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\subsection{Dilepton studies in CR4} |
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\label{sec:cr4} |
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[DO WE NEED TO BETTER SPECIFY THE SELECTION FOR THIS REGION???] |
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\subsubsection{Modeling of Additional Hard Jets in Top Dilepton Events} |
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\label{sec:jetmultiplicity} |
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[THIS SUBSUBSECTION IS DONE...MODULO THE LATEST PLOTS AND THE LATEST |
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NUMBERS IN THE TABLE] |
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Dilepton \ttbar\ events have 2 jets from the top decays, so additional |
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jets from radiation or higher order contributions are required to |
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enter the signal sample. The modeling of addtional jets in \ttbar\ |
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enter the signal sample. In this Section we develop an algorithm |
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to be applied to all \ttll\ MC samples to insure that the distribution |
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of extra jets is properly modelled. |
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The modeling of additional jets in \ttbar\ |
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events is checked in a \ttll\ control sample, |
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selected by requiring |
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\begin{itemize} |
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\item exactly 2 selected electrons or muons with \pt $>$ 20 GeV |
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\item \met\ $>$ 100 GeV |
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\item \met\ $>$ 50 GeV |
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\item $\geq1$ b-tagged jet |
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\item Z-veto |
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\item Z-veto ($|m_{\ell\ell} - 91| > 15$ GeV) |
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\end{itemize} |
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Figure~\ref{fig:dileptonnjets} shows a comparison of the jet |
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multiplicity distribution in data and MC for this two-lepton control |
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\begin{figure}[hbt] |
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\begin{center} |
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\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_mueg.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_diel.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/njets_all_met100_dimu.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu.pdf} |
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\caption{ |
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\label{fig:dileptonnjets}%\protect |
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Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\ |
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In this case only 1 additional jet from radiation may suffice for |
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a \ttll\ event to enter the signal sample. As a result, both the |
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samples with $\ttbar+1$ jet and $\ttbar+\ge2$ jets are relevant for |
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estimating the top dilepton bkg in the signal region. |
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estimating the top dilepton background in the signal region. |
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%In this section we discuss a correction to $ N_{2 lep}^{MC} $ in Equation XXX |
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%due to differences in the modelling of the jet multiplicity in data versus MC. |
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in data. These scale factors are calculated from Fig.~\ref{fig:dileptonnjets} |
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as follows: |
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\begin{itemize} |
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\item $N_{2}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\leq$ 2 |
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\item $N_{2}=$ data yield minus non-dilepton \ttbar\ MC yield for |
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\njets\ =1 or 2. |
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\item $N_{3}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ = 3 |
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\item $N_{4}=$ data yield minus non-dilepton \ttbar\ MC yield for \njets\ $\geq$ 4 |
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\item $M_{2}=$ dilepton \ttbar\ MC yield for \njets\ $\leq$ 2 |
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\item $M_{2}=$ dilepton \ttbar\ MC yield for \njets\ = 1 or 2 |
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\item $M_{3}=$ dilepton \ttbar\ MC yield for \njets\ = 3 |
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\item $M_{4}=$ dilepton \ttbar\ MC yield for \njets\ $\geq$ 4 |
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\end{itemize} |
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\noindent This insures that $K_3 M_3/(M_2 + K_3 M_3 + K_4 M_4) = N_3 / |
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(N_2+N_3+N_4)$ and similarly for the $\geq 4$ jet bin. |
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Table~\ref{tab:njetskfactors} also shows the values of $K_3$ and $K_4$ when the \met\ cut in the control sample definition is changed from 50 GeV to 100 GeV and 150 GeV. |
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% These values of $K_3$ and $K_4$ are not used in the analysis, but |
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This demonstrate that there is no statistically significant dependence of $K_3$ and $K_4$ on the \met\ cut. |
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The factors $K_3$ and $K_4$ are applied to the \ttll\ MC throughout the |
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The factors $K_3$ and $K_4$ (derived with the 100 GeV \met\ cut) are applied to the \ttll\ MC throughout the |
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entire analysis, i.e. |
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whenever \ttll\ MC is used to estimate or subtract |
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a yield or distribution. |
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a yield or distribution. To be explicit, whenever Powheg is used, |
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the Powheg $K_3$ and $K_4$ are used; whenever default MadGraph is |
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used, the MadGraph $K_3$ and $K_4$ are used, etc. |
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% |
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In order to do so, it is first necessary to count the number of |
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additional jets from radiation and exclude leptons mis-identified as |
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\begin{table}[!ht] |
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\begin{center} |
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\begin{tabular}{l|c} |
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\begin{tabular}{l|c|c|c} |
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\cline{2-4} |
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& \multicolumn{3}{c}{ \met\ cut for data/MC scale factors} \\ |
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\hline |
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Jet Multiplicity Sample |
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& Data/MC Scale Factor \\ |
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Jet Multiplicity Sample & 50 GeV & 100 GeV & 150 GeV \\ |
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\hline |
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\hline |
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N jets $= 3$ (sensitive to $\ttbar+1$ extra jet from radiation) & |
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$K_3 = 0.97 \pm 0.03$\\ |
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N jets $= 3$ (sensitive to $\ttbar+1$ extra jet from radiation) |
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& $K_3 = 0.98 \pm 0.02$ & $K_3 = 1.01 \pm 0.03$ & $K_3 = 1.00 \pm 0.08$ \\ |
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N jets $\ge4$ (sensitive to $\ttbar+\ge2$ extra jets from radiation) |
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& $K_4 = 0.91 \pm 0.04$\\ |
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& $K_4 = 0.94 \pm 0.02$ & $K_4 = 0.93 \pm 0.04$ & $K_4 = 1.00 \pm 0.08$ \\ |
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\hline |
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\end{tabular} |
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\caption{Data/MC scale factors used to account for differences in the |
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fraction of events with additional hard jets from radiation in |
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\ttll\ events. \label{tab:njetskfactors}} |
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\ttll\ events. The values derived with the 100 GeV \met\ cut are applied |
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to the \ttll\ MC throughout the analysis. \label{tab:njetskfactors}} |
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\end{center} |
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\end{table} |
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\subsubsection{Validation of the ``Physics'' Modelling of the \ttdl\ |
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MC in CR4} |
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\subsubsection{sec:CR4-valid} |
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[THE TEXT IN THIS SUBSECTION IS ESSENTIALLY COMPLETE] |
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\label{sec:CR4-valid} |
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As mentioned above, $t\bar{t} \to $ dileptons where one of the leptons |
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is somehow lost constitutes the main background. |
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background by looking at the $M_T$ distribution of well identified |
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dilepton events. |
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We construct a transverse mass variable from the leading lepton and |
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the \met\. We distinguish between events with leading electrons and |
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the \met. We distinguish between events with leading electrons and |
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leading muons. |
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The $t\bar{t}$ MC is corrected using the $K_3$ and $K_4$ factors |
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in Table~\ref{tab:cr4mtsf} and are close to unity. |
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The underlying \met\ and $M_T$ distributions are shown in |
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Figures~\ref{fig:cr4met} and~\ref{fig:cr4rest}. The data-MC agreement |
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Figures~\ref{fig:cr4met} and~\ref{fig:cr4mtrest}. The data-MC agreement |
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is quite good. Quantitatively, this is also shown in Table~\ref{tab:cr4yields}. |
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This is a {\bf very} important Table. It shows that for well |
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identified \ttdl\ , the MC can predict the $M_T$ tail. Since the |
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main background is also \ttdl\ except with one ``missed'' lepton, |
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this is a key test. |
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\begin{table}[!h] |
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\begin{center} |
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\begin{tabular}{l||c|c|c|c} |
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{\footnotesize |
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\begin{tabular}{l||c||c|c|c|c|c|c} |
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\hline |
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Sample & CR4A & CR4B & CR4C & CR4D \\ |
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Sample & CR4PRESEL & CR4A & CR4B & CR4C & |
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CR4D & CR4E & CR4F\\ |
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\hline |
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\hline |
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Muon Data/MC-SF & $0.91 \pm 0.04$ & $0.94 \pm 0.07$ & $1.06 \pm 0.13$ & $1.03 \pm 0.22$ \\ |
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$\mu$ Data/MC-SF & $1.01 \pm 0.03$ & $0.96 \pm 0.04$ & $0.99 \pm 0.07$ & $1.05 \pm 0.13$ & $0.91 \pm 0.20$ & $1.10 \pm 0.34$ & $1.50 \pm 0.67$ \\ |
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\hline |
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\hline |
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Electron Data/MC-SF & $0.95 \pm 0.04$ & $1.00 \pm 0.08$ & $0.85 \pm 0.12$ & $0.83 \pm 0.19$ \\ |
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e Data/MC-SF & $0.99 \pm 0.03$ & $0.99 \pm 0.05$ & $0.91 \pm 0.08$ & $0.84 \pm 0.13$ & $0.70 \pm 0.18$ & $0.73 \pm 0.29$ & $0.63 \pm 0.38$ \\ |
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\hline |
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\end{tabular} |
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\end{tabular}} |
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\caption{ Data/MC scale factors for total yields, applied to compare |
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the shapes of the distributions. |
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The uncertainties are statistical only. |
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|
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\begin{table}[!h] |
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\begin{center} |
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\begin{tabular}{l||c|c|c|c} |
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{\footnotesize |
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\begin{tabular}{l||c||c|c|c|c|c|c} |
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\hline |
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Sample & CR4A & CR4B & CR4C & CR4D \\ |
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Sample & CR4PRESEL & CR4A & CR4B & CR4C & |
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CR4D & CR4E & CR4F\\ |
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\hline |
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\hline |
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Muon MC & $199 \pm 7$ & $102 \pm 6$ & $29 \pm 3$ & $8 \pm 1$ \\ |
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Muon Data & $187$ & $108$ & $34$ & $9$ \\ |
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$\mu$ MC & $256 \pm 14$ & $152 \pm 11$ & $91 \pm 9$ & $26 \pm 5$ & $6 \pm 2$ & $4 \pm 2$ & $2 \pm 1$ \\ |
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$\mu$ Data & $251$ & $156$ & $98$ & $27$ & $8$ & $6$ & $4$ \\ |
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\hline |
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Muon Data/MC SF & $0.94 \pm 0.08$ & $1.06 \pm 0.12$ & $1.17 \pm 0.23$ & $1.09 \pm 0.40$ \\ |
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$\mu$ Data/MC SF & $0.98 \pm 0.08$ & $1.02 \pm 0.11$ & $1.08 \pm 0.16$ & $1.04 \pm 0.28$ & $1.29 \pm 0.65$ & $1.35 \pm 0.80$ & $2.10 \pm 1.72$ \\ |
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\hline |
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\hline |
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Electron MC & $203 \pm 8$ & $97 \pm 5$ & $26 \pm 2$ & $8 \pm 1$ \\ |
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Electron Data & $201$ & $102$ & $25$ & $5$ \\ |
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e MC & $227 \pm 13$ & $139 \pm 11$ & $73 \pm 8$ & $21 \pm 4$ & $5 \pm 2$ & $2 \pm 1$ & $1 \pm 1$ \\ |
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e Data & $219$ & $136$ & $72$ & $19$ & $2$ & $1$ & $1$ \\ |
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\hline |
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Electron Data/MC SF & $0.99 \pm 0.08$ & $1.06 \pm 0.12$ & $0.97 \pm 0.21$ & $0.60 \pm 0.29$ \\ |
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e Data/MC SF & $0.96 \pm 0.09$ & $0.98 \pm 0.11$ & $0.99 \pm 0.16$ & $0.92 \pm 0.29$ & $0.41 \pm 0.33$ & $0.53 \pm 0.62$ & $0.76 \pm 0.96$ \\ |
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\hline |
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\end{tabular} |
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\hline |
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$\mu$+e MC & $483 \pm 19$ & $291 \pm 16$ & $164 \pm 13$ & $47 \pm 7$ & $11 \pm 3$ & $6 \pm 2$ & $3 \pm 2$ \\ |
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$\mu$+e Data & $470$ & $292$ & $170$ & $46$ & $10$ & $7$ & $5$ \\ |
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\hline |
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$\mu$+e Data/MC SF & $0.97 \pm 0.06$ & $1.00 \pm 0.08$ & $1.04 \pm 0.11$ & $0.99 \pm 0.20$ & $0.90 \pm 0.37$ & $1.11 \pm 0.57$ & $1.55 \pm 1.04$ \\ |
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\hline |
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\end{tabular}} |
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\caption{ Yields in \mt\ tail comparing the MC prediction (after |
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applying SFs) to data. The uncertainties are statistical only. |
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\label{tab:cr4yields}} |
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\begin{figure}[hbt] |
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\begin{center} |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met50_leadmuo_nj4.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met50_leadele_nj4.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met150_leadmuo_nj4.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met150_leadele_nj4.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met200_leadmuo_nj4.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met200_leadele_nj4.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met250_leadmuo_nj4.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/CR4plots/mt_met250_leadele_nj4.pdf} |
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\caption{ |
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Comparison of the \mt\ distribution in data vs. MC for events |
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with a leading muon (left) and leading electron (right) |
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satisfying the requirements of CR4. The \met\ requirements used are |
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150 GeV (top), 200 GeV (middle) and 250 GeV (bottom). |
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50 GeV (top), 200 GeV (middle) and 250 GeV (bottom). |
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\label{fig:cr4mtrest} |
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} |
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\end{center} |
