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This category of backgrounds includes processes with a single leptonic \W~decay, giving rise to one lepton and \met\ from a single neutrino.
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As a result, the \mt\ variable, constructed from the lepton and the \met, exhibits a kinematic edge at $\mt \sim \mW$. The main contributors
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to this background are \ttlj, \wjets\ and single top, though in the latter case there is a contribution from \tw\ that can give rise to two leptons.
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As shown in Figure.~\ref{fig:mtsinglelepcomp} (left), these backgrounds exhibit a similar \mt\ shape and are thus combined into a single
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background estimate.
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It should be underlined that single lepton events entering the signal sample are in the far \mt~tail for these processes
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and contribute mainly due to the \met\ resolution that smears the \mt\ peak, particularly in the presence of multiple jets.
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Since these types of effects are challenging to model in simulation, the background estimate for this category of processes is cross checked
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in a control sample in data. The control sample is obtained by applying the full selection criteria with the exception of the b-tagging requirement,
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that is reversed, vetoing events with b-tagged jets. The b-tag veto greatly reduces the contamination from \ttbar, which is particularly important
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in the case of \ttll\ which otherwise populates the \mt\ tail. The resulting sample is dominated by \wjets\ events. The derivation of the background
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estimate in this control sample serves to validate the method.
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In addition, the level of agreement between the prediction and the data in the \mt\ tail provides an estimate of the systematic uncertainty for this
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background prediction.
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/mt_singlelepcomp_full.png}%
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\includegraphics[width=0.5\linewidth]{plots/mt_bkgsubt_bveto_met50.png}
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\caption{
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\label{fig:mtsinglelepcomp}%\protect
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Monte Carlo comparison of the shapes (left) of the \mt\ distribution for the main background processes containing a single leptonic \W\ decay (left).
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The \mt\ shape for \ttlj, \wjets\ and single top are similar and thus combined into a single background estimate. Comparison of the MC
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prediction (right) for single lepton processes (blue) and the data after subtracting the non-single lepton background MC prediction (also shown in red).
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The \mt\ distribution in MC is scaled to the data in the \mt\ peak region ($60-100~\GeV$). Since the control sample is dominated by $\Wfourj$ events,
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the MC is not expected to provide an estimate of the overall normalization to better than the $\sim 15\%$ difference observed.}
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\end{center}
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\end{figure}
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The single lepton background contribution to the tail of the \mt\ is derived from MC and normalized to the data in the \mt\ peak region, defined by the
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range $60 < \mt \le 100~\GeV$. In particular, the total yield for the combination of the single lepton + jets samples in MC satisfying $60 < \mt \le 100~\GeV$
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is scaled to match the entries in data satisfying the same \mt\ requirement. The data is corrected for the expected contamination from non-single
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lepton + jets processes, which is obtained from MC. The derivation of this MC to data scale factor is shown in Figure.~\ref{fig:mtsinglelepcomp} (right), where the
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contribution from non-single lepton + jets processes in the \mt\ peak is also shown to be small.
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Scaling to the data yield in the \mt\ peak largely reduces the dependence on the \ttbar\ cross section and cancels systematic uncertainties associated with
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effects such as the luminosity, selection efficiencies, etc$\dots$
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\begin{figure}[!ht]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/mt_met50_bveto.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/mt_met100_bveto.pdf}
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\caption{
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\label{fig:mtbveto}%\protect
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Comparison of data and MC in the b-veto sample after scaling the single lepton samples in the \mt\ peak region ($60-100~\GeV$) for two \met\ requirements
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$\met>50~\GeV$ (left) and $\met>100~\GeV$ (right). The simulation shows reasonable agreement with the data both in the peak and the \mt\ tail, as can also
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be seen the ratios.}
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\end{center}
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\end{figure}
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\begin{figure}[!hb]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/mt_singlelepcomp_full_stack.png}%
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\includegraphics[width=0.5\linewidth]{plots/bkg_comp_err_mt_met100.png}
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\caption{
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\label{fig:mtsamplecomperr}%\protect
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Stacked plot (left) showing the relative sample composition in MC for the main single lepton + jets components, \ttlj, \wjets\ and single top
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sample for the b-veto control selection. Note no scalings are applied and the $\met>50~\GeV$ is shown. Percent change in the total single lepton + jets
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background prediction for variations in the normalization of each single lepton + jets background component (right). Each sample is varied independently and the
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full background prediction is performed.}
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\end{center}
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\end{figure}
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\begin{table}[!ht]
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\begin{center}
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\begin{tabular}{c|c|c}
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\hline
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Sample & $\met>50~\GeV$ & $\met>100~\GeV$ \\
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\hline
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\hline
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Lepton + Jets Prediction & $88 \pm 12$ & $38 \pm 8$ \\
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Data in Signal Region & $106 \pm 13$ & $40 \pm 8$ \\
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\hline
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Data/MC Closure & $1.20 \pm 0.22$ & $1.03 \pm 0.30$ \\
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\hline
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\end{tabular}
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\caption{Summary of closure test in b-veto control sample for two values of the \met\ requirement. The closure serves to estimate the systematic uncertainty for
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the prediction of the single lepton + jets background.\label{tab:ljetsclosure}}
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\end{center}
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\end{table}
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Figure~\ref{fig:mtbveto} shows a comparison of the \mt\ distribution in data and MC in the b-veto control sample for two values of the \met\ cut after scaling
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the single lepton contribution to the \mt\ peak region. The simulation models the \mt\ distribution in data reasonably well. Table~\ref{tab:ljetsclosure} shows
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a comparison of the single lepton + jets prediction and the data in the $\mt>150~\GeV$ region. The prediction and the data are in agreement
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within the statistical uncertainty, which is $30 \%$ for the $\met>100~\GeV$ case. No correction is necessary given the agreement observed and the uncertainty
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serves as an estimate of the systematic uncertainty on the lepton + jets background. It may be noted that the $30\%$ uncertainty applies to the lepton + jets
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background, which constitues $15\%$ of the sample. The resulting uncertainty on the total background is $\approx5\%$, within our uncertainty budget of $\approx10\%$.
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Given the similarities in the shapes of the \mt\ distributions for the various samples, the resulting dependence on the sample composition is small.
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Figure.~\ref{fig:mtsamplecomperr} shows the \mt\ distribution for the single lepton + jets components in MC. The distribution on the right shows the impact of
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varying the relative sample composition on the total single lepton + jets prediction. In this study, each component is varied independently by up to $20\%$ and
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the corresponding change on the prediction is at the level of a few percent and therefore negligible compared to the statistical uncertainty of the closure test.
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It should be noted that despite differences in the \mt\ shape for the various single lepton + jets processes, expected for example due to differences in the \pt\ of the \W,
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this test provides a check for the impact of reconstruction effects, such as the \met\ resolution, that are the dominant contributors to the tail of the \mt\ and similar
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for the \ttlj\ and \wjets\ processes.
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