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Comparing UserCode/claudioc/OSNote2010/limit.tex (file contents):
Revision 1.1 by claudioc, Fri Oct 29 02:29:40 2010 UTC vs.
Revision 1.34 by claudioc, Fri Jan 14 00:02:59 2011 UTC

+\section{Limit on new physics}
+\label{sec:limit}
-<
+Nothing yet.
->
->
+%{\bf \color{red} The numbers in this Section need to be double checked.}
->
->
+\subsection{Limit on number of events}
->
+\label{sec:limnumevents}
->
+As discussed in Section~\ref{sec:results}, we see one event
->
+in the signal region, defined as SumJetPt$>$300 GeV and
->
+\met/$\sqrt{\rm SumJetPt}>8.5$ GeV$^{\frac{1}{2}}$.
->
->
+The background prediction from the SM Monte Carlo is 1.3 events.
->
+%, where the uncertainty comes from
->
+%the jet energy scale (30\%, see Section~\ref{sec:systematics}),
->
+%the luminosity (10\%), and the lepton/trigger
->
+%efficiency (10\%)\footnote{Other uncertainties associated with
->
+%the modeling of $t\bar{t}$ in MadGraph have not been evaluated.
->
+%The uncertainty on $pp \to \sigma(t\bar{t})$ is also not included.}.
->
+The data driven background predictions from the ABCD method
->
+and the $P_T(\ell\ell)$ method are $1.3 \pm 0.8({\rm stat}) \pm 0.3({\rm syst})$
->
+and $2.1 \pm 2.1({\rm stat}) \pm 0.6({\rm syst})$, respectively.
->
->
+These three predictions are in good agreement with each other
->
+and with the observation of one event in the signal region.
->
+We calculate a Bayesian 95\% CL upper limit\cite{ref:bayes.f}
->
+on the number of non SM events in the signal region to be 4.1.
->
+We have also calculated this limit using
->
+% a profile likelihood method
->
+% as implemented in
->
+the cl95cms software\cite{ref:cl95cms},
->
+and we also find 4.1.  (This is not surprising, since cl95cms
->
+also gives baysean upper limits with a flat prior).
->
+These limits were calculated using a background prediction of $N_{BG} = 1.4 \pm 0.8$
->
+events, the error-weighted average of the ABCD and $P_T(\ell\ell)$ background
->
+predictions.  The upper limit is not very sensitive to the choice of
->
+$N_{BG}$ and its uncertainty.
->
->
+To get a feeling for the sensitivity of this search to some
->
+popular SUSY models, we remind the reader of the number of expected
->
+LM0 and LM1 events from Table~\ref{tab:sigcont}: $8.6 \pm 1.6$
->
+events and $3.6 \pm 0.5$ events respectively, where the uncertainties
->
+are from energy scale (Section~\ref{sec:systematics}), luminosity,
->
+and lepton efficiency.
->
->
->
+\subsection{Outreach}
->
+\label{sec:outreach}
->
+Conveying additional useful information about the results of
->
+a generic ``signature-based'' search such as the one described
->
+in this note is a difficult issue.
->
+Here we attempt to present our result in the most general
->
+way.
->
->
+Models of new physics in the dilepton final state
->
+can be confronted in an approximate way by simple
->
+generator-level studies that
->
+compare the expected number of events in 34.0~pb$^{-1}$
->
+with our upper limit of 4.1 events.  The key ingredients
->
+of such studies are the kinematical cuts described
->
+in this note, the lepton efficiencies, and the detector
->
+responses for SumJetPt and \met/$\sqrt{\rm SumJetPt}$.
->
+The muon identification efficiency is $\approx 95\%$;
->
+the electron identification efficiency varies from $\approx$ 63\% at
->
+$P_T = 10$ GeV to 91\% for $P_T > 30$ GeV.  The isolation
->
+efficiency in top events varies from $\approx 83\%$ (muons)
->
+and $\approx 89\%$ (electrons) at $P_T=10$ GeV to
->
+$\approx 95\%$ for $P_T>60$ GeV.
->
+%{\bf \color{red} The following numbers were derived from Fall 10 samples. }
->
+The average detector
->
+responses for SumJetPt and $\met/\sqrt{\rm SumJetPt}$ are
->
+$1.02 \pm 0.05$ and $0.94 \pm 0.05$ respectively, where
->
+the uncertainties are from the jet energy scale uncertainty.
->
+The experimental resolutions on these quantities are 11\% and
->
+\% respectively.
->
->
+To justify the statements in the previous paragraph
->
+about the detector responses, we plot
->
+in Figure~\ref{fig:response} the average response for
->
+SumJetPt and \met/$\sqrt{\rm SumJetPt}$ in MC, as well as the
->
+efficiency for the cuts on these quantities used in defining the
->
+signal region.
->
+% (SumJetPt $>$ 300 GeV and \met/$\sqrt{\rm SumJetPt} > 8.5$
->
+% Gev$^{\frac{1}{2}}$).
->
+%{\bf \color{red} The following numbers were derived from Fall10 samples }
->
+We find that the average SumJetPt response
->
+in the Monte Carlo is about 1.02, with an RMS of order 11\% while
->
+the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an
->
+RMS of 16\%.
->
->
+%Using this information as well as the kinematical
->
+%cuts described in Section~\ref{sec:eventSel} and the lepton efficiencies
->
+%of Figures~\ref{fig:effttbar}, one should be able to confront
->
+%any existing or future model via a relatively simple generator
->
+%level study by comparing the expected number of events in 35 pb$^{-1}$
->
+%with our upper limit of 4.1 events.
->
->
+\begin{figure}[tbh]
->
+\begin{center}
->
+\includegraphics[width=\linewidth]{selectionEffDec10.png}
->
+\caption{\label{fig:response} Left plots: the efficiencies
->
+as a function of the true quantities for the SumJetPt (top) and
->
+tcMET/$\sqrt{\rm SumJetPt}$ (bottom) requirements for the signal
->
+region as a function of their true values.  The value of the
->
+cuts is indicated by the vertical line.
->
+Right plots: The average response and its RMS for the SumJetPt
->
+(top) and tcMET/$\sqrt{\rm SumJetPt}$ (bottom) measurements.
->
+The response is defined as the ratio of the reconstructed quantity
->
+to the true quantity in MC.  These plots are done using the LM0
->
+Monte Carlo, but they are not expected to depend strongly on
->
+the underlying physics.
->
+%{\bf \color{red} These plots were made with Fall10 samples. }
->
+}
->
+\end{center}
->
+\end{figure}
->
->
->
->
+%%%  Nominal
->
+% -----------------------------------------
->
+% observed events                         1
->
+% relative error on acceptance        0.000
->
+% expected background                 1.400
->
+% absolute error on background        0.770
->
+% desired confidence level             0.95
->
+% integration upper limit             30.00
->
+% integration step size              0.0100
->
+% -----------------------------------------
->
+% Are the above correct? y
->
+%    1  16.685     0.29375E-06
->
+%
->
+% limit: less than     4.112 signal events
->
->
->
->
+%%%  Add 20% acceptance uncertainty based on LM0
->
+% -----------------------------------------
->
+% observed events                         1
->
+% relative error on acceptance        0.200
->
+% expected background                 1.400
->
+% absolute error on background        0.770
->
+% desired confidence level             0.95
->
+% integration upper limit             30.00
->
+% integration step size              0.0100
->
+% -----------------------------------------
->
+% Are the above correct? y
->
+%    1  29.995     0.50457E-06
->
+%
->
+% limit: less than     4.689 signal events
->
->
->
+\subsection{mSUGRA scan}
->
+\label{sec:mSUGRA}
->
+We also perform a scan of the mSUGRA parameter space, as recomended
->
+by the SUSY group convenors\cite{ref:scan}.
->
+The goal of the scan is to determine an exclusion region in the
->
+$m_0$ vs. $m_{1/2}$ plane for
->
+$\tan\beta=3$,
->
+sign of $\mu = +$, and $A_{0}=0$~GeV.  This scan is based on events
->
+generated with FastSim.
->
->
+The first order of business is to verify that results using
->
+Fastsim and Fullsim are compatible.  To this end we compare the
->
+expected yield for the LM1 point in FullSim (3.56 $\pm$ 0.06) and
->
+FastSim (3.29 $\pm$ 0.27), where the uncertainties are statistical only.
->
+These two numbers are in agreement, which gives us confidence in
->
+using FastSim for this study.
->
->
+The FastSim events are generated with different values of $m_0$
->
+and $m_{1/2}$ in steps of 10 GeV.  For each point in the
->
+$m_0$ vs. $m_{1/2}$ plane, we compute the expected number of
->
+events at NLO.  We then also calculate an upper limit $N_{UL}$
->
+using cl95cms at each point using the following inputs:
->
+\begin{itemize}
->
+\item Number of BG events = 1.40 $\pm$ 0.77
->
+\item Luminosity uncertainty = 11\%
->
+\item The acceptance uncertainty is calculated at each point
->
+as the quadrature sum of
->
+\begin{itemize}
->
+\item The uncertainty due to JES for that point, as calculated
->
+using the method described in Section~\ref{sec:systematics}
->
+\item A 5\% uncertainty due to lepton efficiencies
->
+\item An uncertaity on the NLO cross-section obtained by varying the
->
+factorization and renormalization scale by a factor of two\cite{ref:sanjay}.
->
+\item The PDF uncertainty on the product of cross-section and acceptance
->
+calculated using the method of Reference~\cite{ref:pdf}.
->
+\end{itemize}
->
+\item We use the ``log-normal'' model for the nuisance parameters
->
+in cl95cms
->
+\end{itemize}
->
->
+An mSUGRA point is excluded if the resulting $N_{UL}$ is smaller
->
+than the expected number of events.  Because of the quantization
->
+of the available MC points in the $m_0$ vs $m_{1/2}$ plane, the
->
+boundaries of the excluded region are also quantized.  We smooth
->
+the boundaries using the method recommended by the SUSY
->
+group\cite{ref:smooth}.  In addition, we show a limit
->
+curve based on the LO cross-section, as well as the
->
+``expected'' limit curve.  The expected limit curve is
->
+calculated using the CLA function also available in cl95cms.
->
+Cross-section uncertainties due to variations of the factorization
->
+and renormalization scale are not included for the LO curve.
->
+The results are shown in Figure~\ref{fig:msugra}
->
->
->
+\begin{figure}[tbh]
->
+\begin{center}
->
+\includegraphics[width=\linewidth]{exclusion_noPDF.pdf}
->
+\caption{\label{fig:msugra}\protect Exclusion curves in the mSUGRA parameter space,
->
+assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs.  THIS IS STILL MISSING
->
+THE PDF UNCERTAINTIES.  WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.}
->
+\end{center}
->
+\end{figure}
->
->
->
+\subsubsection{Check of the nuisance parameter models}
->
+We repeat the procedure outlined above but changing the
->
+lognormal nuisance parameter model to a gaussian or
->
+gamma-function model.  The results are shown in
->
+Figure~\ref{fig:nuisance}.  (In this case,
->
+to avoid smoothing artifacts, we
->
+show the raw results, without smoothing).
->
->
+\begin{figure}[tbh]
->
+\begin{center}
->
+\includegraphics[width=0.5\linewidth]{nuissance.png}
->
+\caption{\label{fig:nuisance}\protect Exclusion curves in the
->
+mSUGRA parameter space,
->
+assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs
->
+using different models for the nuisance parameters.
->
+PDF UNCERTAINTIES ARE NOT INCLUDED.}
->
+\end{center}
->
+\end{figure}
->
->
+We find that different assumptions on the PDFs for the nuisance
->
+parameters make very small differences to the set of excluded
->
+points.
->
+Following the recommendation of Reference~\cite{ref:cousins},
->
+we use the lognormal nuisance parameter model as the default.
->
->
->
+\clearpage
->
->
->
+\subsubsection{Effect of signal contamination}
->
+\label{sec:contlimit}
->
->
+Signal contamination could affect the limit by inflating the
->
+background expectation.  In our case we see no evidence of signal
->
+contamination, within statistics.
->
+The yields in the control regions
->
+$A$, $B$, and $C$ (Table~\ref{tab:datayield}) are just
->
+as expected in the SM, and the check
->
+of the $P_T(\ell \ell)$ method in the control region is
->
+also consistent with expectations (Table~\ref{tab:victory}).
->
+Since we have two data driven methods, with different
->
+signal contamination issues, giving consistent
->
+results that are in agreement with the SM, we
->
+argue for not making any correction to our procedure
->
+because of signal contamination.  In some sense this would
->
+be equivalent to using the SM background prediction, and using
->
+the data driven methods as confirmations of that prediction.
->
->
+Nevertheless, here we explore the possible effect of
->
+signal contamination.  The procedure suggested to us
->
+for the ABCD method is to modify the
->
+ABCD background prediction from $A_D \cdot C_D/B_D$ to
->
+$(A_D-A_S) \cdot (C_D-C_S) / (B_D - B_S)$, where the
->
+subscripts $D$ and $S$ refer to the number of observed data
->
+events and expected SUSY events, respectively, in a given region.
->
+We then recalculate $N_{UL}$ at each point using this modified
->
+ABCD background estimation.  For simplicity we ignore
->
+information from the $P_T(\ell \ell)$
->
+background estimation.  This is conservative, since
->
+the $P_T(\ell\ell)$ background estimation happens to
->
+be numerically larger than the one from ABCD.
->
->
+Note, however, that in some cases this procedure is
->
+nonsensical.  For example, take LM0 as a SUSY
->
+point.  In region $C$ we have a SM prediction of 5.1
->
+events and $C_D = 4$ in agreement with the Standard Model,
->
+see Table~\ref{tab:datayield}.  From the LM0 Monte Carlo,
->
+we find $C_S = 8.6$ events.   Thus, including information
->
+on $C_D$ and $C_S$ should {\bf strengthen} the limit, since there
->
+is clearly a deficit of events in the $C$ region in the
->
+LM0 hypothesis.  Instead, we now get a negative ABCD
->
+BG prediction (which is nonsense, so we set it to zero),
->
+and therefore a weaker limit.
->
->
->
->
->
+\begin{figure}[tbh]
->
+\begin{center}
->
+\includegraphics[width=0.5\linewidth]{sigcont.png}
->
+\caption{\label{fig:sigcont}\protect Exclusion curves in the
->
+mSUGRA parameter space,
->
+assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs
->
+with and without the effects of signal contamination.
->
+PDF UNCERTAINTIES ARE NOT INCLUDED.}
->
+\end{center}
->
+\end{figure}
->
->
+A comparison of the exclusion region with and without
->
+signal contamination is shown in Figure~\ref{fig:sigcont}
->
+(with no smoothing).  The effect of signal contamination is
->
+small, of the same order as the quantization of the scan.
->
->
->
+\subsubsection{mSUGRA scans with different values of tan$\beta$}
->
+\label{sec:tanbetascan}
->
->
+For completeness, we also show the exclusion regions calculated
->
+using $\tan\beta = 10$ (Figure~\ref{fig:msugratb10}).
->
->
+\begin{figure}[tbh]
->
+\begin{center}
->
+\includegraphics[width=\linewidth]{exclusion_tanbeta10.pdf}
->
+\caption{\label{fig:msugratb10}\protect Exclusion curves in the mSUGRA parameter space,
->
+assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.  THIS IS STILL MISSING
->
+THE PDF UNCERTAINTIES.  WE ALSO WANT TO IMPROVE THE SMOOTHING PROCEDURE.}
->
+\end{center}
->
+\end{figure}
->
->
->
->
->
->

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Comparing UserCode/claudioc/OSNote2010/limit.tex (file contents): Revision 1.1 by claudioc, Fri Oct 29 02:29:40 2010 UTC vs. Revision 1.34 by claudioc, Fri Jan 14 00:02:59 2011 UTC

Diff Legend

Comparing UserCode/claudioc/OSNote2010/limit.tex (file contents):
Revision 1.1 by claudioc, Fri Oct 29 02:29:40 2010 UTC vs.
Revision 1.34 by claudioc, Fri Jan 14 00:02:59 2011 UTC