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%\clearpage
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\section{Results}
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\label{sec:results}
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\begin{figure}[tbh]
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\begin{center}
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\includegraphics[width=0.75\linewidth]{abcd_35pb.png}
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\caption{\label{fig:abcdData}\protect Distributions of SumJetPt
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vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo and data. Here we also
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show our choice of ABCD regions.}
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\end{center}
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\end{figure}
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The data, together with SM expectations is presented
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in Figure~\ref{fig:abcdData}. We see 1 event in the
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signal region (region $D$). For more information about
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this one candidate events, see Appendix~\ref{sec:cand}.
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The Standard Model MC expectation is 1.4 events.
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\subsection{Background estimate from the ABCD method}
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\label{sec:abcdres}
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The data yields in the
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four regions are summarized in Table~\ref{tab:datayield}.
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The prediction of the ABCD method is is given by $k_{ABCD} \times (A\times C/B)$ and
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is $1.8 \pm 1.0(stat) \pm 0.4(syst)$ events, where $k_{ABCD} = 1.2 \pm 0.2$ as discussed
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in Sec.~\ref{sec:abcd}.
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\begin{table}[hbt]
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\begin{center}
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\caption{\label{tab:datayield} Data yields in the four
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regions of Figure~\ref{fig:abcdData}, as well as the predicted yield in region D given
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by A $\times$C / B. The quoted uncertainty
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on the prediction in data is statistical only, assuming Gaussian errors.
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We also show the SM Monte Carlo expectations, scaled to 34.85~pb$^{-1}$.}
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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 & A $\times$ C / B \\
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\hline
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$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 7.96 & 33.07 & 4.81 & 1.20 & 1.16 \\
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$t\bar{t}\rightarrow \mathrm{other}$ & 0.15 & 0.85 & 0.09 & 0.04 & 0.02 \\
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$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.03 & 1.47 & 0.10 & 0.10 & 0.00 \\
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$W^{\pm}$ + jets & 0.00 & 0.10 & 0.00 & 0.00 & 0.00 \\
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$W^+W^-$ & 0.19 & 0.29 & 0.02 & 0.07 & 0.02 \\
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$W^{\pm}Z^0$ & 0.03 & 0.04 & 0.01 & 0.01 & 0.00 \\
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$Z^0Z^0$ & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 \\
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single top & 0.28 & 1.00 & 0.04 & 0.01 & 0.01 \\
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\hline
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total SM MC & 8.63 & 36.85 & 5.07 & 1.43 & 1.19 \\
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\hline
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data & 11 & 36 & 5 & 1 & $1.53 \pm 0.86$ \\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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%As a cross-check, we can subtract from the yields in
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%Table~\ref{tab:datayield} the expected DY contributions
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%from Table~\ref{tab:ABCD-DY} in order to get a ``purer''
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%estimate of the $t\bar{t}$ contribution. The result
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%of this exercise is {\color{red} xx} events.
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%\clearpage
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\subsection{Background estimate from the $P_T(\ell\ell)$ method}
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\label{sec:victoryres}
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We first use the $P_T(\ell \ell)$ method to predict the number of events
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in control region A, defined in Sec.~\ref{sec:abcd} as
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$125<{\rm SumJetPt}>300$~GeV and $\met/\sqrt{\rm SumJetPt}>$8.5~GeV$^{1/2}$.
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We count the number of events in region
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$A'$, defined in Sec.~\ref{sec:othBG} by replacing the above $\met/\sqrt{\rm SumJetPt}$
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cut with the same cut on the quantity $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$,
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and find $N_{A'}=6$. We subtract off the expected DY contribution in this region
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$N_{DY} = 2.5 \pm 2.4$, derived in Sec.~\ref{sec:othBG}.
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To predict the yield in region A we take
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$N_A = K \cdot K_C \cdot ( N_{A'} - N_{DY} ) = 6.1 \pm 6.0$
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(statistical uncertainty only, assuming Gaussian errors),
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where we have taken $K = 1.73$ and $K_C = 1$. This yield is consistent
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with the observed yield of 11 events, as shown in
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Table~\ref{tab:victory_control} and displayed in Fig.~\ref{fig:victory} (left).
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Encouraged by the good agreement between predicted and observed yields
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in the control region, we proceed to perform the $P_T(\ell \ell)$ method
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in the signal region ${\rm SumJetPt}>300$~GeV.
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The number of data events in region $D'$, which is defined in
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Section~\ref{sec:othBG} to be the same as region $D$ but with the
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$\met/\sqrt{\rm SumJetPt}$ requirement
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replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement,
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is $N_{D'}=2$.
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We next subtract off the expected DY contribution of
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$N_{DY}$ = $0.4 \pm 0.4$ events, as calculated
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in Sec.~\ref{sec:othBG}. The BG prediction is
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$N_D = K \cdot K_C \cdot (N_{D'}-N_{DY}) = 2.5 \pm 2.2$ (statistical
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uncertainty only, assuming Gaussian errors), where $K=1.54 \pm xx$
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as derived in Sec.~\ref{sec:victory} and $K_C = 1$.
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This prediction is consistent with the observed yield of
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1 event, as summarized in Table~\ref{tab:victory_signal} and Fig.~\ref{fig:victory}
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(right).
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.48\linewidth]{victory_control_35pb.png}
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\includegraphics[width=0.48\linewidth]{victory_signal_35pb.png}
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\caption{\label{fig:victory}\protect Distributions of
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tcMet/$\sqrt{\rm SumJetPt}$ for the control and signal region.
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We show the oberved distributions in both Monte Carlo and data.
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We also show the distributions predicted from
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${P_T(\ell\ell)}/\sqrt{\rm SumJetPt}$ in both MC and data.}
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\end{center}
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\end{figure}
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\begin{table}[hbt]
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\begin{center}
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\caption{\label{tab:victory_control}Results of the dilepton $p_{T}$ template method in the control region
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$125 < \mathrm{sumJetPt} < 300$~GeV$^{1/2}$. The predicted and observed yields for
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the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data
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and MC. The error on the prediction for data is statistical only, assuming
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Gaussian errors.}
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\begin{tabular}{lccc}
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\hline
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& Predicted & Observed & Obs/Pred \\
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\hline
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total SM MC & 7.18 & 8.63 & 1.20 \\
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data & $6.06 \pm 5.95$ & 11 & 1.82 \\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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\begin{table}[hbt]
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\begin{center}
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\caption{\label{tab:victory_signal}Results of the dilepton $p_{T}$ template method in the signal region
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$\mathrm{sumJetPt} > 300$~GeV$^{1/2}$. The predicted and observed yields for
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the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data
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and MC. The error on the prediction for data is statistical only, assuming
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Gaussian errors.}
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\begin{tabular}{lccc}
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\hline
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& Predicted & Observed & Obs/Pred \\
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\hline
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total SM MC & 1.03 & 1.43 & 1.38 \\
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data & $2.53 \pm 2.25$ & 1 & 0.40 \\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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% \clearpage
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\subsection{Summary of results}
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In summary, in the signal region defined as $\mathrm{SumJetPt}>300$~GeV and $\met/\sqrt{\rm SumJetPt} > 8.5$~GeV$^{1/2}$:\\
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We observe 1 event. \\
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We expect 1.4 events from Standard Model MC prediction. \\
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The ABCD data driven method predicts $1.8 \pm 1.0(stat) \pm 0.4(syst)$ events. \\
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The $P_T(\ell\ell)$ method predicts $2.5 \pm 2.2$ events.
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All three background estimates are consistent within their uncertainties.
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We thus take as our best estimate of the Standard Model yield in
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the signal region the MC prediction and assign as an uncertainty the
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maximal deviation with either of the data-driven methods, $N_{BG}=1.4 \pm 1.1$.
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We conclude that we see no evidence for an anomalous
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rate of opposite sign isolated dilepton events
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at high \met and high SumJetPt. The extraction of
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quantitative limits on new physics models is discussed
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in Section~\ref{sec:limit}. |
