cmsnotes/StopSearch/systematics.tex

\section{Systematics Uncertainties in the Background Prediction}
\label{sec:systematics}

The methodology for determining the systematics on the background
predictions has not changed with respect to the nominal analysis.
Because the template method has not changed, the same 
systematic uncertainty is assessed on this prediction (32\%).
The 50\% uncertainty on the WZ and ZZ background is also unchanged.
The systematic uncertainty in the OF background prediction based on 
e$\mu$ events has changed, due to the different composition of this
sample after vetoing events containing b-tagged jets.

As in the nominal analysis, we do not require the e$\mu$ events
to satisfy the dilepton mass requirement and apply a scaling factor K,
extracted from MC, to account for the fraction of e$\mu$ events
which satisfy the dilepton mass requirement. This procedure is used
in order to improve the statistical precision of the OF background estimate.

For the selection used in the nominal analysis, 
the e$\mu$ sample is completely dominated by $t\bar{t}$
events, and we observe that K is statistically consistent with constant with
respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$
background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$
backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant. 
At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$
and VV dominate at high \MET\ (see App.~\ref{app:kinemu}).
Therefore, the sample composition changes
as the \MET\ requirement is varied, and as a result K depends
on the \MET\ requirement. 

We thus measure K in MC separately for each
\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left).
%The systematic uncertainty on K is determined separately for each \MET\
%requirement by comparing the relative difference in K in data vs. MC.
The values of K used are the MC predictions 
%and the total systematic uncertainty on the OF prediction 
%as shown in 
(Table \ref{fig:kvmettable}).
The contribution to the total OF prediction systematic uncertainty 
from K is assessed from the ratio of K in data and MC,
shown in Fig.~\ref{fig:kvmet} (right).
The ratio is consistent with unity to roughly 17\%, 
so we take this value as the systematic from K.
17\% added in quadrature with 7\% from 
the electron to muon efficieny ratio 
(as assessed in the inclusive analysis)
yields a total systematic of $\sim$18\% 
which we round up to 20\%.
For \MET\ $>$ 150, there are no OF events in data inside the Z mass window
so we take a systematic based on the statistical uncertainty
of the MC prediction for K. 
This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV.
%Although we cannot check the value of K in data for \MET\ $>$ 150
%because we find no OF events inside the Z mass window for this \MET\ 
%cut, the overall OF yields with no dilepton mass requirement 
%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC).


%Below Old

%In reevaluating the systematics on the OF prediction, however,
%we observed a different behavior of K as a function of \MET\ 
%as was seen in the inclusive analysis. 

%Recall that K is the ratio of the number of \emu\ events
%inside the Z window to the total number of \emu\ events.
%In the inclusive analysis, it is taken from \ttbar\ MC
%and used to scale the inclusive \emu\ yield in data.
%The yield scaled by K is then corrected for 
%the $e$ vs $\mu$ efficiency difference to obtain the 
%final OF prediction.

%Based on the plot in figure \ref{fig:kvmet}, 
%we choose to use a different
%K for each \MET\ cut and assess a systematic uncertainty
%on the OF prediction based on the difference between 
%K in data and MC. 
%The variation of K as a function of \MET\ is caused 
%by a change in sample composition with increasing \MET.
%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is
%not negligible (as it was in the inclusive analysis)
%because of the b veto. (See appendix \ref{app:kinemu}.)
%At higher \MET, \ttbar\ and diboson backgrounds dominate.


\begin{figure}[hbt]
  \begin{center}
        \includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf}
        \includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf}
        \caption{
          \label{fig:kvmet}\protect 
          The left plot shows
          K as a function of \MET\ in MC (red) and data (black). 
          The bin low edge corresponds to the \MET\ cut, and the 
          bins are inclusive.
          The MC used is a sum of all SM MC used in the yield table of
          section \ref{sec:yields}.
          The right plot is the ratio of K in data to MC.
          The ratio is fit to a line whose slope is consistent with zero
          (the fit parameters are 
          0.9 $\pm$  0.4 for the intercept and
      0.001 $\pm$ 0.005 for the slope).
        }
  \end{center}
\end{figure}


\begin{table}[htb]
\begin{center}
\caption{\label{fig:kvmettable} The values of K used in the OF background prediction. 
The uncertainties shown are the total relative systematic used for the OF prediction,
which is the systematic uncertainty from K added in quadrature with
a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the
inclusive analysis.
}
\begin{tabular}{lcc}
\hline
\MET\ Cut    &    K        &  Relative Systematic \\
\hline
%the met zero row is used only for normalization of the money plot.
%0    &  0.1   &        \\  
30   &  0.12  &  20\%  \\  
60   &  0.13  &  20\%  \\  
80   &  0.12  &  20\%  \\  
100  &  0.12  &  20\%  \\  
150  &  0.09  &  25\%  \\  
200  &  0.06  &  60\%  \\  
\hline
\end{tabular}
\end{center}
\end{table}
Revision:	1.1
Committed:	Sun Jun 24 15:06:07 2012 UTC (12 years, 10 months ago) by benhoob
Content type:	application/x-tex
Branch:	MAIN
Log Message:	Initial commit
#	User	Rev	Content
1	benhoob	1.1	\section{Systematics Uncertainties in the Background Prediction}
2			\label{sec:systematics}
3
4			The methodology for determining the systematics on the background
5			predictions has not changed with respect to the nominal analysis.
6			Because the template method has not changed, the same
7			systematic uncertainty is assessed on this prediction (32\%).
8			The 50\% uncertainty on the WZ and ZZ background is also unchanged.
9			The systematic uncertainty in the OF background prediction based on
10			e$\mu$ events has changed, due to the different composition of this
11			sample after vetoing events containing b-tagged jets.
12
13			As in the nominal analysis, we do not require the e$\mu$ events
14			to satisfy the dilepton mass requirement and apply a scaling factor K,
15			extracted from MC, to account for the fraction of e$\mu$ events
16			which satisfy the dilepton mass requirement. This procedure is used
17			in order to improve the statistical precision of the OF background estimate.
18
19			For the selection used in the nominal analysis,
20			the e$\mu$ sample is completely dominated by $t\bar{t}$
21			events, and we observe that K is statistically consistent with constant with
22			respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$
23			background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$
24			backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant.
25			At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$
26			and VV dominate at high \MET\ (see App.~\ref{app:kinemu}).
27			Therefore, the sample composition changes
28			as the \MET\ requirement is varied, and as a result K depends
29			on the \MET\ requirement.
30
31			We thus measure K in MC separately for each
32			\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left).
33			%The systematic uncertainty on K is determined separately for each \MET\
34			%requirement by comparing the relative difference in K in data vs. MC.
35			The values of K used are the MC predictions
36			%and the total systematic uncertainty on the OF prediction
37			%as shown in
38			(Table \ref{fig:kvmettable}).
39			The contribution to the total OF prediction systematic uncertainty
40			from K is assessed from the ratio of K in data and MC,
41			shown in Fig.~\ref{fig:kvmet} (right).
42			The ratio is consistent with unity to roughly 17\%,
43			so we take this value as the systematic from K.
44			17\% added in quadrature with 7\% from
45			the electron to muon efficieny ratio
46			(as assessed in the inclusive analysis)
47			yields a total systematic of $\sim$18\%
48			which we round up to 20\%.
49			For \MET\ $>$ 150, there are no OF events in data inside the Z mass window
50			so we take a systematic based on the statistical uncertainty
51			of the MC prediction for K.
52			This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV.
53			%Although we cannot check the value of K in data for \MET\ $>$ 150
54			%because we find no OF events inside the Z mass window for this \MET\
55			%cut, the overall OF yields with no dilepton mass requirement
56			%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC).
57
58
59			%Below Old
60
61			%In reevaluating the systematics on the OF prediction, however,
62			%we observed a different behavior of K as a function of \MET\
63			%as was seen in the inclusive analysis.
64
65			%Recall that K is the ratio of the number of \emu\ events
66			%inside the Z window to the total number of \emu\ events.
67			%In the inclusive analysis, it is taken from \ttbar\ MC
68			%and used to scale the inclusive \emu\ yield in data.
69			%The yield scaled by K is then corrected for
70			%the $e$ vs $\mu$ efficiency difference to obtain the
71			%final OF prediction.
72
73			%Based on the plot in figure \ref{fig:kvmet},
74			%we choose to use a different
75			%K for each \MET\ cut and assess a systematic uncertainty
76			%on the OF prediction based on the difference between
77			%K in data and MC.
78			%The variation of K as a function of \MET\ is caused
79			%by a change in sample composition with increasing \MET.
80			%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is
81			%not negligible (as it was in the inclusive analysis)
82			%because of the b veto. (See appendix \ref{app:kinemu}.)
83			%At higher \MET, \ttbar\ and diboson backgrounds dominate.
84
85
86
87
88			\begin{figure}[hbt]
89			\begin{center}
90			\includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf}
91			\includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf}
92			\caption{
93			\label{fig:kvmet}\protect
94			The left plot shows
95			K as a function of \MET\ in MC (red) and data (black).
96			The bin low edge corresponds to the \MET\ cut, and the
97			bins are inclusive.
98			The MC used is a sum of all SM MC used in the yield table of
99			section \ref{sec:yields}.
100			The right plot is the ratio of K in data to MC.
101			The ratio is fit to a line whose slope is consistent with zero
102			(the fit parameters are
103			0.9 $\pm$ 0.4 for the intercept and
104			0.001 $\pm$ 0.005 for the slope).
105			}
106			\end{center}
107			\end{figure}
108
109
110
111			\begin{table}[htb]
112			\begin{center}
113			\caption{\label{fig:kvmettable} The values of K used in the OF background prediction.
114			The uncertainties shown are the total relative systematic used for the OF prediction,
115			which is the systematic uncertainty from K added in quadrature with
116			a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the
117			inclusive analysis.
118			}
119			\begin{tabular}{lcc}
120			\hline
121			\MET\ Cut & K & Relative Systematic \\
122			\hline
123			%the met zero row is used only for normalization of the money plot.
124			%0 & 0.1 & \\
125			30 & 0.12 & 20\% \\
126			60 & 0.13 & 20\% \\
127			80 & 0.12 & 20\% \\
128			100 & 0.12 & 20\% \\
129			150 & 0.09 & 25\% \\
130			200 & 0.06 & 60\% \\
131			\hline
132			\end{tabular}
133			\end{center}
134			\end{table}