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\section{Limit on new physics} |
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\label{sec:limit} |
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Nothing yet. |
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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 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 1.5 $\pm$ 0.9 and |
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$2.5 \pm 2.2$ 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 $N_{BG}=1.4 \pm 1.1$ |
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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 Figure~\ref{fig:response} we provide the response functions for the |
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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 (SumJetPt $>$ 300 GeV and \met/$\sqrt{\rm SumJetPt} > 8.5$ |
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Gev$^{\frac{1}{2}}$). We see that the average SumJetPt response |
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in the Monte Carlo |
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is very close to one, with an RMS of order 10\%. The |
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response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an |
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RMS of 15\%. |
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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]{selectionEff.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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\end{center} |
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\end{figure} |
