claudioc/OSNote2010/results.tex

%\clearpage

\section{Results}
\label{sec:results}

\begin{figure}[tbh]
\begin{center}
\includegraphics[width=0.75\linewidth]{abcd_35pb.png}
\caption{\label{fig:abcdData}\protect Distributions of SumJetPt 
vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo and data.  Here we also
show our choice of ABCD regions.}
\end{center}
\end{figure}

The data, together with SM expectations is presented 
in Figure~\ref{fig:abcdData}.  We see 1 event in the 
signal region (region $D$).  For more information about
this one candidate events, see Appendix~\ref{sec:cand}.
The Standard Model MC expectation is 1.4 events.

\subsection{Background estimate from the ABCD method}
\label{sec:abcdres}

The data yields in the 
four regions are summarized in Table~\ref{tab:datayield}.
The prediction of the ABCD method is is given by $k_{ABCD} \times (A\times C/B)$ and
is $1.8 \pm 1.0(stat) \pm 0.4(syst)$ events, where $k_{ABCD} = 1.2 \pm 0.2$ as discussed
in Sec.~\ref{sec:abcd}.

\begin{table}[hbt]
\begin{center}
\caption{\label{tab:datayield} Data yields in the four
regions of Figure~\ref{fig:abcdData}, as well as the predicted yield in region D given
by A $\times$C / B.  The quoted uncertainty
on the prediction in data is statistical only, assuming Gaussian errors.
We also show the SM Monte Carlo expectations, scaled to 34.85~pb$^{-1}$.}
\begin{tabular}{l||c|c|c|c||c}
\hline
         sample                          &              A   &              B   &              C   &              D   & A $\times$ C / B  \\


\hline
              sample   &                   A   &                   B   &                   C   &                   D   &                PRED  \\
\hline
$t\bar{t}\rightarrow \ell^{+}\ell^{-}$   &   7.96  $\pm$  0.17   &  33.07  $\pm$  0.35   &   4.81  $\pm$  0.13   &   1.20  $\pm$  0.07   &   1.16  $\pm$  0.04  \\
$t\bar{t}\rightarrow \mathrm{other}$     &   0.15  $\pm$  0.02   &   0.85  $\pm$  0.06   &   0.09  $\pm$  0.02   &   0.04  $\pm$  0.01   &   0.02  $\pm$  0.00  \\
$Z^0 \rightarrow \ell^{+}\ell^{-}$       &   0.03  $\pm$  0.03   &   1.47  $\pm$  0.38   &   0.10  $\pm$  0.10   &   0.10  $\pm$  0.10   &   0.00  $\pm$  0.00  \\
    $W^{\pm}$ + jets                     &   0.00  $\pm$  0.00   &   0.10  $\pm$  0.10   &   0.00  $\pm$  0.00   &   0.00  $\pm$  0.00   &   0.00  $\pm$  0.00  \\
            $W^+W^-$                     &   0.19  $\pm$  0.05   &   0.29  $\pm$  0.06   &   0.02  $\pm$  0.02   &   0.07  $\pm$  0.03   &   0.02  $\pm$  0.01  \\
        $W^{\pm}Z^0$                     &   0.03  $\pm$  0.01   &   0.04  $\pm$  0.02   &   0.01  $\pm$  0.01   &   0.01  $\pm$  0.01   &   0.00  $\pm$  0.00  \\
            $Z^0Z^0$                     &   0.00  $\pm$  0.00   &   0.03  $\pm$  0.01   &   0.00  $\pm$  0.00   &   0.00  $\pm$  0.00   &   0.00  $\pm$  0.00  \\
          single top                     &   0.28  $\pm$  0.01   &   1.00  $\pm$  0.03   &   0.04  $\pm$  0.01   &   0.01  $\pm$  0.00   &   0.01  $\pm$  0.00  \\
\hline
         total SM MC                     &   8.63  $\pm$  0.18   &  36.85  $\pm$  0.53   &   5.07  $\pm$  0.17   &   1.43  $\pm$  0.12   &   1.19  $\pm$  0.05  \\
\hline
                data                     &  11                   &  36                   &   5                   &   1                   &   1.53  $\pm$  0.86  \\
\hline
\end{tabular}
\end{center}
\end{table}

%As a cross-check, we can subtract from the yields in 
%Table~\ref{tab:datayield} the expected DY contributions
%from Table~\ref{tab:ABCD-DY} in order to get a ``purer''
%estimate of the $t\bar{t}$ contribution.  The result
%of this exercise is {\color{red} xx} events.

%\clearpage

\subsection{Background estimate from the $P_T(\ell\ell)$ method}
\label{sec:victoryres}

We first use the $P_T(\ell \ell)$ method to predict the number of events 
in control region A, defined in Sec.~\ref{sec:abcd} as 
$125<{\rm SumJetPt}>300$~GeV and $\met/\sqrt{\rm SumJetPt}>$8.5~GeV$^{1/2}$.
We count the number of events in region
$A'$, defined in Sec.~\ref{sec:othBG} by replacing the above $\met/\sqrt{\rm SumJetPt}$
cut with the same cut on the quantity $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$,
and find $N_{A'}=6$. We subtract off the expected DY contribution in this region
$N_{DY} = 2.5 \pm 2.4$, derived in Sec.~\ref{sec:othBG}.
To predict the yield in region A we take 
$N_A = K \cdot K_C \cdot ( N_{A'} - N_{DY} ) = 6.1 \pm 6.0$
(statistical uncertainty only, assuming Gaussian errors),
where we have taken $K = 1.73$ and $K_C = 1$. This yield is consistent
with the observed yield of 11 events, as shown in 
Table~\ref{tab:victory_control} and displayed in Fig.~\ref{fig:victory} (left).

Encouraged by the good agreement between predicted and observed yields
in the control region, we proceed to perform the $P_T(\ell \ell)$ method 
in the signal region ${\rm SumJetPt}>300$~GeV.
The number of data events in region $D'$, which is defined in 
Section~\ref{sec:othBG} to be the same as region $D$ but with the
$\met/\sqrt{\rm SumJetPt}$ requirement 
replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement,
is $N_{D'}=2$.  
We next subtract off the expected DY contribution of 
$N_{DY}$ = $0.4 \pm 0.4$ events, as calculated 
in Sec.~\ref{sec:othBG}. The BG prediction is 
$N_D = K \cdot K_C \cdot (N_{D'}-N_{DY}) = 2.5 \pm 2.2$ (statistical
uncertainty only, assuming Gaussian errors), where $K=1.54 \pm xx$ 
as derived in Sec.~\ref{sec:victory} and $K_C = 1$.
This prediction is consistent with the observed yield of
1 event, as summarized in Table~\ref{tab:victory_signal} and Fig.~\ref{fig:victory}
(right).


\begin{figure}[hbt]
\begin{center}
\includegraphics[width=0.48\linewidth]{victory_control_35pb.png}
\includegraphics[width=0.48\linewidth]{victory_signal_35pb.png}
\caption{\label{fig:victory}\protect Distributions of 
tcMet/$\sqrt{\rm SumJetPt}$ for the control and signal region.
We show the oberved distributions in both Monte Carlo and data.
We also show the distributions predicted from 
${P_T(\ell\ell)}/\sqrt{\rm SumJetPt}$ in both MC and data.}
\end{center}
\end{figure}


\begin{table}[hbt]
\begin{center}
\caption{\label{tab:victory_control}Results of the dilepton $p_{T}$ template method in the control region
$125 < \mathrm{sumJetPt} < 300$~GeV$^{1/2}$. The predicted and observed yields for
the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data
and MC. The error on the prediction for data is statistical only, assuming
Gaussian errors.}
\begin{tabular}{lccc}
\hline
              & Predicted           &   Observed &  Obs/Pred \\
\hline
total SM   MC &      7.18           &       8.63 &      1.20 \\
         data &    $6.06 \pm 5.95$  &         11 &      1.82 \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[hbt]
\begin{center}
\caption{\label{tab:victory_signal}Results of the dilepton $p_{T}$ template method in the signal region
$\mathrm{sumJetPt} > 300$~GeV$^{1/2}$. The predicted and observed yields for
the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data
and MC. The error on the prediction for data is statistical only, assuming
Gaussian errors.}
\begin{tabular}{lccc}
\hline
              & Predicted                &   Observed &  Obs/Pred \\
\hline
total SM   MC &      1.03                &       1.43 &      1.38 \\
         data &    $2.53 \pm 2.25$       &          1 &      0.40 \\
\hline
\end{tabular}
\end{center}
\end{table}


% \clearpage
\subsection{Summary of results}

 In summary, in the signal region defined as $\mathrm{SumJetPt}>300$~GeV and $\met/\sqrt{\rm SumJetPt} > 8.5$~GeV$^{1/2}$:\\ 
We observe 1 event. \\
We expect 1.4 events from Standard Model MC prediction. \\
The ABCD data driven method predicts $1.8 \pm 1.0(stat) \pm 0.4(syst)$ events. \\
The  $P_T(\ell\ell)$ method predicts $2.5 \pm 2.2$ events.
  
All three background estimates are consistent within their uncertainties.
We thus take as our best estimate of the Standard Model yield in 
the signal region the MC prediction and assign as an uncertainty the 
maximal deviation with either of the data-driven methods,  $N_{BG}=1.4 \pm 1.1$.

We conclude that we see no evidence for an anomalous 
rate of opposite sign isolated dilepton events
at high \met and high SumJetPt.  The extraction of 
quantitative limits on new physics models is discussed
in Section~\ref{sec:limit}.
Revision:	1.24
Committed:	Sat Nov 20 15:23:11 2010 UTC (14 years, 5 months ago) by benhoob
Content type:	application/x-tex
Branch:	MAIN
Changes since 1.23:	+14 -11 lines
Log Message:	Add errors to ABCD table
#	User	Rev	Content
1	claudioc	1.22	%\clearpage
2	benhoob	1.7
3	claudioc	1.1	\section{Results}
4			\label{sec:results}
5
6			\begin{figure}[tbh]
7			\begin{center}
8	benhoob	1.7	\includegraphics[width=0.75\linewidth]{abcd_35pb.png}
9	claudioc	1.1	\caption{\label{fig:abcdData}\protect Distributions of SumJetPt
10			vs. MET$/\sqrt{\rm SumJetPt}$ for SM Monte Carlo and data. Here we also
11			show our choice of ABCD regions.}
12			\end{center}
13			\end{figure}
14
15	claudioc	1.2	The data, together with SM expectations is presented
16	benhoob	1.7	in Figure~\ref{fig:abcdData}. We see 1 event in the
17	claudioc	1.17	signal region (region $D$). For more information about
18			this one candidate events, see Appendix~\ref{sec:cand}.
19			The Standard Model MC expectation is 1.4 events.
20	claudioc	1.2
21			\subsection{Background estimate from the ABCD method}
22			\label{sec:abcdres}
23
24			The data yields in the
25			four regions are summarized in Table~\ref{tab:datayield}.
26	benhoob	1.23	The prediction of the ABCD method is is given by $k_{ABCD} \times (A\times C/B)$ and
27			is $1.8 \pm 1.0(stat) \pm 0.4(syst)$ events, where $k_{ABCD} = 1.2 \pm 0.2$ as discussed
28			in Sec.~\ref{sec:abcd}.
29	claudioc	1.2
30	claudioc	1.1	\begin{table}[hbt]
31			\begin{center}
32			\caption{\label{tab:datayield} Data yields in the four
33	benhoob	1.7	regions of Figure~\ref{fig:abcdData}, as well as the predicted yield in region D given
34	benhoob	1.14	by A $\times$C / B. The quoted uncertainty
35	benhoob	1.4	on the prediction in data is statistical only, assuming Gaussian errors.
36	benhoob	1.7	We also show the SM Monte Carlo expectations, scaled to 34.85~pb$^{-1}$.}
37			\begin{tabular}{l\|\|c\|c\|c\|c\|\|c}
38			\hline
39	benhoob	1.14	sample & A & B & C & D & A $\times$ C / B \\
40	benhoob	1.24
41
42	benhoob	1.7	\hline
43	benhoob	1.24	sample & A & B & C & D & PRED \\
44			\hline
45			$t\bar{t}\rightarrow \ell^{+}\ell^{-}$ & 7.96 $\pm$ 0.17 & 33.07 $\pm$ 0.35 & 4.81 $\pm$ 0.13 & 1.20 $\pm$ 0.07 & 1.16 $\pm$ 0.04 \\
46			$t\bar{t}\rightarrow \mathrm{other}$ & 0.15 $\pm$ 0.02 & 0.85 $\pm$ 0.06 & 0.09 $\pm$ 0.02 & 0.04 $\pm$ 0.01 & 0.02 $\pm$ 0.00 \\
47			$Z^0 \rightarrow \ell^{+}\ell^{-}$ & 0.03 $\pm$ 0.03 & 1.47 $\pm$ 0.38 & 0.10 $\pm$ 0.10 & 0.10 $\pm$ 0.10 & 0.00 $\pm$ 0.00 \\
48			$W^{\pm}$ + jets & 0.00 $\pm$ 0.00 & 0.10 $\pm$ 0.10 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 \\
49			$W^+W^-$ & 0.19 $\pm$ 0.05 & 0.29 $\pm$ 0.06 & 0.02 $\pm$ 0.02 & 0.07 $\pm$ 0.03 & 0.02 $\pm$ 0.01 \\
50			$W^{\pm}Z^0$ & 0.03 $\pm$ 0.01 & 0.04 $\pm$ 0.02 & 0.01 $\pm$ 0.01 & 0.01 $\pm$ 0.01 & 0.00 $\pm$ 0.00 \\
51			$Z^0Z^0$ & 0.00 $\pm$ 0.00 & 0.03 $\pm$ 0.01 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 & 0.00 $\pm$ 0.00 \\
52			single top & 0.28 $\pm$ 0.01 & 1.00 $\pm$ 0.03 & 0.04 $\pm$ 0.01 & 0.01 $\pm$ 0.00 & 0.01 $\pm$ 0.00 \\
53	benhoob	1.7	\hline
54	benhoob	1.24	total SM MC & 8.63 $\pm$ 0.18 & 36.85 $\pm$ 0.53 & 5.07 $\pm$ 0.17 & 1.43 $\pm$ 0.12 & 1.19 $\pm$ 0.05 \\
55	claudioc	1.1	\hline
56	benhoob	1.24	data & 11 & 36 & 5 & 1 & 1.53 $\pm$ 0.86 \\
57	claudioc	1.1	\hline
58			\end{tabular}
59			\end{center}
60			\end{table}
61
62	claudioc	1.3	%As a cross-check, we can subtract from the yields in
63			%Table~\ref{tab:datayield} the expected DY contributions
64			%from Table~\ref{tab:ABCD-DY} in order to get a ``purer''
65			%estimate of the $t\bar{t}$ contribution. The result
66			%of this exercise is {\color{red} xx} events.
67	claudioc	1.2
68	claudioc	1.22	%\clearpage
69	benhoob	1.10
70	claudioc	1.2	\subsection{Background estimate from the $P_T(\ell\ell)$ method}
71			\label{sec:victoryres}
72
73	benhoob	1.11	We first use the $P_T(\ell \ell)$ method to predict the number of events
74	benhoob	1.12	in control region A, defined in Sec.~\ref{sec:abcd} as
75	benhoob	1.19	$125<{\rm SumJetPt}>300$~GeV and $\met/\sqrt{\rm SumJetPt}>$8.5~GeV$^{1/2}$.
76	benhoob	1.12	We count the number of events in region
77			$A'$, defined in Sec.~\ref{sec:othBG} by replacing the above $\met/\sqrt{\rm SumJetPt}$
78			cut with the same cut on the quantity $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$,
79	benhoob	1.15	and find $N_{A'}=6$. We subtract off the expected DY contribution in this region
80			$N_{DY} = 2.5 \pm 2.4$, derived in Sec.~\ref{sec:othBG}.
81			To predict the yield in region A we take
82			$N_A = K \cdot K_C \cdot ( N_{A'} - N_{DY} ) = 6.1 \pm 6.0$
83	benhoob	1.11	(statistical uncertainty only, assuming Gaussian errors),
84	benhoob	1.15	where we have taken $K = 1.73$ and $K_C = 1$. This yield is consistent
85			with the observed yield of 11 events, as shown in
86	benhoob	1.11	Table~\ref{tab:victory_control} and displayed in Fig.~\ref{fig:victory} (left).
87
88			Encouraged by the good agreement between predicted and observed yields
89			in the control region, we proceed to perform the $P_T(\ell \ell)$ method
90			in the signal region ${\rm SumJetPt}>300$~GeV.
91	claudioc	1.2	The number of data events in region $D'$, which is defined in
92			Section~\ref{sec:othBG} to be the same as region $D$ but with the
93			$\met/\sqrt{\rm SumJetPt}$ requirement
94	benhoob	1.11	replaced by a $P_T(\ell\ell)/\sqrt{\rm SumJetPt}$ requirement,
95	benhoob	1.13	is $N_{D'}=2$.
96			We next subtract off the expected DY contribution of
97	benhoob	1.14	$N_{DY}$ = $0.4 \pm 0.4$ events, as calculated
98	benhoob	1.13	in Sec.~\ref{sec:othBG}. The BG prediction is
99	benhoob	1.14	$N_D = K \cdot K_C \cdot (N_{D'}-N_{DY}) = 2.5 \pm 2.2$ (statistical
100	benhoob	1.13	uncertainty only, assuming Gaussian errors), where $K=1.54 \pm xx$
101	benhoob	1.11	as derived in Sec.~\ref{sec:victory} and $K_C = 1$.
102	benhoob	1.13	This prediction is consistent with the observed yield of
103	benhoob	1.12	1 event, as summarized in Table~\ref{tab:victory_signal} and Fig.~\ref{fig:victory}
104			(right).
105	benhoob	1.11
106	claudioc	1.1
107	claudioc	1.3	\begin{figure}[hbt]
108			\begin{center}
109	benhoob	1.8	\includegraphics[width=0.48\linewidth]{victory_control_35pb.png}
110			\includegraphics[width=0.48\linewidth]{victory_signal_35pb.png}
111	claudioc	1.3	\caption{\label{fig:victory}\protect Distributions of
112			tcMet/$\sqrt{\rm SumJetPt}$ for the control and signal region.
113			We show the oberved distributions in both Monte Carlo and data.
114			We also show the distributions predicted from
115	benhoob	1.4	${P_T(\ell\ell)}/\sqrt{\rm SumJetPt}$ in both MC and data.}
116	claudioc	1.3	\end{center}
117			\end{figure}
118
119
120	benhoob	1.14
121	benhoob	1.9	\begin{table}[hbt]
122			\begin{center}
123	benhoob	1.13	\caption{\label{tab:victory_control}Results of the dilepton $p_{T}$ template method in the control region
124	benhoob	1.19	$125 < \mathrm{sumJetPt} < 300$~GeV$^{1/2}$. The predicted and observed yields for
125	benhoob	1.9	the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data
126			and MC. The error on the prediction for data is statistical only, assuming
127			Gaussian errors.}
128	benhoob	1.13	\begin{tabular}{lccc}
129	benhoob	1.9	\hline
130			& Predicted & Observed & Obs/Pred \\
131			\hline
132	benhoob	1.14	total SM MC & 7.18 & 8.63 & 1.20 \\
133	benhoob	1.16	data & $6.06 \pm 5.95$ & 11 & 1.82 \\
134	benhoob	1.9	\hline
135			\end{tabular}
136			\end{center}
137			\end{table}
138
139			\begin{table}[hbt]
140			\begin{center}
141	benhoob	1.13	\caption{\label{tab:victory_signal}Results of the dilepton $p_{T}$ template method in the signal region
142	benhoob	1.19	$\mathrm{sumJetPt} > 300$~GeV$^{1/2}$. The predicted and observed yields for
143	benhoob	1.9	the region $\mathrm{tcmet}/\sqrt{\mathrm{sumJetPt}}>$~8.5 are shown for data
144			and MC. The error on the prediction for data is statistical only, assuming
145			Gaussian errors.}
146	benhoob	1.13	\begin{tabular}{lccc}
147	benhoob	1.9	\hline
148	benhoob	1.11	& Predicted & Observed & Obs/Pred \\
149	benhoob	1.9	\hline
150	benhoob	1.14	total SM MC & 1.03 & 1.43 & 1.38 \\
151			data & $2.53 \pm 2.25$ & 1 & 0.40 \\
152	benhoob	1.9	\hline
153			\end{tabular}
154			\end{center}
155			\end{table}
156
157
158	claudioc	1.22	% \clearpage
159	claudioc	1.3	\subsection{Summary of results}
160	benhoob	1.21
161			In summary, in the signal region defined as $\mathrm{SumJetPt}>300$~GeV and $\met/\sqrt{\rm SumJetPt} > 8.5$~GeV$^{1/2}$:\\
162			We observe 1 event. \\
163			We expect 1.4 events from Standard Model MC prediction. \\
164	benhoob	1.23	The ABCD data driven method predicts $1.8 \pm 1.0(stat) \pm 0.4(syst)$ events. \\
165	benhoob	1.21	The $P_T(\ell\ell)$ method predicts $2.5 \pm 2.2$ events.
166
167			All three background estimates are consistent within their uncertainties.
168			We thus take as our best estimate of the Standard Model yield in
169			the signal region the MC prediction and assign as an uncertainty the
170			maximal deviation with either of the data-driven methods, $N_{BG}=1.4 \pm 1.1$.
171
172			We conclude that we see no evidence for an anomalous
173	claudioc	1.1	rate of opposite sign isolated dilepton events
174			at high \met and high SumJetPt. The extraction of
175			quantitative limits on new physics models is discussed
176	benhoob	1.5	in Section~\ref{sec:limit}.