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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 event generator |
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are generated with the leading order (LO) event generator |
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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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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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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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|
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%%%%%%%%%%%%%%% |
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% YM modified before this mark |
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|
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Using MCFM to estimate the total NLO cross section, we found: |
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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^0; \sqrt{s}=14TeV) = 30.5 pb |
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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^0; \sqrt{s}=14TeV) = 19.1 pb |
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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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|
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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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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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|
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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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\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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%# 830x0.173 (== XS x eff.) = 143.59pb |
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|
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|
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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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\subsection{Signal and background Monte Carlo samples} |
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|
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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 $e\nu_e$ or |
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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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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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 |
