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\subsubsection{Selection of W$\rightarrow \mu \nu$ events}
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Different Monte Carlo data samples with different signal compositions were analyzed to study
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the $W \rightarrow \mu \nu$ preselection yield. The goal of the skimming is to reduce
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the disk space for the data storage and physics analysis at Tier-2
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whilst preserving the signal and suppressing
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the backgrounds. As an example of a simple analysis performed at Tier-2 on skimmed data, the efficiency and resolution
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of the muon reconstruction obtained with the CMSSW software were studied as a function of $p_T$ and $\eta$,
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the $W \rightarrow \mu \nu$ signal was selected with isolation cuts and the transverse mass was
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compared with the same distribution obtained from the background.
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The following data samples were considered:
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\begin{itemize}
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\item the electroweak soup (3.4M events, 50\% $W \rightarrow \mu \nu$ and 50\% DY)
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\item the soft muons (1.8M events, 50\% minimum bias and 50\% $J/\Psi$, $p_T > 4$ GeV)
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\end{itemize}
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The skim jobs were running at the PIC and CNAF Tier-1 over FEVT (full events). The output was sent at the LNL Tier-2
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in AODSIM format (Analysis Object format). For the $W \rightarrow \mu \nu$ channel the skim consists of the selection
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of events having at least one muon (StandAlone muon reconstructed object) with $ p_T > 10$ GeV.
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Table~\ref{tab:wmunu_datareduction} summarizes the reduction of the disk space for the data storage due to the skimming.
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The efficiency of the electroweak soup data skimming results to be 16\% (0.55M events / 3.4M events).
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%
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\begin{table}[htb]
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\begin{center}
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\caption{Data reduction due to the skimming in term of number of events and disk space}
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\label{tab:wmunu_datareduction}
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\vspace{3mm}
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\begin{tabular}{|l|l|l|}
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\hline
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& Input & Output \\
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\hline
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EWK soup & FEVT , 3.4 Mevts , 5.1 TB & AODSIM , 0.55 Mevts , 0.82 GB \\
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\hline
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Soft muons & FEVT , 1.8 Mevts , 2.7 TB & AODSIM , 0.94 Mevts , 1.4 GB \\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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The selection efficiency for the $W \rightarrow \mu \nu$ skimming of the soft muon sample
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was 50\% (0.94M events / 1.8M events). The ``Soft Muon soup'' consisted
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of the mixing of approximately 1M events of $J/\Psi$ inclusively
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produced in pp collision with 1M events
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of $pp \rightarrow \mu+X$ events from a minimum bias sample, preselected with a requirement
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of $p_{T}(m)> 4 $GeV/c at the generator level. The analysis was performed with a sample of 0.12M events.
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Figure~\ref{fig:wmunu_ptnorm} shows the transverse momentum of muons for the different electroweak
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and soft muon soup components with cross section normalization.
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Figure~\ref{fig:wmunu_mtnorm} shows the transverse mass for the W boson candidate
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(reconstructed with the missing $E_T$ estimation).
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Figures~\ref{fig:wmunu_ptnormiso} and ~\ref{fig:wmunu_mtnormiso} show the muon $p_T$ and
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W boson $E_T$ distributions after muon isolation cuts.
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\begin{2figures}{hbt}
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\centering
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\includegraphics[angle=90, width=1 \linewidth]{figs/norma_pt} &
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\includegraphics[angle=90, width=1 \linewidth]{figs/norma_mt} \\
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\caption[]{Transverse momentum of muons after the skimming
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selection for the different electroweak soup and soft muons components with the cross section normalization.}
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\label{fig:wmunu_ptnorm} &
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\caption{Transverse mass of W bosons candidate after the skimming selection.}
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\label{fig:wmunu_mtnorm}
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\end{2figures}
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\begin{2figures}{hbt}
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\centering
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\includegraphics[angle=90, width=1 \linewidth]{figs/norma_pt_isol} &
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\includegraphics[angle=90, width=1 \linewidth]{figs/norma_mt_isol} \\
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\caption[]{Transverse momentum of muons after the isolation cuts.}
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\label{fig:wmunu_ptnormiso} &
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\caption{Transverse mass of W bosons candidate after the isolation cuts.}
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\label{fig:wmunu_mtnormiso}
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\end{2figures}
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