Measurement of WW+WZ Production Cross Section in lvjj Channel in L=4.6 fb-1
Barbara Alvarez3, Florencia Canelli1, Ricardo Eusebi4, Craig Group4, Martina Hurwitz1, Bruno Casal Larana2, Enrique Palencia4, Bernd Stelzer5
1University of Chicago
2Universidad de Cantabria
3Universidad de Oviedo
5Institute for Particle Physics Canada, Simon Fraser University
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
(p-value) is 2.9×10-8 (5.4σ).
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.
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.
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.
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 signal-to-background 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 Mjj < 55 GeV and Mjj > 120 GeV.
Predicted and observed EPD for events with Mjj < 55 and Mjj > 120
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.