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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}. To
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accomodate 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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This analysis is studying the final state of on-shell $W$ and $Z$
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boson, both of them decaying leptonically. The fully final leptonic
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final 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 $p_T$ dependance 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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\begin{table}[tbh]
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\begin{tabular}{llllll} \hline
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Sample & Generator & Sample name & Events & $\sigma \cdot \epsilon \cdot k$ & k-factor \\ \hline
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WZ & Pythia & /WZ/CMSSW\_1\_6\_7-CSA07-1195663763/RECO & 58897 & 0.585 pb & 1.92 \\
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$Zb\bar{b}$ & COMPHEP & /comphep-bbll/CMSSW\_1\_6\_7-CSA07-1198677426/RECO & 143.59 pb & 2.4 \\
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``Chowder'' & ALPGEN & /CSA07AllEvents/CMSSW\_1\_6\_7-CSA07-Chowder-A1-PDAllEvents-ReReco-100pb/RECO & 25 M & event weights & - \\
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\hline
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\end{tabular}
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\caption{Monte Carlo samples used in this analysis}
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\end{table}
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