CMS


AcknowledgmentsAcknowledgments Many thanks to:Many thanks to:

Jochen SchiekJochen Schiek Markus ElsingMarkus Elsing Teddy TodorovTeddy Todorov Thomas SpeerThomas Speer Marian IvanovMarian Ivanov Matt NeedhamMatt Needham Gerhard RavenGerhard Raven Jeroen van TilburgJeroen van Tilburg Tom AtkinsonTom Atkinson Sebastian FleischmannSebastian Fleischmann Wolfgang LiebigWolfgang Liebig Matthias WinklerMatthias Winkler

track reconstruction in the lhc experiments

Documents