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\section{Data Driven Background Estimation Methods}
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\label{sec:datadriven}
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We have developed two data-driven methods to
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estimate the background in the signal region.
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The first one explouts the fact that
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\met and \met$/\sqrt{\rm SumJetPt}$ are nearly
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uncorrelated for the $t\bar{t}$ background
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(Section~\ref{sec:abcd}); the second one
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is based on the fact that in $t\bar{t}$ the
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$P_T$ of the dilepton pair is on average
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nearly the same as the $P_T$ of the pair of neutrinos
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from $W$-decays, which is reconstructed as \met in the
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detector.
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in 30 pb$^{-1}$ we expect $\approx$ 1 SM event in
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the signal region. The expectations from the LMO
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and LM1 SUSY benchmark points are {\color{red} XX} and
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{\color{red} XX} events respectively.
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\subsection{ABCD method}
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\label{sec:abcd}
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We find that in $t\bar{t}$ events \met and
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\met$/\sqrt{\rm SumJetPt}$ are nearly uncorrelated.
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This is demonstrated in Figure~\ref{fig:uncor}.
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Thus, we can use an ABCD method in the \met$/\sqrt{\rm SumJetPt}$ vs
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sumJetPt plane to estimate the background in a data driven way.
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\begin{figure}[htb]
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\begin{center}
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\includegraphics[width=0.75\linewidth]{uncorrelated.pdf}
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\caption{\label{fig:uncor}\protect Distributions of SumJetPt
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in MC $t\bar{t}$ events for different intervals of
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MET$/\sqrt{\rm SumJetPt}$.}
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\end{center}
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\end{figure}
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\begin{figure}[htb]
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\begin{center}
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\includegraphics[width=0.75\linewidth]{abcdMC.jpg}
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\caption{\label{fig:abcdMC}\protect Distributions of SumJetPt
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vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo. Here we also
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show our choice of ABCD regions. {\color{red} We need a better
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picture with the letters A-B-C-D and with the numerical values
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of the boundaries clearly indicated.}}
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\end{center}
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\end{figure}
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Our choice of ABCD regions is shown in Figure~\ref{fig:abcdMC}.
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The signal region is region D. The expected number of events
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in the four regions for the SM Monte Carlo, as well as the BG
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prediction AC/B is given in Table~\ref{tab:abcdMC} for an integrated
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luminosity of 30 pb$^{-1}$. The ABCD method is accurate
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to about 10\%.
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\begin{table}[htb]
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\begin{center}
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\caption{\label{tab:abcdMC} Expected SM Monte Carlo yields for
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30 pb$^{-1}$ in the ABCD regions.}
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\begin{tabular}{|l|c|c|c|c||c|}
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\hline
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Sample & A & B & C & D & AC/D \\ \hline
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ttdil & 6.4 & 28.4 & 4.2 & 1.0 & 0.9 \\
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Zjets & 0.0 & 1.3 & 0.2 & 0.0 & 0.0 \\
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Other SM & 0.6 & 2.1 & 0.2 & 0.1 & 0.0 \\ \hline
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total MC & 7.0 & 31.8 & 4.5 & 1.1 & 1.0 \\ \hline
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\end{tabular}
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\end{center}
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\end{table}
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