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\subsection{Single Lepton Top MC Modelling Validation from CR2}
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\label{sec:cr2}
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The \mt\ tail for single-lepton top events (\ttsl\ and single top) is dominated by jet resolution effects. The \W\ cannot be far off-shell because $\mW < \mtop$.
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The modeling of the \mt\ tail from jet resolution effects can be studied
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using \zjets\ data and MC samples. However, as we will show below,
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this test is statistically limited and can only be performed for the
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\met\ requirements corresponding to SRA and SRB.
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\Z\ events are selected by requiring exactly 2 good leptons (satisfying ID
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and isolation requirements) and requiring the \mll\ to be in the range
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$81-101$ GeV.
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Events with additional isolated tracks are vetoed, as in Section~\ref{sec:tkveto}.
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To reduce \ttbar\ backgrounds, events with a CSVM tag %H
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are removed.
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The positive lepton is treated as a neutrino and so is added to the MET: \met\ $\rightarrow$ \pt(\Lepp) + \met,
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and the \mt\ is recalculated with the negative lepton: \mt(\Lepm, \met).
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The resulting ``pseudo-\mt'' is dominated by jet resolution effects, since no off-shell
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\Z\ production enters the sample due to the \mll\ requirement.
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This section describes how well the MC predicts the tail of ``pseudo-\mt''.
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The underlying distributions are shown in Fig.~\ref{fig:cr2met}.
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%and~\ref{fig:cr2mtrest}.
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We then perform the exact same type of Data/MC comparison and analysis as
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described for CR1 in Section~\ref{sec:cr1}. For CR1 we collected
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the data/MC tail information in
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Table~\ref{tab:cr1yields}; the equivalent for CR2 is
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Table~\ref{tab:cr2yields} (for CR2 the statistics are not sufficient to split electrons and muons).
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The last line of Table~\ref{tab:cr2yields} gives the data/MC scale factors
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for the \ttbar\ lepton $+$ jets $M_T$ tail ($SFR_{top}$). This is
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calculated in the same way as $SFR_{wjets}$ of Table~\ref{tab:cr1yields}.
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Just as in CR1, there is an excess of data in the tails, as reflected
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in the values of $SFR_{top}$. There are insufficient events to derive scale factors for
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$\met\ > 150$~GeV. As a result, the scale factors derived from CR2 are
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not used for the central prediction of the single-lepton top
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background. They serve as a valuable cross check of the predictions
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described in Section~\ref{sec:ttp}. The single lepton top predictions
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obtained for SRA and SRB using the $SFR_{top}$ values described here
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are consistent with the default predictions.
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\begin{table}[!h]
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\begin{center}
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{\footnotesize
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\begin{tabular}{l||c|c||c|c}
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\hline
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Sample & CR2PRESEL0 &CR2PRESEL1 & CR2A & CR2B \\
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\hline
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\hline
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MC & $32 \pm 2$ & $28 \pm 2$ & $10 \pm 1$ & $10 \pm 1$ \\
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Data & $50$ & $45$ & $17$ & $17$ \\
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\hline
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Data/MC & $1.56 \pm 0.24$ & $1.63 \pm 0.27$ & $1.68 \pm 0.45$ & $1.74 \pm 0.48$ \\
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\hline
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\hline
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\hline
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DY MC & $25 \pm 2$ & $20 \pm 2$ & $5 \pm 1$ & $5 \pm 1$ \\
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DY Data & $42 \pm 7$ & $38 \pm 7$ & $12 \pm 4$ & $12 \pm 4$ \\
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\hline
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DY Data/MC & $1.73 \pm 0.32$ & $1.85 \pm 0.37$ & $2.37 \pm 0.96$ & $2.58 \pm 1.16$ \\
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\hline
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\hline
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\hline
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$SFR_{top}$ & $1.64 \pm 0.40$ & $1.74 \pm 0.46$ & $2.02 \pm 0.68$ & $2.16 \pm 0.75$ \\
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\hline
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\end{tabular}}
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\caption{ Yields in \mt\ tail comparing the \zjets\ MC prediction (after
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applying SFs) to data without subtracting the non-\zjets\ components (top table) and with subtracting the non-\zjets\ components (bottom table).
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CR2PRESEL refers to a sample with $\met>50$ GeV and $\mt>150$ GeV.
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\label{tab:cr2yields}}
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\end{center}
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\end{table}
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%\hline
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%$N_{1l-top}$ SF & - & - & $172 \pm 58$ & $119 \pm 42$ \\
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%\hline
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%$N_{1l-top}$ Opt/Pess & - & - & $256 \pm 131$ & $120 \pm 50$ \\
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\begin{figure}[hbt]
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\begin{center}
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% \includegraphics[width=0.5\linewidth]{plots/CR2plots/met_scaled_nj4_emucomb.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR2plots/met_lepcor_scaled_nj4_emucomb.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR2plots/mt_lepcor_scaled_nj4_emucomb.pdf}
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\includegraphics[width=0.5\linewidth]{plots/CR2plots/mt_lepcor_scaled_met50_nj4_emucomb.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR2plots/mt_lepcor_scaled_met100_nj4_emucomb.pdf}
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\caption{
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Comparison of the pseudo-\met\ (top, left), pseudo-\mt\ (top,
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right and bottom) distributions in data vs. MC for events
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satisfying the requirements of CR2, combining both the muon and
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electron channels. The pseudo-\mt\ distributions are shown
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before any additional requirements (top, right) and after
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requiring pseudo-\met $>$50 GeV (bottom, left) and pseudo-\met
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$>$ 100 GeV (bottom, right).
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\label{fig:cr2met}
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}
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\end{center}
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\end{figure}
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%\begin{figure}[hbt]
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% \begin{center}
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% \includegraphics[width=0.5\linewidth]{plots/CR2plots/mt_lepcor_scaled_met150_nj4_emucomb.pdf}%
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% \includegraphics[width=0.5\linewidth]{plots/CR2plots/mt_lepcor_scaled_met200_nj4_emucomb.pdf}
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% \includegraphics[width=0.5\linewidth]{plots/CR2plots/mt_lepcor_scaled_met250_nj4_emucomb.pdf}%
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% \includegraphics[width=0.5\linewidth]{plots/CR2plots/mt_lepcor_scaled_met300_nj4_emucomb.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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% satisfying the requirements of CR2, combining both the muon and
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% electron channels. The pseudo-\met\ requirements used are
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% 150 GeV (top, left), 200 GeV (top, right), 250 GeV (bottom,
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% left) and 300 GeV (bottom, right).
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%\label{fig:cr2mtrest}
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%}
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% \end{center}
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%\end{figure}
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\clearpage
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