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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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were generated with the leading order event generator PYTHIA~\cite{Sjostrand:2003wg}, ALPGEN or COMPHEP. To
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accommodate NLO effect constant k-factors were applied.
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Additionally the cross section calculator MCFM~\cite{Campbell:2005} was used to determine
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the next-to-leading order differential cross section for the WZ
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production process. To estimate the PDF uncertainty for the signal
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process at NLO the NLO event generator MC@NLO 3.1~\cite{Frixione:2002ik} together with PDF set
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CTEQ6M was used.
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\subsection{Signal Definition}
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The goal of the analysis is to study the final state of on-shell $W$
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and $Z$ boson, both of them decaying leptonically. The leptonic final
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state $l^+ l^- l^\pm \nu$ also receives a contribution from the
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$W\gamma *$ process, where the $\gamma *$ stands for a virtual photon
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through the $WW\gamma$ vertex. In this analysis, only events with $l^+
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l^-$ invariant mass consistent with $Z$ mass will be considered. CMS
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detector have a very good energy resolution for electrons and muons,
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the mass windows will be $\pm 10$ GeV around 91 GeV.
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Using MCFM to estimate the total NLO cross section, we found:
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\begin{equation}
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\sigma_{NLO} ( pp \rightarrow W^+Z^0; \sqrt{s}=14TeV) = 30.5 pb
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\end{equation}
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\begin{equation}
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\sigma_{NLO} ( pp \rightarrow W^-Z^0; \sqrt{s}=14TeV) = 19.1 pb
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\end{equation}
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The LO and NLO distribution of \Z transverse momentum are shown of
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figure~\ref{fig:LOvsNLO} for the case of $W^+$ on the left and $W^-$
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on the right side. The ratio NLO/LO is also presented on the figure
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and it is increasing as $P_T(Z)$ increased. In the following analysis
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we consider a constant $k-factor$ of 1.84 as we concentrate on the
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first data taking. On the other side, if in the future one wants to
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use such distribution to study the effect of possible anomalous triple
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gauge couplings, it will be necessary to take the $p_T$ dependence of
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this $k-factor$ into account.
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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{$P_T(Z)$ in $W^-Z$ events on the left and $W^+Z$ events on the right
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distribution for LO and NLO calculation. The ratio NLO/LO is also given.
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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 has been produced using PYTHIA
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generator. The decay for the \W has been forced to be in $e\nu_e$ or
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$\mu\nu_{mu}$ or $\tau\nu_{\tau}$ while the \Z is decaying into electrons
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or muons only.
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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 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 been produced using PYTHIA generator.
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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 $CMSSW\_1\_4_\_6$ 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 $CMSSW\_1\_6_\_7$
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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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%$ZZ\rightarrow ll l'l'$& 0.846 &
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\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}
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\end{table}
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