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}.

\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/$\sqrt{\rm SumJetPt}$.
{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 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
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 very close to one, with an RMS of order 11\% while
the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.96 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:	1.30
Committed:	Mon Dec 13 08:59:00 2010 UTC (14 years, 4 months ago) by benhoob
Content type:	application/x-tex
Branch:	MAIN
Changes since 1.29:	+5 -4 lines
Log Message:	Removed notes about Fall10 samples
#	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			uncertainty. The results are shown in Fig.~\ref{fig:msugra}.
45
46			\begin{figure}[tbh]
47			\begin{center}
48			\includegraphics[width=0.6\linewidth]{msugra.png}
49			\caption{\label{fig:msugra}\protect Exclusion curve in the mSUGRA parameter space,
50			assuming $\tan\beta=10$, sign of $\mu = +$ and $A_{0}=0$~GeVs.}
51			\end{center}
52			\end{figure}
53
54	claudioc	1.2
55	claudioc	1.10	Conveying additional useful information about the results of
56			a generic ``signature-based'' search such as the one described
57	claudioc	1.11	in this note is a difficult issue. The next paragraph represent
58	claudioc	1.10	our attempt at doing so.
59
60			Other models of new physics in the dilepton final state
61			can be confronted in an approximate way by simple
62			generator-level studies that
63	benhoob	1.23	compare the expected number of events in 34.0~pb$^{-1}$
64	claudioc	1.10	with our upper limit of 4.1 events. The key ingredients
65			of such studies are the kinematical cuts described
66			in this note, the lepton efficiencies, and the detector
67	benhoob	1.21	responses for SumJetPt and \met/$\sqrt{\rm SumJetPt}$.
68			{LOOKING AT THE 38X MC PLOTS BY EYE, THE FOLLOWING QUANTITIES LOOK ABOUT RIGHT.}
69	claudioc	1.10	The muon identification efficiency is $\approx 95\%$;
70			the electron identification efficiency varies from $\approx$ 63\% at
71			$P_T = 10$ GeV to 91\% for $P_T > 30$ GeV. The isolation
72			efficiency in top events varies from $\approx 83\%$ (muons)
73			and $\approx 89\%$ (electrons) at $P_T=10$ GeV to
74	benhoob	1.30	$\approx 95\%$ for $P_T>60$ GeV.
75			%{\bf \color{red} The following numbers were derived from Fall 10 samples. }
76	dbarge	1.29	The average detector
77	claudioc	1.10	responses for SumJetPt and $\met/\sqrt{\rm SumJetPt}$ are
78	dbarge	1.28	$1.00 \pm 0.05$ and $0.96 \pm 0.05$ respectively, where
79	claudioc	1.10	the uncertainties are from the jet energy scale uncertainty.
80	dbarge	1.28	The experimental resolutions on these quantities are 11\% and
81			16\% respectively.
82	claudioc	1.10
83			To justify the statements in the previous paragraph
84			about the detector responses, we plot
85			in Figure~\ref{fig:response} the average response for
86	claudioc	1.8	SumJetPt and \met/$\sqrt{\rm SumJetPt}$ in MC, as well as the
87			efficiency for the cuts on these quantities used in defining the
88	claudioc	1.9	signal region.
89			% (SumJetPt $>$ 300 GeV and \met/$\sqrt{\rm SumJetPt} > 8.5$
90			% Gev$^{\frac{1}{2}}$).
91	benhoob	1.30	%{\bf \color{red} The following numbers were derived from Fall10 samples }
92	claudioc	1.9	We find that the average SumJetPt response
93	dbarge	1.28	in the Monte Carlo is very close to one, with an RMS of order 11\% while
94			the response of \met/$\sqrt{\rm SumJetPt}$ is approximately 0.96 with an
95			RMS of 16\%.
96	claudioc	1.8
97	claudioc	1.10	%Using this information as well as the kinematical
98			%cuts described in Section~\ref{sec:eventSel} and the lepton efficiencies
99			%of Figures~\ref{fig:effttbar}, one should be able to confront
100			%any existing or future model via a relatively simple generator
101			%level study by comparing the expected number of events in 35 pb$^{-1}$
102			%with our upper limit of 4.1 events.
103	claudioc	1.8
104			\begin{figure}[tbh]
105			\begin{center}
106	dbarge	1.25	\includegraphics[width=\linewidth]{selectionEffDec10.png}
107	claudioc	1.8	\caption{\label{fig:response} Left plots: the efficiencies
108			as a function of the true quantities for the SumJetPt (top) and
109			tcMET/$\sqrt{\rm SumJetPt}$ (bottom) requirements for the signal
110			region as a function of their true values. The value of the
111			cuts is indicated by the vertical line.
112			Right plots: The average response and its RMS for the SumJetPt
113			(top) and tcMET/$\sqrt{\rm SumJetPt}$ (bottom) measurements.
114			The response is defined as the ratio of the reconstructed quantity
115			to the true quantity in MC. These plots are done using the LM0
116			Monte Carlo, but they are not expected to depend strongly on
117	benhoob	1.20	the underlying physics.
118	benhoob	1.30	%{\bf \color{red} These plots were made with Fall10 samples. }
119			}
120	claudioc	1.8	\end{center}
121			\end{figure}
122	benhoob	1.22
123
124
125			%%% Nominal
126			% -----------------------------------------
127			% observed events 1
128			% relative error on acceptance 0.000
129			% expected background 1.400
130			% absolute error on background 0.770
131			% desired confidence level 0.95
132			% integration upper limit 30.00
133			% integration step size 0.0100
134			% -----------------------------------------
135			% Are the above correct? y
136			% 1 16.685 0.29375E-06
137			%
138			% limit: less than 4.112 signal events
139
140
141
142			%%% Add 20% acceptance uncertainty based on LM0
143			% -----------------------------------------
144			% observed events 1
145			% relative error on acceptance 0.200
146			% expected background 1.400
147			% absolute error on background 0.770
148			% desired confidence level 0.95
149			% integration upper limit 30.00
150			% integration step size 0.0100
151			% -----------------------------------------
152			% Are the above correct? y
153			% 1 29.995 0.50457E-06
154			%
155	dbarge	1.25	% limit: less than 4.689 signal events