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Outline

Unfolding jet multiplicity and leading jet p T spectra in jet production in association with W and Z Bosons. Christos Lazaridis University of Wisconsin-Madison on behalf of the V+Jets group November 28, 2011. Outline. Analysis flow Unfolding overview Unfolding methods Validation

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Outline

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  1. Unfolding jet multiplicityand leading jet pT spectrain jet production in association with W and Z Bosons Christos LazaridisUniversity of Wisconsin-Madisonon behalf of the V+Jets groupNovember 28, 2011

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

  3. Analysis Flow Fit distributions A L L E V EN T S Electron Selection ZCandidates Correct yields for reconstruction efficiency Signal yields vs. # jets Unfold jet multiplicity and leading jet pT Jet Selection • Ratio plots • σ(Ζ+n jets) / σ(Ζtotal) • σ(Ζ+n jets) /σ(Ζ+(n-1) jets) Unfolding

  4. Unfolding Overview Responsematrices # jets Leading jet pT Unfolding • 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 studies

  5. Unfolding MethodsSingular Value Decomposition Unfolding • 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

  6. Unfolding MethodsBayes Unfolding • 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

  7. Studying unfolding methods : SVDZ+Jetsleading jet pT Method: SVD; kTERM= 5 (optimal) Method: SVD; kTERM = 10 Unfolding

  8. Studying unfolding methods : BayesZ+Jetsleading jet pT Method: Bayes; #iterations: 2 (optimal) Method: Bayes; #iterations: 4 For >3 iterations we start getting increasing disagreement Unfolding s

  9. Validation of unfolding 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

  10. Validating jet multiplicity unfoldingZ+Jets • Unfolding performed on exclusive jet bins • Ratio is comparison of reconstructed events beforeand after unfolding with the generated MadGraphn-jets distribution MadGraph Z2, SVD (5) MadGraph Z2, Bayes (4) Pythia Z2, SVD (5) Generated Reconstructed Unfolded Generated Reconstructed Unfolded Generated Reconstructed Unfolded Reconstructed/Generated Reconstructed/Generated Reconstructed/Generated Unfolded/Generated Unfolded/Generated Unfolded/Generated Unfolding • 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

  11. Validating jet multiplicity unfoldingW+Jets • Closure test performed to verify that unfolding works as expected • Response matrix derived from MadGraph Z2 W+Jets sample Unfolding MadGraph Z2 W+Jets Unfolding Pythia Z2 W+Jets Generated Reconstructed Unfolded Generated Reconstructed Unfolded Reconstructed/Generated • Unfolded/Generated Unfolding

  12. Validating leading jet pT unfoldingZ+Jets MadGraph Z2, SVD (5) MadGraph D6T, Bayes (5) Pythia Z2, SVD (5) Generated Reconstructed Unfolded Generated Reconstructed Unfolded Generated Reconstructed Unfolded Reconstructed/Generated Reconstructed/Generated Reconstructed/Generated Unfolded/Generated Unfolded/Generated Unfolded/Generated Unfolding • 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

  13. Unfolding Exclusive Jet MultiplicityApplication to data : Z(ee) + Jets Exclusive jet multiplicity Generated MC Reconstructed Data Unfolded Data • 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 Reconstructed/Generated • Unfolded/Generated Exclusive jet multiplicity Unfolding

  14. Unfolding Leading Jet pTApplication to data : Z(ee) + Jets Leading jet pT Generated MC Reconstructed Data Unfolded Data • 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 pTregion Ratio with MadGraph Z2 MC Reconstructed/Generated • Unfolded/Generated Leading Jet pT Unfolding

  15. Error propagation in unfolding 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

  16. 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 0 Ratio with Monte Carlo Inclusive Jet Multiplicity Unfolding

  17. 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 Ratio with Monte Carlo Inclusive Jet Multiplicity Unfolding

  18. 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 • TuningPythia 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 Events/GeV Ratio with Monte Carlo Unfolding

  19. Conclusions Unfolding

  20. Backup slides

  21. Samples systematicstudies MadGraph samples normalized by MCFM NLO cross sections Unfolding • 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

  22. V+Jets unfolding plots Closure test Unfolding exclusive jet multiplicity Unfolding

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