---
abstract: '0.3in We present a combined measurement of the production cross section of $VZ$ ($V=W$ or $Z$) events in final states containing charged leptons (electrons or muons) or neutrinos, and heavy flavor jets, using data collected by the CDF and DØ detectors at the Fermilab Tevatron Collider. The analyzed samples of $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV correspond to integrated luminosities of – . Assuming the ratio of the production cross sections $\sigma(WZ)$ and $\sigma(ZZ)$ as predicted by the standard model, we measure the sum of the $WZ$ and $ZZ$ cross sections to be . This is consistent with the standard model prediction and corresponds to a significance of  standard deviations above the background-only hypothesis.'
author:
- 'The TEVNPH Working Group[^1]'
title: 'Combined CDF and measurement of $\bm{WZ}$ and $\bm{ZZ}$ production in final states with $\bm{b}$-tagged jets\'
---

0.5in

*Preliminary Results for the Moriond 2012 Conferences*

Introduction {#intro}
============

0[[@dzWHl; @dzZHv; @dzZHl]]{}

Studies on the production of $VV$ ($V=W,Z$) boson pairs provide an important test of the electroweak sector of the standard model (SM). In $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV, the next-to-leading order (NLO) SM cross sections for these processes are $\sigma(WW)=\wwnlo\pm\wwnloe$ pb, $\sigma(WZ)=\wznlo\pm\wznloe$ pb and $\sigma(ZZ)=\zznlo\pm\zznloe$ pb [@dibo]. These cross sections assume both $\gamma^{*}$ and $Z^{\circ}$ components in the neutral current exchange and corresponding production of dilepton final states in the region 75 $\leq m_{\ell^+\ell^-} \leq$ 105 GeV/$c^2$. Measuring a significant departure in cross section or deviations in the predicted kinematic distributions would indicate the presence of anomalous gauge boson couplings [@bib:anocoups] or new particles in extensions of the SM [@bib:newphen]. The $VV$ production in $\pp$ collisions at the Fermilab Tevatron Collider has been observed in fully leptonic decay modes [@bib:leptonic] and in semi-leptonic decay modes [@bib:hadronic], where the combined $WW+WZ$ cross section was measured.

Recently, the DØ experiment presented evidence for $WZ$ and $ZZ$ production in semileptonic decays with a $b$-tagged final state [@dzDibosonCombo]. The $WZ$ and $ZZ$ production cross sections, as well as their sum, were measured in final states where one of the $Z$ bosons decays into $\bb$ (although there is some signal contribution from $\wcs$, $\zcc$) and the other weak boson decays to charged leptons or neutrinos ($\wlv$, $\zvv$, or $\zll$, with $\ell=e,\mu$). In this note we report an improved measurement of the $WW+ZZ$ production cross section in such final states based on the combination of the results from [@dzDibosonCombo], with a corresponding new set of CDF analyses [@cdfDibosonCombo]. This analysis is relevant as a proving ground for the combined Tevatron search for a low-mass Higgs boson produced in association with a weak boson and decaying into a $\bb$ pair [@bib:higgs] since it shares the same selection criteria as well as analysis and combination techniques.

Summary of Contributing Analyses {#analyses}
================================

This result is the combination of three CDF analyses  and three analyses 0 outlined in Table \[tab:chans\]. These analyses utilize data corresponding to integrated luminosities ranging from  to  , collected with the CDF [@cdf] and  [@dzero] detectors at the Fermilab Tevatron Collider, and they are organized into multiple sub-channels for each different configuration of final state particles. To facilitate proper combination of signals, the analyses from a given experiment are constructed to use mutually exclusive event selections.

In the  analyses , events containing an isolated electron or muon, and two or three jets are selected (exactly two jets in the case of the CDF analysis). The presence of a neutrino from the $W$ decay is inferred from a large imbalance of transverse momentum ($\met$). The  analyses  select events containing large $\met$ and two or three jets (exactly two jets in the case of the analysis). Finally, in the  analyses   events are required to contain two electrons or two muons and at least two jets. In the case of the CDF  analysis, events with two or three jets are analyzed separately. In the  and   analyses as well as the CDF  analysis, each lepton flavor of the $W/Z$ boson decay ($\ell=e,\mu$) is treated as an independent channel. In the case of the CDF  analysis lepton types are separated into four different channels based on their purity and location within the detector. To ensure that event samples used for the different analyses do not overlap, the  analyses reject events in which a second isolated electron or muon is identified, and the  analyses reject events in which any isolated electrons or muons are identified.

To isolate the $\zbb$ decays, algorithms for identifying jets consistent with the decay of a heavy-flavor quark are applied to the jets in each event candidate ($b$-tagging). All of the analyses, as well as the CDF  and  analyses, use multivariate discriminants based on sets of kinematic variables sensitive to displaced decay vertices and tracks within jets with large transverse impact parameters relative to the hard-scatter vertices. The algorithm is a boosted decision tree discriminant which builds upon the previously utilized neural network $b$-tagging tool [@bib:btagnn], while the CDF algorithm [@bib:HOBIT] is based on a neural network discriminant. In both cases, a spectrum of increasingly stringent $b$-tagging operating points is constructed through the use of progressively higher requirements on the minimum output of the $b$-tagging discriminant. The analyses are separated into two groups: a double-tag (DT) group in which two of the jets are $b$-tagged with a loose tag requirement ( and ) or one loose and one tight tag requirement (); and an orthogonal single-tag (ST) group in which only one jet has a loose ( and ) or tight () $b$-tag. A typical per-jet $b$ efficiency and fake rate for the loose (tight) $b$-tag selection is about 80% (50%) and 10% (0.5%), respectively. The corresponding efficiency for jets from $c$-quarks is 45% (12%). The  and  analyses also use the output of the $b$-tagging algorithm as an additional input to the discriminants used in the final signal extraction. Candidate events in the CDF and  analyses are also separated into channels based on tight and loose tagging definitions. Events with two tight tags (TT), one tight and one loose tag (TL), two loose tags (LL), and a single tight tag (Tx) are used by both analyses. The CDF  analysis also considers events with a single loose tag (Lx). A typical per-jet efficiency and fake rate for the CDF loose (tight) neural network $b$-tag selection is about 70% (45%) and 7% (0.6%), respectively. The CDF   analysis utilizes a tight $b$-tagging algorithm [@bib:SecVtx] based on reconstruction of a displaced secondary vertex and a loose $b$-tagging algorithm [@bib:JetProb] that assigns a likelihood for the tracks within a jet to have originated from a displaced vertex. Based on the output of these algorithms events with two tight tags (SS) and those with one tight tag and one loose tag (SJ) are separated into independent analysis channels. The signal in all of the double-tag samples is expected to be primarily composed of events with $\zbb$ decays, with smaller contributions from $\zcc$ and $\wcs$ decays. In the single-tag samples, which are defined by less stringent requirements on the $b$-jet content of the event, the contributions from the three decay modes are comparable.

  Experiment             Channel            Luminosity ()   Reference
  ------------ --------------------------- --------------- -----------
  CDF           ,  TT/TL/Tx/LL/Lx, 2 jets        9.5        [@cdfWHl]
  CDF              ,  SS/SJ, 2/3 jets            9.5        [@cdfZHv]
  CDF           ,  TT/TL/Tx/LL, 2/3 jets         9.5        [@cdfZHl]
                   ,  ST/DT, 2/3 jets            7.5        [@dzWHl]
                    ,  ST/DT, 2 jets             8.4        [@dzZHv]
                 ,  ST/DT, $\geq$ 2 jets         7.5        [@dzZHl]

  : \[tab:chans\]List of analysis channels and their corresponding integrated luminosities. See Sect. \[analyses\] for details ($\ell=e, \mu$).

The primary background is from $W/Z$+jets, which is modeled with  [@alpgen] by both CDF and DØ. The backgrounds from multijet production are measured from control samples in the data. At DØ the other backgrounds are generated with  and  [@singletop], with  [@pythia] providing parton-showering and hadronization. At CDF most backgrounds from other SM processes are modeled using  Monte Carlo samples. Background rates are normalized either to next-to-leading order (NLO) or higher-order theory calculations or to data control samples. The DØ  and both experiment’s  analyses normalize $W/Z$+jets backgrounds to data, whereas the the CDF  and both experiment’s   analyses normalize them to the predictions from . The fraction of the $W/Z$+jets in which the jets arise from heavy quarks ($b$ or $c$) is obtained from NLO calculations using  [@mcfm] at DØ while at CDF the prediction from  is corrected based on a data control region. The background from  events is normalized to the approximate NNLO cross section [@ttbar_xsec]. The $s$-channel and $t$-channel cross sections for the production of single-top quarks are from approximate NNLO+NNLL calculations [@schan_top_xsec] and approximate NNNLO+NLL calculations [@tchan_top_xsec], respectively. The background from $WW$ events is normalized to NLO calculations from  [@dibo]. All Monte Carlo samples are passed through detailed [geant]{}-based simulations [@geant] of the CDF and D0 detectors.

The analyses use multivariate discriminants (MVA) based on decision trees as the final variables for extracting the $VZ$ signal from the backgrounds. These decision trees are trained to discriminate the $VZ$ signal from the backgrounds using the same set of discriminant variables as in the corresponding Higgs analyses. The CDF analyses follow the same strategy, using neural network-based discriminants instead for signal-to-background discrimination.

Systematic Uncertainties
========================

Systematic uncertainties differ between experiments and analyses, and they affect the normalizations and the differential distributions (shapes) of the predicted signal and background templates in correlated ways. The combined result incorporates the sensitivity of predictions to values of nuisance parameters and takes into account correlations in these parameters both within each individual experiment and between experiments. The largest uncertainty contributions and their correlations between and within the two experiments are discussed here. Further details on the individual analyses are available in Refs. .

### Correlated Systematics between CDF and 

The uncertainties on measurements of the integrated luminosities are 5.9% (CDF) and 6.1% (). Of these values, 4% arises from the uncertainty on the inelastic $\pp$ scattering cross section, which is correlated between CDF and DØ. CDF and also share the assumed values and uncertainties on the cross sections for $WW$ production and top-quark production processes ( and single top).

In most analyses determination of the multijet (“QCD”) background involves data control samples, and the methods used differ between CDF and DØ, and even between analyses within the collaborations. Therefore, there is no assumed correlation in the predicted rates of this background between analysis channels. Likewise, calibrations of quantities such as the fake lepton rate, $b$-tag efficiencies, and mistag rates are performed by each collaboration using independent data samples and different methods, and are treated as uncorrelated. Similarly, different techniques are used to estimate background rates for $W/Z$+heavy flavor backgrounds and the associated uncertainties are taken as uncorrelated.

### Correlated Systematic Uncertainties for CDF

The dominant systematic uncertainties for the CDF analyses are shown in Appendix Tables \[tab:cdfsystwh1\] and \[tab:cdfsystwh2\] for the  channels, in Table \[tab:cdfsystzhvv\] for the channels, and in Tables \[tab:cdfllbb1\] and \[tab:cdfllbb2\] for the  channels. Each source induces a correlated uncertainty across all of CDF’s channels’ signal and background contributions which are sensitive to that source. The largest uncertainties on signal arise from measured $b$-tagging efficiencies, jet energy scale, and other Monte Carlo modeling. Shape dependencies of templates on jet energy scale, $b$-tagging, and gluon radiation (“ISR” and “FSR”) are taken into account for some analyses (see tables). Uncertainties on background event rates vary significantly for the different processes. The backgrounds with the largest systematic rate uncertainties are in general quite small. Such uncertainties are constrained through fits to the nuisance parameters and do not affect the result significantly. Since normalizations for the $W/Z$+heavy flavor backgrounds are obtained from data in the and  analyses, the corresponding rate uncertainties associated with each analysis are treated as uncorrelated even within CDF.

### Correlated Systematic Uncertainties for 

The  and  analyses carry an uncertainty on the integrated luminosity of 6.1% [@lumi], while the overall normalization of the  analysis is determined from the NNLO $Z/\gamma^*$ cross section [@dyxsec] in data events near the peak of $\zll$ decays. The uncertainty from the identification and energy measurement of jets is $\sim$7%. The uncertainty arising from the $b$-tagging rate ranges from 1 to 10%. All analyses include uncertainties associated with lepton measurement and acceptances, which range from 1 to 9% depending on the final state. The largest contribution for all analyses is the theoretical uncertainty on the background cross sections at 7-20% depending on the analysis channel and specific background. The uncertainty on the expected multijet background is dominated by the statistics of the data sample from which it is estimated. Further details on the systematic uncertainties are given in Tables \[tab:d0systwh\]-\[tab:d0llbb1\]. All systematic uncertainties originating from a common source are taken to be 100% correlated, as detailed in Table \[tab:corr\].

Measurement of the $\bm{WZ+ZZ}$ Cross Section
=============================================

The total $VZ$ cross section is determined from a maximum likelihood fit of the MVA distributions for the background and signal samples from the contributing analyses to the data. The cross section for the signal ($WZ+ZZ$) is a free parameter in the fit, but the ratio of the $WZ$ and $ZZ$ cross sections is fixed to the SM prediction. Events from $WW$ production are considered as a background. The fit is performed simultaneously on the distributions in all sub-channels. As a consistency check, we also determine the Bayesian posterior probability by integrating over the nuisance parameters. Here we report only the results from the maximum likelihood fit, but the results from the Bayesian method are consistent.

![image](dbFigs/tevDibosonCondensedFit_combo_Subtract.eps){height="0.2\textheight"}

The combined fit for the total $VZ$ cross section distributions yields . This measurement is consistent with the NLO SM prediction of $\sigma(WW+WZ)=\vznlo\pm\vznloe$ pb [@dibo], as well as with the individual measurements from [@dzDibosonCombo], $\sigma(WW+WZ)=5.0 \pm 1.6$ pb, and from CDF [@cdfDibosonCombo], $\sigma(WW+WZ)=4.1 ^{+1.4}_{-1.3}$ pb. Based on the measured central value for the $VZ$ cross section and its uncertainties, the observed significance is estimated to be  standard deviations (s.d.), while the expected significance is $\sim 4.8$ s.d.

To visualize the sensitivity of the combined analysis, we calculate the expected signal over background ($s/b$) in each bin of the MVA distributions from the contributing analyses. Bins with similar $s/b$ are then combined to produce a single distribution, shown in Fig. \[fig:rfsub\]. The binning was chosen to keep the background fluctuations roughly of the same size as in the dijet mass distributions. Figure \[fig:mjj\] shows the distributions of the invariant mass of the dijet system, summed over all channels from CDF and DØ, after adjusting the signal and background predictions according to the results of the fit. Figure \[fig:mjj\_sub\] shows the background subtracted dijet mass distributions after the fit, demonstrating the presence of a hadronic resonance in the data consistent with the SM expectation, both in shape and normalization.

  ------------------------------------------------------ ------------------------------------------------------ ------------------------------------------------------
   ![image](dbFigs/tevDBmjjST_combo.eps){width="2.4in"}   ![image](dbFigs/tevDBmjjDT_combo.eps){width="2.4in"}   ![image](dbFigs/tevDBmjjAT_combo.eps){width="2.4in"}
                       [**(a)**]{}                                            [**(b)**]{}                                            [**(c)**]{}
  ------------------------------------------------------ ------------------------------------------------------ ------------------------------------------------------

  --------------------------------------------------------------- --------------------------------------------------------------- ---------------------------------------------------------------
   ![image](dbFigs/tevDBmjjST_combo_Subtract.eps){width="2.4in"}   ![image](dbFigs/tevDBmjjDT_combo_Subtract.eps){width="2.4in"}   ![image](dbFigs/tevDBmjjAT_combo_Subtract.eps){width="2.4in"}
                            [**(a)**]{}                                                     [**(b)**]{}                                                     [**(c)**]{}
  --------------------------------------------------------------- --------------------------------------------------------------- ---------------------------------------------------------------

Summary
=======

In summary, we combine analyses in the , , and  ($\ell=e,~\mu$) final states from the CDF and DØ experiments to observe, with a significance of  s.d., the production of $VZ$ ($V=W$ or $Z$) events. The analyzed samples correspond to  to   of $\pp$ collisions at $\sqrt{s}=1.96$ TeV. We measure the total cross section for $VZ$ production to be . This result demonstrates the ability of the Tevatron experiments to measure a SM production process with cross section of the same order magnitude as that expected for Higgs production from the same set of background-dominated final states containing two heavy-flavor jets used in our low mass Higgs searches.

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Additional Material
===================

  Source                                                 
  --------------------- ---------- ---------- ---------- --
  Luminosity             $\times$   $\times$             
  Normalization                                          
  Jet Energy Scale       $\times$   $\times$   $\times$  
  Jet ID                 $\times$   $\times$   $\times$  
  Electron ID/Trigger    $\times$   $\times$   $\times$  
  Muon ID/Trigger        $\times$   $\times$   $\times$  
  $b$-Jet Tagging        $\times$   $\times$   $\times$  
  Background $\sigma$    $\times$   $\times$   $\times$  
  Background Modeling                                    
  Multijet Background                                    
  Signal $\sigma$        $\times$   $\times$   $\times$  

  : \[tab:corr\]The correlation matrix for the D0 analysis channels. Uncertainties marked with an $\times$ are considered 100% correlated across the affected channels. Otherwise the uncertainties are not considered correlated, or do not apply to the specific channel. The systematic uncertainties on the background cross section ($\sigma$) and the normalization are each subdivided according to the different background processes in each analysis.

[^1]: The Tevatron New-Phenomena and Higgs Working Group can be contacted at TEVNPHWG@fnal.gov. More information can be found at http://tevnphwg.fnal.gov/.
