Abstract
We present a measurement of the WW+WZ production cross section in the channel with an
identified electron or muon, large missing transverse energy, and two
jets in 4.6 fb^{1} of CDF II data. The analysis employs a
matrix element technique which calculates event probability densities
for signal and background hypotheses. We combine the probabilities to
form a discriminant variable which is evaluated for signal and
background Monte Carlo events. The resulting template distributions
are fit to the data using a binned likelihood approach. We measure a
cross section of 16.5^{+3.3}_{3.0} pb. The probability that the
observed excess originated from a background fluctuation
(pvalue) is 2.9×10^{8} (5.4σ).
Event Selection
This analysis uses events from leptonic decay of one of the W
bosons and hadronic decay of the other W or Z boson.
We require a single, wellisolated lepton with high transverse energy,
large missing transverse energy, and exactly two
hightransverseenergy jets. Events with additional jets or leptons
are vetoed to suppress Z+jets and top pair backgrounds.
Cosmic ray and conversion events are also removed. The QCD multijet
background is suppressed partially with the high missing transverse
energy cut, and with additional cuts on the transverse mass of the
leptonic W candidate and on the the direction of the missing
energy.
Backgrounds need to have wellmodeled shapes and normalizations. The
largest background is due to W+jets events, which are modeled
using the Alpgen fixedorder Monte Carlo generator and a Pythia parton
shower. The normalization of the W+jets background is a free
parameter in the final signal extraction. The QCD multijet
background is much smaller; it is modeled using events from jet
triggers where the lepton identification requirements have been
loosened. The normalization of the QCD multijet background is
determined by fitting the missing transverse energy spectrum in the
data to a sum of expected contributions. Z+jets, top pair,
and single top backgrounds are all relatively small backgrounds; both
their shapes and normalizations are modeled using the Monte Carlo.
Fit to the missing transverse energy to determine the normalization of the QCD multijet background in four lepton categories.
Process  Expected number of events 
WW signal  1262 ± 114 
WZ signal  196 ± 22 
W+jets  35637 ± 686 
Z+jets  1700 ± 223 
QCD multijet  1514 ± 606 
top pair  293 ± 39 
single top  276 ± 41 
Number of expected events for signal and background
processes.
Analysis Method
This analysis is based on a Matrix Element method applied to maximize
the use of information in the events [2,3]. We calculate event
probability densities under the signal and background hypotheses as
follows. Given a set of measured variables of each event (the
4vectors of the lepton and the two jets), we calculate the
probability densities that these variables could result from a given
underlying interaction (signal and background). The probability is
constructed by integrating over the partonlevel differential
crosssection, which includes the matrix element for the process, the
parton distribution functions, and the detector resolutions. This
analysis calculates probabilities for several different underlying
processes: WW, WZ, single top (schannel
and tchannel), Wbbbar, Wccbar,
Wc+jet, Wgj, and Wgg.
Transfer functions are used to include detector effects. Lepton
quantities and jet angles are considered to be well measured.
However, jet energies are not, and their resolution is parameterized
from Monte Carlo simulation to create a jet resolution transfer
function. We integrate over the quark energies and over the
zmomentum of the neutrino to create a final probability density.
We use the probabilities to construct a discriminant variable for each
event, referred to as the Event Probability Discriminant, or EPD.
WW and WZ are combined to form a single signal
probability. The EPD is defined as:
The templates of the EPD for background and signal processes
(normalized to unit area) are shown below. The signal distribution
falls less steeply than the background.
Templates of the EPD for signal
and background processes, normalized to unit area.
The effectiveness of the discriminant in separating signal and
background can also be shown by plotting the invariant mass of the two
jets in bins of EPD. The majority of the background is in bins of low
EPD, and quickly the discriminant isolates events with a mass close to
the W mass, as expected for signal events. As the value of
the EPD increases, the signaltobackground ratio is expected to
improve.
Shape of the dijet invariant mass in bins of EPD
To quantify the WW+WZ content in the data, we perform a
binned maximum likelihood fit. We fit a linear combination of signal
and background shapes of the event probability discriminant to the
data. The background normalizations (except for W+jets) are
Gaussian constrained in the fit, with the width of the Gaussian
determined by the uncertainties on the process cross section and the
selection efficiency. The W+jets normalization is a free
parameter. All sources of systematic uncertainty are included as
nuisance parameters in the likelihood function. Sources of systematic
uncertainties can affect the normalization and shape for a given
process. Correlations between both are taken into account. The
likelihood function is reduced through a standard Bayesian
marginalization technique.
Validation of the Method
We compare the distribution of many kinematic variables predicted by
Monte Carlo simulation for signal and background to the data. In
particular, we compare the distributions of the input variables to
ensure the data matches the Monte Carlo prediction. We assign a shape
uncertainty on the background if mismodeling is observed, using events
with M_{jj} < 55 GeV and M_{jj} > 120 GeV.
E_{T} and η of the two jets, E_{T} of the
lepton, missing transverse energy, dijet invariant mass, and Δ
η between the two jets, shown as a stacked plot for the prediction
with the data points superimposed. The hatched band corresponds to
the uncertainty in the shape of the background.
Predicted and observed EPD for events with M_{jj} < 55 and M_{jj} > 120
Systematic Uncertainties
Systematic uncertainties can affect both the normalization and the
shape of background and signal processes. The normalization
uncertainty includes changes to the event yield due to the systematic
effect, and the shape uncertainty includes changes to the template
histograms. Both of these effects are included in the likelihood
function.
A complete list of systematic uncertainties is given below.
 The jet energy scale systematic is obtained by changing the jet
energy scale by 1 standard deviation (SD) and recalculating the event
yield and the discriminant template histograms. We apply shape and
normalization uncertainties to the signal template and background
templates.
 We assign a shape uncertainty to the background templates
associated with mismodeling in the p_{T} of the dijet system
and in the η of the second jet. The systematically changed
template is derived from Monte Carlo events reweighted to agree with
data in the region with M_{jj} < 55 and M_{jj} >
120.
 We vary the factorization and renormalization scele
(Q^{2}) in the Monte Carlo samples that have been created with
the ALPGEN Monte Carlo program. An uncertainty on the shape of the
W+jets background is applied.
 We increase or decrease the amount of initial state radiation in
the Monte Carlo and recalculate the event yield for the signal.
 We increase or decrease the amount of final state radiation in
the Monte Carlo and recalculate the event yield for the signal.
 We vary the eigenvectors in the CTEQ parton distribution function
tables to determine the uncertainty from this effect. We also include
the effect of using different versions of CTEQ and of using MRST with
different values of Λ_{QCD}. This results in a
normalization uncertainty on the signal.
 We assign a small uncertainty to the signal acceptance associated
with the jet energy resolution.
 We assign normalization uncertainties to background processes:
for Z+jets, top pairs, and single top production the
uncertainty in the production cross sections are used; for QCD
multijets a 40% uncertainty is applied, and the W+jets
normalization is a free parameter in the fit.
 We include an uncertainty on event detection efficiency due to the
lepton ID scale factors that we apply to our Monte Carlo samples
 We include a 6% uncertainty on our measured luminosity.
We run pseudoexperiments to determine the expected effects of the
systematic uncertainties. We find that the measurement is already
nearly systematically limited, with an expected statistical
uncertainty of 14% and expected systematic uncertainty of 16%. The
most important systematic uncertainties are the jet energy scale
uncertainty, contributing 8% to the total, the Q^{2} scale
uncertainty, contributing 7%, and the luminosity uncertainty,
contributing 6%. The total expected uncertainty is 21%.
Results

The likelihood fit of the sum of signal and background Event Probability Discriminant templates to data gave a cross section of $\sigma $_{WW+WZ} = 16.5^{+3.3}_{3.0} pb. The significance of the signal is 5.4 σ.

