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\subsection{W+Jets MC Modelling Validation from CR1}
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\label{sec:cr1}
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The estimate of the uncertainty on this background is based on CR1,
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defined by applying the full signal selection, including the isolated track veto, but requiring 0 b-tags
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(CSV medium working point as described in Sec.~\ref{sec:selection}).
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The sample is dominanted by \wjets\ and is thus used to validate the MC modelling of this background.
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In Table~\ref{tab:cr1mtsf} we show the amount that we need to scale the \wjets\ MC
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by in order to have agreement between data and Monte Carlo in the $M_T$ peak
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region, defined as $50 < M_T < 80$ GeV, for the
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different signal regions. (Recall, the signal regions have different
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\met\ requirements). These scale factors are not terribly
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important, but it is reassuring that they are not too different from
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1.
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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|c|c|c|c}
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\hline
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Sample & CR1PRESEL & CR1A & CR1B & CR1C & CR1D & CR1E &
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CR1F & CR1G\\
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\hline
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\hline
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$\mu$ \mt-SF & $0.92 \pm 0.02$ & $0.97 \pm 0.03$ & $0.90 \pm 0.04$ & $0.91 \pm 0.06$ & $0.93 \pm 0.09$ & $0.98 \pm 0.13$ & $0.94 \pm 0.18$ & $0.96 \pm 0.25$ \\
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\hline
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\hline
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e \mt-SF & $0.94 \pm 0.02$ & $0.90 \pm 0.04$ & $0.84 \pm 0.05$ & $0.80 \pm 0.07$ & $0.83 \pm 0.10$ & $0.77 \pm 0.13$ & $0.86 \pm 0.20$ & $0.87 \pm 0.29$ \\
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\hline
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\end{tabular}}
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\caption{ \mt\ peak Data/MC scale factors applied to \wjets\
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samples. No scaling is made for backgrounds from other
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processes. CR1PRESEL refers to a sample with $\met>50$ GeV.
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The uncertainties are statistical only.
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\label{tab:cr1mtsf}}
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\end{center}
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\end{table}
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Next, in Fig~\ref{fig:cr1met},~\ref{fig:cr1mtrest},
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and~\ref{fig:cr1mtrest2}, we show plots of \met\ and then $M_T$
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for different \met\ requirements corresponding to those defining our signal regions.
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It is clear that there are more events in the $M_T$ tail than
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predicted
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from MC. This implies that we need to rescale the MC \wjets\
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background
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in the tail region.
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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|c|c|c|c}
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\hline
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Sample & CR1PRESEL & CR1A & CR1B & CR1C & CR1D & CR1E &
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CR1F & CR1G\\
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\hline
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\hline
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$\mu$ MC & $480 \pm 22$ & $173 \pm 5$ & $114 \pm 4$ & $40 \pm 2$ & $16 \pm 1$ & $8 \pm 1$ & $4 \pm 1$ & $2 \pm 1$ \\
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$\mu$ Data & $629$ & $238$ & $139$ & $45$ & $12$ & $8$ & $3$ & $2$ \\
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\hline
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$\mu$ Data/MC & $1.31 \pm 0.08$ & $1.37 \pm 0.10$ & $1.22 \pm 0.11$ & $1.12 \pm 0.18$ & $0.75 \pm 0.23$ & $0.99 \pm 0.37$ & $0.75 \pm 0.45$ & $0.96 \pm 0.72$ \\
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\hline
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\hline
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e MC & $330 \pm 8$ & $118 \pm 4$ & $79 \pm 3$ & $29 \pm 2$ & $13 \pm 1$ & $5 \pm 1$ & $3 \pm 1$ & $2 \pm 0$ \\
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e Data & $473$ & $174$ & $100$ & $36$ & $16$ & $5$ & $5$ & $2$ \\
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\hline
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e Data/MC & $1.43 \pm 0.07$ & $1.47 \pm 0.12$ & $1.27 \pm 0.14$ & $1.23 \pm 0.22$ & $1.26 \pm 0.34$ & $1.07 \pm 0.51$ & $1.80 \pm 0.91$ & $1.26 \pm 0.97$ \\
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\hline
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\hline
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$\mu$+e MC & $810 \pm 23$ & $291 \pm 7$ & $192 \pm 5$ & $69 \pm 3$ & $29 \pm 2$ & $13 \pm 1$ & $7 \pm 1$ & $4 \pm 1$ \\
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$\mu$+e Data & $1102$ & $412$ & $239$ & $81$ & $28$ & $13$ & $8$ & $4$ \\
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\hline
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$\mu$+e Data/MC & $1.36 \pm 0.08$ & $1.42 \pm 0.13$ & $1.24 \pm 0.15$ & $1.17 \pm 0.23$ & $0.97 \pm 0.31$ & $1.02 \pm 0.51$ & $1.18 \pm 0.69$ & $1.09 \pm 0.96$ \\
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\hline
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\hline
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\hline
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$\mu$ W MC & $300 \pm 23$ & $84 \pm 5$ & $52 \pm 4$ & $20 \pm 2$ & $9 \pm 2$ & $5 \pm 1$ & $3 \pm 1$ & $1 \pm 1$ \\
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$\mu$ W Data & $449 \pm 26$ & $149 \pm 16$ & $78 \pm 12$ & $25 \pm 7$ & $5 \pm 4$ & $5 \pm 3$ & $2 \pm 2$ & $1 \pm 1$ \\
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\hline
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$\mu$ W Data/MC & $1.50 \pm 0.14$ & $1.77 \pm 0.21$ & $1.49 \pm 0.26$ & $1.25 \pm 0.38$ & $0.56 \pm 0.39$ & $0.98 \pm 0.62$ & $0.60 \pm 0.73$ & $0.94 \pm 1.14$ \\
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\hline
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\hline
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e W MC & $192 \pm 8$ & $55 \pm 4$ & $36 \pm 3$ & $14 \pm 2$ & $6 \pm 1$ & $3 \pm 1$ & $2 \pm 1$ & $1 \pm 0$ \\
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e W Data & $335 \pm 22$ & $111 \pm 13$ & $58 \pm 10$ & $20 \pm 6$ & $10 \pm 4$ & $3 \pm 2$ & $4 \pm 2$ & $1 \pm 1$ \\
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\hline
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e W Data/MC & $1.74 \pm 0.14$ & $2.02 \pm 0.29$ & $1.58 \pm 0.32$ & $1.49 \pm 0.50$ & $1.50 \pm 0.70$ & $1.10 \pm 0.80$ & $2.27 \pm 1.55$ & $1.51 \pm 1.96$ \\
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\hline
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\hline
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$\mu$+e W MC & $493 \pm 24$ & $139 \pm 6$ & $89 \pm 5$ & $33 \pm 3$ & $16 \pm 2$ & $8 \pm 1$ & $4 \pm 1$ & $2 \pm 1$ \\
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$\mu$+e W Data & $785 \pm 59$ & $260 \pm 37$ & $135 \pm 28$ & $45 \pm 16$ & $15 \pm 9$ & $8 \pm 7$ & $6 \pm 5$ & $3 \pm 3$ \\
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\hline
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$\mu$+e W Data/MC & $1.59 \pm 0.14$ & $1.87 \pm 0.28$ & $1.53 \pm 0.33$ & $1.35 \pm 0.50$ & $0.95 \pm 0.58$ & $1.03 \pm 0.83$ & $1.29 \pm 1.13$ & $1.16 \pm 1.65$ \\
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\hline
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\hline
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\hline
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$SFR_{wjet}$ & $1.48 \pm 0.26$ & $1.64 \pm 0.38$ & $1.38 \pm 0.30$ & $1.26 \pm 0.39$ & $0.96 \pm 0.45$ & $1.02 \pm 0.67$ & $1.23 \pm 0.92$ & $1.12 \pm 1.31$ \\
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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. CR1PRESEL refers to a sample with $\met>50$
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GeV and $\mt>150$ GeV. See text for details.
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% The uncertainties are statistical only.
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\label{tab:cr1yields}}
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\end{center}
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\end{table}
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The rescaling is explored
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in Table~\ref{tab:cr1yields},
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where we compare the data and MC yields in the $M_T$ signal regions
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and in a looser control region. Note that the
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MC is normalized in the $M_T$ peak region by rescaling
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the \wjets\ component according to Table~\ref{tab:cr1mtsf}.
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We also derive data/MC scale factors.
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As shown in Table~\ref{tab:cr1yields}, these are derived in two different ways, separately for muons and
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electrons and then combined, as follows:
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\begin{itemize}
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\item For the first three sets of scale factors, above the triple horizontal
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line, we calculate the scale factor as the amount by which we would
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need to rescale {\bf all} MC (\wjets\ , \ttbar\ , single top, rare) in
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order to have data-MC agreement in the $M_T$ tail.
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\item For the next three set of scale factors, below the triple horizontal
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line, we calculate the scale factor as the amount by which we would
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need
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to scale \wjets\ keeping all other
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components fixed in order to have data-MC agreement in the tail.
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\end{itemize}
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\noindent The true \wjets\ scale factor is somewhere in between these
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two extremes. We also note that there is no statistically significant
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difference between the electron and muon samples. We use these data
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to extract a data/MC scale factor for \wjets\ which will be used to
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rescale the \wjets\ MC tail. This scale factor is listed in the last
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line of the Table, and is called $SFR_{wjets}$. It is calculated as
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follows.
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\begin{itemize}
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\item Separately for each signal region
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\item As the average of the two methods described above
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\item Including the statistical uncertainty
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\item Adding in quadrature to the uncertainty one-half of the
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deviation from 1.0
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\end{itemize}
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/met_met50_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/met_met50_leadele_nj4.pdf}
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met100_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met100_leadele_nj4.pdf}
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\caption{
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Comparison of the \met\ (top) and \mt\ for $\met>100$ (bottom) distributions 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 CR1.
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\label{fig:cr1met}
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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/CR1plots/mt_met150_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met150_leadele_nj4.pdf}
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met200_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met200_leadele_nj4.pdf}
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met250_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/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 CR1. The \met\ requirements used are
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150 GeV (top), 200 GeV (middle) and 250 GeV (bottom).
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\label{fig:cr1mtrest}
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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/CR1plots/mt_met300_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met300_leadele_nj4.pdf}
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met350_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met350_leadele_nj4.pdf}
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met400_leadmuo_nj4.pdf}%
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\includegraphics[width=0.5\linewidth]{plots/CR1plots/mt_met400_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 CR1. The \met\ requirements used are
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300 GeV (top), 350 GeV (middle) and 400 GeV (bottom).
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\label{fig:cr1mtrest2}
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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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