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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
IntroductionIntroduction
After the track fit one usually forgets aboutthe measurements and
only cares about a compact representation
of the tracks
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Overall strategiesOverall strategies
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.
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Overall strategiesOverall strategies
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
The ATLAS DetectorThe ATLAS Detector
Weight: 7000 t
44 m
22
m
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
ATLAS Inner DetectorATLAS Inner Detector
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Wolfgang LiebigWolfgang Liebig
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
CMSCMS
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Thomas SpeerThomas Speer
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
LHCbLHCb
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Matt NeedhamMatt Needham
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Tracking beyond Tracking beyond the Kalman filterthe Kalman filter
Deterministic Annealing Deterministic Annealing FilterFilter
Gaussian-sum filterGaussian-sum filter
ATLAS + CMSATLAS + CMS
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Sebastian FleischmannSebastian Fleischmann
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
ATLAS: resolution as function of noiseATLAS: resolution as function of noise
fast simulationfast simulation
preliminarypreliminary
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
CMS: tracks in high-pt CMS: tracks in high-pt b-jetsb-jets
Matthias WinklerMatthias Winkler
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Momentum residualsMomentum residuals
ATLAATLASS
CMSCMS
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
Effective 1
resolution vs. true
momentum
Effective 2
resolution vs. true
momentum
ATLASATLAS
CMSCMS
Effective 1 and
2 resolution vs. true
momentum
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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
A. Strandlie, LHC Detector Alignment Workshop, 5.9.2006
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