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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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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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|
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\subsection{Signal definition} |
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|
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\subsection{Signal and Background Monte Carlo samples} |
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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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|
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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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|
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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{$p_T(Z)$ 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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|
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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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|
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|
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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 lepton is 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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The background to the \WZ final state can be divided in physics and |
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instrumental. Physics background includes the contributions from |
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either converted photons that produce isolated leptons misidentified |
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as a decay products of $\W$ or $\Z$ bosons, or genuine leptons from |
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diboson processes. The only non-negligible physics backgrounds are |
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$\Z\gamma$ and $\Z\Z$ processes officially produced with {\sl PYTHIA} |
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generator. |
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|
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The instrumental backgrounds are all include jets that are misidentified |
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as isolated leptons. These include production of $\W$ and $\Z$ bosons |
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with jets and $t\bar{t}$ processes. We summarize the instrumental background |
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processes below. |
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|
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\begin{itemize} |
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\item $\Z + jets$: this background is one of the dominant to the \WZ final state. Although |
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the misidentification rate for a jet to be misidentified as a lepton is quite small, the |
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$\Z+jets$ cross-section is 35 times larger than the signal one. We use the {\sl ALPGEN} |
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generated official samples of $\Z+jet$ production Monte Carlo samples for different |
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values of the jet transverse momentum. |
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\item $t\bar{t}$: each of the top quarks decay into a $\W b$ pair producing at least two |
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leptons and two $b$-quark jets. Although this process does not have a genuine $\Z$ |
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candidate and can be suppressed be a $\Z$ candidate invariant mass requirement, |
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the probability for a $b$-quark jet to decay semi-leptonically and be misidentified |
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as a lepton is higher than that from a light-quark jets. The cross-section of the $t\bar{t}$ |
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production is also exceed by about 15 times the cross-section of the \WZ production. |
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Thus, this background is also one of the most dominant. We use the official $t\bar{t}$ |
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samples produced with {\sl ALPGEN} generator to estimate this background. |
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\item $\Z + b\bar{b}$: this process is produced by the {\sl COMPHEP} |
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generator and have a genuine $\Z$ candidate in the final state. One of the $b$-quark |
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jets are misidentified as the third lepton from the $\W$ boson. |
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\item $\W+jets$: in this process, the \W boson produces a genuine lepton, |
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while the other two leptons are misidentified jets. As the misidentification |
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probability is low, this channel does not contribute significantly to the \WZ |
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final state. The additional \Z candidate invariant mass requirement suppresses |
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this background further. We use the officially produced sample of $\W+jets$ processes |
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for different number of jets in the final state generated by the {\sl ALPGEN} |
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generator. |
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\end{itemize} |
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|
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All the samples we use in this study are a part of the CSA07 production and |
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are generated using $\mathrm{CMSSW}\_1\_4_\_6$ using the full {\sl GEANT} |
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simulation of the CMS detector. The digitization and reconstruction are |
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done using a newer $\mathrm{CMSSW}\_1\_6_\_7$ release with a |
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misalignment/miscalibration of the detector scenario expected |
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to be achieved after collection of $\sim$ 100~pb$^{-1}$ of data. |
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All {\sl ALPGEN} samples are mixed together in further referred to as to a |
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``Chowder soup''. |
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|
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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 isolation |
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discriminants. |
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|
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Analysis of the samples is done using CMSSW$\_1\_6\_7$ CMS software |
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release. 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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|
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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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$\Z\Z$ inclusive & 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 100 pb$^{-1}$ scenario} |
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\end{table} |
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|
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|
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|
