Abstract
We present an observation of WW+WZ production in the channel with an
identified electron or muon, large missing transverse energy, and two
jets in 2.7 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 17.7 ± 3.9 pb. The probability that the
observed excess originated from a background fluctuation
(pvalue) is 3.5×10^{8} (5.4σ) and the
expected pvalue in pseudoexperiments is
2.1×10^{7} (5.1σ).
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. These cuts are much more stringent for electron events than
muon events, resulting in a significantly lower acceptance for
electron events than for muon events.
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.
Process  Expected number of events 
WW signal  441 ± 28 
WZ signal  79 ± 6 
W+jets  9425 ± 283 
Z+jets  546 ± 82 
QCD multijet  252 ± 101 
top pair  111 ± 15 
single top  90 ± 9 
Total predicted  10944 ± 313 
Observed  10948 
Total number of expected events for signal and background
processes. The observed and predicted totals agree by construction,
since a fit to the data provides the number of QCD multijet and W+jet
events
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 much less steeply than the background.
The effectiveness of the discriminant in separating signal and
background can also be shown by plotting the dijet mass in bins of EPD
range. The shape of the dijet mass over the full EPD range is shown
at left below, while the dijet mass in EPD bins is shown at right.
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 also gets larger.
To quantify the WW+WZ content in the data, we perform a binned
maximum likelihood fit to the data. 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. 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 define control
regions according to the dijet invariant mass
(M_{jj}) of the event, which will be close to the
mass of the W for signallike events.
The input variables to the signal and background event probability calculations for events with M_{jj}<55 GeV (left) and M_{jj}>120 GeV (right).
ΔR between the two jets in the control regions.
Distribution of the event probability discriminant in the control regions.
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.
Systematics from various sources are taken into account. One systematic accounts for a mismodeling observed when plotting the dijet mass sidebands:
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 a small rate
uncertainty on the background.
 We assign a shape uncertainty to the background templates
associated with dijet mass mismodeling. The systematically changed
template is derived from Monte Carlo events reweighted according to
their dijet mass to agree with data.
 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.
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} = 17.7 ± 3.9 pb. 

Pseudoexperiments were carried out to determine the probability (pvalue) that a background fluctuation would produce the observed excess. The median expected pvalue was found to be 2.1×10^{7} (5.1σ), whereas the observed pvalue was 3.5×10^{8} (5.4σ). 
