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We present the results of studies aimed at an experimental measurement of WZ/ZZ diboson production in the dilepton + dijet final state using 6.6 fb-1 of data recorded with the CDF detector at the Fermilab Tevatron collider. We select events by identifying those that contain two charged leptons with a reconstructed invariant mass near the mass of the Z boson, two hadronic jets, and low transverse missing energy. We introduce a new quark-gluon neural network discriminant that quantizes the spatial spread of the energy and track momenta contained within a jet. We use this variable to correct our background modeling for differing jet energy scales for gluon-like and quark-like jets. We attempt to extract our signal through a fit to the dijet mass spectrum in three channels: a heavy-flavor tagged channel, a light-flavor tagged channel, and an untagged channel. We do not see a significant presence of signal, and present a limit on the measured cross section of 1.3 x SM = 6.6 pb at 95% CL, compared to the expected limit of 2.3 times the Standard Model.
Standard Model (SM) diboson production (WW, WZ, and ZZ) is topologically to associated Higgs production, where a Higgs boson is produced together with a W or Z boson. In the case of a low mass Higgs, the most common decay mode is to a bottom quark pair. Thus, searches for diboson production in semi-hadronic decay modes provide a great testing ground in searches for low mass Higgs bosons. We present here the results of a search for WZ and ZZ production where one Z decays to a pair of charged electrons or muons, while the other W or Z boson decays hadronically.
Trigger and Basic Selection Requirements
Our event selection requires:
- two electrons or muons with pT > 20 GeV/c;
- a reconstructed dilepton mass with 76 GeV/c2 < Mll < 106 GeV/c2, consistent with the mass of the Z boson;
- a reconstructed Z transverse momentum > 10 GeV/c;
- at least two jets with ET > 20 GeV;
- no events with a large (> 25 GeV) transverse momentum imbalance, to reduce contribution from top quark pair production.
A New Artificial Neural-Network Based Quark-Gluon Discriminant
The dominant background to WZ/ZZ production in the dilepton + jets decay channel is the production of jets with a leptonic Z boson decay. Thus, in signal events the two most energetic jets should almost exclusively come from the hadronization of quarks, while in the processes contributing to generic Z + jets, many of these jets will originate from gluons, motivating a quark-gluon discriminant. One way in which quarks and gluons differ is that gluon jets tend to have their energy spatially spread out more than quark jets. The discriminant uses three total neural networks to produce a final QG discriminant value. There are separate networks for separating quark jets and gluon jets by looking at the distribution of the distance between tower pairs inside of them, weighted by their energy content, and the distance between track pairs inside of them, weighted by their momentum content. We train a two neural networks to use these distributions to separate quark jets ("signal") and gluon jets ("background") from an ALPGEN Z to mu,mu + 2 partons sample. Thus, every jet is assigned a Tower NN value and a Track NN value. These two NN output values are combined with other variables to form a third neural network, whose output is the final QG discriminant.
The distribution of the distance (ΔR = √( (Δη)2 + (Δφ)2 ) ) between pairs of towers within a jet (left) and pairs of tracks within a jet (right) for the typical gluon and quark jet. A distribution like this is made for each jet, and used as the input into two neural networks toi discriminate between quarks and gluons.
The output NN values for the Tower neural network (left) and the Track neural network (right) used to discriminate between quark and gluon jets. These distributions are used as inputs into the final quark/gluon (QG) discriminant, shown below.
We calibrate differences in the response of the jet Tower and Track NN quantities in data and Monte Carlo simulation using jets from a W+1 jet selection sample. The final QG discriminant output in that W + 1 jet samples is shown below. The calibration greatly improves agreement between data and MC---we assign an additional systematic later.
The distribution of the final QG neural network values in our W + 1 jet selection, before and after calibrations are applied to the Track and Tower NN values.
Studies of Z-Jet Balancing
We investigate the relationship between Z-Jet balancing (the ratio of the Jet ET over the reconstructed Z PT as a function of a variety of jet variables. We find that the Monte Carlo simulation modeling our data does not agree well with the data, especially in the relationship between Z-Jet balancing and the Jet QG value. We find much better modeling when we lower the jet energy scale (JES) for only gluon jets in MC down by 2 standard deviations. We apply this correction throughout the analysis.
The distribution of of the Z-Jet balancing as a function of the jet QG value. We find the best fit to data to be lowering the JES in gluons by 2 standard deviatioms, but to do no such shift for quark jets.
The distribution of of the Z-Jet balancing as a function of the jet pseudorapidity (left) and jet ET
We conduct a scan, varying the JES for jets match to quarks and gluons in MC separately, and calculating a χ2 of the difference between data and MC in the Z-jet balancing as a function of the jet QG value (using 20 bins between -1 and 1). We find the best fir to be for moving the gluon JES down by 2 σ, while leaving the quark JES at its nominal value.
Signal and Background Modeling
We model our WZ+ZZ signal using a Pythia Monte Carlo simulation. We consider the following main backgrounds to our dilepton + dijet signal:
- Electroweak (EWK): Z boson+jets processes that pass our selection requirements. They are estimated using Alpgen Monte Carlo simulations.
- Fakes: Events where we have one real lepton and one lepton faked by a jet. We use a data-driven estimate for these backgrounds, using same-sign dilepton events to estimate muon fakes, and using electron-jet pairs to model electron fakes. The latter is assigned a fake rate dependent on the ET and η of the jet, derived from jet-triggered data.
- Top quark pair production, where we have tt → lnu,lnu,bb. We estimate this background using a Pythia Monte Carlo simulation.
- WW production. This is indistinguishable from the signal in the non-btagged region. This background is evaluated using a Pythia Monte Carlo simulation.
(Left) The dilepton mass distribution of the events in our Z + 2 jet selection region. (Right) The total predicted number of events from our modeling. Comparisons to the bumber of data events are shown below.
Additional plots showing the modeling of various jet kinematic variables are located here.
We extract our signal by conducting a fit to the dijet mass distribution between 30 GeV/c2 and 200 GeV/c2We separate the events passing our Z + 2 (or more) jets selection into three separate fitting channels: a heavy-flavor tag channel, a light-flavor tag channel, and a no-tag channel. We use the jet bness neural network tagger to pick out b jets. We define a "sum" in order to combine the neural network values for each jet. Events with Sum Jet bness > 0.0 enter our heavy flavor tag region. We define a similar "sum" to combine the two jet QG values. Events which fail the heavy-flavor tag requirement but have a sum QG value > 0.0 enter our light flavor tag region. Events which fail both tagging cuts enter our no-tag region.
The sum of the jet bness values with MC scaled absolutely (left) and normalized to the data (right). Events with sum bness values greater than 0.0 enter our heavy-flavor tagged region.
The sum of the jet QG values with MC scaled absolutely (left) and normalized to the data (right). Events which fail the heavy-flavor tag requirement and with sum QG values greater than 0.0 enter our light-flavor tagged region.
The number of events in each channel is shown below, along with the dijet mass distribution in each channel. Additional plots showing the modeling of various jet kinematic variables in the different tagging channels are located here
Predicted/observed number of events in the Z + 2 jet selection region.
Dijet mass in our Z + 2 jet Heavy-Flavor Tag Region with MC scaled absolutely (left) and normalized to the data (right).
Dijet mass in our Z + 2 jet Light-Flavor Tag Region with MC scaled absolutely (left) and normalized to the data (right).
Dijet mass in our Z + 2 jet No-Tag Region with MC scaled absolutely (left) and normalized to the data (right).
Additionally, plots showing the dijet mass in a W + 2 jet selection may be found here.
When fitting for the data in each channel, we use the following templates in the fit:
- Z + jets background: Our largest background, we allow the Z + jets background normalization to float unconstrained and independently in the three different channels, allowing us to avoid uncertainties due to the relative fraction of heavy flavor jets, quark jets, and gluon jets in the various channels.
- tt: We constrain the top pair production normalization to its measured cross section with an uncertainty of 6%.
- WW: We also constrain the WW normalization to its measured cross section with an uncertainty of 6%.
- Fakes: We constrain the normalization on the fakes to +/-25%. As this is a data-driven background template, no other uncertainties are applied to it.
- WZ/ZZ: Our signal's normalization is allowed to float unconstrained in the fit, but unlike the Z + jets background, not independently between channels.
In performing the fit, we simultaneously fit for the following systematic errors:
- Jet Energy Scale (JES): We raise and lower the JES by ±1σ, obtaining templates reflecting both a change in the number of events and different background and signal shapes.
- Q2 (Q2): We use higher and lower Q2 MC samples to evaluate a shape only systematic for the EWK background template.
- Sum bness Cut: We raise and lower the bness cuts in MC to affect the efficiency/mistag rate of a cut. The uncertainty is derived from a ttbar dilepton sample and a W + 2 jets sample. The distribution of the sum of the jet bness values, and the evaluated efficiencies and mistag rates in data and MC are shown below:
- Sum QG Value Cut: Similarly, we raise and lower the QG cuts in MC according, where the efficiencies are calculated in a ttbar lepton + jets sample, and a W + 2 jets sample. The distribution of the sum of the jet bness values, and the evaluated efficiencies and mistag rates in data and MC are shown below:
The systematics included as nuisance paramters in the fit to the data are summarized in the following table:
Summary of systematic uncertainties included in the fit.
We additionally consider acceptance uncertainties from the jet energy resolution lepton energy scale, lepton energy resolution, intial and final state radation, PDFs, and Luminosity (6%).
Summary of the acceptance uncertainties included in this analysis.
The fit returns no signal events. We construct Feldman-Cousins bands in order to set a limit on the measured cross section, given our result. We find that we set a limit at 1.3 x SM at 95% CL, or σWZ+ZZ < 6.6 pb. Given a measurement that returned the SM cross section, the expected limit is at 2.3 x SM.
The number of events fit for in each template in the final fit to the data distribution of the dijet mass in the three channels.
The result of the final fit to the data distribution of dijet mass in the three channels. The top panel shows the stacked templates scaled to the fit; the bottom panel shows the difference between data and the fitted background.
Feldman-Cousins bands, showing our measured result, and the limit we set on the measured cross section of 1.3 x SM.