Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part XII)

Intr

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Introduction to Hadronic Final State Reconstruction in Collider Experiments

(Part XII)

Introduction to Hadronic Final State Reconstruction in Collider Experiments

(Part XII)

Peter LochPeter LochUniversity of ArizonaUniversity of Arizona

Tucson, ArizonaTucson, ArizonaUSAUSA

Peter LochPeter LochUniversity of ArizonaUniversity of Arizona

Tucson, ArizonaTucson, ArizonaUSAUSA

2P. LochP. Loch

U of ArizonaU of ArizonaApril 15, 2010April 15, 2010

Preliminaries

Plots for this sessionPlots for this session Most if not all plots shown in this session are meant as examples and for Most if not all plots shown in this session are meant as examples and for

illustration purposesillustration purposes Educational showcases to highlight certain features of energy scales and Educational showcases to highlight certain features of energy scales and

calorimeter responsecalorimeter response

They do not represent the up-to-date estimates for ATLAS jet They do not represent the up-to-date estimates for ATLAS jet reconstruction performancereconstruction performance In general much better than the (old) results shown here!In general much better than the (old) results shown here! Not many new plots can be shown in public yet!Not many new plots can be shown in public yet!

The performance plots shown are published The performance plots shown are published Reflection of state-of-art at a given moment in timeReflection of state-of-art at a given moment in time No experimental collision data available at that time!No experimental collision data available at that time!

3P. LochP. Loch


Summary Of Jet Inputs

Experiment and simulationExperiment and simulation Calorimeter towersCalorimeter towers

2-dim signal objects from all cells or only 2-dim signal objects from all cells or only cells surviving noise suppression cells surviving noise suppression (topological towers in ATLAS)(topological towers in ATLAS)

Calorimeter clustersCalorimeter clusters 3-dim signal objects with implied noise 3-dim signal objects with implied noise

suppression (topological clusters in ATLAS)suppression (topological clusters in ATLAS)

TracksTracks Reconstructed inner detector tracks – only Reconstructed inner detector tracks – only

charged particles with pT > pTcharged particles with pT > pTthresholdthreshold = 500 = 500 MeV – 1 GeV (typically)MeV – 1 GeV (typically)

Simulation onlySimulation only Generated stable particlesGenerated stable particles

Typically Typically ττlablab > 10 ps to be a signal source > 10 ps to be a signal source

towerstowers

clustersclusters

particlesparticles

trackstracks

4P. LochP. Loch


Image Of Jets In Calorimeter

5P. LochP. Loch


Calorimeter Jet Response

Calorimeter jet responseCalorimeter jet response Electromagnetic energy scaleElectromagnetic energy scale

Available for all signal Available for all signal definitionsdefinitions

No attempt to compensate or No attempt to compensate or correct signal for limited correct signal for limited calorimeter acceptancecalorimeter acceptance

Global hadronic energy scaleGlobal hadronic energy scale All signal definitions, but All signal definitions, but

specific calibrations for each specific calibrations for each definitiondefinition

Calibrations normalized to Calibrations normalized to reconstruct full true jet energy reconstruct full true jet energy in “golden regions” of in “golden regions” of calorimetercalorimeter

Local hadronic energy scaleLocal hadronic energy scale Topological clusters onlyTopological clusters only No jet context – calibration No jet context – calibration

insufficient to recover insufficient to recover calorimeter acceptance calorimeter acceptance limitations – no corrections for limitations – no corrections for total loss in dead material and total loss in dead material and magnetic field charged magnetic field charged particles losses)particles losses)

0,tower particletowers in particles in

jet jet0,jet

0,jet 0,tower particletowers in particles i

jet

reconstructed calorimeter jet

Unbiased and noise-suppressed towers:

E EEp p p

0,clusterclusters in

jet0,jet

0,jet 0,clusterclust

njet

matched particle

ers injet

reconstructed ca

jet(truth reference)

lorimeter jet

Topological cell clusters:

EEp p

particleparticles in

jet


jet

matched particle

2 2jet jet jett owers clusters

jet(truth reference)

Note at any scale:

0 for , 1m E p N N

E

p

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cell cell 0,cell DMcells in

jetrec,jet

0,jetrec,jetcell cell 0,cell DM

cells in 0,jetjet

Cell based calibration for all calorimeter signals and jets in "golden spot":

( , )

( , )

w E E

Epp w p Ep



jet


jet

matched particle jet(truth reference)

(cells are extracted fr

E

p

om unbiased or noise suppressed

towers or topological clusters forming the jet)

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rec,cluster particleclusters in particles in

jet jetrec,jet

rec,jet rec,cluster particletowers in p

jet


Locally calibrated clusters only:

E EEp p p

articles in

jet

matched particle jet(truth reference)

8P. LochP. Loch


Jet Energy Scale

Final Jet Energy Scale (JES)Final Jet Energy Scale (JES) Final jet calibrationFinal jet calibration

All corrections appliedAll corrections applied

Best estimate of true (particle) jet energyBest estimate of true (particle) jet energy Flat response as function of pTFlat response as function of pT Uniform response across whole calorimeterUniform response across whole calorimeter

Relative energy resolutionRelative energy resolution Depends on the calorimeter jet response – calibration applies compensation correctionsDepends on the calorimeter jet response – calibration applies compensation corrections

Resolution improvements by including jet signal featuresResolution improvements by including jet signal features Requires corrections sensitive to measurable jet variablesRequires corrections sensitive to measurable jet variables Can use signals from other detectorsCan use signals from other detectors

Determination with simulationsDetermination with simulations Measure residual deviations of the calorimeter jet response from truth jet energyMeasure residual deviations of the calorimeter jet response from truth jet energy

Derive corrections from the calorimeter response at a given scale as function of pT (linearity) Derive corrections from the calorimeter response at a given scale as function of pT (linearity) and pseudorapidity (uniformity) for all particle jetsand pseudorapidity (uniformity) for all particle jets

Use numerical inversion to parameterize correctionsUse numerical inversion to parameterize corrections Conversion from truth variable dependence of response to reconstructed variable responseConversion from truth variable dependence of response to reconstructed variable response

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Signal Linearity

From simulations From simulations Compare calorimeter response with particle Compare calorimeter response with particle

jet energy as function of the particle jet jet energy as function of the particle jet energyenergy

All jets, all regions, full kinematic coverageAll jets, all regions, full kinematic coverage Residual deviation from linearityResidual deviation from linearity

Depend on calorimeter energy scale – large Depend on calorimeter energy scale – large for electromagnetic energy scale and local for electromagnetic energy scale and local calibration due to missing jet level calibration due to missing jet level correctionscorrections

Small for global calibration due to jet Small for global calibration due to jet energy normalizationenergy normalization

Corrections can be extracted from residualsCorrections can be extracted from residuals A bit tricky – need to use numerical A bit tricky – need to use numerical

inversion (see later)inversion (see later)

From experimentFrom experiment Validate and extract calibrations from collision Validate and extract calibrations from collision

datadata W boson mass in hadronic decay is jet W boson mass in hadronic decay is jet

energy scale referenceenergy scale reference pT balance of electromagnetic signal (Z pT balance of electromagnetic signal (Z

boson, photon) and jetboson, photon) and jet Note change of reference scaleNote change of reference scale

In-situ channels provide interaction In-situ channels provide interaction (parton) level truth reference!(parton) level truth reference!

Global CalibrationGlobal Calibration

Local CalibrationLocal Calibration

tower jet closure test for calibrated calorimeter response

cluster jet closure test

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Signal Uniformity

SimulationsSimulations Compare calorimeter response Compare calorimeter response

with particle jet energy as with particle jet energy as function of the jet directionfunction of the jet direction All jets in full kinematic rangeAll jets in full kinematic range

Residual non-uniformities Residual non-uniformities expected in cracksexpected in cracks Only jets in “golden regions” Only jets in “golden regions”

used for calibrationused for calibration

From experimentFrom experiment Di-jet pT balanceDi-jet pT balance

Balance pT of well calibrated jet Balance pT of well calibrated jet in “golden region” with jet in in “golden region” with jet in other calorimeter regions other calorimeter regions

Can also use photon pT balance Can also use photon pT balance with jets outside of “golden with jets outside of “golden region”region”



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Relative Jet Energy Resolution

SimulationsSimulations Measure fluctuations of Measure fluctuations of

calorimeter jet energy as calorimeter jet energy as function of truth jet energyfunction of truth jet energy All jets in full kinematic range All jets in full kinematic range

and in various regions of and in various regions of pseudo-rapiditypseudo-rapidity

From experimentFrom experiment Di-jet final statesDi-jet final states

Measure relative fluctuations Measure relative fluctuations of jet energies in back-to-back of jet energies in back-to-back (pT) balanced di-jets(pT) balanced di-jets



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JES Calibration Parameterizations

Golden rule of calorimetric energy measurementGolden rule of calorimetric energy measurement The fully calibrated calorimeter signal is most probably the true jet (or particle) The fully calibrated calorimeter signal is most probably the true jet (or particle)

energyenergy Interpretation holds only for symmetrically distributed fluctuations – mean value is Interpretation holds only for symmetrically distributed fluctuations – mean value is

identical to average value identical to average value

The resolution of the measurement is given by the characteristics of the signal The resolution of the measurement is given by the characteristics of the signal fluctuationsfluctuations Can only be strictly and correctly understood in case of Gaussian response distributionsCan only be strictly and correctly understood in case of Gaussian response distributions

We need a normally distributed response!We need a normally distributed response!

Problem for all calibration techniquesProblem for all calibration techniques Residual deviations from expected jet reconstruction performance must be measure Residual deviations from expected jet reconstruction performance must be measure

as function of true quantitiesas function of true quantities Only then is the fluctuation of the response Only then is the fluctuation of the response RR = = EErecoreco//EEtruetrue really Gaussian after calibration really Gaussian after calibration

But need to apply corrections to measured jetsBut need to apply corrections to measured jets Need parameterization as function of reconstructed quantitiesNeed parameterization as function of reconstructed quantities Simple re-binning does not maintain the Gaussian characteristics of the fluctuations – hard Simple re-binning does not maintain the Gaussian characteristics of the fluctuations – hard

to control error!to control error!

Use numerical inversion to transfer the calibrations from true to measured Use numerical inversion to transfer the calibrations from true to measured parametersparameters Maintains Gaussian character Maintains Gaussian character

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Understanding Response Fluctuations

Toy model Toy model Generate flat jet energy Generate flat jet energy

spectrumspectrum Uniform energy distribution for Uniform energy distribution for

EEjetjet in [ in [EEminmin,,EEmaxmax]]

Smear true jet energy with Smear true jet energy with GaussianGaussian Assume perfect average Assume perfect average

calibrationcalibration Width of distribution follows Width of distribution follows

calorimetric energy resolution calorimetric energy resolution function function

Calculate the response Calculate the response In bins of In bins of EEtruetrue and in bins of and in bins of

EEsmearsmear = = EErecoreco

Repeat exercise with steeply Repeat exercise with steeply falling energy spectrumfalling energy spectrum

smear reco true

22

true

smear true

2

Calibrated response:

Calorimeter resolution function (no noise):

Smeared energy:

is a random number following the Gaussian PD

1 1(

F:

) exp2

e2

i.

E

E

E E E

ac

E E

E E r

g r

r

r

smear true

true

. distributed around 0 with a width of 1Response fluctuations:

with 0E E

R RE

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Response Distributions

true( )p E const 4true true( )p E E

Lower edge of Lower edge of EE spectrum spectrum

Center of Center of EE spectrum spectrum

High end of High end of EE spectrum spectrum

smea

t

r

rue

binned in binned in

EE

15P. LochP. Loch


Response Distributions

true( )p E const 4true true( )p E E

Lower edge of Lower edge of EE spectrum spectrum

Center of Center of EE spectrum spectrum

High end of High end of EE spectrum spectrum

smea

t

r

rue

binned in binned in

EE

16P. LochP. Loch


Numerical Inversion

( )trueR E

( )recR E

( )true trueR E E

trueE

Transfer of response function from dependence on true variable to dependence on measured variable

rec true true( ) ( )R E R R E E

rec true true( )E R E E

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Numerical Inversion Functions

Often simple functionsOften simple functions Address residual energy (pT) Address residual energy (pT)

and direction dependence of and direction dependence of calorimeter jet responsecalorimeter jet response Determine response Determine response

functions functions RR in bins of true jet in bins of true jet pT and reconstructed pT and reconstructed pseudo-rapidity pseudo-rapidity ηηrec,jetrec,jet

Apply numerical inversion to Apply numerical inversion to determine calibration determine calibration functions in reconstructed functions in reconstructed variable space (variable space (ppT,rec,jetT,rec,jet,, η ηrec,jetrec,jet ) )

Use calibration functions to Use calibration functions to get jet energy scaleget jet energy scale Technique can be applied to Technique can be applied to

locally or globally calibrated locally or globally calibrated jet response, with likely jet response, with likely different calibration different calibration functions functions

truth,jet1T,truth,jet r

1T,truth

eco,jet T,truth,jet reco,jet

,jet r

reco

eco,jet T,truth,jet reco,jet

T,

,jett ruth,

truth,jet re

rec,jet

jet

( , ) (

with and

then apply numerical inversio

( , ) ( ,

, )

(

n

,

)

f p R p

f p

ER p p

E

numericalinversion

co,jet T,reco,jet reco,jet) ( , )f p

T,truth,jet rec,jet( , )f p

T,rec,jet rec,jet( , )f p

T,trT,r uthec,jet ,jet(GeV) ( Vor Ge )p p

18P. LochP. Loch


Numerical Inversion Functions

Often simple functionsOften simple functions Address residual energy (pT) Address residual energy (pT)

and direction dependence of and direction dependence of calorimeter jet responsecalorimeter jet response Determine response Determine response

functions functions RR in bins of true jet in bins of true jet pT and reconstructed pT and reconstructed pseudo-rapidity pseudo-rapidity ηηrec,jetrec,jet

Apply numerical inversion to Apply numerical inversion to determine calibration determine calibration functions in reconstructed functions in reconstructed variable space (variable space (ppT,rec,jetT,rec,jet,, η ηrec,jetrec,jet ) )

Use calibration functions to Use calibration functions to get jet energy scaleget jet energy scale Technique can be applied to Technique can be applied to

locally or globally calibrated locally or globally calibrated jet response, with likely jet response, with likely different calibration different calibration functions functions

reco,jet

reco,jet

calib,jet

calib,jet

cell cell 0,cell DMcells in

jet

T,reco,jet reco,jet 0,jetcell cell 0,cell DM

cells in 0,jetjet

, wi

global cal

( , )

( , )( ,

ibration

)

:

E

p

Ep

w E E

f p pw p E

p

2T,reco,jet reco,jet reco,jet

rec,clusterclusters in

jetcalib,jetT,reco,jet reco,jet

calib,jet rec,

th 1 ta

clustertower

nh

s inje

local cali

( , )

bration:

p p

EE

f pp p

t

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Erec,jet Versus Etruth,jet

Why not use direct relation Why not use direct relation between reconstructed and true between reconstructed and true energy?energy? Same simulation data inputSame simulation data input

Has been used in some Has been used in some experimentsexperiments

Dependence on truth energy Dependence on truth energy spectrumspectrum Need to make sure calibration Need to make sure calibration

sample is uniform in truth sample is uniform in truth energyenergy

Alternatively, unfold driving Alternatively, unfold driving truth energy spectrum truth energy spectrum

Residual non-gaussian behaviour Residual non-gaussian behaviour of truth energy distributionof truth energy distribution Error on reconstructed energy Error on reconstructed energy

hard to understandhard to understand Could still use response Could still use response

distribution → same issues as distribution → same issues as discussed on previous slide!discussed on previous slide!

rec,jet(GeV)E

truth,jet(GeV)E

4truth,jetcross-section E

4truth,jetweight E

truth,jet(GeV)E

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truth,jet(GeV)E

rec,jet(GeV)E

truth,jet(GeV)E

4truth,jetcross-section E

4truth,jetweight E

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truth,jet(GeV)E

rec,jet(GeV)E

truth,jet(GeV)E

truth,jet rec,jet 1( ), [ , [i ih E E E E

rec,jett ruth,jet 1( ), [ , [i ih E E E E

4truth,jett ruth,jet

rec,jet 1

( ) ,

[ , [i i

h E E

E E E

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Systematic Error

Strategy from simulationsStrategy from simulations Determine all calibrations with fixed conditionsDetermine all calibrations with fixed conditions

Ideal detector model – everything is alignedIdeal detector model – everything is aligned Fixed (best) GEANT4 shower model – from testbeam evaluationsFixed (best) GEANT4 shower model – from testbeam evaluations Fixed calorimeter signal definition – e.g., towersFixed calorimeter signal definition – e.g., towers Fixed jet definition – like seeded cone with size 0.7Fixed jet definition – like seeded cone with size 0.7 Fixed final state – QCD di-jets preferredFixed final state – QCD di-jets preferred

Study change in performance for changing conditions with ideal calibration Study change in performance for changing conditions with ideal calibration appliedapplied Detector misalignment and changes in material budgetsDetector misalignment and changes in material budgets Different shower GEANT4 modelDifferent shower GEANT4 model Different calorimeter signal definitions – e.g., clustersDifferent calorimeter signal definitions – e.g., clusters Different jet definitions – e.g., kT, AntikT, different cone or cone sizes…Different jet definitions – e.g., kT, AntikT, different cone or cone sizes… Different physics final state – preferably more busy ones like SUSY, ttbar,…Different physics final state – preferably more busy ones like SUSY, ttbar,…

Use observed differences as systematic error estimatesUse observed differences as systematic error estimates Use of collision dataUse of collision data

Compare triggered final states with simulationsCompare triggered final states with simulations Level of comparison represents understanding of measurement – systematic Level of comparison represents understanding of measurement – systematic

error (at least for standard final states)error (at least for standard final states) Use in-situ final states to validate calibrationUse in-situ final states to validate calibration

Careful about biases and reference levels (see session 9)Careful about biases and reference levels (see session 9)

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Performance Evaluation

Calibration functions determined with “perfect” detector description and Calibration functions determined with “perfect” detector description and one reference jet definitionone reference jet definition Validate performance in perfect detector Validate performance in perfect detector

Signal linearity & resolutionSignal linearity & resolution Quality of calibration for a real detectorQuality of calibration for a real detector

A priori unknown real detector A priori unknown real detector Absolute and relative alignments, inactive material distributions Absolute and relative alignments, inactive material distributions

Estimate effect of distorted (real) detectorEstimate effect of distorted (real) detector Implement realistic assumptions for misalignment in simulationsImplement realistic assumptions for misalignment in simulations Small variations of inactive material thicknesses and locationsSmall variations of inactive material thicknesses and locations But use “perfect” calibration for reconstructionBut use “perfect” calibration for reconstruction

Change jet signalsChange jet signals Tower or clustersTower or clusters

E.g, change from reference calorimeter signalE.g, change from reference calorimeter signal Different jet finderDifferent jet finder

E.g., use kT instead of cone E.g., use kT instead of cone Different configurationDifferent configuration

E.g., use narrow jets (cone size 0.4) instead of wide jets (0.7)E.g., use narrow jets (cone size 0.4) instead of wide jets (0.7)

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Signal Linearity & Resolution

Response Response Linear within +/-1% after calibration applied Linear within +/-1% after calibration applied

for pT>100 GeVfor pT>100 GeV Clear improvement compared to basic signal Clear improvement compared to basic signal

scalescale Problems with low pT regimeProblems with low pT regime

ATLAS limit pT>20-40 GeV, depending on ATLAS limit pT>20-40 GeV, depending on luminosityluminosity

May be resolution bias – under studyMay be resolution bias – under study

ResolutionResolution Jet energy resolution clearly improved by Jet energy resolution clearly improved by

calibration as wellcalibration as well Slight dependence on calibration strategySlight dependence on calibration strategy

Close to required performanceClose to required performance

65%3%

E E

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Characterizes “real” detector jet Characterizes “real” detector jet response response Variation of response with directionVariation of response with direction Changing inactive material Changing inactive material

distributiondistribution Cracks between calorimeter Cracks between calorimeter

modulesmodules

Variations Variations No strong dependence on No strong dependence on

calorimeter signal definitioncalorimeter signal definition Towers/clustersTowers/clusters

ATLAS cone jet performs better in ATLAS cone jet performs better in crack region at low pT crack region at low pT

Signal Uniformity

narrow jetsnarrow jets


Rel

ativ

e T

ower

Jet

Res

pon

sep T

(G

eV)

Clu

ster

-Tow

er D

iffe

ren

ce (

%)

η

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Deviation From Signal Linearity

Estimated effect of a distorted detector Estimated effect of a distorted detector

Effect of detector distortion depends on jet size, calo signal choice, and kinematic domain

Effect of detector distortion depends on jet size, calo signal choice, and kinematic domain

ATLAS MC(preliminary)

rec,jett ruth,jet distorted

rec,jett ruth,jet ideal

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E E

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Resolution Direction Dependence

Larger fluctuations for kT jets at Larger fluctuations for kT jets at low pTlow pT Vacuum effect for tower jets?Vacuum effect for tower jets? Less pronounced for cluster jetsLess pronounced for cluster jets

Noise suppression important in Noise suppression important in this domainthis domain

Very similar resolutions at high pTVery similar resolutions at high pT No strong dependence on jet No strong dependence on jet

definitiondefinition No strong dependence on No strong dependence on

calorimeter signal definitioncalorimeter signal definition No significant noise contribution No significant noise contribution

anymoreanymore

η


2 2

cluster tower

for 0

for 0

E E

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Different Final States: Quark Jets

tt qqb tt qqb

(high mulitplicity jets)SUSY

q

(high mulitplicity jets)SUSY

q

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Documents

Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part XII)