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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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|
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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 additional 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 ensure that the distribution |
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of extra jets is properly modelled. |
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|
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|
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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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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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|
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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 demonstrate that there is no statistically significant dependence of $K_3$ and $K_4$ on the \met\ cut. |
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Table~\ref{tab:njetskfactors} also shows the values of $K_3$ and $K_4$ for different values of the \met\ cut in the control sample definition. |
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% These values of $K_3$ and $K_4$ are not used in the analysis, but |
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This demonstrates that there is no statistically significant dependence of $K_3$ and $K_4$ on the \met\ cut. |
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|
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|
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The factors $K_3$ and $K_4$ (derived with the 50 GeV \met\ cut) 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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|
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\begin{table}[!ht] |
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\begin{center} |
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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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{\footnotesize |
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\begin{tabular}{l|c|c|c|c|c|c} |
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\cline{2-7} |
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& \multicolumn{6}{c}{ \met\ cut for data/MC scale factors} \\ |
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\hline |
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Jet Multiplicity Sample & 50 GeV & 100 GeV & 150 GeV \\ |
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Sample & 50 GeV & 100 GeV & 150 GeV & 200 GeV & 250 GeV & 300 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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& $K_3 = 0.98 \pm 0.02$ & $K_3 = 1.01 \pm 0.03$ & $K_3 = 1.00 \pm 0.08$ \\ |
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N jets $\ge4$ (sensitive to $\ttbar+\ge2$ extra jets from radiation) |
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& $K_4 = 0.94 \pm 0.02$ & $K_4 = 0.93 \pm 0.04$ & $K_4 = 1.00 \pm 0.08$ \\ |
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N jets $= 3$ |
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& $K_3 = 0.98 \pm 0.02$ & $K_3 = 1.01 \pm 0.03$ & $K_3 = 1.00 \pm 0.08$ & $K_3 = 1.03 \pm 0.18$ & $K_3 = 1.29 \pm 0.51$ & $K_3 = 1.58 \pm 1.23$ \\ |
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N jets $\ge4$ |
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& $K_4 = 0.94 \pm 0.02$ & $K_4 = 0.93 \pm 0.04$ & $K_4 = 1.00 \pm 0.08$ & $K_4 = 1.07 \pm 0.18$ & $K_4 = 1.30 \pm 0.48$ & $K_4 = 1.65 \pm 1.19$ \\ |
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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 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. The values derived with the 50 GeV \met\ cut are applied |
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\ttll\ events. |
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The N jets $= 3$ scale factor, $K_3$, is sensitive to $\ttbar+1$ extra jet from radiation, while |
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the N jets $\ge4$ scale factor, $K_4$, is sensitive to $\ttbar+\ge2$ extra jets from radiation. |
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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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MC in CR4} |
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\label{sec:CR4-valid} |
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|
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[THE TEXT IN THIS SUBSECTION IS ESSENTIALLY COMPLETE] |
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|
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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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The object of this test is to validate the $M_T$ distribution of this |
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|
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The $t\bar{t}$ MC is corrected using the $K_3$ and $K_4$ factors |
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from Section~\ref{sec:jetmultiplicity}. It is also normalized to the |
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total data yield separately for the \met\ requirements of signal |
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regions A, B, C, and D. These normalization factors are listed |
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total data yield separately for the \met\ requirements of the various signal |
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regions. These normalization factors are listed |
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in Table~\ref{tab:cr4mtsf} and are close to unity. |
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|
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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: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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|
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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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|
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\begin{table}[!h] |
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\begin{center} |
