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\clearpage
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\section{Matching efficiency for \WZ\ events}
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\label{app:wzmatch}
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In Tables~\ref{tab:wz-matcheffi-Zee} and \ref{tab:wz-matcheffi-Zmumu} we
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display the fraction of reconstructed \WZ events with correctly-matched leptons.
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It can be seen that the lepton associated with the \W boson decay is correctly matched
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to the true Monte Carlo lepton in more than 91\% of the cases for $3e$, 93\% for $3\mu$, and more
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than 99\% for other categories , even for events with several lepton candidates available to be associated
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to the \W boson decay. The choice to take the lepton candidate with the leading $p_T$ is,
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therefore, justified.
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{llcc} \hline
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& & \multicolumn{2}{c}{Generated decay} \\
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& & \multicolumn{2}{c}{$\Z \to ee $} \\
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Selection channel & & $\W \to e\nu$ & $\W \to \mu\nu$ \\
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\hline \hline
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\multicolumn{4}{c}{all} \\ \hline
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$3e$ & all & 1644 events & 3 events \\
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$3e$ & matched \Z & 93$\pm$1\% & 100\%\\
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$3e$ & matched \W & 92$\pm$1\% & 0\\
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$3e$ & matched \WZ & 91$\pm$1\% & 0\\
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\hline \hline
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\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
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$3e$ & all & 1602 events & 0 events \\
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$3e$ & matched \Z & 94$\pm$1\% & 0\\
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$3e$ & matched \W & 92$\pm$1\% & 0\\
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$3e$ & matched \WZ & 91$\pm$1\% & 0\\
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\hline \hline
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\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
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$3e$ & all & 42 events & 3 events \\
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$3e$ & matched \Z & 93$\pm$4\% & 100\%\\
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$3e$ & matched \W & 91 $\pm$5\% & 0\\
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$3e$ & matched \WZ & 91$\pm$5\% & 0\\
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\hline \hline
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\multicolumn{4}{c}{all} \\ \hline
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$2e1\mu$ & all & 0 events & 1746 events \\
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$2e1\mu$ & matched \Z & 0 & 100\%\\
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$2e1\mu$ & matched \W & 0 & 100\%\\
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$2e1\mu$ & matched \WZ & 0 & 100\%\\
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\hline \hline
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\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
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$2e1\mu$ & all & 0 events & 1715 events \\
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$2e1\mu$ & matched \Z & 0 & 100\%\\
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$2e1\mu$ & matched \W & 0 & 100\%\\
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$2e1\mu$ & matched \WZ & 0 & 100\%\\
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\hline \hline
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\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
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$2e1\mu$ & all & 0 & 31 \\
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$2e1\mu$ & matched \Z & 0 & 100\%\\
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$2e1\mu$ & matched \W & 0 & 100\%\\
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$2e1\mu$ & matched \WZ & 0 & 100\% \\ \hline \hline
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\end{tabular}
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\end{center}
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\caption{Fractions of events with correctly matched leptons
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to true decay product of \W and \Z decays for final states
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with generated $\Z\to ee$ decays}
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\label{tab:wz-matcheffi-Zee}
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\end{table}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{llcc} \hline
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& & \multicolumn{2}{c}{Generated decay:} \\
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& & \multicolumn{2}{c}{$\Z \to \mu\mu $} \\
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Selection channel & & $\W \to e\nu$ & $\W \to \mu\nu$
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\\
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\hline \hline
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\multicolumn{4}{c}{all} \\ \hline
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$2\mu1e$ & all & 1895 events & 2 events \\
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$2\mu1e$ & matched \Z & 100\% & 100\%\\
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$2\mu1e$ & matched \W & 99$\pm$1\% & 0\\
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$2\mu1e$ & matched \WZ & 99$\pm$1\% & 0\\
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\hline \hline
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\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
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$2\mu1e$ & all & 1847 events & 0 events \\
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$2\mu1e$ & matched \Z & 100\% & 0\\
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$2\mu1e$ & matched \W & 99$\pm$1\% & 0\\
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$2\mu1e$ & matched \WZ & 99$\pm$1\% & 0\\
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\hline \hline
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\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
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$2\mu1e$ & all & 48 events & 2 events \\
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$2\mu1e$ & matched \Z & 100\% & 100\%\\
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$2\mu1e$ & matched \W & 94$\pm$3.5\%& 0\\
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$2\mu1e$ & matched \WZ & 94$\pm$3.5\% & 0\\
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\hline \hline
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\multicolumn{4}{c}{all} \\ \hline
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$3\mu$ & all & 0 events & 2251 events \\
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$3\mu$ & matched \Z & 0 & 94$\pm$1\%\\
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$3\mu$ & matched \W & 0 & 93$\pm$1\%\\
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$3\mu$ & matched \WZ & 0 & 93$\pm$1\%\\
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\hline \hline
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\multicolumn{4}{c}{exactly 1 \W lepton candidate} \\ \hline
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$3\mu$ & all & 0 events & 2207 events \\
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$3\mu$ & matched \Z & 0 & 94$\pm$1\%\\
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$3\mu$ & matched \W & 0 & 93$\pm$1\%\\
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$3\mu$ & matched \WZ & 0 & 93$\pm$1\%\\
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\hline \hline
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\multicolumn{4}{c}{more than 1 \W lepton candidate} \\ \hline
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$3\mu$ & all & 0 events & 44 events \\
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$3\mu$ & matched \Z & 0 & 91$\pm$4\%\\
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$3\mu$ & matched \W & 0 & 91$\pm$4\%\\
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$3\mu$ & matched \WZ & 0 & 91$\pm$4\%\\ \hline \hline
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\end{tabular}
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\end{center}
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\caption{Fractions of MC \WZ events with correctly matched leptons
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to true decay product of \W and \Z decays for final states
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with generated $\Z\to \mu\mu$ decays}
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\label{tab:wz-matcheffi-Zmumu}
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\end{table}
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