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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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The first one exploits 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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from $W$-decays, which is reconstructed as \met in the |
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detector. |
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|
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In 30 pb$^{-1}$ we expect $\approx$ 1 SM event in |
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In 35 pb$^{-1}$ we expect 1.4 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 5.6 and |
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2.2 events respectively. |
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and LM1 SUSY benchmark points are 6.5 and |
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2.6 events respectively. |
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%{\color{red} I took these |
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%numbers from the twiki, rescaling from 11.06 to 30/pb. |
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%They seem too large...are they really right?} |
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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 are 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\%. {\color{red} Avi wants some statement about stability |
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wrt changes in regions. I am not sure that we have done it and |
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I am not sure it is necessary (Claudio).} |
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luminosity of 35 pb$^{-1}$. The ABCD method is accurate |
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to about 20\%. |
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%{\color{red} Avi wants some statement about stability |
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%wrt changes in regions. I am not sure that we have done it and |
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%I am not sure it is necessary (Claudio).} |
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|
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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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35 pb$^{-1}$ in the ABCD regions, as well as the predicted yield in |
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the signal region given by A$\times$C/B. Here 'SM other' is the sum |
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of non-dileptonic $t\bar{t}$ decays, $W^{\pm}$+jets, $W^+W^-$, |
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$W^{\pm}Z^0$, $Z^0Z^0$ and single top.} |
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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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$Z^0$ + jets & 0.00 & 1.16 & 0.08 & 0.08 & 0.00 \\ |
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SM other & 0.65 & 2.31 & 0.17 & 0.14 & 0.05 \\ |
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\hline |
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total SM MC & 8.61 & 36.54 & 5.05 & 1.41 & 1.19 \\ |
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\hline |
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Sample & A & B & C & D & AC/D \\ \hline |
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ttdil & 6.9 & 28.6 & 4.2 & 1.0 & 1.0 \\ |
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Zjets & 0.0 & 1.3 & 0.1 & 0.1 & 0.0 \\ |
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Other SM & 0.5 & 2.0 & 0.1 & 0.1 & 0.0 \\ \hline |
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total MC & 7.4 & 31.9 & 4.4 & 1.2 & 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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|
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|
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Monte Carlo studies give values of $K$ that are typically between 1.5 and 1.6, |
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depending on selection details. |
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depending on selection details. |
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%%%TO BE REPLACED |
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%Given the integrated luminosity of the |
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%present dataset, the determination of $K$ in data is severely statistics |
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%limited. Thus, we take $K$ from $t\bar{t}$ Monte Carlo as |
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|
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%\begin{center} |
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%$ K_{MC} = \frac{\int_0^{\infty} {\cal N}(\met)~~d\met~}{\int_{50}^{\infty} {\cal N}(\met)~~d\met~}$ |
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%\end{center} |
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|
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%\noindent {\color{red} For the 11 pb result we have used $K$ from data.} |
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|
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There are several effects that spoil the correspondance between \met and |
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$P_T(\ell\ell)$: |
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An additional source of concern is that the CMS Madgraph $t\bar{t}$ MC does |
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not include effects of spin correlations between the two top quarks. |
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We have studied this effect at the generator level using Alpgen. We find |
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that the bias is a the few percent level. |
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that the bias is at the few percent level. |
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|
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%%%TO BE REPLACED |
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%Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
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%naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
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%be corrected by a factor of {\color{red} $ K_{\rm{fudge}} =1.2 \pm 0.3$ |
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%(We still need to settle on thie exact value of this. |
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%For the 11 pb analysis it is taken as =1.)} . The quoted |
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%uncertainty is based on the stability of the Monte Carlo tests under |
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%variations of event selections, choices of \met algorithm, etc. |
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%For example, we find that observed/predicted changes by roughly 0.1 |
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%for each 1.5\% change in the average \met response. |
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|
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Based on the results of Table~\ref{tab:victorybad}, we conclude that the |
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naive data driven background estimate based on $P_T{(\ell\ell)}$ needs to |
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be corrected by a factor of {\color{red} $1.2 \pm 0.3$ (We need to talk |
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about this)} . The quoted |
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uncertainty is based on the stability of the Monte Carlo tests under |
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be corrected by a factor of $ K_C = X \pm Y$. |
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The value of this correction factor as well as the systematic uncertainty |
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will be assessed using 38X ttbar madgraph MC. In the following we use |
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$K_C = 1$ for simplicity. Based on previous MC studies we foresee a correction |
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factor of $K_C \approx 1.2 - 1.5$, and we will assess an uncertainty |
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based on the stability of the Monte Carlo tests under |
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variations of event selections, choices of \met algorithm, etc. |
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For example, we find that observed/predicted changes by roughly 0.1 |
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for each 1.5\% change in the average \met response. |
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|
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|
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|
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|
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The LM points are benchmarks for SUSY analyses at CMS. The effects |
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of signal contaminations for a couple such points are summarized |
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in Table~\ref{tab:sigcontABCD} and~\ref{tab:sigcontPT}. |
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Signal contamination is definitely an important |
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in Table~\ref{tab:sigcont}. Signal contamination is definitely an important |
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effect for these two LM points, but it does not totally hide the |
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presence of the signal. |
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|
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|
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\begin{table}[htb] |
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\begin{center} |
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\caption{\label{tab:sigcontABCD} Effects of signal contamination |
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for the background predictions of the ABCD method including LM0 or |
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LM1. Results |
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are normalized to 30 pb$^{-1}$.} |
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\begin{tabular}{|c||c|c||c|c|} |
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\hline |
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SM & LM0 & BG Prediction & LM1 & BG Prediction \\ |
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Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline |
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1.2 & 5.6 & 3.7 & 2.2 & 1.3 \\ |
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\caption{\label{tab:sigcont} Effects of signal contamination |
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for the two data-driven background estimates. The three columns give |
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the expected yield in the signal region and the background estimates |
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using the ABCD and $P_T(\ell \ell)$ methods. Results are normalized to 35~pb$^{-1}$.} |
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\begin{tabular}{lccc} |
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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}[htb] |
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\begin{center} |
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\caption{\label{tab:sigcontPT} Effects of signal contamination |
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for the background predictions of the $P_T(\ell\ell)$ method including LM0 or |
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LM1. Results |
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are normalized to 30 pb$^{-1}$. {\color{red} Does this BG prediction include |
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the fudge factor of 1.4 or watever because the method is not perfect.}} |
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\begin{tabular}{|c||c|c||c|c|} |
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\hline |
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SM & LM0 & BG Prediction & LM1 & BG Prediction \\ |
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Background & Contribution& Including LM0 & Contribution & Including LM1 \\ \hline |
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1.2 & 5.6 & 2.2 & 2.2 & 1.5 \\ |
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& Yield & ABCD & $P_T(\ell \ell)$ \\ |
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\hline |
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SM only & 1.41 & 1.19 & 0.96 \\ |
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SM + LM0 & 7.88 & 4.24 & 2.28 \\ |
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SM + LM1 & 3.98 & 1.53 & 1.44 \\ |
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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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|
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|
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%\begin{table}[htb] |
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%\begin{center} |
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%\caption{\label{tab:sigcontABCD} Effects of signal contamination |
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%for the background predictions of the ABCD method including LM0 or |
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%LM1. Results |
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%are normalized to 30 pb$^{-1}$.} |
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%\begin{tabular}{|c|c||c|c||c|c|} |
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%\hline |
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%SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\ |
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%Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline |
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%1.2 & 1.0 & 6.8 & 3.7 & 3.4 & 1.3 \\ |
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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}[htb] |
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%\begin{center} |
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%\caption{\label{tab:sigcontPT} Effects of signal contamination |
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%for the background predictions of the $P_T(\ell\ell)$ method including LM0 or |
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%LM1. Results |
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%are normalized to 30 pb$^{-1}$.} |
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%\begin{tabular}{|c|c||c|c||c|c|} |
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%\hline |
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%SM & BG Prediction & SM$+$LM0 & BG Prediction & SM$+$LM1 & BG Prediction \\ |
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%Background & SM Only & Contribution & Including LM0 & Contribution & Including LM1 \\ \hline |
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%1.2 & 1.0 & 6.8 & 2.2 & 3.4 & 1.5 \\ |
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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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|
