from bubble bubble chambers chambers to to the the LHC LHC

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Track

Track reconstruction reconstruction – – from

from bubble bubble chambers chambers to to the the LHC LHC

Talk given at

Talk given at thethe ViennaViennaConferenceConferenceononInstrumentation, Instrumentation, FebruaryFebruary19. 200419. 2004 Are Are StrandlieStrandlie, ,

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ThisThis talk talk willwill be a be a reviewreview ofof somesome tracktrack reconstruction

reconstruction methodsmethods

DisclaimerDisclaimer::

TheThe reviewreview is is not not exhaustiveexhaustive ((consultconsult book by book by FrühwirthFrühwirth et al.)!et al.)!

The The selection of itemsselection of items is a consequence of my is a consequence of my personal experience and preference

personal experience and preference

→ main emphasis is on

→ main emphasis is on developments having taken developments having taken place at CERN

place at CERN or in the context of CERN experimentsor in the context of CERN experiments

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Elements Elements bothboth from from tracktrack findingfinding ((patternpattern recognition

recognition) and ) and tracktrack fittingfitting ((estimationestimation ofof track

track parametersparameters) ) willwill be be treatedtreated

Main Main focusfocus is is onon methodsmethods for for tracktrack fittingfitting

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Outline Outline

IntroductionIntroduction

BoundariesBoundaries betweenbetween tracktrack findingfinding and and tracktrack fitting

fitting

LeastLeast--squaressquares methodsmethods and and treatmenttreatment ofof material

material effectseffects

Adaptive Adaptive methodsmethods

SummarySummary, , discussiondiscussion and and outlookoutlook

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Introduction Introduction

EnormousEnormous developmentsdevelopments withinwithin thethe fieldsfields ofof accelerators

accelerators, , detectorsdetectors and and computingcomputing technologies

technologies have have takentaken placeplace during during thethe last 50 last 50 years

years

Data rates have in general Data rates have in general increasedincreased::

most most eventsevents in in earlyearly bubblebubble chamberchamber experimentsexperiments werewere studiedstudied manuallymanually

data rate at LHC has to be data rate at LHC has to be reducedreduced online by more online by more thanthan fivefive ordersorders ofof magnitudemagnitude!!

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Introduction Introduction

TrackingTracking detectorsdetectors have have evolvedevolved from from bubblebubble chambers

chambers to to gaseousgaseous and and solidsolid--statestate electronic

electronic detectorsdetectors

ComputersComputers have have evolvedevolved from from largelarge mainframes

mainframes to to desktopsdesktops and and laptopslaptops withwith computing

computing powerpower severalseveral ordersorders ofof magnitude

magnitude largerlarger thanthan whatwhat waswas availableavailable somesome decades

decades agoago

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Introduction Introduction

EnvironmentEnvironment for data for data analysisanalysis has has continuously

continuously changedchanged over over thethe yearsyears

MethodsMethods for for data data analysisanalysis have have evolvedevolved accordingly

accordingly

Even Even thoughthough thisthis talk in talk in somesome sensesense willwill present present a a historicalhistorical reviewreview ofof tracktrack reconstructionreconstruction

methods

methods, , focusfocus willwill alsoalso be be onon longlong--termterm evolutions

evolutions and trends and trends withinwithin thisthis changingchanging environment

environment

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Boundaries Boundaries

TrackTrack reconstructionreconstruction is is traditionallytraditionally divideddivided intointo twotwo separate parts:

separate parts:

tracktrack findingfinding or or patternpattern recognitionrecognition

tracktrack fittingfitting (estimation(estimation ofof tracktrack parameters)parameters)

TrackTrack findingfinding in in earlyearly bubblebubble chamberchamber experimentsexperiments waswas donedone in a purelyin a purely manual waymanual way::

eventsevents werewere inspectedinspected onon a a scanningscanning tabletable

machinesmachines measuringmeasuring bubblebubble positionspositions onon thethe eventevent image image werewere guidedguided by an operatorby an operator

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Boundaries Boundaries

CERN CERN 2m 2m bubblebubble

chamber chamber

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Boundaries Boundaries

simplified simplified sketch

sketch –– beam beam perpendicular perpendicular

to slide to slide

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Boundaries

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Boundaries Boundaries

CERN BEBC CERN BEBC ––

BigBig EuropeanEuropean Bubble

Bubble ChamberChamber

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Boundaries Boundaries

SignificantSignificant effortsefforts werewere putput intointo thethe automationautomation ofof pattern

pattern recognitionrecognition in in bubblebubble chamberchamber experimentsexperiments

OneOne ofof thethe most most popularpopular methodsmethods waswas thethe HoughHough transform

transform ((HoughHough, , ProcProc. . ConfConf. . HighHigh EnergyEnergy AccAcc. Instr., . Instr., CERN, 1959)

CERN, 1959) ::

dividingdividing picturepicture intointo segmentssegments small enoughsmall enough to assumeto assume tracks

tracks beingbeing straight linesstraight lines

accumulatesaccumulates setssets ofof binsbins in histogramin histogram for eachfor each ofof thethe measurements

measurements in segmentin segment

measurementsmeasurements lyinglying alongalong straight lines show straight lines show upup as as peakspeaks in in histogram

histogram

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Boundaries Boundaries

bubble bubble chamber chamber picture

picture andand subdivision subdivision intointo segmentssegments

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Boundaries Boundaries

oneone segmentsegment

projection

projection ofof transform transform

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Boundaries Boundaries

Parameters Parameters ofof tracktrack elements from elements from eacheach ofof thethe segments

segments werewere used to used to combinecombine elements elements from

from differentdifferent segments segments intointo completecomplete tracks

tracks

ThisThis methodmethod waswas later later discovereddiscovered by by thethe image

image processingprocessing communitycommunity and and furtherfurther developed

developed therethere ^(Duda⁽^Duda and Hart, 1973)and Hart, 1973)

HoughHough transformtransform is still is still todaytoday amongamong mainstream

mainstream toolstools in in thatthat fieldfield

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Boundaries Boundaries

WhenWhen electronicelectronic experimentsexperiments enteredentered thethe arena in arena in thethe early

early 70’s, 70’s, newnew challengeschallenges hadhad to be to be facedfaced by by thethe reconstruction

reconstruction programsprograms

higherhigher data ratesdata rates

usuallyusually more material in more material in trackingtracking regionregion

In In thisthis environmentenvironment thethe numbernumber ofof fakefake candidatescandidates after

after tracktrack findingfinding couldcould be be quitequite largelarge

IntermediateIntermediate stepstep betweenbetween tracktrack findingfinding and and tracktrack fitting

fitting waswas sometimessometimes usefuluseful ((EichingerEichinger and Regler, CERN and Regler, CERN 8181--06 1981)06 1981)

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Boundaries Boundaries

A A popularpopular methodmethod ofof gettinggetting rid rid ofof manymany ofof thethe fakes

fakes withoutwithout submittingsubmitting thethe candidatecandidate to to thethe full

full tracktrack fitfit::

→ → PrincipalPrincipal ComponentsComponents AnalysisAnalysis (PCA)(PCA)

making making useuse ofof feature feature thatthat tracktrack onlyonly occupiesoccupies subspace

subspace ofof full full coordinatecoordinate spacespace

PCA –PCA – trainedtrained onon a seta set ofof goodgood trackstracks –– used to used to determine

determine thisthis subspacesubspace

given given tracktrack candidatecandidate: : veryvery fast to fast to decidedecide whetherwhether candidate

candidate is a is a goodgood tracktrack or notor not

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Boundaries Boundaries

With With inventioninvention ofof KalmanKalman filter filter for for tracktrack reconstruction

reconstruction thethe boundaryboundary becamebecame eveneven more

more fuzzyfuzzy::

couldcould be used for be used for tracktrack findingfinding and fitting and fitting concurrently

concurrently due to due to recursiverecursive nature nature ofof filterfilter

ApplicationApplication ofof KalmanKalman filter as filter as tracktrack finderfinder waswas pioneered

pioneered by by P.BilloirP.Billoir in DELPHI in DELPHI experiment

experiment at LEP at LEP ^(Billoir⁽^Billoir,^{, Comp}^Comp^{. Phys}^.^Phys.^.Comm. (CPC) ^Comm. (CPC) 1989)

1989)

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Boundaries Boundaries

It It waswas triedtried outout onon real datareal data for for thethe first time in first time in ZEUS

ZEUS experimentexperiment at DESYat DESY ^(Billoir⁽^Billoir ^{and Qian}^and^{Qian, NIM}^{, NIM}

A 1990) A 1990)

TheThe methodmethod waswas generalizedgeneralized by R. by R. MankelMankel to to possibly

possibly propagatepropagate severalseveral tracktrack candidatescandidates concurrently

concurrently in in HERAHERA--B B experimentexperiment at at DESYDESY ⁽⁽^Mankel^Mankel, NIM A 1997), NIM A 1997)

Is Is todaytoday by far by far thethe most most widelywidely used used methodmethod for for tracktrack findingfinding and fittingand fitting

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Boundaries Boundaries

principle

principle ofof method method

result

result from from eventevent in DELPHI TPC in DELPHI TPC

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Boundaries Boundaries

reconstructed reconstructed

event

event fromfrom ZEUSZEUS

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Boundaries Boundaries

Main

Main TrackerTracker inin HERAHERA--BB

principle

principle ofof concurrentconcurrent track

track evolutionevolution

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Boundaries Boundaries

At LHC, At LHC, boundariesboundaries betweenbetween tracktrack findingfinding and and fitting

fitting willwill becomebecome eveneven more diffusemore diffuse thanthan at at LEPLEP

In In highhigh--levellevel triggeringtriggering in CMS in CMS experimentexperiment at at LHC,

LHC, thethe conceptconcept ofof partialpartial reconstructionreconstruction has has beenbeen introducedintroduced::

stopstop tracktrack findingfinding onceonce enoughenough informationinformation is is available

available to to answeranswer a a specificspecific questionquestion

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Boundaries Boundaries

ExampleExample: ”is : ”is therethere a a tracktrack withwith transversetransverse momentum

momentum aboveabove a a certaincertain cutcut in a in a specificspecific region?”

region?”

in CMS in CMS ~5 ~5 measurementsmeasurements in a in a goodgood tracktrack is is enough

enough

ifif candidatecandidate is is acceptedaccepted, , thethe remainingremaining tracktrack seedsseeds areare not not exploredexplored

ApplicationApplication ofof thisthis conceptconcept willwill allowallow advancedadvanced analyses

analyses suchsuch as as bb--tagging tagging alreadyalready at trigger at trigger level

level ^{(CMS Data}^{(CMS Data}^Acq^Acq^{. and}^{. and}^High^High^-^-^Level^Level Trigger TDR 2002)Trigger TDR 2002)

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Boundaries Boundaries

QuiteQuite recentlyrecently developeddeveloped adaptive adaptive methodsmethods willwill alsoalso be be appliedapplied at LHCat LHC

SuchSuch methodsmethods –– developeddeveloped to to copecope withwith largelarge amounts

amounts ofof ambiguitiesambiguities and and noisenoise –– defersdefers thethe final

final assignmentassignment ofof measurementsmeasurements to to trackstracks to to thethe tracktrack fitfit

For For thesethese methodsmethods parts parts ofof tracktrack findingfinding has has beenbeen postponedpostponed to to thethe last last phasesphases ofof thethe tracktrack fitfit

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Least

Least - - squares squares methods methods

LeastLeast--squaressquares methodsmethods have a have a longlong traditiontradition in in track

track fittingfitting

AlreadyAlready from from bubblebubble chamberchamber experimentsexperiments theythey have have constituted

constituted thethe defaultdefault classclass ofof methodsmethods for for estimating

estimating tracktrack parametersparameters

In In earlyearly bubblebubble chamberchamber experimentsexperiments::

usualusual practicepractice to to neglectneglect effectseffects ofof multiple Coulomb multiple Coulomb scattering

scattering during theduring the estimationestimation (Jobes(Jobes and Shaylorand Shaylor, Rep. , Rep. ProgProg. . Phys. 1972)Phys. 1972)

errorserrors ofof multiple multiple scatteringscattering werewere afterwardsafterwards addedadded to to covariance

covariance matrixmatrix ofof estimatedestimated parametersparameters

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Least

Least - - squares squares methods methods

ImportantImportant stepstep forwardforward due to due to LaurikainenLaurikainen et et al. al. ^{(NIM 1972)}^{(NIM 1972)} ::

introducedintroduced thethe conceptconcept ofof breakpointsbreakpoints

fittedfitted deflectiondeflection angles angles explicitelyexplicitely

accuracyaccuracy ofof estimatesestimates improvedimproved

choicechoice ofof positionspositions ofof breakpointsbreakpoints somewhatsomewhat arbitrary

arbitrary

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Least

Least - - squares squares methods methods

New New challengeschallenges hadhad to be to be facedfaced by by reconstructionreconstruction programs

programs whenwhen electronicelectronic experimentsexperiments camecame onon stage stage in in earlyearly 70’s70’s

Prime Prime exampleexample: : Split Split FieldField Magnet (SFM)Magnet (SFM) detectordetector at at thethe CERN CERN IntersectingIntersecting StorageStorage Rings (ISR)Rings (ISR)

preciseprecise treatmenttreatment ofof material material effectseffects in wire in wire chamberschambers waswas needed

needed

alsoalso importantimportant effectseffects from from crossingcrossing beam pipe at beam pipe at shallowshallow angles

angles

correctcorrect approachapproach pioneeredpioneered by by M. ReglerM. Regler (CERN 73(CERN 73--2 1973)2 1973)

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Least

Least - - squares squares methods methods

SFM SFM detectordetector at CERN ISRat CERN ISR

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Least

Least - - squares squares methods methods

excerpt

excerpt from from paperpaper by by NagyNagy et al.et al.

((NuclNucl. . PhysPhys. B 1979). B 1979)

correct

correct weightingweighting enabled

enabled veryvery preciseprecise cross

cross--sectionsection measurementsmeasurements

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Least

Least - - squares squares methods methods

CorrectCorrect treatmenttreatment ofof multiple multiple scatteringscattering waswas essential

essential alsoalso for for experimentsexperiments at CERN SPSat CERN SPS

In In WA6 WA6 experimentexperiment at CERN proper at CERN proper treatmenttreatment ofof particleparticle deflectionsdeflections in airin air due to multiple due to multiple

scattering

scattering waswas neededneeded for reliable for reliable estimatesestimates ofof track

track parametersparameters

FormalismFormalism developeddeveloped by M. Regler by M. Regler waswas alsoalso used in

used in thisthis experimentexperiment ⁽⁽^Fidecaro^Fidecaro ^{et al.,}^{et al.,}^Nucl^Nucl^.^.^Phys^Phys^{. B}^{. B}

1980) 1980)

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Least

Least - - squares squares methods methods

WA6 WA6

experiment experiment

at at CERNCERN

SPSSPS

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Least

Least - - squares squares methods methods

perfectly

perfectly flatflat probability probability distribution distribution after

after cuttingcutting awayaway

nonnon--elasticelastic events events

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Least

Least - - squares squares methods methods

In In thethe UA1UA1 Nobel Nobel prizeprize experimentexperiment, material , material effectseffects could

could be neglectedbe neglected for for particlesparticles aboveabove 200 GeV200 GeV/c/c due to

due to veryvery small small amountsamounts ofof material in material in CentralCentral Detector

Detector (M. (M. PimiPimiää, CERN, private communication), CERN, private communication)

UA1 UA1 CentralCentral DetectorDetector providedprovided

preciseprecise measurementsmeasurements perpendicularperpendicular to to fieldfield

bad bad resolutionresolution elsewhereelsewhere

TrackTrack findingfinding and fitting and fitting waswas donedone in in projectionprojection perpendicular

perpendicular to to fieldfield

Fast, Fast, approximateapproximate circlecircle fitfit due to V. due to V. KarimKarimäkiäki was was used as least

used as least--squares estimator squares estimator (NIM A 1991)(NIM A 1991)

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Least

Least - - squares squares methods methods

In WA13 In WA13 experimentexperiment at CERN, a at CERN, a newnew formulationformulation ofof leastleast--squaressquares methodmethod waswas developeddeveloped

ThisThis methodmethod –– thethe so-so-calledcalled progressive progressive methodmethod due to P.

due to P. BilloirBilloir –– includesincludes measurementsmeasurements recursively

recursively intointo thethe fitfit (NIM 1984)(NIM 1984)

EstimatesEstimates ofof tracktrack parameters parameters areare updatedupdated eacheach time time information

information from from newnew measurementmeasurement is is includedincluded

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Least

Least - - squares squares methods methods

layout layout ofof

WA13 WA13

experiment experiment

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Least

Least - - squares squares methods methods

During During developmentdevelopment ofof reconstructionreconstruction software for software for DELPHI

DELPHI experimentexperiment at LEP at LEP collidercollider at CERN, it at CERN, it waswas realized

realized by R. Frühwirthby R. Frühwirth that progressive method was that progressive method was equivalent to

equivalent to KalmanKalman filterfilter (NIM A 1987)(NIM A 1987)

Immediate implications:Immediate implications:

existence of Kalmanexistence of Kalman smoothersmoother

easy to obtain easy to obtain optimal estimates anywhere along the optimal estimates anywhere along the track

track

enables enables efficient outlier rejectionefficient outlier rejection, as track parameter , as track parameter

predictions are calculated from all other measurements in a predictions are calculated from all other measurements in a track

track

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Least

Least - - squares squares methods methods

from Fr

from Frühwirth’sühwirth’s seminal paper seminal paper

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Least

Least - - squares squares methods methods

AnotherAnother importantimportant effecteffect needingneeding treatmenttreatment during

during estimationestimation is is energyenergy lossloss

IonizationIonization loss is loss is oftenoften regardedregarded as as deterministic

deterministic correctioncorrection to to tracktrack modelmodel

ElectronsElectrons needneed specialspecial treamenttreament::

suffersuffer from from bremsstrahlungbremsstrahlung energyenergy lossloss

dominant dominant componentcomponent ofof energyenergy loss loss aboveabove ~100 ~100 MeV/cMeV/c

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Least

Least - - squares squares methods methods

distribution

distribution ofof relative

relative energyenergy lossloss

strongly

strongly peakedpeaked withwith longlong tailtail

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Least

Least - - squares squares methods methods

A A full full spectrumspectrum ofof electronelectron trackstracks waswas treatedtreated withinwithin unbiased

unbiased leastleast--squaressquares estimationestimation for for thethe first time by first time by Stampfer

Stampfer et al.et al. ^{(CPC 1994)}^{(CPC 1994)}

BremsstrahlungBremsstrahlung waswas treatedtreated as as stochasticstochastic processprocess

First First twotwo momentsmoments ofof distributiondistribution due to modeldue to model by by Bethe

Bethe and and HeitlerHeitler ^(Proc⁽^Proc.^.^Royal^Royal Soc. London 1934)^Soc. London 1934) includedincluded in in Kalman

Kalman filterfilter

MethodMethod originallyoriginally testedtested outout onon data from DELPHIdata from DELPHI and and shownshown to be to be superior to conventionalsuperior to conventional

treatments treatments

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Least

Least - - squares squares methods methods

residual

residual andand pull

pull distributionsdistributions standard

standard approach approach

Kalman Kalman

filter filter

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Adaptive

Adaptive methods methods

LeastLeast--squaressquares methodmethod is is optimaloptimal whenwhen

tracktrack modelmodel is linearis linear

probabilityprobability densitiesdensities areare GaussianGaussian

TrackTrack modelmodel cancan oftenoften be be linearizedlinearized

ProbabilityProbability densitydensity functionsfunctions ((pdfpdf) ) areare oftenoften notnot Gaussian

Gaussian::

measurementmeasurement errorserrors cancan have longhave long tailstails or or eveneven be closebe close to to flatflat

multiple multiple scatteringscattering errorserrors have have GaussianGaussian corecore butbut longlong, , single

single--scatteringscattering tailstails

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Adaptive

Adaptive methods methods

Proper Proper treatmenttreatment ofof suchsuch effectseffects leads to leads to methodsmethods going

going beyondbeyond pure pure leastleast--squaressquares

VeryVery interestinginteresting specialspecial case:case:

pdfspdfs areare restrictedrestricted to Gaussianto Gaussian mixturesmixtures

ResultingResulting estimatorestimator:: GaussianGaussian--sumsum filter (GSF) filter (GSF)

(Fr(Frühwirthühwirth, CPC 1997), CPC 1997)

ResemblesResembles in in thisthis case a case a setset ofof KalmanKalman filters filters runningrunning in in parallelparallel

BothBoth measurementmeasurement errorserrors and material and material uncertainties

uncertainties areare in general in general GaussianGaussian mixturesmixtures

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Adaptive

Adaptive methods methods

VeryVery thoroughthorough studystudy ofof multiple multiple scatteringscattering in in context

context ofof tracktrack reconstructionreconstruction has has beenbeen performed

performed by by FrFrühwirthühwirth and and ReglerRegler ^{(NIM A}^{(NIM A}

2001) 2001) ::

full full pdfpdf obtained by obtained by successive (numerical) successive (numerical) convolutions

convolutions of single-of single-scattering densityscattering density

precise, precise, twotwo--component Gaussiancomponent Gaussian--mixture mixture approximation

approximation of density obtained and of density obtained and

parameterized as function of material thickness parameterized as function of material thickness

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Adaptive

Adaptive methods methods

comparison

comparison withwith simulation

simulation comparison

comparison withwith MoliereMoliere

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Adaptive

Adaptive methods methods

ReconstructionReconstruction ofof electronselectrons lends lends itselfitself to to treatment

treatment by GSFby GSF::

energyenergy loss loss distributiondistribution is is highlyhighly nonnon--GaussianGaussian

First First attemptattempt mademade by Frühwirthby Frühwirth and and Frühwirth-Frühwirth- Schnatter

Schnatter ^{(CPC 1998)}^{(CPC 1998)}

“proof“proof--of of ––principle” type of studyprinciple” type of study

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Adaptive

Adaptive methods methods

residual residual

distributions distributions

ofof inverse inverse momentum momentum

ofof GSF GSF

and and KalmanKalman filterfilter

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Adaptive

Adaptive methods methods

More More recentlyrecently, , GaussianGaussian--mixturemixture approximations

approximations ofof thethe BetheBethe--HeitlerHeitler distributions

distributions have have beenbeen calculatedcalculated ^(Frühwirth^(Frühwirth, CPC , CPC 2003)

2003)

These have been used in a more These have been used in a more realistic realistic implementation of a GSF

implementation of a GSF in the CMS tracker in the CMS tracker at CERN

at CERN (Adam et al., Proc. CHEP’03 2003)(Adam et al., Proc. CHEP’03 2003)

Results indicate that Results indicate that improvements can be improvements can be mademade with respect to standard with respect to standard KalmanKalman filterfilter

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Adaptive

Adaptive methods methods

example

example ofof estimated

estimated pdfpdf from GSF from GSF

residual residual distributions distributions

ofof inverseinverse momentum momentum

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Adaptive

Adaptive methods methods

probability probability distributions distributions ofof estimatedestimated

inverse inverse momentum momentum

KFKF GSFGSF

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Adaptive

Adaptive methods methods

Neural Neural networksnetworks becamebecame veryvery popularpopular toolstools for data for data analysis

analysis in in thethe 80’s80’s

A A HopfieldHopfield neural netneural net waswas developeddeveloped for patternfor pattern recognition

recognition in in trackingtracking detectorsdetectors

→ Denby→ Denby--PetersonPeterson neural networkneural network (Denby(Denby, CPC 1988; , CPC 1988;

Peterson

Peterson, NIM A 1989), NIM A 1989)

MethodMethod waswas implementedimplemented in ALEPH in ALEPH experimentexperiment at at CERN and

CERN and claimedclaimed to to yieldyield resultsresults compatiblecompatible withwith standard

standard tracktrack findingfinding ^(Stimpfl⁽^Stimpfl-^-^Abele^Abele ^&^&Garrido, CPC 1991)^Garrido, CPC 1991)

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Adaptive

Adaptive methods methods

event

event withwith generatedgenerated links links and and convergedconverged resultresult

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Adaptive

Adaptive methods methods

AlternativesAlternatives to to meanmean--fieldfield annealingannealing for for minimization

minimization ofof energyenergy have have beenbeen foundfound inferior

inferior ^(Diehl⁽^Diehl et al., NIM A 1997)et al., NIM A 1997)

efficiency efficiency evolution

evolution ofof energy

energy

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Adaptive

Adaptive methods methods

MethodMethod relatedrelated to to HopfieldHopfield netnet butbut withwith explicit

explicit referencereference to to tracktrack modelmodel::

ElasticElastic Arms Arms algorithmalgorithm ((OhlssonOhlsson et al., CPC 1992)et al., CPC 1992)

AttemptAttempt to to speed speed upup methodmethod by by formulatingformulating it it as as singlesingle--tracktrack algorithmalgorithm has has beenbeen mademade

(Fr(Frühwirthühwirth and and StrandlieStrandlie, CPC 1999), CPC 1999)