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\section{Significance of observation of \WZ signal for different final state signatures}
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\label{sec:Significance_4Cat}
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Here we provide the results of the procedure described in Section~\ref{ssec:pseudoExperiments}
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of the note using the background and signal estimated with matrix method using categories
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in instrumental background given in Table~\ref{tab:FinalXC} (see Figs.~\ref{fig:sls} and \ref{fig:sl_full_new}),
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and that without using instrumental background categorization given in Table~\ref{tab:FinalNoFit}
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(see Figs.~\ref{fig:sls_noFit} and \ref{fig:sl_full_new_noFit}). In both cases
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the systematic uncertainties correspond to 300 \invpb scenario.
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It is important to note that the significance plots are valid as far as the numbers in Tables
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\ref{tab:FinalXC} and \ref{tab:FinalNoFit} are simply scaled with luminosity. In reality,
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increase of the luminosity will result in increase of the systematic effects due to the assumption
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that the misidentified lepton is associated from \W lepton decays. On the other hand, increase
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in luminosity also result in better understanding of the background processes and, thus, two
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effects can cancel each other.
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In summary, we estimate that with 300 \invpb, 3.4 $ < S_L < $ 10.1 at 95\% C.L. for the method
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where individual instrumental background sources are considered, and 5.0 $< S_L <$ 11.7
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at 95\% C.L. with the method where all instrumental sources of background are treated as one.
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\begin{figure}[bt]
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\subfigure[$3e$]
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{
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\includegraphics[width=3.2in] {figs/sl1.eps}
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}
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\subfigure[$2e1\mu$]
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{
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\includegraphics[width=3.2in] {figs/sl2.eps}
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}
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\\
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\subfigure[$2\mu 1e$]
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{
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\includegraphics[width=3.2in] {figs/sl3.eps}
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}
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\subfigure[$3\mu$]
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{
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\includegraphics[width=3.2in] {figs/sl4.eps}
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}
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\caption{Expected value of $S_L$ (black line) and its 68\% (red band) and
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95\% (green band) CL bands as a function of integrated luminosity
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for (a) $3e$, (b) $2e1\mu$, (c) $2\mu 1e$, and (d) $3\mu$ final state signatures.}
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\label{fig:sls}
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\end{figure}
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\begin{figure}[!tb]
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\begin{center}
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\scalebox{0.8}{\includegraphics{figs/sl_full_new.eps}}
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\caption{Expected value of $S_L$ (black line) and its 68\% (red band) and
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95\% (green band) CL bands as a function of integrated luminosity
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for all final state signatures combined.}
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\label{fig:sl_full_new}
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\end{center}
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\end{figure}
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\begin{figure}[bt]
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\subfigure[$3e$]
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{
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\includegraphics[width=3.2in] {figs/sl1_noCat.eps}
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}
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\subfigure[$2e1\mu$]
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{
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\includegraphics[width=3.2in] {figs/sl2_noCat.eps}
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}
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\\
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\subfigure[$2\mu 1e$]
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{
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\includegraphics[width=3.2in] {figs/sl3_noCat.eps}
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}
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\subfigure[$3\mu$]
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{
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\includegraphics[width=3.2in] {figs/sl4_noCat.eps}
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}
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\caption{Expected value of $S_L$ (black line) and its 68\% (red band) and
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95\% (green band) CL bands as a function of integrated luminosity
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for (a) $3e$, (b) $2e1\mu$, (c) $2\mu 1e$, and (d) $3\mu$ final state signatures
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when no categorization of instrumental background is assumed.}
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\label{fig:sls_noFit}
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\end{figure}
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\begin{figure}[!tb]
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\begin{center}
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\scalebox{0.8}{\includegraphics{figs/sl_full_new_noCat.eps}}
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\caption{Expected value of $S_L$ (black line) and its 68\% (red band) and
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95\% (green band) CL bands as a function of integrated luminosity
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for all final state signatures combined.}
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\label{fig:sl_full_new_noFit}
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\end{center}
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\end{figure}
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