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

Christos Lazaridis, University of Wisconsin-Madison Outline Analysis flow Unfolding overview Unfolding methods Validation Unfolding data Error propagation Final results Conclusions November 28, 2011 Unfolding 2

Christos Lazaridis, University of Wisconsin-Madison Analysis Flow November 28, 2011 Unfolding 3 Electron Selection ALLEVENTSALLEVENTS ALLEVENTSALLEVENTS Jet Selection Jet Selection Z Candidates Signal yields vs. # jets Unfold jet multiplicity and leading jet p T Fit distributions Correct yields for reconstruction efficiency Ratio plots σ(Ζ+n jets) / σ(Ζ total ) σ(Ζ+n jets) / σ(Ζ+(n-1) jets) Ratio plots σ(Ζ+n jets) / σ(Ζ total ) σ(Ζ+n jets) / σ(Ζ+(n-1) jets)

Christos Lazaridis, University of Wisconsin-Madison 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 p T – Matrix is inverted and applied to data Used Singular Value Decomposition method to unfold data Bayesian method also evaluated – Used for systematic studies November 28, 2011 Unfolding 4 Response matrices # jets Leading jet p T

Christos Lazaridis, University of Wisconsin-Madison Unfolding Methods Singular 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 = USV T U(mxm), V(nxn) : Orthogonal matrices – Columns of U, V : left & right singular vectors S(mxn) : Diagonal matrix with non-negative diagonal elements – S ii ≥0 : singular values – Regularization parameter k SVD 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 5

Christos Lazaridis, University of Wisconsin-Madison Unfolding Methods Bayes Iterative method – Starting with an initial set of probabilities p i – Obtaining an improved estimate via Probability an event is observed in bin i in terms of response matrix R and prior probability p i – Regularization parameter determines number of iterations November 28, 2011 Unfolding 6

Christos Lazaridis, University of Wisconsin-Madison Studying unfolding methods : SVD Z+Jets leading jet p T November 28, 2011 Unfolding 7 Method: SVD; kTERM = 5 (optimal)Method: SVD; kTERM = 10

Christos Lazaridis, University of Wisconsin-Madison Studying unfolding methods : Bayes Z+Jets leading jet p T s November 28, 2011 Unfolding 8 Method: Bayes; #iterations: 2 (optimal)Method: Bayes; #iterations: 4 For >3 iterations we start getting increasing disagreement

Christos Lazaridis, University of Wisconsin-Madison 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 Unfolding 9

Christos Lazaridis, University of Wisconsin-Madison Validating jet multiplicity unfolding Z+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 November 28, 2011 Unfolding 10 MadGraph Z2, SVD (5) MadGraph Z2, Bayes (4) Pythia Z2, SVD (5) Generated Reconstructed Unfolded Generated Reconstructed Unfolded Generated Reconstructed Unfolded Reconstructed/Generated Unfolded/Generated Reconstructed/Generated Unfolded/Generated Reconstructed/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 Unfolding performed on exclusive jet bins Ratio is comparison of reconstructed events before and after unfolding with the generated MadGraph n-jets distribution

Christos Lazaridis, University of Wisconsin-Madison Validating jet multiplicity unfolding W+Jets November 28, Unfolding Closure test performed to verify that unfolding works as expected Response matrix derived from MadGraph Z2 W+Jets sample Generated Reconstructed Unfolded Generated Reconstructed Unfolded Reconstructed/Generated Unfolded/Generated Unfolding MadGraph Z2 W+Jets Unfolding Pythia Z2 W+Jets

Christos Lazaridis, University of Wisconsin-Madison Validating leading jet p T unfolding Z+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 p T region – Minimizing bin-to-bin migrations Best results given by SVD with k term = 5 November 28, 2011 Unfolding 12 MadGraph Z2, SVD (5) MadGraph D6T, Bayes (5) Pythia Z2, SVD (5) Generated Reconstructed Unfolded Generated Reconstructed Unfolded Generated Reconstructed Unfolded Reconstructed/Generated Unfolded/Generated Reconstructed/Generated Unfolded/Generated Reconstructed/Generated Unfolded/Generated

Christos Lazaridis, University of Wisconsin-Madison Unfolding Exclusive Jet Multiplicity Application to data : Z(ee) + Jets November 28, 2011 Unfolding 13 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 MC Reconstructed Data Unfolded Data Reconstructed/Generated Unfolded/Generated Exclusive jet multiplicity

Christos Lazaridis, University of Wisconsin-Madison Unfolding Leading Jet p T Application to data : Z(ee) + Jets November 28, 2011 Unfolding 14 Leading jet p T Corrected leading jet p T Response matrix from the Z+Jets, Z2 Tune MadGraph Monte Carlo Unfolding leads to better agreement Indication that Monte Carlo underestimates in the low p T region Generated MC Reconstructed Data Unfolded Data Reconstructed/Generated Unfolded/Generated Leading Jet p T Ratio with MadGraph Z2 MC

Christos Lazaridis, University of Wisconsin-Madison 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 Unfolding 15

Christos Lazaridis, University of Wisconsin-Madison Final cross section ratios σ(Ζ+n jets) / σ(Ζ total ) November 28, 2011 Unfolding 16 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 P YTHIA fails to describe data – Result of the Parton Shower mechanism for higher-order corrections Ratio with Monte Carlo Inclusive Jet Multiplicity 0

Christos Lazaridis, University of Wisconsin-Madison Final cross section ratios σ(Ζ+n jets) / σ(Ζ+(n-1) jets) November 28, 2011 Unfolding 17 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 P YTHIA does not model data as well as expected Inclusive Jet Multiplicity Ratio with Monte Carlo

Christos Lazaridis, University of Wisconsin-Madison Unfolded Leading Jet p T Spectrum Transverse momentum spectrum of leading jet – Contents of each bin scaled by bin size Pythia Monte Carlo does not model leading jet p T spectrum well – Tuning P YTHIA 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, Unfolding Ratio with Monte Carlo Events/GeV

Christos Lazaridis, University of Wisconsin-Madison Conclusions November 28, 2011 Unfolding 19

Backup slides

Christos Lazaridis, University of Wisconsin-Madison 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) tt bar + 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 November 28, 2011 Unfolding 21 MadGraph samples normalized by MCFM NLO cross sections systematic studies

Christos Lazaridis, University of Wisconsin-Madison V+Jets unfolding plots November 28, 2011 Unfolding 22 Closure testUnfolding exclusive jet multiplicity