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\section{Limit on new physics}
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\label{sec:limit}
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{\bf \color{red} The numbers in this Section need to be double checked.}
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As discussed in Section~\ref{sec:results}, we see one event
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in the signal region, defined as SumJetPt$>$300 GeV and
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\met/$\sqrt{\rm SumJetPt}>8.5$ GeV$^{\frac{1}{2}}$.
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The background prediction from the SM Monte Carlo is
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1.4 $\pm$ 0.5 events, where the uncertainty comes from
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the jet energy scale (30\%, see Section~\ref{sec:systematics}),
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the luminosity (10\%), and the lepton/trigger
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efficiency (10\%)\footnote{Other uncertainties associated with
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the modeling of $t\bar{t}$ in MadGraph have not been evaluated.}.
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The data driven background predictions from the ABCD method
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and the $P_T(\ell\ell)$ method are 1.5 $\pm$ 0.9 and
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$1.8^{+2.5}_{-1.8}$ events respectively.
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These three predictions are in good agreement with each other
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and with the observation of one event in the signal region.
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We calculate a Bayesian 95\% CL upper limit\cite{ref:bayes.f}
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on the number of non SM events in the signal region to be 4.1.
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This was calculated using a background prediction of $N_{BG}=1.4 \pm 1.0$
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events. The upper limit is not very sensitive to the choice of
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$N_{BG}$ and its uncertainty.
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To get a feeling for the sensitivity of this search to some
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popular SUSY models, we remind the reader of the number of expected
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LM0 and LM1 events from Table~\ref{tab:sigcont}: $6.5 \pm 1.3$
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events and $2.6 \pm 0.4$ respectively, where the uncertainties
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are from energy scale (Section~\ref{sec:systematics}), luminosity,
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and lepton efficiency.
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In Figures XX and YY we provide the response functions for the
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SumJetPt and \met/$\sqrt{\rm SumJetPt}$ cuts used in our analysis,
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{\em i.e.} the efficiencies of the experimental cuts as a function of
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the true quantities. Using this information as well as the kinematical
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cuts described in Section~\ref{sec:eventSel} and the lepton efficiencies
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of Figures~\ref{fig:effttbar}, one should be able to confront
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any existing or future model via a relatively simple generator
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level study by comparing the expected number of events in 35 pb$^{-1}$
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with our upper limit of 4.1 events. |
