Measurement of the WW Production Cross Section at CDF Using 3.6 fb-1 of Data

Doug Benjamin, Dean Andrew Hidas, Mark Kruse, Eric James, Sergo Jindariani, Britney Rutherford, Roman Lysak, Aidan Robson, Rick St. Denis, Peter Bussey, Matthew Herndon, Jennifer Pursley, Simone Pagan Griso, Donatella Lucchesi

Please see CDF public note 9753 for more details on the analysis presented here. You can email the authors with any questions you have regarding this analysis.

CDF - WW Cross Section using 3.6 fb-1

At CDF using 3.6 fb-1 of data we measure the WW production cross section to be:

Signal Region

Events are selected which contain 2 leptons with opposite charge (any combination of electrons and muons) and significant missing transverse energy. This signature is characteristic of two W bosons decaying leptonically, where the final state consists of two leptons and two neutrinos which escape undetected giving rise to an apparent missing energy. The expected number of signal and background events is shown in the table below along with the number of events observed in data. This table includes systematic uncertainties only.

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Signal Region Plots

Below are a number of kinematic distributions for signal and background predictions in the signal region, shown with the data for comparison. More details about the selection and kinematic plots are given in the accompanying note.

EPS versions of these plots can be found here

Control Regions

In order to ensure that simulation is properly modeling the data, several control regions which are orthogonal to the signal regions are investigated. A small sample of these regions is presented graphically below. For more details on these control regions please see the HWW public webpage. The plots below represent the following control regions:

  • Drell-Yan control region: Requires low missing tranverse energy and a dilepton mass between 76 and 106 GeV. The purpose of this region is to check the modeling of selection efficiencies for all lepton types.

EPS versions of these plots can be found here

  • Low missing transverse energy (Met) significance control region: Requires the missing transverse energy divided by the square root of the sum of all calorimeter energy in the event to be low. The purpose of this region is to check the model of mismeasured unclustered energy or lepton energy.

EPS versions of these plots can be found here

  • Same sign control region: Requires two like-sign dileptons. The purpose of this region is to check the modeling of the Wgamma and fake lepton (W+jets) backgrounds.

EPS versions of these plots can be found here

Matrix Elements and Likelihood Ratios

This measurement makes use of matrix element based likelihood ratios. A per-event probability is assigned according to a matrix element based calculation of the leading order cross section for 4 different processes (WW, ZZ, Wgamma, and W+jet) given the measured event kinematics. The probability is given by

where the variables are defined as follows:
  • - This represents the observed lepton momenta vectors as well as the two transverse components of the missing transverse energy.
  • - This is a normalization factor based on the total leading order cross section and detector acceptances.
  • - This refers to the leading-order cross section.
  • - The true lepton 4-momenta which are integrated over.
  • - Detector efficiencies and acceptances.
  • - A generalized detector resolution function.
MCFM is used for the leading order matrix element calculations. A likelihood ratio is then formed using the event probabilities for signal and background like events. The likelihood ratio used in this measurement is LRWW which is given by
where i are the background processes modeled and ki is the relative fraction of the i-th mode such that the sum over all ki equals 1.

LRWW distributions for signal and background-like events are shown below. These distributions are used in the maximum likelihood fit described below.

EPS versions of these plots can be found here

Systematic Uncertainties

Many systematic uncertainties are considered in this analysis. A table of systematics used in this analysis is given below followed by brief explanations of what these uncertainties are. Systematics in itallics are correlated across all processes in both the generation of simulated experiments as well as in the likelihood fit itself.
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  • Cross Section - Uncertainty on the theoretical cross sections for each process.
  • PDF Model - Uncertainty in acceptance from varying the PDF (CTEQ6m) eigenvectors.
  • Higher-order Diagrams - Uncertainty in acceptance from potential higher-order electroweak corrections, assessed by comparing leading order PYTHIA to MC@NLO Monte Carlo for the WW signal.
  • Jet Modeling - Uncertainty on acceptance due to the modeling of initial state radiation jets by the Monte Carlo. The effect is largest for those processes with zero jets at leading order.
  • Conversion Modeling - Uncertainty in acceptance due to the uncertainty on the efficiency of photon conversion removal.
  • Jet Fake Rates - Uncertainty in acceptance from uncertainties on the calculated probabilities that a jet will be falsely identified as a lepton.
  • MC Run Dependence - Uncertainty in acceptance for those Monte Carlo samples which do not span the entire run range of data used in this analysis.
  • Lepton ID Efficiencies - Uncertainty in acceptance due to the measured lepton identification efficiencies.
  • Trigger Efficiencies - Uncertainty in acceptance due to the trigger efficiency measurement.
  • Luminosity - Standard 5.9% uncertainty on the luminosity measurement.

Likelihood Fit and Results

A binned likelihood is formed from the Poisson probabilities of the expected and observed number of events in each bin. The likelihood is given by

where the Sc are nuisance parameters associated with each systematic and ni are the number of data events in the i-th bin. The expected number of events in each bin is given by

.
Here (NkExp)i is the expected number of events from the process k in the i-th bin. fck is the fractional uncertainty associated with the systematic Sc which were previously described. αk is a normalization parameter for each process, which is set to unity for all processes except for WW. αWW is a freely floating parameter in the fit which is used to measure the WW cross section. Sc are also floating parameters in the fit, however they are constrained by the Gaussian terms in the likelihood. In this respect, the WW cross section is a free parameter in the fit while the systematics are allowed to vary within their uncertainties.

The figures below show the fitted value for the WW cross section as well as the contributions from systematic variations for all processes in the fit. The figure on the left additionally shows the nominal prediction for signal plus background as a dashed line. The second figure is a simplified version of the first figure.

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Summary of Past and Current Measurements

This figure is a summary of results from CDF and D0 in Run II. The individual results can be found here:

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