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\section{Signal and Background Modeling}
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\label{sec:gen}
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\subsection{Monte Carlo generators}
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The signal and background samples for the full detector simulation
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are generated with the leading order (LO) event generators
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{\sl PYTHIA}~\cite{Sjostrand:2003wg}, {\sl ALPGEN} and {\sl COMPHEP}.
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To accommodate next-to-leading (NLO) effects, constant $k$-factors are applied.
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Additionally, the cross section calculator {\sl MCFM}~\cite{Campbell:2005}
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is used to determine the NLO differential cross section for the $\WZ$
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production. To estimate the uncertainty on the cross-section
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due to the choice of the PDF, we use NLO event generator
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{\sl MC@NLO 3.1}~\cite{Frixione:2002ik} together with CTEQ6M PDF set.
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\subsection{Signal definition}
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The goal of this analysis is to study the associative production of the on-shell
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$W$ and $\Z$ bosons that decay into three leptons and a neutrino. In the
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following we refer to a lepton to as either a muon or an electron, unless
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specified otherwise. The leptonic final state $\ell^+ \ell^- \ell^\pm \nu$ also receives a
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contribution from the $W\gamma^*$ production, where the $\gamma^*$ stands for a
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virtual photon through the $WW\gamma$ vertex. In this analysis, we
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restrict this contribution by requiring the $\ell^+\ell^-$ invariant mass to be
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consistent with the nominal $\Z$ boson mass. As CMS detector has a very
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good energy resolution for electrons and muons, the mass window
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is set to be $\pm$ 10 GeV around 91 GeV.
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Using {\sl MCFM} we estimate the total NLO $\WZ$ cross-section to be
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\begin{equation}
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\sigma_{NLO} ( pp \rightarrow W^+\Z; \sqrt{s}=14~{\rm TeV}) = 30.5~{\rm pb},
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\end{equation}
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\begin{equation}
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\sigma_{NLO} ( pp \rightarrow W^-\Z; \sqrt{s}=14~{\rm TeV}) = 19.1~{\rm pb}.
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\end{equation}
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The LO and NLO distributions of the \Z boson transverse momentum are
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shown in Fig.~\ref{fig:LOvsNLO} with the case of $W^+$ on the left and $W^-$
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on the right side. The NLO/LO ratio, $k$-factor, is also presented on the figure,
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and it is increasing with $p_T(\Z)$. The $p_T$ dependence of the $k$-factor
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becomes important when a proper NLO description of the $\Z$ boson transverse
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momentum must be obtained, $e.g$ to measure the strength of the $WWZ$ coupling.
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As the focus of this analysis is to prepare for the cross-section measurement,
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we take a $p_{T}$-averaged value of the $k$-factor, equal to 1.84.
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\begin{figure}[!bt]
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\begin{center}
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\scalebox{0.8}{\includegraphics{figs/LOvsNLOZPtWminuns.eps}\includegraphics{figs/LOvsNLOZPtWplus.eps}}
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\caption{$p_T(Z)$ distribution for LO (solid black histogram) and NLO (dashed black histogram)
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in $W^-\Z$ events (left) and $W^+\Z$ events (right). The ratio NLO/LO is also given as a red
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solid line.
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}
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\label{fig:LOvsNLO}
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\end{center}
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\end{figure}
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%# for bbll:
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%#CS NLO ((Z/gamma*->l+l-)bb) = 830pb = 345 pb * 2.4, where:
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%#- 345 pb is LO CS calculated with precision of ~0.15%
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%#- 2.4 is MCMF calculated k-factor with precision ~30% (!)
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%# 830x0.173 (== XS x eff.) = 143.59pb
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\subsection{Signal and background Monte Carlo samples}
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The signal Monte Carlo sample is produced using {\sl PYTHIA}
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generator. The decay for the \W has been forced to $e\nu_e$,
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$\mu\nu_{\mu}$ or $\tau\nu_{\tau}$ final state, while the \Z decays
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into electrons or muons only.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% YM changes implemented up to here
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The main background that we have to consider are all final states
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having at least two isolated leptons from the same flavor and with
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opposite charge. The third one can be a real isolated lepton or a misidentified
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lepton. The probability to misidentify one isolated lepton is rather low, so
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this is why we can considerer safely starting from two
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leptons. Moreover we will apply a cut on the invariant mass of the two
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isolated leptons so most of the background that we have to study are:\\
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\begin{itemize}
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\item $W+jets$: $W$ boson will give us one isolated leptons. The probability that 2 additional jets will be misidentified as isolated lepton is very low and the criteria on the lepton invariant mass will definitely reduce such background. This channel is nevertheless useful to study other background for which data sample are not available such as $Wb\bar{b}$. The sample studied for this analysis, has been produced using ALPGEN generator per jet multiplicity bin.
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\item $Z + jets$: $Z$ boson is common between signal and background. The third isolated lepton can come from a misidentified lepton. The cross section of production of this channel is around 35 time greater than the signal.The sample studied for this analysis, has been produced using ALPGEN generator per jet bin.
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\item $t\bar{t}$: top quark will decay to \W$b$ pair where each $W$ can decay via an isolated leptons. This leptons will have opposite charged. Even though combining the two leptons, we will not obtain a peak around the \Z mass, the cross section of this process is around 15 time the cross section of the signal. The sample studied for this analysis, has been produced using ALPGEN generator per jet bin. The third lepton will come from a semi leptonic decay of a $b$ quark which will be isolated.
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\item $Z + b\bar{b}$: the presence of $Z$ boson will select such events. Moreover due to the semi leptonic decay of a $b$ quark, a third lepton can be easily identified and consider as isolated. The sample used has been produced by COMPHEP generator.
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\item $ZZ$: the inclusive cross section production is smaller than the signal studied but due to branching fraction and if we consider $Z\rightarrow b\bar{b}$ decay, some events can pass the analysis selection. This process has be
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en produced using PYTHIA generator.
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\item $Z\gamma$: TO BE ADDED
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\end{itemize}
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All the different sample studied are part of the CSA07 production and
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have been generated using $\mathrm{CMSSW}\_1\_4_\_6$ and went through the full
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GEANT simulation of the CMS detector using the same release. The
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digitization and reconstruction have been done using $\mathrm{CMSSW}\_1\_6_\_7$
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release with a misalignment/miscalibration of the detector expected
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after 100~pb$^{-1}$ of data. All ALPGEN samples are mixed together in
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``Chowder soup''.
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The summary of all datasets used for signal and background is given in
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table~\ref{tab:MC}. We use the RECO production level to access to
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low-level detector information, such as reconstructed hits. This lets
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us to use full granularity of the CMS sub-detectors to use a isolation
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discriminants.
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Analysis of the samples is done using CMSSW$\_1\_6\_7$ CMS software release.
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The information is stored in ROOT trees using a code in
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CVS:/UserCode/Vuko/WZAnalysis, which is based on Physics Tools candidates.
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\begin{table}[!tb]
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%\begin{tabular}{llllll} \hline
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%Sample & Generator & Sample name & Events & $\sigma \cdot \epsilon
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%\cdot k$ & k-factor \\ \hline WZ & Pythia &
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%/WZ/CMSSW\_1\_6\_7-CSA07-1195663763/RECO & 58897 & 0.585 pb & 1.92 \\
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%$Zb\bar{b}$ & COMPHEP &
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%/comphep-bbll/CMSSW\_1\_6\_7-CSA07-1198677426/RECO & 143.59 pb & 2.4
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%\\ ``Chowder'' & ALPGEN &
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%/CSA07AllEvents/CMSSW\_1\_6\_7-CSA07-Chowder-A1-PDAllEvents-ReReco-100pb/RECO
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%& 25 M & event weights & - \\
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\begin{tabular}{|c|c|c|c|c|} \hline
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Sample & cross section [pb] & Events & Dataset name \\ \hline
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$WZ$ & 1.12 & 59K & /WZ/CMSSW$\_1\_6\_7$-CSA07-1195663763\\ \hline
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$Z b\bar{b}$ & 830*0.173 (NLO) & 1.9M & /comphep-bbll/CMSSW$\_1\_6\_7$-CSA07-1198677426\\ \hline
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Chowder & Event Weight & $\sim$ 21M & /CSA07AllEvents/\\ & & & CMSSW$\_1\_6\_7$-CSA07-Chowder-A1-PDAllEvents-ReReco
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-100pb\\ \hline
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$ZZ$ inclusif & 16.1 (NLO) & $\sim$ 140k & /ZZ$\_$incl/CMSSW$\_1\_6\_7$-CSA07-1194964234/RECO\\ \hline
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$Z\gamma \rightarrow e^+e^-\gamma$ & 1.08 (NLO) & $\sim$125k &/Zeegamma/CMSSW$\_1\_6\_7$-CSA07-1198935518/RECO \\ \hline
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$Z\gamma \rightarrow \mu^+\mu^-\gamma$ & 1.08 (NLO) & $\sim$ 93k & /Zmumugamma/CMSSW$\_1\_6\_7$-CSA07-1194806860/RECO\\ \hline
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\end{tabular}
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\label{tab:MC}
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\caption{Monte Carlo samples used in this analysis using 100pb$^{-1}$ scenario}
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\end{table}
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