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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_jsonv3.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.}
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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 1.3 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 $A \times C / B = 1.3 \pm 0.8({\rm stat}) \pm 0.3({\rm syst})$.
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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 34.0~pb$^{-1}$.}
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\begin{tabular}{l||c|c|c|c||c}
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%%%official json v3 33.96/pb, 38X MC (D6T for ttbar and DY)
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\hline
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sample & A & B & C & D & PRED \\
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\hline
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$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 8.44 $\pm$ 0.18 & 32.83 $\pm$ 0.35 & 4.78 $\pm$ 0.14 & 1.07 $\pm$ 0.06 & 1.23 $\pm$ 0.05 \\
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$t\bar{t}\rightarrow \mathrm{other}$ & 0.12 $\pm$ 0.02 & 0.78 $\pm$ 0.05 & 0.16 $\pm$ 0.02 & 0.02 $\pm$ 0.01 & 0.02 $\pm$ 0.01 \\
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$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.17 $\pm$ 0.08 & 1.18 $\pm$ 0.22 & 0.04 $\pm$ 0.04 & 0.12 $\pm$ 0.07 & 0.01 $\pm$ 0.01 \\
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$W^{\pm}$ + jets & 0.00 $\pm$ 0.00 & 0.09 $\pm$ 0.09 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 \\
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$W^+W^-$ & 0.11 $\pm$ 0.01 & 0.29 $\pm$ 0.02 & 0.02 $\pm$ 0.01 & 0.03 $\pm$ 0.01 & 0.01 $\pm$ 0.00 \\
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$W^{\pm}Z^0$ & 0.01 $\pm$ 0.00 & 0.04 $\pm$ 0.00 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 \\
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$Z^0Z^0$ & 0.01 $\pm$ 0.00 & 0.02 $\pm$ 0.00 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 \\
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single top & 0.29 $\pm$ 0.01 & 1.04 $\pm$ 0.03 & 0.04 $\pm$ 0.01 & 0.01 $\pm$ 0.00 & 0.01 $\pm$ 0.00 \\
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\hline
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total SM MC & 9.14 $\pm$ 0.20 & 36.26 $\pm$ 0.43 & 5.05 $\pm$ 0.14 & 1.27 $\pm$ 0.10 & 1.27 $\pm$ 0.05 \\
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\hline
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data & 12 & 37 & 4 & 1 & 1.30 $\pm$ 0.78 \\
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\hline
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LM0 & 4.04 $\pm$ 0.19 & 4.45 $\pm$ 0.20 & 13.92 $\pm$ 0.36 & 8.63 $\pm$ 0.27 & 12.63 $\pm$ 0.88 \\
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LM1 & 0.52 $\pm$ 0.02 & 0.26 $\pm$ 0.02 & 1.64 $\pm$ 0.04 & 3.56 $\pm$ 0.06 & 3.33 $\pm$ 0.27 \\
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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 $N_{A'}=5$. We subtract off the expected DY contribution in this region
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$N_{DY} = 1.3 \pm 0.9$, derived in Sec.~\ref{sec:othBG}.
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To predict the yield in region A we take
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$N_A = K \cdot K_C \cdot ( N_{A'} - N_{DY} ) = 9.0 \pm 6.0$
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where we have taken $K = 1.7$ and $K_C = 1.4$.
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This uncertainty takes into account the statistical uncertainties in $N_{A'}$ and $N_{DY}$,
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assuming Gaussian errors. This yield is consistent
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with the observed yield of 12 events, as shown in
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Table~\ref{tab:victory} 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 $N_{D'}=1$.
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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}.
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The BG prediction is
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$N_D = K \cdot K_C \cdot (N_{D'}-N_{DY}) = 2.1 \pm 2.1({\rm stat}) \pm 0.6({\rm syst})$
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where $K=1.5$ as derived in Sec.~\ref{sec:victory} and $K_C = 1.4 \pm 0.4$.
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This prediction is consistent with the observed yield of 1 event, as summarized
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in Table~\ref{tab:victory} and Fig.~\ref{fig:victory} (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_jsonv3.png}
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\includegraphics[width=0.48\linewidth]{victory_signal_jsonv3.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}Results of the dilepton $p_{T}$ template method in the control region
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($125 < \mathrm{SumJetPt} < 300$~GeV) and signal region ($\mathrm{SumJetPt} > 300$~GeV). The predicted and
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observed yields for the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}} > 8.5$~GeV$^{1/2}$. The errors are
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statistical only, assuming Gaussian errors. Note that the correction factor $K_C$ has been applied to
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the data but not to the MC. }
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\begin{tabular}{l|cc|cc}
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\hline
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& Control Region & & Signal Region & \\
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\hline
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& Predicted & Observed & Predicted & Observed \\
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\hline
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total SM MC & 6.45 & 9.14 & 0.92 & 1.27 \\
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data & $9.0 \pm 6.0$ & 12 & $2.1 \pm 2.1$ & 1 \\
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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 1.3 events from Standard Model MC prediction. \\
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The ABCD data driven method predicts $1.3 \pm 0.8({\rm stat}) \pm 0.3({\rm syst})$ events. \\
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The $P_T(\ell\ell)$ method predicts $2.1 \pm 2.1({\rm stat}) \pm 0.6({\rm syst})$ 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 average of the predicted yields from the 2 data-driven methods,
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weighted by their uncertainties.
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This procedure gives an expected background yield $N_{BG}=1.4 \pm 0.8$.
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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}. |
