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\section{Limit on new physics} |
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\label{sec:limit} |
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|
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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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\subsection{Limit on number of events} |
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\label{sec:limnumevents} |
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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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|
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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 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 1.5 $\pm$ 0.9 and |
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$2.5 \pm 2.2$ events, respectively. |
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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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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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We have also calculated this limit using |
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% a profile likelihood method |
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% as implemented in |
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the cl95cms software\cite{ref:cl95cms}, |
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and we also find 4.1. (This is not surprising, since cl95cms |
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also gives baysean upper limits with a flat prior). |
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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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|
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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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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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|
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In Figure~\ref{fig:response} we provide the response functions for the |
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|
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\subsection{Outreach} |
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\label{sec:outreach} |
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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. |
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Here we attempt to present our result in the most general |
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way. |
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|
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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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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. |
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%{\bf \color{red} The following numbers were derived from Fall 10 samples. } |
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The average detector |
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responses for SumJetPt and $\met/\sqrt{\rm SumJetPt}$ are |
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$1.02 \pm 0.05$ 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 11\% and |
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16\% respectively. |
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|
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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 Fall10 samples } |
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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\%; |
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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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in the Monte Carlo is about 1.02, with an RMS of order 11\% while |
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the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an |
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RMS of 16\%. |
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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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|
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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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\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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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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the underlying physics. |
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%{\bf \color{red} These plots were made with Fall10 samples. } |
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} |
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\end{center} |
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\end{figure} |
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|
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|
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|
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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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|
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|
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|
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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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|
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|
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\subsection{mSUGRA scan} |
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\label{sec:mSUGRA} |
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We also perform a scan of the mSUGRA parameter space, as recomended |
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by the SUSY group convenors\cite{ref:scan}. |
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The goal of the scan is to determine an exclusion region in the |
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$m_0$ vs. $m_{1/2}$ plane for |
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$\tan\beta=3$, |
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sign of $\mu = +$, and $A_{0}=0$~GeV. This scan is based on events |
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generated with FastSim. |
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|
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The first order of business is to verify that results using |
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Fastsim and Fullsim are compatible. To this end we compare the |
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expected yield for the LM1 point in FullSim (3.56 $\pm$ 0.06) and |
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FastSim (3.29 $\pm$ 0.27), where the uncertainties are statistical only. |
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These two numbers are in agreement, which gives us confidence in |
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using FastSim for this study. |
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|
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The FastSim events are generated with different values of $m_0$ |
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and $m_{1/2}$ in steps of 10 GeV. For each point in the |
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$m_0$ vs. $m_{1/2}$ plane, we compute the expected number of |
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events at NLO. We then also calculate an upper limit $N_{UL}$ |
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using cl95cms at each point using the following inputs: |
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\begin{itemize} |
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\item Number of BG events = 1.40 $\pm$ 0.77 |
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\item Luminosity uncertainty = 11\% |
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\item The acceptance uncertainty is calculated at each point |
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as the quadrature sum of |
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\begin{itemize} |
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\item The uncertainty due to JES for that point, as calculated |
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using the method described in Section~\ref{sec:systematics} |
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\item A 5\% uncertainty due to lepton efficiencies |
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\item An uncertaity on the NLO cross-section obtained by varying the |
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factorization and renormalization scale by a factor of two\cite{ref:sanjay}. |
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\item The PDF uncertainty on the product of cross-section and acceptance |
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calculated using the method of Reference~\cite{ref:pdf}. |
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\end{itemize} |
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\item We use the ``log-normal'' model for the nuisance parameters |
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in cl95cms |
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\end{itemize} |
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|
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An mSUGRA point is excluded if the resulting $N_{UL}$ is smaller |
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than the expected number of events. Because of the quantization |
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of the available MC points in the $m_0$ vs $m_{1/2}$ plane, the |
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boundaries of the excluded region are also quantized. We smooth |
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the boundaries using the method recommended by the SUSY |
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group\cite{ref:smooth}. In addition, we show a limit |
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curve based on the LO cross-section, as well as the |
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``expected'' limit curve. The expected limit curve is |
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calculated using the CLA function also available in cl95cms. |
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Cross-section uncertainties due to variations of the factorization |
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and renormalization scale are not included for the LO curve. |
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The results are shown in Figure~\ref{fig:msugra} |
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|
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|
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\begin{figure}[tbh] |
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\begin{center} |
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\includegraphics[width=\linewidth]{exclusion_noPDF.pdf} |
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\caption{\label{fig:msugra}\protect Exclusion curves in the mSUGRA parameter space, |
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assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs. THIS IS STILL MISSING |
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THE PDF UNCERTAINTIES. WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.} |
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\end{center} |
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\end{figure} |
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|
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|
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\subsubsection{Check of the nuisance parameter models} |
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We repeat the procedure outlined above but changing the |
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lognormal nuisance parameter model to a gaussian or |
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gamma-function model. The results are shown in |
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Figure~\ref{fig:nuisance}. (In this case, |
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to avoid smoothing artifacts, we |
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show the raw results, without smoothing). |
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|
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\begin{figure}[tbh] |
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\begin{center} |
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\includegraphics[width=0.5\linewidth]{nuissance.png} |
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\caption{\label{fig:nuisance}\protect Exclusion curves in the |
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mSUGRA parameter space, |
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assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
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using different models for the nuisance parameters. |
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PDF UNCERTAINTOES ARE NOT INCLUDED.} |
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\end{center} |
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\end{figure} |
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|
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We find that the set of excluded points is identical for the |
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lognormal and gamma models. There are small differences for the |
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gaussian model. Following the recommendation of Reference~\cite{ref:cousins}, |
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we use the lognormal nuisance parameter model. |
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|
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|
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\clearpage |
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|
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|
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\subsubsection{Effect of signal contamination} |
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\label{sec:contlimit} |
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Signal contamination could affect the limit by inflating the |
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background expectation. In our case we see no evidence of signal |
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contamination, within statistics. |
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The yields in the control regions |
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$A$, $B$, and $C$ (Table~\ref{tab:datayield}) are just |
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as expected in the SM, and the check |
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of the $P_T(\ell \ell)$ method in the control region is |
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also consistent with expectations (Table~\ref{tab:victory}). |
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Since we have two data driven methods, with different |
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signal contamination issues, giving consistent |
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results that are in agreement with the SM, we |
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argue for not making any correction to our procedure |
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because of signal contamination. In some sense this would |
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be equivalent to using the SM background prediction, and using |
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the data driven methods as confirmations of that prediction. |
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|
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Nevertheless, here we explore the possible effect of |
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signal contamination. The procedure suggested to us |
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is the following: |
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\begin{itemize} |
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\item At each point in mSUGRA space we modify the |
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ABCD background prediction from $A_D \cdot C_D/B_D$ to |
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$(A_D-A_S) \cdot (C_D-C_S) / (B_D - B_S)$, where the |
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subscripts $D$ and $S$ referes to the number of observed data |
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events and expected SUSY events, respectively, in a given region. |
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\item Similarly, at each point in mSugra space we modify the |
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$P_T(\ell\ell)$ background prediction from |
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$K \cdot K_C \cdot D'_D$ to $K \cdot K_C \cdot (D'_D - D'_S)$, |
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where the subscript $D$ and $S$ are defined as above. |
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\item At each point in mSUGRA space we recalculate $N_{UL}$ |
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using the weighted average of the modified $ABCD$ and |
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$P_T(\ell\ell)$ method predictions. |
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\end{itemize} |
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|
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\noindent This procedure results in a reduced background prediction, |
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and therefore a less stringent $N_{UL}$. |
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|
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Note, however, that in some cases this procedure is |
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nonsensical. For example, take LM0 as a SUSY |
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point. In region $C$ we have a SM prediction of 5.1 |
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events and $C_D = 4$ in agreement with the Standard Model, |
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see Table~\ref{tab:datayield}. From the LM0 Monte Carlo, |
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we find $C_S = 8.6$ events. Thus, including information |
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on $C_D$ and $C_S$ should {\bf strengthen} the limit, since there |
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is clearly a deficit of events in the $C$ region in the |
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LM0 hypothesis. Instead, we now get a negative ABCD |
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BG prediction (which is nonsense, so we set it to zero), |
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and therefore a weaker limit. |
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|
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\begin{figure}[tbh] |
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\begin{center} |
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\includegraphics[width=0.5\linewidth]{sigcont.png} |
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\caption{\label{fig:sigcont}\protect Exclusion curves in the |
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mSUGRA parameter space, |
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assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs |
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with and without the effects of signal contamination. |
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PDF UNCERTAINTIES ARE NOT INCLUDED.} |
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\end{center} |
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\end{figure} |
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|
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Despite these reservations, we follow the procedure suggested |
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to us. A comparison of the exclusion region with and without |
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the signal contamination is shown in Figure~\ref{fig:sigcont} |
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(with no smoothing). The effect of signal contamination is |
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small. |
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|
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\subsubsection{mSUGRA scans with different values of tan$\beta$} |
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\label{sec:tanbetascan} |
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|
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For completeness, we also show the exclusion regions calculated |
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using $\tan\beta = 10$ (Figure~\ref{fig:msugratb10}). |
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|
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\begin{figure}[tbh] |
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\begin{center} |
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\includegraphics[width=\linewidth]{exclusion_tanbeta10.pdf} |
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\caption{\label{fig:msugratb10}\protect Exclusion curves in the mSUGRA parameter space, |
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assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs. THIS IS STILL MISSING |
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THE PDF UNCERTAINTIES. WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.} |
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\end{center} |
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\end{figure} |
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|
