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 (p-value) is 3.5×10^-8 (5.4σ) and the expected p-value in pseudo-experiments 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, well-isolated lepton with high transverse energy, large missing transverse energy, and exactly two high-transverse-energy 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 multi-jet 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 well-modeled shapes and normalizations. The largest background is due to W+jets events, which are modeled using the Alpgen fixed-order 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 multi-jet 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 multi-jet 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

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 4-vectors 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 parton-level differential cross-section, 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 (s-channel and t-channel), Wbb-bar, Wcc-bar, 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 z-momentum 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 signal-to-background 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 signal-like 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:

• 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 mis-modeling. 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 (Q²) 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 multi-jets 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.
	Pseudo-experiments were carried out to determine the probability (p-value) that a background fluctuation would produce the observed excess. The median expected p-value was found to be 2.1×10-7 (5.1σ), whereas the observed p-value was 3.5×10-8 (5.4σ).

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