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\clearpage |
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\section{Results} |
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\label{sec:results} |
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%\noindent {\color{red} In the 11 pb everything is very |
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%simple because there are a few zeros. This text is written |
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%for the full dataset under the assumption that some of these |
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%numbers will not be zero anymore.} |
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\begin{figure}[tbh] |
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\begin{center} |
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\includegraphics[width=0.75\linewidth]{abcdData.png} |
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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 $\color{red} 0$ |
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events in the signal region (region $D$). The Standard Model |
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MC expectation is {\color{red} 0.4} events. |
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in Figure~\ref{fig:abcdData}. We see 1 event in the |
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signal region (region $D$). The Standard Model MC |
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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 $AC/B$ and |
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is 0.5 events. |
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(see Table~\ref{tab:datayield}. |
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The prediction of the ABCD method is is given by $A\times C/B$ and |
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is 1.5 $\pm$ 0.9 events (statistical uncertainty only, assuming |
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Gaussian errors), as shown in Table~\ref{tab:datayield}. |
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|
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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}. The quoted uncertainty |
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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.} |
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\begin{tabular}{|l|c|c|c|c||c|} |
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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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&A & B & C & D & AC/B \\ \hline |
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Data &3 & 6 & 1 & 0 & $0.5^{+0.6}_{-0.5}$ \\ |
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SM MC &2.5 &11.2 & 1.5 & 0.4 & 0.4 \\ |
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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 & $1.53\pm0.86$ \\ |
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\hline |
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\end{tabular} |
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\end{center} |
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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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|
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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}>$8.5. |
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We count the number of events in region |
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$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 $N_{D'}=1$. Thus the BG prediction is |
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$N_D = K \cdot K_C \cdot N_{D'} = 1.5$ |
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where $K=1.5 \pm xx$ as derived in Sec.~\ref{sec:victory} and |
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$K_C = 1$. |
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Note that if we were to subtract off from region $D'$ |
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the {\color{red} 0.4 $\pm$ 0.4} DY events estimated from |
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Section~\ref{sec:othBG}, the background |
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prediction would change to $N_D=0.9 \pm xx$ events. |
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|
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%%%TO BE REPLACED |
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%{\color{red}As mentioned previously, for the 11/pb analysis |
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%we use the $K$ factor from data and take $K=1$. |
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%This will change for the full dataset. We will also pay |
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%more attention to the statistical errors.} |
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|
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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 $N_{D'}=1$. Thus the BG prediction is |
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%$N_D = K \cdot K_{\rm fudge} \cdot N_{D'} = 1.5$ |
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%where we used $K=1.5 \pm xx$ and $K_{\rm fudge}=1.0 \pm 0.0$. |
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%Note that if we were to subtract off from region $D'$ |
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%the {\color{red} 0.4 $\pm$ 0.4} DY events estimated from |
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%Section~\ref{sec:othBG}, the background |
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%prediction would change to $N_D=0.9 \pm xx$ events. |
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%{\color{red} When we do this with a real |
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%$K_{\rm fudge}$, the fudge factor will be different |
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%after the DY subtraction.} |
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|
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As a cross-check, we use the $P_T(\ell \ell)$ |
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method to also predict the number of events in the |
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control region $120<{\rm SumJetPt}<300$ GeV and |
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\met/$\sqrt{\rm SumJetPt} > 8.5$. We predict |
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$5.6^{+x}_{-y}$ events and we observe 4. |
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The results of the $P_T(\ell\ell)$ method are |
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summarized in Figure~\ref{fig:victory}. |
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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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|
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\begin{figure}[hbt] |
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\begin{center} |
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\includegraphics[width=0.48\linewidth]{victory_control.png} |
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\includegraphics[width=0.48\linewidth]{victory_sig.png} |
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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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\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. 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 & 1.06 \\ |
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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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|
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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. 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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|
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\subsection{Summary of results} |
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To summarize: we see no evidence for an anomalous |
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rate of opposite sign isolated dilepton events |
