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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.
1	>	%\section{Systematics Uncertainties on the Background Prediction}
2	>	%\label{sec:systematics}
3
4	+	\subsection{Uncertainty on the \ttll\ Acceptance}
5
6	+	The \ttbar\ background prediction is obtained from MC, with corrections
7	+	derived from control samples in data. The uncertainty associated with
8	+	the theoretical modeling of the \ttbar\ production and decay is
9	+	estimated by comparing the background predictions obtained using
10	+	alternative MC samples. It should be noted that the full analysis is
11	+	performed with the alternative samples under consideration,
12	+	including the derivation of the various data-to-MC scale factors.
13	+	The variations considered are
14	+
15	+	\begin{itemize}
16	+	\item Top mass: The alternative values for the top mass differ
17	+	from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}}
18	+	= 166.5~\GeV$.
19	+	\item Jet-parton matching scale: This corresponds to variations in the
20	+	scale at which the Matrix Element partons from Madgraph are matched
21	+	to Parton Shower partons from Pythia. The nominal value is
22	+	$x_q>20~\GeV$. The alternative values used are $x_q>10~\GeV$ and
23	+	$x_q>40~\GeV$.
24	+	\item Renormalization and factorization scale: The alternative samples
25	+	correspond to variations in the scale $\times 2$ and $\times 0.5$. The nominal
26	+	value for the scale used is $Q^2 = m_{\mathrm{top}}^2 +
27	+	\sum_{\mathrm{jets}} \pt^2$.
28	+	\item Alternative generators: Samples produced with different
29	+	generators include MC@NLO and Powheg (NLO generators) and
30	+	Pythia (LO). It may also be noted that MC@NLO uses Herwig6 for the
31	+	hadronisation, while POWHEG uses Pythia6.
32	+	\item Modeling of taus: The alternative sample does not include
33	+	Tauola and is otherwise identical to the Powheg sample.
34	+	\item The PDF uncertainty is estimated following the PDF4LHC
35	+	recommendations[CITE]. The events are reweighted using alternative
36	+	PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the
37	+	alternative eigenvector variations and the ``master equation''. In
38	+	addition, the NNPDF2.1 set with 100 replicas. The central value is
39	+	determined from the mean and the uncertainty is derived from the
40	+	$1\sigma$ range. The overall uncertainty is derived from the envelope of the
41	+	alternative predictions and their uncertainties.
42	+	\end{itemize}
43
44
45		\begin{figure}[hbt]
46		\begin{center}
47	<	\includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf}
91	<	\includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf}
47	>	\includegraphics[width=0.8\linewidth]{plots/n_dl_syst_comp.png}
48		\caption{
49	<	\label{fig:kvmet}\protect
50	<	The left plot shows
51	<	K as a function of \MET\ in MC (red) and data (black).
52	<	The bin low edge corresponds to the \MET\ cut, and the
53	<	bins are inclusive.
54	<	The MC used is a sum of all SM MC used in the yield table of
55	<	section \ref{sec:yields}.
56	<	The right plot is the ratio of K in data to MC.
57	<	The ratio is fit to a line whose slope is consistent with zero
58	<	(the fit parameters are
59	<	0.9 $\pm$  0.4 for the intercept and
60	<	0.001 $\pm$ 0.005 for the slope).
61	<	}
62	<	\end{center}
63	<	\end{figure}
64	<
65	<
66	<
67	<	\begin{table}[htb]
68	<	\begin{center}
69	<	\caption{\label{fig:kvmettable} The values of K used in the OF background prediction.
70	<	The uncertainties shown are the total relative systematic used for the OF prediction,
71	<	which is the systematic uncertainty from K added in quadrature with
72	<	a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the
73	<	inclusive analysis.
74	<	}
75	<	\begin{tabular}{lcc}
76	<	\hline
77	<	\MET\ Cut    &    K        &  Relative Systematic \\
78	<	\hline
79	<	%the met zero row is used only for normalization of the money plot.
80	<	%0    &  0.1   &        \\
81	<	30   &  0.12  &  20\%  \\
82	<	60   &  0.13  &  20\%  \\
83	<	80   &  0.12  &  20\%  \\
84	<	100  &  0.12  &  20\%  \\
85	<	150  &  0.09  &  25\%  \\
86	<	200  &  0.06  &  60\%  \\
87	<	\hline
88	<	\end{tabular}
89	<	\end{center}
90	<	\end{table}
49	>	\label{fig:ttllsyst}%\protect
50	>	Comparison of the \ttll\ central prediction with those using
51	>	alternative MC samples. The blue band corresponds to the
52	>	total statistical error for all data and MC samples. The
53	>	alternative sample predictions are indicated by the
54	>	datapoints. The uncertainties on the alternative predictions
55	>	correspond to the uncorrelated statistical uncertainty from
56	>	the size of the alternative sample only.}
57	>	\end{center}
58	>	\end{figure}
59	>
60	>
61	>
62	>	%
63	>	%
64	>	%The methodology for determining the systematics on the background
65	>	%predictions has not changed with respect to the nominal analysis.
66	>	%Because the template method has not changed, the same
67	>	%systematic uncertainty is assessed on this prediction (32\%).
68	>	%The 50\% uncertainty on the WZ and ZZ background is also unchanged.
69	>	%The systematic uncertainty in the OF background prediction based on
70	>	%e$\mu$ events has changed, due to the different composition of this
71	>	%sample after vetoing events containing b-tagged jets.
72	>	%
73	>	%As in the nominal analysis, we do not require the e$\mu$ events
74	>	%to satisfy the dilepton mass requirement and apply a scaling factor K,
75	>	%extracted from MC, to account for the fraction of e$\mu$ events
76	>	%which satisfy the dilepton mass requirement. This procedure is used
77	>	%in order to improve the statistical precision of the OF background estimate.
78	>	%
79	>	%For the selection used in the nominal analysis,
80	>	%the e$\mu$ sample is completely dominated by $t\bar{t}$
81	>	%events, and we observe that K is statistically consistent with constant with
82	>	%respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$
83	>	%background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$
84	>	%backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant.
85	>	%At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$
86	>	%and VV dominate at high \MET\ (see App.~\ref{app:kinemu}).
87	>	%Therefore, the sample composition changes
88	>	%as the \MET\ requirement is varied, and as a result K depends
89	>	%on the \MET\ requirement.
90	>	%
91	>	%We thus measure K in MC separately for each
92	>	%\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left).
93	>	%%The systematic uncertainty on K is determined separately for each \MET\
94	>	%%requirement by comparing the relative difference in K in data vs. MC.
95	>	%The values of K used are the MC predictions
96	>	%%and the total systematic uncertainty on the OF prediction
97	>	%%as shown in
98	>	%(Table \ref{fig:kvmettable}).
99	>	%The contribution to the total OF prediction systematic uncertainty
100	>	%from K is assessed from the ratio of K in data and MC,
101	>	%shown in Fig.~\ref{fig:kvmet} (right).
102	>	%The ratio is consistent with unity to roughly 17\%,
103	>	%so we take this value as the systematic from K.
104	>	%17\% added in quadrature with 7\% from
105	>	%the electron to muon efficieny ratio
106	>	%(as assessed in the inclusive analysis)
107	>	%yields a total systematic of $\sim$18\%
108	>	%which we round up to 20\%.
109	>	%For \MET\ $>$ 150, there are no OF events in data inside the Z mass window
110	>	%so we take a systematic based on the statistical uncertainty
111	>	%of the MC prediction for K.
112	>	%This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV.
113	>	%%Although we cannot check the value of K in data for \MET\ $>$ 150
114	>	%%because we find no OF events inside the Z mass window for this \MET\
115	>	%%cut, the overall OF yields with no dilepton mass requirement
116	>	%%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC).
117	>	%
118	>	%
119	>	%%Below Old
120	>	%
121	>	%%In reevaluating the systematics on the OF prediction, however,
122	>	%%we observed a different behavior of K as a function of \MET\
123	>	%%as was seen in the inclusive analysis.
124	>	%
125	>	%%Recall that K is the ratio of the number of \emu\ events
126	>	%%inside the Z window to the total number of \emu\ events.
127	>	%%In the inclusive analysis, it is taken from \ttbar\ MC
128	>	%%and used to scale the inclusive \emu\ yield in data.
129	>	%%The yield scaled by K is then corrected for
130	>	%%the $e$ vs $\mu$ efficiency difference to obtain the
131	>	%%final OF prediction.
132	>	%
133	>	%%Based on the plot in figure \ref{fig:kvmet},
134	>	%%we choose to use a different
135	>	%%K for each \MET\ cut and assess a systematic uncertainty
136	>	%%on the OF prediction based on the difference between
137	>	%%K in data and MC.
138	>	%%The variation of K as a function of \MET\ is caused
139	>	%%by a change in sample composition with increasing \MET.
140	>	%%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is
141	>	%%not negligible (as it was in the inclusive analysis)
142	>	%%because of the b veto. (See appendix \ref{app:kinemu}.)
143	>	%%At higher \MET, \ttbar\ and diboson backgrounds dominate.
144	>	%
145	>	%
146	>	%
147	>	%
148	>	%\begin{figure}[hbt]
149	>	%  \begin{center}
150	>	%       \includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf}
151	>	%       \includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf}
152	>	%       \caption{
153	>	%         \label{fig:kvmet}\protect
154	>	%         The left plot shows
155	>	%         K as a function of \MET\ in MC (red) and data (black).
156	>	%         The bin low edge corresponds to the \MET\ cut, and the
157	>	%         bins are inclusive.
158	>	%         The MC used is a sum of all SM MC used in the yield table of
159	>	%         section \ref{sec:yields}.
160	>	%         The right plot is the ratio of K in data to MC.
161	>	%         The ratio is fit to a line whose slope is consistent with zero
162	>	%         (the fit parameters are
163	>	%         0.9 $\pm$  0.4 for the intercept and
164	>	%      0.001 $\pm$ 0.005 for the slope).
165	>	%       }
166	>	%  \end{center}
167	>	%\end{figure}
168	>	%
169	>	%
170	>	%
171	>	%\begin{table}[htb]
172	>	%\begin{center}
173	>	%\caption{\label{fig:kvmettable} The values of K used in the OF background prediction.
174	>	%The uncertainties shown are the total relative systematic used for the OF prediction,
175	>	%which is the systematic uncertainty from K added in quadrature with
176	>	%a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the
177	>	%inclusive analysis.
178	>	%}
179	>	%\begin{tabular}{lcc}
180	>	%\hline
181	>	%\MET\ Cut    &    K        &  Relative Systematic \\
182	>	%\hline
183	>	%%the met zero row is used only for normalization of the money plot.
184	>	%%0    &  0.1   &        \\
185	>	%30   &  0.12  &  20\%  \\
186	>	%60   &  0.13  &  20\%  \\
187	>	%80   &  0.12  &  20\%  \\
188	>	%100  &  0.12  &  20\%  \\
189	>	%150  &  0.09  &  25\%  \\
190	>	%200  &  0.06  &  60\%  \\
191	>	%\hline
192	>	%\end{tabular}
193	>	%\end{center}
194	>	%\end{table}

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