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\subsubsection{$M_{W}$ measurement exercise}
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The analyzed dataset for this exercise is
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{%\it
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/CSA06-103-os-EWKSoup0-0/RECOSIM/CMSSW$\_$1$\_$0$\_$5-eg$\_$ZeeFilter-1161162341}
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which contains $76\,494$ events. The jobs have been submitted using
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CMSSW 1.0.5 and CRAB 1.4.0, and have run on the Rome Tier-2 CPUs.
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$Z \to e^+ e^- $ events are treated by ignoring one randomly chosen lepton to
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mimic $W \to e \nu$ events. $Z$ events with an invariant mass of the
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electron-positron pair $M_{e^+e^-} > $ 50~GeV are then selected using the
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criteria applied in the $W$ mass analysis~\cite{CMSNOTE2006-061}: one
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electron inside the pseudorapidity region $|\eta|<$2.4 and with
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transverse energy greater than 29~GeV; missing transverse energy
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$E^{T}_{missing}>$ 25~GeV; the momentum of the
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system recoiling against the boson below 20~GeV; and,
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finally, no jets in the event with tranverse momentum greater
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30~GeV. Electrons are chosen among electron candidates, requiring a
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geometrical matching between the supercluster and the associated track
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($|\phi_{SC} - \phi_{track}|<$0.1 and $|\eta_{SC} -
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\eta_{track}|<$0.006) and a matching between the energy of the
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supercluster and the momentum measured from the track
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(0.8$<E_{SC}/P_{track}<$2.5). The missing transverse energy is measured
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from the energy deposited in the calorimeters towers and the jets are
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obtained with the iterative cone algorithm.
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Variables relevant to this analysis are the transverse energy of
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the lepton, the missing transverse energy and the invariant transverse
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mass of the lepton pair. Their spectra and the corresponding
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resolutions are shown in Fig.~\ref{fig:mw-ET}, \ref{fig:mw-MET} and
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\ref{fig:mw-MT}.
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\begin{figure}[h]
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\centering
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\includegraphics[width=0.49\textwidth]{figs/wmass_ete.pdf}
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\includegraphics[width=0.49\textwidth]{figs/wmass_ete_resolution.pdf}
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\caption{The electron transverse energy distribution in $Z \to e^+
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e^- $ decays (left) and the corresponding resolution (right).
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\label{fig:mw-ET}}
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\end{figure}
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\begin{figure}[h]
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\centering
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\includegraphics[width=0.49\textwidth]{figs/wmass_met.pdf}
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\includegraphics[width=0.49\textwidth]{figs/wmass_met_resolution.pdf}
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\caption{The missing transverse energy distribution
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in $Z \to e^+ e^- $ events with one lepton removed (left) and the
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resolution for one MET component (right).
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\label{fig:mw-MET}}
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\end{figure}
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\begin{figure}[h]
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\centering
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\includegraphics[width=0.49\textwidth]{figs/wmass_mt.pdf}
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\includegraphics[width=0.49\textwidth]{figs/wmass_mt_resolution.pdf}
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\caption{The transverse mass spectrum in $Z \to e^+ e^- $ events
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with one lepton removed (left) and its resolution (right).
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\label{fig:mw-MT}}
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\end{figure}
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