Notes/WZCSA07/selection.tex

\section{Event reconstruction}
\label{sec:eventReconstruction}

We categorize \WZ\ three-lepton final state as following
\begin{itemize}
\item $3e$: for \WZ events with $\W \to e \nu$ and $\Z\to \epem$.
\item $2e1\mu$: for \WZ events with $\W \to \mu \nu$ and $\Z\to \epem$.
\item $2\mu 1e$: for \WZ events with $\W \to e \nu$ and $\Z\to \mumu$.
\item $3\mu$: for \WZ events with $\W \to \mu \nu$ and $\Z\to \mumu$.
\end{itemize}


\subsection{Trigger selection and efficiencies}

Events stemming from the three-lepton final states of $\WZ$ production
are collected by the electron and/or muon triggers. For each channel,
a minimun number of HLT requirements is chosen while keeping 
the HLT efficiency for selected events close to 100\%. The same 
HLT requirements are used for channels with the same \Z decay mode:
\begin{itemize}
\item for $3e$ and $2e1\mu$: HLTSingleElectron or HLTDoubleElectronRelaxed
\item for $2\mu1e$ and $3\mu$: HLTSingleMuonIso
\end{itemize}
The HLT efficiencies for all modes for events passing the full 
selection described in this section are given in table~\ref{tab:hlteff}.

\begin{table}[tbph]
\begin{center}

\begin{tabular}{llc} \hline \hline
Channel    &   HLT selection                                   & HLT efficiency \\ \hline 
$3e$       &   HLTSingleElectron or HLTDoubleElectronRelaxed   &  0.996         \\
$2e1\mu$   &   HLTSingleElectron or HLTDoubleElectronRelaxed   &  0.969         \\
$2\mu 1e$  &   HLTSingleMuonIso                                &  0.966         \\
$3\mu$     &   HLTSingleMuonIso                                &  0.994         \\ \hline \hline
\end{tabular}

\end{center}
\caption{HLT Efficiencies for all the events in the generated phase space that 
  have been retained  by the complete event selection.}
\label{tab:hlteff}
\end{table}


\begin{figure}[tbp]
  \begin{center}
  \scalebox{0.7}{\includegraphics{figs/mu_isol.eps}}
  \caption{Muon isolation variables for the muon associated
    to the \W boson decay in $2e1\mu$ events: in the left plot 
    we illustrate the sum of calorimetric energy in a $\Delta R=0.3$ cone
    around the muon candidate; in the right plot we display the sum of 
    transverse momenta of tracks within a $\Delta R = 0.25$ cone around
    the muon candidate. The normalization of signal and background
    distributions is arbitrary.
}
  \label{fig:mu_isol}
  \end{center}
\end{figure}

\begin{figure}[tb]
  \begin{center}
  \scalebox{0.6}{\includegraphics{figs/mu_SIP.eps}}
  \caption{
    Muon impact parameter significance distribution 
    in $2e1\mu$ events. The normalization of signal and background
    distributions is arbitrary.
  }
  \label{fig:mu_SIP}
  \end{center}
\end{figure}


\subsection{Lepton identification}
\label{sec:leptonId}

The requirements used for electron identification in this analysis are described
in~\cite{noteElectronID}.

Muon candidates are selected from global muons, which are reconstructed
by combining measurements in the muon chambers and the central tracker.
An additional isolation criterion is imposed to require the energy
measured in the calorimeters within a $\Delta R = 0.3$ cone around the
muon to be smaller than 3 GeV and the sum of the $p_T$ of tracks
within a $\Delta R = 0.25$ cone around the muon must be smaller than 2 GeV.
These cuts reduce the background from muons originated in
\b-quark decays of the $\Zbbbar$ background, which are close to tracks
and clusters from the other \b-quark decay products.
The signal and background distributions of these isolation variables 
are shown in Figure~\ref{fig:mu_isol} for the muon in $2e1\mu$ candidate 
events.

%Figures~\ref{fig:muonisol} and ~\ref{fig:muonisoleffi} show the
%performance of the isolation cut. The distribution of the isolation
%variables for the $\Z\b\bbar(\epem\b\bbar)$ is particularly
%interesting, since muons only stem from  \b-quark decays.

The significance of the muon impact parameter in the plane
transverse to the beam, $S_{IP}$, discriminates against leptons from
heavy-quark decays in all standard model background processes. This
variable is defined as the ratio between the measured impact parameter
and its uncertainty: $S_{IP}=IP/\sigma_{IP}$, and is required to
satisfy $S_{IP}<3$. This requirement is applied only for muon candidates
and not for electrons. For electron candidates, a significant fraction of the
background comes from misidentified light quark jets. Thus,
the requirement on the impact parameter significance does not 
increase the significance of the $\W\to e$ channels, as can be seen in 
Fig.~\ref{fig:wl_IP_SvsCut}. The distribution of $S_{IP}$ for the muon 
in $2e1\mu$ candidate events is shown in Figure~\ref{fig:mu_SIP}.

The muons fullfilling all these requirements will be called ``tight'', while global
muons without requirements on isolation or impact parameter significance are called ``loose''.

\begin{figure}[p]
  \begin{center}
  \scalebox{0.6}{\includegraphics{figs/wl_IP_eff.eps}}
  \caption{Efficiency for signal and background as a function
    of the requirement on the \W-boson lepton impact parameter
    significance. All other criteria but the one on impact parameter 
    significance are applied.
%    Only events with 81 GeV $< M_Z < $ 101 \gev 
%    are considered.
  }
  \label{fig:wl_IP_eff}
  \end{center}
%\end{figure}

%\begin{figure}[bt]
  \begin{center}
  \scalebox{0.6}{\includegraphics{figs/wl_IP_SvsCut.eps}}
  \caption{Signal significance as a function of requirement on
    the \W-boson lepton impact parameter significance. All other criteria but 
    the requirement on the impact parameter significance are applied.
%    Only events with 81 GeV $< M_Z < $ 101 \gev are considered.
  }
  \label{fig:wl_IP_SvsCut}
  \end{center}
\end{figure}


\begin{table}[tbp]
\begin{tabular}{|l|c|c|c|c|} \hline
              &  $3e$ & $2e1\mu$ & $2\mu 1e$ & $3\mu$ \\ \hline \hline
\multicolumn{5}{|c|}{Lepton selection} \\ \hline
Electrons     &   \multicolumn{3}{|c|}{{\tt SimpleLoose} requirements for \Z reconstruction} & \\
              &   \multicolumn{3}{|c|}{{\tt SimpleTight} requirements for \W} &  \\ \hline
Muons         &  &  \multicolumn{3}{|c|}{ Track Isolation:$ {\tt IsoTrack}(\Delta R= 0.25) < 2 \gev$}  \\
              &  &  \multicolumn{3}{|c|}{ Calorimetric Isolation:$  {\tt IsoCalo}(\Delta R = 0.3)  < 5 \gev$}  \\
              &  &  \multicolumn{3}{|c|}{$S_{IP}=IP/\sigma_{IP}<3$ }  \\ \hline
HLT requirement & \multicolumn{2}{|c|}{ HLTSingleElectron or HLTDoubleElectronRelaxed}
                & \multicolumn{2}{|c|}{  HLTSingleMuonIso} \\ \hline
\multicolumn{5}{|c|}{\Z reconstruction} \\ \hline
Lepton cuts   &  \multicolumn{4}{|c|}{for both \Z leptons: $p_T > 15$ GeV} \\
Mass window   &  \multicolumn{4}{|c|}{$50 \gev < M_Z < 120 \gev $ } \\
Second \Z veto &  \multicolumn{4}{|c|}{No independent second \Z candidate with $50 \gev < M_Z < 120 \gev $ } \\ \hline
\multicolumn{5}{|c|}{\W lepton selection} \\ \hline

Other cuts    &     &        & $\Delta R(\mu_Z,e_W)>0.1$ &  \\ \hline
Signal region  &    \multicolumn{4}{|c|}{$81 \gev < M_Z < 101 \gev $ } \\ \hline \hline

\end{tabular}
\caption{Summary of the criteria we use to select \WZ\ final state}
\label{tab:allcuts}
\end{table}


\begin{figure}[p]
  \begin{center}
  \scalebox{0.6}{\includegraphics{figs/wlpt_cuteff.eps}}
  \caption{Efficiency for signal and background as a function
    of the cut value on the \W-boson lepton transverse momentum.
    All other cuts but the cut on this variable are applied.
    Only events with 81 GeV $< M_Z < $ 101 \gev 
    are considered.}
  \label{fig:wlpt_cuteff}
  \end{center}
%\end{figure}

%\begin{figure}[bt]
  \begin{center}
  \scalebox{0.6}{\includegraphics{figs/wlpt_cutS.eps}}
  \caption{Signal significance as a function of the cut value on 
    the \W-boson lepton transverse momentum. All other cuts but 
    the cut on this variable are applied. Only events with 
    81 GeV $< M_Z < $ 101 \gev are considered.}
  \label{fig:wlpt_cutS}
  \end{center}
\end{figure}


\subsection{\WZ candidate selection}

Events are accepted if they contain at least three charged leptons,
either electrons or muons, with $p_T > 15\,\mathrm{GeV}$ and $| \eta | < 2.5$ for
electrons,$| \eta | < 2.4$ for muons, as discussed in Section~\ref{sec:leptonId}.

The \WZ candidate selection proceeds from building all possible
\Z-boson candidates from same-flavour opposite-charge lepton pairs.
For $\Z \to ee$ decays, electron candidates have to fulfill the loose requirements
defined in~\cite{noteElectronID}.

Events are retained if the mass of the \Z boson candidate is 
within 20 GeV of the \Z boson mass, $m_Z$. The event is
rejected if a second \Z candidate is found. This second \Z boson candidate is formed 
using all possible same-flavour opposite-charge combinations which are left 
after removing the two leptons already used for the first \Z boson candidate. This 
secondary \Z boson veto helps to suppress $\Z\Z$ events. 
%The invariant 
%mass distribution for accepted \Z candidates is shown in
%Figure~\ref{fig:zcandidates}.

% and the \Z mass resolution is shown in
%Figure~\ref{fig:dzmass}.

After the \Z boson candidate is identified, the remaining leptons in the event
are required, for electrons, to pass the tight criteria described in~\cite{noteElectronID}
or, for muons, all criteria described in section~\ref{sec:leptonId}.
If more than one lepton candidate satisfies the tight requirements, the one with the
highest $p_T$ is associated with \W boson decay. This lepton's $p_T$ is effective
discriminant against \Zbbbar and \Zjets production (see Fig.~\ref{fig:wlpt_cuteff}).
We require the transverse momentum to exceed 20 GeV, as it maximizes
the significance of the \WZ\ signal with respect to background as shown in 
Fig.~\ref{fig:wlpt_cutS}.

An additional requirement on the isolation between electron and muon candidates is applied
for the $2\mu 1e$ channel, by demanding the value of $\Delta R$ between the electron 
candidate associated with the \W boson decay and any of the two muons associated with 
the \Z boson decay to be greater than 0.1.
 
This requirement allows suppressing the contribution of $\Z \to \mu\mu$
decays, where one of the two muons radiates a photon which is reconstructed
as an electron, possibly after conversion.
% ADD THE PLOT TO JUSTIFY THIS COMMENT
% This can be seen as a peak in the dimuon
%invariant mass at  around 60 GeV in Fig.~\ref{fig:Z2mu1e_60GeVPeak}.

The summary of the selection criteria is given in Table~\ref{tab:allcuts}.

The expected number of the events satisfying the sequential steps of the selection
is listed in Tables~\ref{tab:sel-effA}.  
In Table~\ref{tab:wz-effimatrix} we list the total selection efficiency for  different
\W and \Z boson decay modes. It can be seen lepton candidates from \W and \Z
boson decays are almost always are reconstructed with the correct flavor. As expected,
there is a small contribution from $\W \to \tau \nu_\tau \to \ell \nu_\ell \nu_\tau$
decays. However, this contribution is suppressed, mostly due to $p_T$ requirement
on the third lepton, as leptons from $\tau$ decays are not as energetic as those from
$\W \to \ell \nu$ processes.

In Tables~\ref{tab:wz-matcheffi-Zee} and \ref{tab:wz-matcheffi-Zmumu} we
display the fraction of reconstructed \WZ events with correctly-matched leptons.
It can be seen that the lepton associated with the \W boson decay is correctly matched 
to the true Monte Carlo lepton from the \W boson decay in more than 90\% of 
the cases, even for events with several lepton candidates available to be associated 
to the \W boson decay. The choice to take the lepton candidate with the leading $p_T$ is,
therefore, justified.

\begin{table}[p]
  \begin{center}

\begin{tabular}{lcc|cc|cc|cc|} \hline
\multicolumn{9}{c}{ {\bf $3e$ Channel}} \\ \hline  \hline
Step   & $\WZ \to 3e\nu$ &  $ \epsilon$  & $\Z+jets$ &  $ \epsilon$  & $t\bar{t}+jets$ &  $ \epsilon$  & $b\bar{b}\ell\ell$ &  $ \epsilon$\\ \hline
All events       & 185 &         & $5.82\cdot 10^6$ &    & $8.27\cdot 10^5$ &    & $1.44\cdot 10^5$ &  \\
Found $\Z \to ee$         & 73.9 & 39.9\%        & $5.02\cdot 10^5$ & 8.63\%    & $2.92\cdot 10^3$ & 0.353\%   & $2.78\cdot 10^4$ & 19.4\% \\
Second \Z veto            & 73.9 & 100\%         & $5.02\cdot 10^5$ & 100\%     & $2.92\cdot 10^3$ & 99.9\%    & $2.78\cdot 10^4$ & 100\% \\
Found $\W \to e\nu$          & 37.4 & 50.6\%        & 310 & 0.062\%       & 13.8 & 0.474\%       & 171 & 0.61\% \\
\W lepton $p_T$ cut          & 32.5 & 86.7\%        & 86.8 & 28\%  & 8.26 & 59.7\%        & 23.4 & 13.7\% \\
Passes HLT               & 32.3 & 99.6\%        & 86.8 & 100\%         & 8.26 & 100\%         & 23.3 & 99.7\% \\
\Z mass window    & 29.5 & 91.2\%        & 51.9 & 59.8\%        & 3.26 & 39.5\%        & 17.3 & 74\% \\
 \hline
  Overall efficiency  &  &  15.9\% &  &  0.00089\% &  &  0.00039\% &  &  0.012\% \\
\hline

\multicolumn{9}{c}{ {\bf $2e1\mu$ Channel}} \\ \hline  \hline
Step   & $\WZ \to 2e1\mu\nu$ &  $ \epsilon$  & $\Z+jets$ &  $ \epsilon$  & $t\bar{t}+jets$ &  $ \epsilon$  & $b\bar{t}\ell\ell$ &  $ \epsilon$\\ \hline
All events       & 185 &         & $5.82\cdot 10^6$ &    & $8.27\cdot 10^5$ &    & $1.44\cdot 10^5$ &  \\
Found $\Z \to ee$         & 63.8 & 34.5\%        & $5.02\cdot 10^5$ & 8.63\%    & $2.92\cdot 10^3$ & 0.35\%   & $2.78\cdot 10^4$ & 19.4\% \\
Second \Z veto            & 63.7 & 99.9\%        & $5.02\cdot 10^5$ & 100\%     & $2.92\cdot 10^3$ & 99.9\%    & $2.78\cdot 10^4$ & 100\% \\
Found $\W \to \mu\nu$        & 42.6 & 66.8\%        & $2.19\cdot 10^3$ & 0.44\%   & 55.6 & 1.91\%        & 748 & 2.69\% \\
\W lepton $p_T$ cut          & 35.1 & 82.5\%        & 9.58 & 0.44\%       & 16.4 & 29.5\%        & 9.49 & 1.27\% \\
Passes HLT               & 34.3 & 97.6\%        & 8.32 & 86.9\%        & 14.1 & 86\%  & 9.12 & 96.1\% \\
\Z mass window    & 30.8 & 89.8\%        & 7.31 & 87.9\%        & 3.76 & 26.7\%        & 8 & 87.8\% \\
 \hline
  Overall efficiency  &  &  16.7\% &  &  0.00013\% &  &  0.00045\% &  &  0.0056\% \\
\hline

\multicolumn{9}{c}{ {\bf $2\mu1e$ Channel}} \\ \hline  \hline
Step   & $\WZ \to 2\mu1e$ &  $ \epsilon$  & $\Z+jets$ &  $ \epsilon$  & $t\bar{t}+jets$ &  $ \epsilon$  & $b\bar{b}\ell\ell$ &  $ \epsilon$\\ \hline
All events       & 190 &         & $5.82\cdot 10^6$ &    & $8.27\cdot 10^5$ &    & $1.44\cdot 10^5$ &  \\
Found $\Z \to \mu\mu$     & 75.2 & 39.7\%        & $5.77\cdot 10^5$ & 9.92\%    & $2.78\cdot 10^3$ & 0.336\%   & $3.19\cdot 10^4$ & 22.2\% \\
Second \Z veto            & 75.2 & 100\%         & $5.77\cdot 10^5$ & 100\%     & $2.77\cdot 10^3$ & 99.9\%    & $3.19\cdot 10^4$ & 100\% \\
Found $\W \to e\nu$          & 44 & 58.5\%  & 702 & 0.12\%        & 15.1 & 0.54\%       & 213 & 0.67\% \\
\W lepton $p_T$ cut                  & 38.4 & 87.2\%        & 464 & 66.2\%         & 10.3 & 68\%  & 50.5 & 23.7\% \\
$\Delta R(e,\mu)$ cut    & 38.4 & 99.9\%        & 93 & 20\%    & 7.15 & 69.6\%        & 23.3 & 46\% \\
Passes HLT                       & 37.3 & 97.1\%        & 88.8 & 95.5\%        & 6.62 & 92.7\%        & 23.1 & 99.4\% \\
\Z mass window    & 33.6 & 90.1\%        & 50.3 & 56.6\%        & 2.84 & 42.9\%        & 18.8 & 81.4\% \\
 \hline
  Overall efficiency  &  &  17.7\% &  &  0.00086\% &  &  0.00034\% &  &  0.013\% \\
\hline
%\end{tabular}
%\begin{tabular}{lcc|cc|cc|cc|} \hline
\multicolumn{9}{c}{ {\bf $3\mu$ Channel}} \\ \hline  \hline
Step   & $\WZ \to 3\mu$ &  $ \epsilon$  & $\Z+jets$ &  $ \epsilon$  & $t\bar{t}+jets$ &  $ \epsilon$  & $b\bar{b}\ell\ell$ &  $ \epsilon$\\ \hline
All events       & 189 &         & $5.82\cdot 10^6$ &    & $8.27\cdot 10^5$ &    & $1.44\cdot 10^5$ &  \\
Found $\Z \to \mu\mu$     & 83.8 & 44.3\%        & $5.77\cdot 10^5$ & 9.92\%    & $2.78\cdot 10^3$ & 0.336\%   & $3.19\cdot 10^4$ & 22.2\% \\
Second \Z veto            & 83.6 & 99.8\%        & $5.77\cdot 10^5$ & 100\%     & $2.77\cdot 10^3$ & 99.9\%    & $3.19\cdot 10^4$ & 100\% \\
Found $\W \to \mu\nu$        & 51.8 & 62\%  & $2.52\cdot 10^3$ & 0.44\%   & 34.8 & 1.25\%        & 810 & 2.54\% \\
\W lepton $p_T$ cut                  & 42.5 & 81.9\%        & 1.84 & 0.07\%       & 1.16 & 3.33\%        & 8.89 & 1.1\% \\
Passes HLT                       & 42.2 & 99.4\%        & 1.84 & 100\%         & 1.16 & 100\%         & 8.89 & 100\% \\
\Z mass window    & 38.5 & 91.1\%        & 1.84 & 100\%         & 1.16 & 100\%         & 7.78 & 87.5\% \\
 \hline
Overall efficiency  &  &  20.3\% &  &  0.000032\% &  &  0.00014\% &  &  0.0054\% \\
\hline
\end{tabular}

\caption{Expected number of signal and background events passing the different
  selections steps together with the efficiency of each requirement and total efficiency of
  selection criteria in the \WZ, \Zbbbar, \Zjets and \ttjets samples for an integrated luminosity 
  of 1 \invfb.}
\label{tab:sel-effA}
\end{center}
\end{table}

\begin{table}[p]
\begin{center}
\begin{tabular}{l|ccccc}
\hline \hline
   & \multicolumn{5}{c}{$\Z \to ee$ and \W decay modes below} \\
Reconstruction channel  &  $e \nu$
   &  $\mu \nu $
   &  $\tau \nu \to e \nu \nu  $
   &  $\tau \nu \to \mu \nu \nu $
   &  $\tau \nu \to {\rm hadrons~} \nu$
\\ \hline
$3e$       &  17.4\%  &  0.0319\%  &  6.42\%  &  0\%  &  0.162\% \\
$2e1\mu$   &  0\%  &  18.6\%  &  0\%  &  5.53\%  &  0.0485\% \\
$2\mu1e$   &  0\%  &  0\%  &  0\%  &  0\%  &  0\% \\
$3\mu$     &  0\%  &  0\%  &  0\%  &  0\%  &  0\% \\
\hline \hline

 & \multicolumn{5}{c}{$\Z \to \mu\mu$ and \W decay modes below} \\
 Reconstruction channel  &  $e\nu$
   &  $\mu\nu$
   &  $\tau\nu \to e\nu\nu$
   &  $\tau\nu \to \mu\nu\nu$
   &  $\tau\nu \to {\rm hadrons~}\nu$
\\ \hline
$3e$        &  0\%  &  0\%  &  0\%  &  0\%  &  0\% \\
$2e1\mu$   &  0.0104\%  &  0\%  &  0\%  &  0\%  &  0\% \\
$2\mu1e$   &  19.6\%  &  0.0208\%  &  5.56\%  &  0\%  &  0.18\% \\
$3\mu$     &  0\%  &  23.4\%  &  0.0573\%  &  6.77\%  &  0.0164\% \\
\hline \hline
\end{tabular}
\end{center}
\caption{Selection efficiency for signal events in the four selection channels for the different 
  generated \W and \Z decay channels.}
\label{tab:wz-effimatrix}

%\end{table}
%\begin{table}[tbp]
\begin{center}
\begin{tabular}{llcc} \hline
  & & \multicolumn{2}{c}{Generated decay} \\ 
  & & \multicolumn{2}{c}{$\Z \to ee $} \\
Selection channel  &    &  $\W \to e\nu$   &  $\W \to \mu\nu$ \\ 
\hline \hline
\multicolumn{4}{c}{all} \\ \hline
$3e$        & all & 1644 events         & 3 events    \\
$3e$        & matched \Z & 93$\pm$1\% & 100\%\\
$3e$        & matched \W & 92$\pm$1\% & 0\\
$3e$        & matched \WZ & 91$\pm$1\% & 0\\
\hline \hline

\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
$3e$        & all & 1602  events       & 0 events    \\
$3e$        & matched \Z & 94$\pm$1\% & 0\\
$3e$        & matched \W & 92$\pm$1\% & 0\\
$3e$        & matched \WZ & 91$\pm$1\% & 0\\
\hline \hline

\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
$3e$        & all & 42 events  & 3 events   \\
$3e$        & matched \Z & 93$\pm$4\% & 100\%\\
$3e$        & matched \W & 91 $\pm$5\% & 0\\
$3e$        & matched \WZ & 91$\pm$5\% & 0\\
\hline \hline

\multicolumn{4}{c}{all} \\ \hline
$2e1\mu$   & all & 0  events   & 1746 events \\
$2e1\mu$   & matched \Z & 0 & 100\%\\
$2e1\mu$   & matched \W & 0 & 100\%\\
$2e1\mu$   & matched \WZ & 0 & 100\%\\
\hline \hline

\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
$2e1\mu$   & all & 0 events    & 1715 events \\
$2e1\mu$   & matched \Z & 0 & 100\%\\
$2e1\mu$   & matched \W & 0 & 100\%\\
$2e1\mu$   & matched \WZ & 0 & 100\%\\
\hline \hline

\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
$2e1\mu$   & all & 0     & 31   \\
$2e1\mu$   & matched \Z & 0 & 100\%\\
$2e1\mu$   & matched \W & 0 & 100\%\\
$2e1\mu$   & matched \WZ & 0 & 100\% \\ \hline \hline
\end{tabular}
\end{center}
\caption{Fractions of events with correctly matched leptons
  to true decay product of \W and \Z decays for final states
  with generated $\Z\to ee$ decays}
\label{tab:wz-matcheffi-Zee}
\end{table}


\begin{table}[tbp]
\begin{center}
\begin{tabular}{llcc} \hline
  & & \multicolumn{2}{c}{Generated decay:} \\ 
 & & \multicolumn{2}{c}{$\Z \to \mu\mu $} \\
Selection channel  &    &  $\W \to e\nu$   &  $\W \to \mu\nu$
\\ 
\hline \hline
\multicolumn{4}{c}{all} \\ \hline
$2\mu1e$   & all & 1895 events  & 2 events   \\
$2\mu1e$   & matched \Z & 100\% & 100\%\\
$2\mu1e$   & matched \W & 99$\pm$1\% & 0\\
$2\mu1e$   & matched \WZ & 99$\pm$1\% & 0\\
\hline \hline

\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
$2\mu1e$   & all & 1847 events & 0 events    \\
$2\mu1e$   & matched \Z & 100\% & 0\\
$2\mu1e$   & matched \W & 99$\pm$1\% & 0\\
$2\mu1e$   & matched \WZ & 99$\pm$1\% & 0\\
\hline \hline

\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
$2\mu1e$   & all & 48 events   & 2 events    \\
$2\mu1e$   & matched \Z & 100\% & 100\%\\
$2\mu1e$   & matched \W & 94$\pm$3.5\%& 0\\
$2\mu1e$   & matched \WZ & 94$\pm$3.5\% & 0\\
\hline \hline

\multicolumn{4}{c}{all} \\ \hline
$3\mu$     & all & 0 events   & 2251 events \\
$3\mu$     & matched \Z & 0 & 94$\pm$1\%\\
$3\mu$     & matched \W & 0 & 93$\pm$1\%\\
$3\mu$     & matched \WZ & 0 & 93$\pm$1\%\\
\hline \hline

\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
$3\mu$     & all & 0 events    & 2207 events \\
$3\mu$     & matched \Z & 0 & 94$\pm$1\%\\
$3\mu$     & matched \W & 0 & 93$\pm$1\%\\
$3\mu$     & matched \WZ & 0 & 93$\pm$1\%\\
\hline \hline

\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
$3\mu$     & all & 0 events    & 44 events  \\
$3\mu$     & matched \Z & 0 & 91$\pm$4\%\\
$3\mu$     & matched \W & 0 & 91$\pm$4\%\\
$3\mu$     & matched \WZ & 0 & 91$\pm$4\%\\ \hline \hline
\end{tabular}
\end{center}
\caption{Fractions of MC \WZ events with correctly matched leptons
  to true decay product of \W and \Z decays for final states
  with generated $\Z\to \mu\mu$ decays}
\label{tab:wz-matcheffi-Zmumu}
\end{table}


\subsection{Complementary studies: can we use the neutrino?}

In $\WZ \to  \ell^{\pm}\nu \ellell (\ell=e,\mu)$ events, the neutrino
coming from the \W-boson decay leaves the detector with a significant
amount of energy, which should reflect in a large transverse missing
energy measurement. On the other side, no large MET is expected for 
the  most  important background categories, especially \Zjets,
\Zbbbar, \ZZ and \Zgamma. This expectation is confirmed, as can be 
seen in Figure~\ref{fig:met}.

Another variable sensitive to the presence of the neutrino 
is the W transverse mass $m_T^W$, obtained by combining the missing 
energy vector and the lepton associated to the \W-boson decay.
The distribution of $m_T^W$ is shown in Figure~\ref{fig:mtw}.
The signal yield could be extracted from that distribution.
This requires however additional studies and it has not been
done at this stage.

%\subsection{Signal extraction}
%\input D0Matrix
\input zjetbackground


\section{Systematic uncertainties}
\input Sys


\begin{figure}[bt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/met_by_channel.eps}}
  \caption{Missing transverse energy for the four signal categories. 
    The distributions  show the number of expected events 
    for $1 fb^{-1}$. Only events with 81 GeV $< M_Z < $ 101 \gev 
    are shown. All selection cuts are applied.}
  \label{fig:met}
  \end{center}
\end{figure}

\begin{figure}[bt]
  \begin{center}
  \scalebox{0.8}{\includegraphics{figs/mtw_by_channel.eps}}
  \caption{\W transverse mass for the four signal categories. 
    The distributions  show the number of expected events 
    for $1 fb^{-1}$. Only events with 81 GeV $< M_Z < $ 101 GeV are shown.
    All selection cuts are applied.}
  \label{fig:mtw}
  \end{center}
\end{figure}


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