Unfolding jet multiplicity and leading jet p T spectra in jet production in association with W and Z...

Unfolding jet multiplicityand leading jet pT spectra

in jet production in association with W and Z Bosons

Christos LazaridisUniversity of Wisconsin-Madison

on behalf of the V+Jets group

November 28, 2011

Christos Lazaridis, University of Wisconsin-Madison

Outline

• Analysis flow• Unfolding overview• Unfolding methods• Validation • Unfolding data• Error propagation• Final results• Conclusions

November 28, 2011Unfolding

2


Analysis Flow


3

Electron SelectionA

LL

EVENTS Jet

Selection

ZCandidat

es

Signal yields vs. # jets Unfold jet

multiplicity and leading jet

pT

Fit distributions

Correct yields for

reconstruction efficiency

Ratio plots• σ(Ζ+n jets) / σ(Ζtotal)• σ(Ζ+n jets) / σ(Ζ+(n-1) jets)


Unfolding Overview• Measured distributions get “smeared”

– Due to detector resolution and efficiency effects

– “True” (particle-level) distribution differs from measured

• Jet distributions are unfolded– “Response matrix” created

based on Monte Carlo– Correlates generated with

reconstructed quantities• Number of jets• Leading jet pT

– Matrix is inverted and applied to data• Used Singular Value Decomposition

method to unfold data• Bayesian method also evaluated

– Used for systematic studiesNovember 28, 2011

Unfolding4

Responsematrices

# jets

Leading jet pT

Unfolding5 Christos Lazaridis, University of Wisconsin-Madison

Unfolding MethodsSingular Value Decomposition

– Unfolding resembles a Fourier expansion • Low frequencies systematic differences between MC and data• High frequencies statistical fluctuations in data• Regularization parameter effectively determines up to which

frequencies the terms in the expansion are kept

– Factorizing A = USVT

• U(mxm), V(nxn) : Orthogonal matrices– Columns of U, V : left & right singular vectors

• S(mxn) : Diagonal matrix with non-negative diagonal elements – Sii ≥0 : singular values

– Regularization parameter kSVD

• Small value may bias the unfolding result towards MC truth• Large value may give a result dominated by unphysically

enhanced statistical fluctuations

November 28, 2011


Unfolding MethodsBayes

• Iterative method– Starting with an initial set of

probabilities pi

– Obtaining an improved estimate via

• Probability an event is observed in bin i in terms of response matrix R and prior probability pi

– Regularization parameter determines number of iterations

November 28, 2011


Studying unfolding methods : SVDZ+Jets leading jet pT


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Method: SVD; kTERM = 5 (optimal) Method: SVD; kTERM = 10


Studying unfolding methods : BayesZ+Jets leading jet pT

• s

November 28, 2011

Method: Bayes; #iterations: 2 (optimal) Method: Bayes; #iterations: 4

For >3 iterations we start getting increasing

disagreement


Validation of unfolding

• Three types of tests to verify procedure– Unfolding distribution using the same signal

MC used to derive the Response Matrix– Unfolding distribution of a signal MC

different than the one used to derive the RM

– Unfolding distribution obtained in a data-like mixture of MC signal and background samples that should reflect the corresponding mixture in data• Background subtraction and efficiency

corrections are applied before unfolding

November 28, 2011


Validating jet multiplicity unfoldingZ+Jets

• Closure test performed to verify that unfolding works as expected:– Response matrix from the Z+Jets, Z2 Tune MadGraph Monte Carlo– Tests performed with:

• Z2 Tune, MadGraph MC – different event set

• D6T Tune, MadGraph MC• Z2 Tune, Pythia 6 MC


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MadGraph Z2, SVD (5) MadGraph Z2, Bayes (4) Pythia Z2, SVD (5)GeneratedReconstructedUnfolded

GeneratedReconstructedUnfolded


Reconstructed/Generated

Unfolded/Generated


Unfolded/Generated


Unfolded/Generated

• Unfolding performed on exclusive jet bins• Ratio is comparison of reconstructed events

before and after unfolding with the generated MadGraph n-jets distribution

11Unfolding


Validating jet multiplicity unfoldingW+Jets

November 28, 2011

• Closure test performed to verify that unfolding works as expected• Response matrix derived from MadGraph Z2 W+Jets sample

GeneratedReconstructed

Unfolded

GeneratedReconstructed

Unfolded

Reconstructed/GeneratedUnfolded/Generated

Unfolding MadGraph Z2 W+Jets Unfolding Pythia Z2 W+Jets


Validating leading jet pT unfoldingZ+Jets

• Same procedure as with number of jets unfolding• To select optimal bin width, the jet resolution was studied

– Bin sizes correspond ~2σ of the jet resolution in that pT region

– Minimizing bin-to-bin migrations

• Best results given by SVD with kterm= 5


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MadGraph Z2, SVD (5) MadGraph D6T, Bayes (5) Pythia Z2, SVD (5)GeneratedReconstructedUnfolded




Unfolded/Generated


Unfolded/Generated


Unfolded/Generated


Unfolding Exclusive Jet MultiplicityApplication to data : Z(ee) + Jets

November 28, 2011Unfolding13

Exclusive jet multiplicity• Response matrix from Z+Jets, Z2 Tune MadGraph Monte Carlo

• Data yields corrected for selection efficiency

• Improved agreement after unfolding

Ratio with MadGraph Z2 Tune

Generated MCReconstructed Data

Unfolded Data


Exclusive jet multiplicity


Unfolding Leading Jet pTApplication to data : Z(ee) + Jets


Leading jet pT• Corrected leading jet pT

• Response matrix from the Z+Jets, Z2 Tune MadGraph Monte Carlo

• Unfolding leads to better agreement

• Indication that Monte Carlo underestimates in the low pT region

Generated MCReconstructed Data

Unfolded Data


Leading Jet pT

Ratio with MadGraph Z2 MC


Error propagation in unfolding

• Unfolding is performed on the uncorrelated n-jet bins – n=0-3, n>=4

• Unfolded exclusive jet rates are used to compute the inclusive rates

• Uncertainties are divided in three categories:– Statistical (from the fit)– Systematics uncorrelated across bins (lepton efficiency)– Systematics correlated across bins (jet counting)

• The unfolding procedure is run multiple times to determine final values with proper uncertainty estimate:– Using statistical errors only– Using statistical + uncorrelated systematics– Using central values shifted by correlated systematics– Using unfolding alternatives in algorithm, response matrix, w/o PU

November 28, 2011


Final cross section ratiosσ(Ζ+n jets) / σ(Ζtotal)


• σ(Ζ+n-jets) / σ(Ζ+≥0-jet) ratio– Luminosity uncertainty cancels out– Event selection uncertainty reduced

• Data points– Error bars correspond to statistical

errors

• Systematic uncertainties– Jet counting

• Yellow band– Unfolding

• Blue striped band

• Good agreement between data and MadGraph

• PYTHIA fails to describe data– Result of the Parton Shower

mechanism for higher-order corrections

Ratio with Monte Carlo

Inclusive Jet Multiplicity

0


Final cross section ratiosσ(Ζ+n jets) / σ(Ζ+(n-1) jets)


• σ(Ζ+n jets) / σ(Ζ+(n-1) jets) ratio– Reduces jet energy scale

uncertainty

• Data points– Error bars correspond to

statistical errors

• Systematic uncertainties– Jet counting

• Yellow band

– Unfolding• Blue striped band

• Good agreement between data and MadGraph

• PYTHIA does not model data as well as expected

Inclusive Jet Multiplicity


18Unfolding


Unfolded Leading Jet pT Spectrum• Transverse momentum

spectrum of leading jet– Contents of each bin scaled by

bin size

• Pythia Monte Carlo does not model leading jet pT spectrum well– Tuning PYTHIA Parton Shower

parameters can improve this

• Z2 Tune agrees more with data than D6T tune– Underlying event description not

optimal– Tunes developed based on

Tevatron data• Re-tuning based on LHC data

November 28, 2011


Even

ts/G

eV


Conclusions


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Backup slides


Samples• December 22 reprocessed data

• Used only certified data • Corresponding to 36.1 pb-1

• Monte Carlo samples:

• Z+Jets• MadGraph, Tune Z2• MadGraph, Tune D6T• Pythia 6, Tune Z2

• Backgrounds:• W+Jets, Tune Z2 (MadGraph)

• ttbar + Jets, Tune Z2 (MadGraph)

• EM enriched QCD, Tune Z2 (Pythia)• BCtoE QCD, Tune Z2 (Pythia)

• Samples include PU corresponding to the latest 2010 collision runs


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MadGraph samples normalized by MCFM NLO

cross sections

systematicstudies


V+Jets unfolding plots


Closure test Unfolding exclusive jet multiplicity

Unfolding jet multiplicity and leading jet p T spectra in jet production in association with W and Z...

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