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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 1.3 events.
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%, 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 uncertainty on $pp \to \sigma(t\bar{t})$ is also not included.}.
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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 $1.3 \pm 0.8({\rm stat}) \pm 0.3({\rm syst})$
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and $2.1 \pm 2.1({\rm stat}) \pm 0.6({\rm syst})$, 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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We have also calculated this limit using a profile likelihood method
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as implemented in the cl95cms software, and we also find 4.1.
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These limits were calculated using a background prediction of $N_{BG} = 1.4 \pm 0.8$
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events, the error-weighted average of the ABCD and $P_T(\ell\ell)$ background
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predictions. 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}: $8.6 \pm 1.6$
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events and $3.6 \pm 0.5$ events 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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We also performed a scan of the mSUGRA parameter space. We set $\tan\beta=10$,
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sign of $\mu = +$, $A_{0}=0$~GeV, and scan the $m_{0}$ and $m_{1/2}$ parameters
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in steps of 10~GeV. For each scan point, we exclude the point if the expected
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yield in the signal region exceeds 4.7, which is the 95\% CL upper limit
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based on an expected background of $N_{BG}=1.4 \pm 0.8$ and a 20\% acceptance
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uncertainty. The results are shown in Fig.~\ref{fig:msugra}.
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\begin{figure}[tbh]
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\begin{center}
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\includegraphics[width=0.6\linewidth]{msugra.png}
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\caption{\label{fig:msugra}\protect Exclusion curve in the mSUGRA parameter space,
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assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.}
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\end{center}
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\end{figure}
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Conveying additional useful information about the results of
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a generic ``signature-based'' search such as the one described
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in this note is a difficult issue. The next paragraph represent
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our attempt at doing so.
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Other models of new physics in the dilepton final state
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can be confronted in an approximate way by simple
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generator-level studies that
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compare the expected number of events in 34.0~pb$^{-1}$
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with our upper limit of 4.1 events. The key ingredients
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of such studies are the kinematical cuts described
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in this note, the lepton efficiencies, and the detector
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responses for SumJetPt and \met/$\sqrt{\rm SumJetPt}$.
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{LOOKING AT THE 38X MC PLOTS BY EYE, THE FOLLOWING QUANTITIES LOOK ABOUT RIGHT.}
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The muon identification efficiency is $\approx 95\%$;
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the electron identification efficiency varies from $\approx$ 63\% at
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$P_T = 10$ GeV to 91\% for $P_T > 30$ GeV. The isolation
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efficiency in top events varies from $\approx 83\%$ (muons)
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and $\approx 89\%$ (electrons) at $P_T=10$ GeV to
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$\approx 95\%$ for $P_T>60$ GeV. {\bf \color{red} The following quantities were calculated
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with Spring10 samples. } The average detector
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responses for SumJetPt and $\met/\sqrt{\rm SumJetPt}$ are
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$1.00 \pm 0.05$ and $0.94 \pm 0.05$ respectively, where
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the uncertainties are from the jet energy scale uncertainty.
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The experimental resolutions on these quantities are 10\% and
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14\% respectively.
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To justify the statements in the previous paragraph
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about the detector responses, we plot
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in Figure~\ref{fig:response} the average response for
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SumJetPt and \met/$\sqrt{\rm SumJetPt}$ in MC, as well as the
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efficiency for the cuts on these quantities used in defining the
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signal region.
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% (SumJetPt $>$ 300 GeV and \met/$\sqrt{\rm SumJetPt} > 8.5$
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% Gev$^{\frac{1}{2}}$).
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{\bf \color{red} The following numbers were derived from Spring10 samples, They should be the same for the Fall10 samples; this needs to be verified .}
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We find that the average SumJetPt response
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in the Monte Carlo is very close to one, with an RMS of order 10\% while
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the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an
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RMS of 14\%.
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%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.
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\begin{figure}[tbh]
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\begin{center}
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\includegraphics[width=\linewidth]{selectionEffDec10.png}
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\caption{\label{fig:response} Left plots: the efficiencies
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as a function of the true quantities for the SumJetPt (top) and
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tcMET/$\sqrt{\rm SumJetPt}$ (bottom) requirements for the signal
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region as a function of their true values. The value of the
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cuts is indicated by the vertical line.
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Right plots: The average response and its RMS for the SumJetPt
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(top) and tcMET/$\sqrt{\rm SumJetPt}$ (bottom) measurements.
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The response is defined as the ratio of the reconstructed quantity
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to the true quantity in MC. These plots are done using the LM0
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Monte Carlo, but they are not expected to depend strongly on
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the underlying physics.
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{\bf \color{red} These plots were made with Fall10 samples. } }
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\end{center}
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\end{figure}
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%%% Nominal
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% -----------------------------------------
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% observed events 1
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% relative error on acceptance 0.000
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% expected background 1.400
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% absolute error on background 0.770
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% desired confidence level 0.95
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% integration upper limit 30.00
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% integration step size 0.0100
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% -----------------------------------------
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% Are the above correct? y
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% 1 16.685 0.29375E-06
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%
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% limit: less than 4.112 signal events
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%%% Add 20% acceptance uncertainty based on LM0
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% -----------------------------------------
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% observed events 1
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% relative error on acceptance 0.200
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% expected background 1.400
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% absolute error on background 0.770
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% desired confidence level 0.95
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% integration upper limit 30.00
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% integration step size 0.0100
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% -----------------------------------------
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% Are the above correct? y
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% 1 29.995 0.50457E-06
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%
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% limit: less than 4.689 signal events
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