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Comparing UserCode/claudioc/OSNote2010/limit.tex (file contents):
Revision 1.28 by dbarge, Mon Dec 13 03:02:37 2010 UTC vs.
Revision 1.37 by claudioc, Fri Jan 21 03:47:11 2011 UTC

+%{\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$^{\frac{1}{2}}$.
+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, and we also find 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
+are from energy scale (Section~\ref{sec:systematics}), luminosity,
+and lepton efficiency.
-–
+We also performed a scan of the mSUGRA parameter space. We set $\tan\beta=10$,
-–
+sign of $\mu = +$, $A_{0}=0$~GeV, and scan the $m_{0}$ and $m_{1/2}$ parameters
-–
+in steps of 10~GeV. For each scan point, we exclude the point if the expected
-–
+yield in the signal region exceeds 4.7, which is the 95\% CL upper limit
-–
+based on an expected background of $N_{BG}=1.4 \pm 0.8$ and a 20\% acceptance
-–
+uncertainty. The results are shown in Fig.~\ref{fig:msugra}.
-–
-–
+\begin{figure}[tbh]
-–
+\begin{center}
-–
+\includegraphics[width=0.6\linewidth]{msugra.png}
-–
+\caption{\label{fig:msugra}\protect Exclusion curve in the mSUGRA parameter space,
-–
+assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.}
-–
+\end{center}
-–
+\end{figure}
-–
-+
+\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.  The next paragraph represent
-<
+our attempt at doing so.
->
+in this note is a difficult issue.
->
+Here we attempt to present our result in the most general
->
+way.
-<
+Other models of new physics in the dilepton final state
->
+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$^{-1}$
+of such studies are the kinematical cuts described
+in this note, the lepton efficiencies, and the detector
+responses for SumJetPt and \met/$\sqrt{\rm SumJetPt}$.
-–
+{LOOKING AT THE 38X MC PLOTS BY EYE, THE FOLLOWING QUANTITIES LOOK ABOUT RIGHT.}
+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 quantities were calculated
-<
+with Spring10 samples. } The average detector
->
+$\approx 95\%$ 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
-<
+$1.00 \pm 0.05$ and $0.96 \pm 0.05$ respectively, where
->
+$1.02 \pm 0.05$ 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.
+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 }
->
+%{\bf \color{red} The following numbers were derived from Fall10 samples }
+We find that the average SumJetPt response
-<
+in the Monte Carlo is very close to one, with an RMS of order 11\% while
-<
+the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.96 with an
->
+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
+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. } }
->
+%{\bf \color{red} These plots were made with Fall10 samples. }
->
+}
+\end{center}
+\end{figure}
+%    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 A 13\% PDF uncertainty on the product of cross-section and acceptance.
-+
+This uncertainty was calculated using the method of Reference~\cite{ref:pdf} for a
-+
+number of points in the $m_0$ vs. $m_{1/2}$ plane, and was found to be
-+
+approximately independent of mSUGRA parameters, see Table~\ref{tab:pdf}.
-+
+\end{itemize}
-+
+\item We use the ``log-normal'' model for the nuisance parameters
-+
+in cl95cms
-+
+\end{itemize}
-+
+We actually calculate three different values of $N_{UL}$:
-+
+\begin{enumerate}
-+
+\item Observed $N_{UL}$ asssuming the NLO cross-section.
-+
+\item Observed $N_{UL}$ asssuming the LO cross-section. In this case
-+
+uncertainties due to PDFs and renormlization/factorization scales are not
-+
+included.
-+
+\item Expected $N_{UL}$ sssuming the NLO cross-section.  This is
-+
+calculated using the the CLA function also available in cl95cms.
-+
+\end{enumerate}
-+
-+
+\begin{table}[hbt]
-+
+\begin{center}
-+
+\caption{\label{tab:pdf} PDF uncertainties on the product of
-+
+cross-section and acceptance for a number of representative points
-+
+in the mSUGRA plane.}
-+
+\begin{tabular}{c|c|c|c|c|c}
-+
+$\tan\beta$ & $m_0$ & $m_{1/2}$ & sign of $\mu$ & $A_0$ & uncertanity (\%)   \\ \hline
-+
+          & 50    & 260       & +             &  0    & $^{+13}_{-9}$ \\
-+
+          & 50    & 270       & +             &  0    & $^{+13}_{-9}$ \\
-+
+          & 60    & 260       & +             &  0    & $^{+14}_{-9}$ \\
-+
+          & 200   & 200       & +             &  0    & $^{+12}_{-9}$ \\
-+
+          & 200   & 210       & +             &  0    & $^{+13}_{-10}$ \\
-+
+          & 210   & 200       & +             &  0    & $^{+11}_{-8}$ \\
-+
+          & 200   & 140       & +             &  0    & $^{+16}_{-12}$ \\
-+
+          & 140   & 150       & +             &  0    & $^{+08}_{-8}$ \\
-+
+          & 150   & 140       & +             &  0    & $^{+14}_{-10}$ \\
-+
+         & 60    & 260       & +             &  0    & $^{+16}_{-11}$ \\
-+
+         & 100   & 260       & +             &  0    & $^{+14}_{-10}$ \\
-+
+         & 100   & 260       & +             &  0    & $^{+12}_{-9}$ \\
-+
+         & 90    & 260       & +             &  0    & $^{+15}_{-10}$ \\
-+
+         & 240   & 260       & +             &  0    & $^{+10}_{-8}$ \\
-+
+         & 240   & 260       & +             &  0    & $^{+13}_{-10}$  \\ \hline
-+
+\end{tabular}
-+
+\end{center}
-+
+\end{table}
-+
-+
-+
+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.  The excluded points
-+
+are shown in Figure~\ref{fig:tanbeta3raw}; in this Figure we also show
-+
+ad-hoc curves that represent the excluded regions.
-+
+In Figure~\ref{fig:msugra} we show our results compared with
-+
+results from previous experiments.
-+
-+
-+
+\begin{figure}[tbh]
-+
+\begin{center}
-+
+\includegraphics[width=0.4\linewidth]{tanbeta3_NLO_observed.png}
-+
+\includegraphics[width=0.4\linewidth]{tanbeta3_NLO_expected.png}
-+
+\includegraphics[width=0.4\linewidth]{tanbeta3_LO_observed.png}
-+
+\caption{\label{fig:tanbeta3raw}\protect Excluded points in the
-+
+$m_0$ vs. $m_{1/2}$ plane for $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0$~GeVs.
-+
+Top left: observed, using the NLO cross-section.
-+
+Top right: expected using the NLO cross-section.
-+
+Bottom left: observed, using the LO cross-section.
-+
+The curves are meant to represent the excluded regions.}
-+
+\end{center}
-+
+\end{figure}
-+
-+
-+
+\begin{figure}[tbh]
-+
+\begin{center}
-+
+\includegraphics[width=\linewidth]{exclusion.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.}
-+
+\end{center}
-+
+\end{figure}
-+
-+
-+
-+
+\clearpage
-+
-+
+\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 Observed NLO 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. (Note: this
-+
+plot was made without the PDF uncertainties.}
-+
+\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 Observed NLO 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.
-+
+Note: 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 region calculated
-+
+using $\tan\beta = 10$ (Figure~\ref{fig:msugratb10}).
-+
-+
-+
+\begin{figure}[tbh]
-+
+\begin{center}
-+
+\includegraphics[width=0.4\linewidth]{tanbeta10_NLO_observed.png}
-+
+\caption{\label{fig:tanbeta10raw}\protect Excluded points in the
-+
+$m_0$ vs. $m_{1/2}$ plane for $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.
-+
+This plot is made using the NLO cross-sections.
-+
+The curves is meant to represent the excluded region.}
-+
+\end{center}
-+
+\end{figure}
-+
-+
+\begin{figure}[tbh]
-+
+\begin{center}
-+
+\includegraphics[width=\linewidth]{exclusion_tanbeta10.pdf}
-+
+\caption{\label{fig:msugratb10}\protect Exclusion curve in the mSUGRA parameter space,
-+
+assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.}
-+
+\end{center}
-+
+\end{figure}
-+
-+
-+
-+
-+
-+

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Comparing UserCode/claudioc/OSNote2010/limit.tex (file contents): Revision 1.28 by dbarge, Mon Dec 13 03:02:37 2010 UTC vs. Revision 1.37 by claudioc, Fri Jan 21 03:47:11 2011 UTC

Diff Legend

Comparing UserCode/claudioc/OSNote2010/limit.tex (file contents):
Revision 1.28 by dbarge, Mon Dec 13 03:02:37 2010 UTC vs.
Revision 1.37 by claudioc, Fri Jan 21 03:47:11 2011 UTC