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\section{Acceptance and efficiency systematics}
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\label{sec:systematics}
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This is a search for new physics contributions to
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events with high \met and lots of jet activity.
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As seen in Section~\ref{sec:results}, there is no
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evidence for a contribution beyond SM expectations.
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Strictly speaking it is impossible to talk about
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``acceptance and efficiency systematics'' because these kinds of
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systematics only apply to a well defined final state.
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Nevertheless, we can make general statements about the
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systematic uncertainties, including quantitative
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estimates of the systematic uncertainties associated with
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a few specific processes.
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The systematic uncertainty on the lepton acceptance consists
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of two parts: the trigger efficiency uncertainty and the
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ID and isolation of uncertainty. We discuss these in turn.
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The trigger efficiency
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for two leptons of $P_T>10$ GeV, with one lepton of
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$P_T>20$ GeV is very high, except in some corners
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of phase space, see Section~\ref{sec:trgEff}.
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We estimate the efficiency uncertainty to be a few percent,
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mostly in the low $P_T$ region.
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\begin{figure}[tbh]
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\begin{center}
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\includegraphics[width=0.75\linewidth]{eff_11.png}
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\caption{\label{fig:effttbar}\protect
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Identification and isolation efficiencies for
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leptons from $t \to W \to \ell$ and
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$t \to W \to \tau \to \ell$ in
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$t\bar{t}$ events.}
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\end{center}
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\end{figure}
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\begin{table}[hbt]
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\begin{center}
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\caption{\label{tab:tagandprobe} Tag and probe results on $Z \to \ell \ell$
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on data and MC. We quote ID efficiency given isolation and
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the isolation efficiency given ID.}
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\begin{tabular}{|l||c|c|}
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\hline
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& Data T\&P & MC T\&P \\ \hline
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$\epsilon(id|iso)$ electrons & $0.909\pm0.006$ & 0.926 \\
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$\epsilon(iso|id)$ electrons & $0.987\pm0.003$ & 0.985 \\
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$\epsilon(id|iso)$ muons & $0.955\pm0.003$ & 0.953 \\
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$\epsilon(iso|id)$ muons & $0.984\pm0.003$ & 0.981 \\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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The ID efficiencies in MC are shown in
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Figures~\ref{fig:effttbar}
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for the leptons from $t \to W \to \ell$ and $t \to W \to \tau \to \ell$.
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Tag and probe studies show that these are correct to about 2\%,
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see Table~\ref{tab:tagandprobe}.
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Note that the isolation efficiency depends on the jet activity in
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the final state. For example, in MC we find that the
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lepton isolation efficiency differs by $\approx 4\%$
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{\bf per lepton} between $Z$ events and $t\bar{t}$ events\cite{ref:top}.
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\noindent {\bf This figure should be cut off at 100 GeV, and
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the y-axis should be zero-suppressed}
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Another significant source of systematic uncertainty is
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associated with the jet and $\met$ energy scale. The impact
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of this uncertainty is final-state dependent. Final
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states characterized by lots of hadronic activity and \met are
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less sensitive than final states where the \met and SumJetPt
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are typically close to the requirement. To be more quantitative,
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we have used the method of Reference~\cite{ref:top} to evaluate
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the systematic uncertainties on the acceptance for $t\bar{t}$
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and two benchmark SUSY points. The uncertainties are calculated
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assuming a 5\% uncertainty to the hadronic energy scale in CMS.
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For $t\bar{t}$ we find uncertainties of 8\% (baseline
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selection) and 30\% (signal region D); for LM0 and LM1 we find
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14\% and 6\% respectively for signal region D. |
