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\section{Systematic uncertainties on the background prediction}
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\label{sec:syst}
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This section summarizes the systematic uncertainties on the predicted
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backgrounds from \ttbar, both in the semileptonic and dileptonic decay
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modes, and from rare processes.
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For each signal region, the dominant \ttbar\ background component is normalized
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to the sideband region, so the statistical
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uncertainties in the data and MC yields in the sideband regions
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contribute to the background predictions in the signal regions.
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This normalization is repeated after varying the
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rare background yield by $\pm50$\% to estimate the associated systematic uncertainty.
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The uncertainty from the limited number of events in the MC samples
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used to derive the predictions also contributes.
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The dominant source of systematic uncertainty arises from the \mt\ and
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\mbb\ extrapolation scale factors are derived in a sample
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with (1 or )2 b-tags for the ($1$)$2\ell$ channels. The uncertainty is derived from control regions
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where the MC prediction derived using the extraplation scale factor can be directly compared to data.
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For the single lepton channel, the stability of the \mt\ scale factors to
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\met\ resolution effects are investigated in the sample with 1 or 2
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b-tags and by tightening the requirement on additional jets.
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For the dilepton channel, the dependence of the \mbb\ scale factors on the
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b-jet multiplicity is studied in the $1\ell$ \mt\ sideband region by
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increasing the requirement on additional b-tags.
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The stability of the background predictions is also verified by
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comparing the prediction derived using the nominal \MADGRAPH sample
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with those using samples generated with \POWHEG and \MCATNLO.
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The resulting background predictions are consistent within the systematic
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uncertainties, so no additional uncertainty is assessed from this test.
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The systematic uncertainties are summarized in Table~\ref{tab:relunc_summary}.
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\begin{table}[!h]
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\begin{center}
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\caption{Summary of the relative uncertainties (in \%) on the total
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background predictions. All uncertainties are derived for the total
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background prediction and are treated as uncorrelated from each other.}
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\begin{tabular}{l||c|c|c|c}
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\hline
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Sample & 1l + 3b & 1l + $\ge$4b & 2l + 3b & 2l + $\ge$4b \\
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\hline
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\hline
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Stat. & $9.3$ & $8.7$ & $20.8$ & $27.3$ \\
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SF uncertainty & $7.8$ & $4.2$ & $10.0$ & $30.0$ \\
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Top $\pt$ Modeling & $2.6$ & $0.6$ & $0.7$ & $4.7$ \\
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rare bkg. Norm & $3.6$ & $0.8$ & $1.4$ & $5.6$ \\
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Subdominant $\ttbar$ Norm & $1.0$ & $0.1$ & - & - \\
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\hline
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Total & $13.0$ & $9.7$ & $23.2$ & $41.2$ \\
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\hline
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\end{tabular}
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\label{tab:relunc_summary}
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\end{center}
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\end{table}
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