claudioc/OSNote2010/limit.tex

\section{Limit on new physics}
\label{sec:limit}

%{\bf \color{red} The numbers in this Section need to be double checked.}

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, and we also find 4.1.
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.

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}.
This figure is still preliminary: 
\begin{itemize}
\item The process dependent k-factors from Prospino were not yet available
when the figure was made.  We took a flat k=1.4.
\item The PDF uncertainties were still missing.
\item The limits from other experiments are missing.  Wwe are hoping to 
converge on a common format for this plot with other SUSY analyses, so 
we have not made any attempt to make the plot look pretty (!).
\item As mentioned above, we took a constant acceptance uncertainty
instead of calculating the uncertainty point by point.
\end{itemize}

\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}


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.

Other 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 
16\% 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 
Revision:	1.31
Committed:	Tue Dec 14 05:53:07 2010 UTC (14 years, 4 months ago) by claudioc
Content type:	application/x-tex
Branch:	MAIN
CVS Tags:	v3
Changes since 1.30:	+16 -5 lines
Log Message:	version 3
#	User	Rev	Content
1	claudioc	1.1	\section{Limit on new physics}
2			\label{sec:limit}
3	claudioc	1.2
4	claudioc	1.10	%{\bf \color{red} The numbers in this Section need to be double checked.}
5	claudioc	1.2
6			As discussed in Section~\ref{sec:results}, we see one event
7			in the signal region, defined as SumJetPt$>$300 GeV and
8			\met/$\sqrt{\rm SumJetPt}>8.5$ GeV$^{\frac{1}{2}}$.
9
10	benhoob	1.22	The background prediction from the SM Monte Carlo is 1.3 events.
11	benhoob	1.15	%, where the uncertainty comes from
12			%the jet energy scale (30\%, see Section~\ref{sec:systematics}),
13			%the luminosity (10\%), and the lepton/trigger
14			%efficiency (10\%)\footnote{Other uncertainties associated with
15			%the modeling of $t\bar{t}$ in MadGraph have not been evaluated.
16			%The uncertainty on $pp \to \sigma(t\bar{t})$ is also not included.}.
17	claudioc	1.2	The data driven background predictions from the ABCD method
18	benhoob	1.22	and the $P_T(\ell\ell)$ method are $1.3 \pm 0.8({\rm stat}) \pm 0.3({\rm syst})$
19			and $2.1 \pm 2.1({\rm stat}) \pm 0.6({\rm syst})$, respectively.
20	claudioc	1.2
21			These three predictions are in good agreement with each other
22			and with the observation of one event in the signal region.
23	benhoob	1.5	We calculate a Bayesian 95\% CL upper limit\cite{ref:bayes.f}
24	benhoob	1.17	on the number of non SM events in the signal region to be 4.1.
25	benhoob	1.18	We have also calculated this limit using a profile likelihood method
26			as implemented in the cl95cms software, and we also find 4.1.
27	benhoob	1.22	These limits were calculated using a background prediction of $N_{BG} = 1.4 \pm 0.8$
28			events, the error-weighted average of the ABCD and $P_T(\ell\ell)$ background
29			predictions. The upper limit is not very sensitive to the choice of
30	claudioc	1.2	$N_{BG}$ and its uncertainty.
31
32			To get a feeling for the sensitivity of this search to some
33			popular SUSY models, we remind the reader of the number of expected
34	benhoob	1.22	LM0 and LM1 events from Table~\ref{tab:sigcont}: $8.6 \pm 1.6$
35			events and $3.6 \pm 0.5$ events respectively, where the uncertainties
36	claudioc	1.2	are from energy scale (Section~\ref{sec:systematics}), luminosity,
37	benhoob	1.23	and lepton efficiency.
38
39			We also performed a scan of the mSUGRA parameter space. We set $\tan\beta=10$,
40			sign of $\mu = +$, $A_{0}=0$~GeV, and scan the $m_{0}$ and $m_{1/2}$ parameters
41			in steps of 10~GeV. For each scan point, we exclude the point if the expected
42			yield in the signal region exceeds 4.7, which is the 95\% CL upper limit
43			based on an expected background of $N_{BG}=1.4 \pm 0.8$ and a 20\% acceptance
44	claudioc	1.31	uncertainty.
45			The results are shown in Fig.~\ref{fig:msugra}.
46			This figure is still preliminary:
47			\begin{itemize}
48			\item The process dependent k-factors from Prospino were not yet available
49			when the figure was made. We took a flat k=1.4.
50			\item The PDF uncertainties were still missing.
51			\item The limits from other experiments are missing. Wwe are hoping to
52			converge on a common format for this plot with other SUSY analyses, so
53			we have not made any attempt to make the plot look pretty (!).
54			\item As mentioned above, we took a constant acceptance uncertainty
55			instead of calculating the uncertainty point by point.
56			\end{itemize}
57	benhoob	1.23
58			\begin{figure}[tbh]
59			\begin{center}
60			\includegraphics[width=0.6\linewidth]{msugra.png}
61			\caption{\label{fig:msugra}\protect Exclusion curve in the mSUGRA parameter space,
62			assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.}
63			\end{center}
64			\end{figure}
65
66	claudioc	1.2
67	claudioc	1.10	Conveying additional useful information about the results of
68			a generic ``signature-based'' search such as the one described
69	claudioc	1.11	in this note is a difficult issue. The next paragraph represent
70	claudioc	1.10	our attempt at doing so.
71
72			Other models of new physics in the dilepton final state
73			can be confronted in an approximate way by simple
74			generator-level studies that
75	benhoob	1.23	compare the expected number of events in 34.0~pb$^{-1}$
76	claudioc	1.10	with our upper limit of 4.1 events. The key ingredients
77			of such studies are the kinematical cuts described
78			in this note, the lepton efficiencies, and the detector
79	benhoob	1.21	responses for SumJetPt and \met/$\sqrt{\rm SumJetPt}$.
80	claudioc	1.10	The muon identification efficiency is $\approx 95\%$;
81			the electron identification efficiency varies from $\approx$ 63\% at
82			$P_T = 10$ GeV to 91\% for $P_T > 30$ GeV. The isolation
83			efficiency in top events varies from $\approx 83\%$ (muons)
84			and $\approx 89\%$ (electrons) at $P_T=10$ GeV to
85	benhoob	1.30	$\approx 95\%$ for $P_T>60$ GeV.
86			%{\bf \color{red} The following numbers were derived from Fall 10 samples. }
87	dbarge	1.29	The average detector
88	claudioc	1.10	responses for SumJetPt and $\met/\sqrt{\rm SumJetPt}$ are
89	claudioc	1.31	$1.02 \pm 0.05$ and $0.94 \pm 0.05$ respectively, where
90	claudioc	1.10	the uncertainties are from the jet energy scale uncertainty.
91	dbarge	1.28	The experimental resolutions on these quantities are 11\% and
92			16\% respectively.
93	claudioc	1.10
94			To justify the statements in the previous paragraph
95			about the detector responses, we plot
96			in Figure~\ref{fig:response} the average response for
97	claudioc	1.8	SumJetPt and \met/$\sqrt{\rm SumJetPt}$ in MC, as well as the
98			efficiency for the cuts on these quantities used in defining the
99	claudioc	1.9	signal region.
100			% (SumJetPt $>$ 300 GeV and \met/$\sqrt{\rm SumJetPt} > 8.5$
101			% Gev$^{\frac{1}{2}}$).
102	benhoob	1.30	%{\bf \color{red} The following numbers were derived from Fall10 samples }
103	claudioc	1.9	We find that the average SumJetPt response
104	claudioc	1.31	in the Monte Carlo is about 1.02, with an RMS of order 11\% while
105			the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.94 with an
106	dbarge	1.28	RMS of 16\%.
107	claudioc	1.8
108	claudioc	1.10	%Using this information as well as the kinematical
109			%cuts described in Section~\ref{sec:eventSel} and the lepton efficiencies
110			%of Figures~\ref{fig:effttbar}, one should be able to confront
111			%any existing or future model via a relatively simple generator
112			%level study by comparing the expected number of events in 35 pb$^{-1}$
113			%with our upper limit of 4.1 events.
114	claudioc	1.8
115			\begin{figure}[tbh]
116			\begin{center}
117	dbarge	1.25	\includegraphics[width=\linewidth]{selectionEffDec10.png}
118	claudioc	1.8	\caption{\label{fig:response} Left plots: the efficiencies
119			as a function of the true quantities for the SumJetPt (top) and
120			tcMET/$\sqrt{\rm SumJetPt}$ (bottom) requirements for the signal
121			region as a function of their true values. The value of the
122			cuts is indicated by the vertical line.
123			Right plots: The average response and its RMS for the SumJetPt
124			(top) and tcMET/$\sqrt{\rm SumJetPt}$ (bottom) measurements.
125			The response is defined as the ratio of the reconstructed quantity
126			to the true quantity in MC. These plots are done using the LM0
127			Monte Carlo, but they are not expected to depend strongly on
128	benhoob	1.20	the underlying physics.
129	benhoob	1.30	%{\bf \color{red} These plots were made with Fall10 samples. }
130			}
131	claudioc	1.8	\end{center}
132			\end{figure}
133	benhoob	1.22
134
135
136			%%% Nominal
137			% -----------------------------------------
138			% observed events 1
139			% relative error on acceptance 0.000
140			% expected background 1.400
141			% absolute error on background 0.770
142			% desired confidence level 0.95
143			% integration upper limit 30.00
144			% integration step size 0.0100
145			% -----------------------------------------
146			% Are the above correct? y
147			% 1 16.685 0.29375E-06
148			%
149			% limit: less than 4.112 signal events
150
151
152
153			%%% Add 20% acceptance uncertainty based on LM0
154			% -----------------------------------------
155			% observed events 1
156			% relative error on acceptance 0.200
157			% expected background 1.400
158			% absolute error on background 0.770
159			% desired confidence level 0.95
160			% integration upper limit 30.00
161			% integration step size 0.0100
162			% -----------------------------------------
163			% Are the above correct? y
164			% 1 29.995 0.50457E-06
165			%
166	dbarge	1.25	% limit: less than 4.689 signal events