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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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%{\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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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 1.5 $\pm$ 0.9 and |
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$1.8^{+2.5}_{-1.8}$ events respectively. |
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and the $P_T(\ell\ell)$ method are $1.5 \pm 0.9({\rm stat}) \pm 0.3({\rm syst})$ |
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and $4.3 \pm 3.0({\rm stat}) \pm 1.2({\rm syst})$, 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 baysean 95\% CL upper limit\cite{ref:bayes.f} |
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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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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 $N_{BG}=1.7 \pm 1.1$ |
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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:sigcontABCD}: $5.6 \pm 1.1$ |
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events and $2.2 \pm 0.3$ respectively, where the uncertainties |
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LM0 and LM1 events from Table~\ref{tab:sigcont}: $6.3 \pm 1.3$ |
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events and $2.6 \pm 0.4$ |
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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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and lepton efficiency. Note that these expected SUSY yields |
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are computed using LO cross-sections, and are therefore underestimated. |
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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. |
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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 35 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/$\sqrt{\rm SumJetPt}$. These |
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quantities have been evaluated with Spring10 MC samples. |
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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. 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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We find 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\% while |
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the |
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response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an |
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RMS of 14\%. |
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|
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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} |
