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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	+	[DESCRIBE HERE ONE BY ONE THE UNCERTAINTIES THAT ARE PRESENT IN THE SPREADSHHET
5	+	FROM WHICH WE CALCULATE THE TOTAL UNCERTAINTY. WE KNOW HOW TO DO THIS
6	+	AND
7	+	WE HAVE THE TECHNOLOGY FROM THE 7 TEV ANALYSIS TO PROPAGATE ALL
8	+	UNCERTAINTIES
9	+	CORRECTLY THROUGH.  WE WILL DO IT ONCE WE HAVE SETTLED ON THE
10	+	INDIVIDUAL PIECES WHICH ARE STILL IN FLUX]
11	+
12	+	In this Section we discuss the systematic uncertainty on the BG
13	+	prediction.  This prediction is assembled from the event
14	+	counts in the peak region of the transverse mass distribution as
15	+	well as Monte Carlo
16	+	with a number of correction factors, as described previously.
17	+	The
18	+	final uncertainty on the prediction is built up from the uncertainties in these
19	+	individual
20	+	components.
21	+	The calculation is done for each signal
22	+	region,
23	+	for electrons and muons separately.
24	+
25	+	The choice to normalizing to the peak region of $M_T$ has the
26	+	advantage that some uncertainties, e.g., luminosity, cancel.
27	+	It does however introduce complications because it couples
28	+	some of the uncertainties in non-trivial ways.  For example,
29	+	the primary effect of an uncertainty on the rare MC cross-section
30	+	is to introduce an uncertainty in the rare MC background estimate
31	+	which comes entirely from MC.   But this uncertainty also affects,
32	+	for example,
33	+	the $t\bar{t} \to$ dilepton BG estimate because it changes the
34	+	$t\bar{t}$ normalization to the peak region (because some of the
35	+	events in the peak region are from rare processes).  These effects
36	+	are carefully accounted for.  The contribution to the overall
37	+	uncertainty from each BG source is tabulated in
38	+	Section~\ref{sec:bgunc-bottomline}.
39	+	First, however, we discuss the uncertainties one-by-one and we comment
40	+	on their impact on the overall result, at least to first order.
41	+	Second order effects, such as the one described, are also included.
42	+
43	+	\subsection{Statistical uncertainties on the event counts in the $M_T$
44	+	peak regions}
45	+	These vary between XX and XX \%, depending on the signal region
46	+	(different
47	+	signal regions have different \met\ requirements, thus they also have
48	+	different $M_T$ regions used as control.
49	+	Since
50	+	the major BG, eg, $t\bar{t}$ are normalized to the peak regions, this
51	+	fractional uncertainty is pretty much carried through all the way to
52	+	the end.  There is also an uncertainty from the finite MC event counts
53	+	in the $M_T$ peak regions.  This is also included, but it is smaller.
54	+
55	+	\subsection{Uncertainty from the choice of $M_T$ peak region}
56	+	IN 7 TEV DATA WE HAD SOME SHAPE DIFFERENCES IN THE MTRANS REGION THAT
57	+	LED US TO CONSERVATIVELY INCLUDE THIS UNCERTAINTY.  WE NEED TO LOOK
58	+	INTO THIS AGAIN
59	+
60	+	\subsection{Uncertainty on the Wjets cross-section and the rare MC cross-sections}
61	+	These are taken as 50\%, uncorrelated.
62	+	The primary effect is to introduce a 50\%
63	+	uncertainty
64	+	on the $W +$ jets and rare BG
65	+	background predictions, respectively.  However they also
66	+	have an effect on the other BGs via the $M_T$ peak normalization
67	+	in a way that tends to reduce the uncertainty.  This is easy
68	+	to understand: if the $W$ cross-section is increased by 50\%, then
69	+	the $W$ background goes up.  But the number of $M_T$ peak events
70	+	attributed to $t\bar{t}$ goes down, and since the $t\bar{t}$ BG is
71	+	scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$
72	+	BG goes down.
73	+
74	+	\subsection{Scale factors for the tail-to-peak ratios for lepton +
75	+	jets top and W events}
76	+	These tail-to-peak ratios are described in Section~\ref{sec:ttp}.
77	+	They are studied in CR1 and CR2.  The studies are described
78	+	in Sections~\ref{sec:cr1} and~\ref{sec:cr2}), respectively, where
79	+	we also give the uncertainty on the scale factors.
80	+
81	+	\subsection{Uncertainty on extra jet radiation for dilepton
82	+	background}
83	+	As discussed in Section~\ref{sec:jetmultiplicity}, the
84	+	jet distribution in
85	+	$t\bar{t} \to$
86	+	dilepton MC is rescaled by the factors $K_3$ and $K_4$ to make
87	+	it agree with the data.  The XX\% uncertainties on $K_3$ and $K_4$
88	+	comes from data/MC statistics.  This
89	+	result directly in a XX\% uncertainty on the dilepton BG, which is by far
90	+	the most important one.
91	+
92	+
93	+	\subsection{Uncertainty on the \ttll\ Acceptance}
94	+
95	+	The \ttbar\ background prediction is obtained from MC, with corrections
96	+	derived from control samples in data. The uncertainty associated with
97	+	the theoretical modeling of the \ttbar\ production and decay is
98	+	estimated by comparing the background predictions obtained using
99	+	alternative MC samples. It should be noted that the full analysis is
100	+	performed with the alternative samples under consideration,
101	+	including the derivation of the various data-to-MC scale factors.
102	+	The variations considered are
103	+
104	+	\begin{itemize}
105	+	\item Top mass: The alternative values for the top mass differ
106	+	from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}}
107	+	= 166.5~\GeV$.
108	+	\item Jet-parton matching scale: This corresponds to variations in the
109	+	scale at which the Matrix Element partons from Madgraph are matched
110	+	to Parton Shower partons from Pythia. The nominal value is
111	+	$x_q>20~\GeV$. The alternative values used are $x_q>10~\GeV$ and
112	+	$x_q>40~\GeV$.
113	+	\item Renormalization and factorization scale: The alternative samples
114	+	correspond to variations in the scale $\times 2$ and $\times 0.5$. The nominal
115	+	value for the scale used is $Q^2 = m_{\mathrm{top}}^2 +
116	+	\sum_{\mathrm{jets}} \pt^2$.
117	+	\item Alternative generators: Samples produced with different
118	+	generators include MC@NLO and Powheg (NLO generators) and
119	+	Pythia (LO). It may also be noted that MC@NLO uses Herwig6 for the
120	+	hadronisation, while POWHEG uses Pythia6.
121	+	\item Modeling of taus: The alternative sample does not include
122	+	Tauola and is otherwise identical to the Powheg sample.
123	+	This effect was studied earlier using 7~TeV samples and found to be negligible.
124	+	\item The PDF uncertainty is estimated following the PDF4LHC
125	+	recommendations[CITE]. The events are reweighted using alternative
126	+	PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the
127	+	alternative eigenvector variations and the ``master equation''. In
128	+	addition, the NNPDF2.1 set with 100 replicas. The central value is
129	+	determined from the mean and the uncertainty is derived from the
130	+	$1\sigma$ range. The overall uncertainty is derived from the envelope of the
131	+	alternative predictions and their uncertainties.
132	+	This effect was studied earlier using 7~TeV samples and found to be negligible.
133	+	\end{itemize}
134
135
136	+	\begin{figure}[hbt]
137	+	\begin{center}
138	+	\includegraphics[width=0.8\linewidth]{plots/n_dl_syst_comp.png}
139	+	\caption{
140	+	\label{fig:ttllsyst}%\protect
141	+	Comparison of the \ttll\ central prediction with those using
142	+	alternative MC samples. The blue band corresponds to the
143	+	total statistical error for all data and MC samples. The
144	+	alternative sample predictions are indicated by the
145	+	datapoints. The uncertainties on the alternative predictions
146	+	correspond to the uncorrelated statistical uncertainty from
147	+	the size of the alternative sample only.}
148	+	\end{center}
149	+	\end{figure}
150	+
151	+	\clearpage
152	+
153	+	%
154	+	%
155	+	%The methodology for determining the systematics on the background
156	+	%predictions has not changed with respect to the nominal analysis.
157	+	%Because the template method has not changed, the same
158	+	%systematic uncertainty is assessed on this prediction (32\%).
159	+	%The 50\% uncertainty on the WZ and ZZ background is also unchanged.
160	+	%The systematic uncertainty in the OF background prediction based on
161	+	%e$\mu$ events has changed, due to the different composition of this
162	+	%sample after vetoing events containing b-tagged jets.
163	+	%
164	+	%As in the nominal analysis, we do not require the e$\mu$ events
165	+	%to satisfy the dilepton mass requirement and apply a scaling factor K,
166	+	%extracted from MC, to account for the fraction of e$\mu$ events
167	+	%which satisfy the dilepton mass requirement. This procedure is used
168	+	%in order to improve the statistical precision of the OF background estimate.
169	+	%
170	+	%For the selection used in the nominal analysis,
171	+	%the e$\mu$ sample is completely dominated by $t\bar{t}$
172	+	%events, and we observe that K is statistically consistent with constant with
173	+	%respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$
174	+	%background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$
175	+	%backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant.
176	+	%At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$
177	+	%and VV dominate at high \MET\ (see App.~\ref{app:kinemu}).
178	+	%Therefore, the sample composition changes
179	+	%as the \MET\ requirement is varied, and as a result K depends
180	+	%on the \MET\ requirement.
181	+	%
182	+	%We thus measure K in MC separately for each
183	+	%\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left).
184	+	%%The systematic uncertainty on K is determined separately for each \MET\
185	+	%%requirement by comparing the relative difference in K in data vs. MC.
186	+	%The values of K used are the MC predictions
187	+	%%and the total systematic uncertainty on the OF prediction
188	+	%%as shown in
189	+	%(Table \ref{fig:kvmettable}).
190	+	%The contribution to the total OF prediction systematic uncertainty
191	+	%from K is assessed from the ratio of K in data and MC,
192	+	%shown in Fig.~\ref{fig:kvmet} (right).
193	+	%The ratio is consistent with unity to roughly 17\%,
194	+	%so we take this value as the systematic from K.
195	+	%17\% added in quadrature with 7\% from
196	+	%the electron to muon efficieny ratio
197	+	%(as assessed in the inclusive analysis)
198	+	%yields a total systematic of $\sim$18\%
199	+	%which we round up to 20\%.
200	+	%For \MET\ $>$ 150, there are no OF events in data inside the Z mass window
201	+	%so we take a systematic based on the statistical uncertainty
202	+	%of the MC prediction for K.
203	+	%This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV.
204	+	%%Although we cannot check the value of K in data for \MET\ $>$ 150
205	+	%%because we find no OF events inside the Z mass window for this \MET\
206	+	%%cut, the overall OF yields with no dilepton mass requirement
207	+	%%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC).
208	+	%
209	+	%
210	+	%%Below Old
211	+	%
212	+	%%In reevaluating the systematics on the OF prediction, however,
213	+	%%we observed a different behavior of K as a function of \MET\
214	+	%%as was seen in the inclusive analysis.
215	+	%
216	+	%%Recall that K is the ratio of the number of \emu\ events
217	+	%%inside the Z window to the total number of \emu\ events.
218	+	%%In the inclusive analysis, it is taken from \ttbar\ MC
219	+	%%and used to scale the inclusive \emu\ yield in data.
220	+	%%The yield scaled by K is then corrected for
221	+	%%the $e$ vs $\mu$ efficiency difference to obtain the
222	+	%%final OF prediction.
223	+	%
224	+	%%Based on the plot in figure \ref{fig:kvmet},
225	+	%%we choose to use a different
226	+	%%K for each \MET\ cut and assess a systematic uncertainty
227	+	%%on the OF prediction based on the difference between
228	+	%%K in data and MC.
229	+	%%The variation of K as a function of \MET\ is caused
230	+	%%by a change in sample composition with increasing \MET.
231	+	%%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is
232	+	%%not negligible (as it was in the inclusive analysis)
233	+	%%because of the b veto. (See appendix \ref{app:kinemu}.)
234	+	%%At higher \MET, \ttbar\ and diboson backgrounds dominate.
235	+	%
236	+	%
237	+	%
238	+	%
239	+	%\begin{figure}[hbt]
240	+	%  \begin{center}
241	+	%       \includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf}
242	+	%       \includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf}
243	+	%       \caption{
244	+	%         \label{fig:kvmet}\protect
245	+	%         The left plot shows
246	+	%         K as a function of \MET\ in MC (red) and data (black).
247	+	%         The bin low edge corresponds to the \MET\ cut, and the
248	+	%         bins are inclusive.
249	+	%         The MC used is a sum of all SM MC used in the yield table of
250	+	%         section \ref{sec:yields}.
251	+	%         The right plot is the ratio of K in data to MC.
252	+	%         The ratio is fit to a line whose slope is consistent with zero
253	+	%         (the fit parameters are
254	+	%         0.9 $\pm$  0.4 for the intercept and
255	+	%      0.001 $\pm$ 0.005 for the slope).
256	+	%       }
257	+	%  \end{center}
258	+	%\end{figure}
259	+	%
260	+	%
261	+	%
262	+	%\begin{table}[htb]
263	+	%\begin{center}
264	+	%\caption{\label{fig:kvmettable} The values of K used in the OF background prediction.
265	+	%The uncertainties shown are the total relative systematic used for the OF prediction,
266	+	%which is the systematic uncertainty from K added in quadrature with
267	+	%a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the
268	+	%inclusive analysis.
269	+	%}
270	+	%\begin{tabular}{lcc}
271	+	%\hline
272	+	%\MET\ Cut    &    K        &  Relative Systematic \\
273	+	%\hline
274	+	%%the met zero row is used only for normalization of the money plot.
275	+	%%0    &  0.1   &        \\
276	+	%30   &  0.12  &  20\%  \\
277	+	%60   &  0.13  &  20\%  \\
278	+	%80   &  0.12  &  20\%  \\
279	+	%100  &  0.12  &  20\%  \\
280	+	%150  &  0.09  &  25\%  \\
281	+	%200  &  0.06  &  60\%  \\
282	+	%\hline
283	+	%\end{tabular}
284	+	%\end{center}
285	+	%\end{table}
286	+
287	+	\subsection{Uncertainty from the isolated track veto}
288	+	This is the uncertainty associated with how well the isolated track
289	+	veto performance is modeled by the Monte Carlo.  This uncertainty
290	+	only applies to the fraction of dilepton BG events that have
291	+	a second e/$\mu$ or a one prong $\tau \to h$, with
292	+	$P_T > 10$ GeV in $|\eta| < 2.4$.  This fraction is 1/3 (THIS WAS THE
293	+	7 TEV NUMBER, CHECK).  The uncertainty for these events
294	+	is XX\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto}
295	+
296	+	\subsubsection{Isolated Track Veto: Tag and Probe Studies}
297	+	\label{sec:trkveto}
298	+
299	+	[EVERYTHING IS 7TEV HERE, UPDATE WITH NEW RESULTS \\
300	+	ADD TABLE WITH FRACTION OF EVENTS THAT HAVE A TRUE ISOLATED TRACK]
301	+
302	+	In this section we compare the performance of the isolated track veto in data and MC using tag-and-probe studies
303	+	with samples of Z$\to$ee and Z$\to\mu\mu$. The purpose of these studies is to demonstrate that the efficiency
304	+	to satisfy the isolated track veto requirements is well-reproduced in the MC, since if this were not the case
305	+	we would need to apply a data-to-MC scale factor in order to correctly predict the \ttll\ background. This study
306	+	addresses possible data vs. MC discrepancies for the {\bf efficiency} to identify (and reject) events with a
307	+	second {\bf genuine} lepton (e, $\mu$, or $\tau\to$1-prong). It does not address possible data vs. MC discrepancies
308	+	in the fake rate for rejecting events without a second genuine lepton; this is handled separately in the top normalization
309	+	procedure by scaling the \ttlj\ contribution to match the data in the \mt\ peak after applying the isolated track veto.
310	+	Furthermore, we test the data and MC
311	+	isolated track veto efficiencies for electrons and muons since we are using a Z tag-and-probe technique, but we do not
312	+	directly test the performance for hadronic tracks from $\tau$ decays. The performance for hadronic $\tau$ decay products
313	+	may differ from that of electrons and muons for two reasons. First, the $\tau$ may decay to a hadronic track plus one
314	+	or two $\pi^0$'s, which may decay to $\gamma\gamma$ followed by a photon conversion. As shown in Figure~\ref{fig:absiso},
315	+	the isolation distribution for charged tracks from $\tau$ decays that are not produced in association with $\pi^0$s are
316	+	consistent with that from $\E$s and $\M$s. Since events from single prong $\tau$ decays produced in association with
317	+	$\pi^0$s comprise a small fraction of the total sample, and since the kinematics of $\tau$, $\pi^0$ and $\gamma\to e^+e^-$
318	+	decays are well-understood, we currently demonstrate that the isolation is well-reproduced for electrons and muons only.
319	+	Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed.
320	+	As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%,
321	+	leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background
322	+	due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as neglgigible.
323	+
324	+	The tag-and-probe studies are performed in the full 2011 data sample, and compared with the DYJets madgraph sample.
325	+	All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV.
326	+	We compare the distributions of absolute track isolation for probe electrons/muons in data vs. MC. The contributions to
327	+	this isolation sum are from ambient energy in the event from underlying event, pile-up and jet activitiy, and hence do
328	+	not depend on the \pt\ of the probe lepton. We therefore restrict the probe \pt\ to be $>$ 30 GeV in order to suppress
329	+	fake backgrounds with steeply-falling \pt\ spectra. To suppress non-Z backgrounds (in particular \ttbar) we require
330	+	\met\ $<$ 30 GeV and 0 b-tagged events.
331	+	The specific criteria for tags and probes for electrons and muons are:
332	+
333	+	%We study the isolated track veto efficiency in bins of \njets.
334	+	%We are interested in events with at least 4 jets to emulate the hadronic activity in our signal sample. However since
335	+	%there are limited statistics for Z + $\geq$4 jet events, we study the isolated track performance in events with
336	+
337	+
338	+	\begin{itemize}
339	+	\item{Electrons}
340	+
341	+	\begin{itemize}
342	+	\item{Tag criteria}
343	+
344	+	\begin{itemize}
345	+	\item Electron passes full analysis ID/iso selection
346	+	\item \pt\ $>$ 30 GeV, $|\eta|<2.5$
347	+
348	+	\item Matched to 1 of the 2 electron tag-and-probe triggers
349	+	\begin{itemize}
350	+	\item \verb=HLT_Ele17_CaloIdVT_CaloIsoVT_TrkIdT_TrkIsoVT_SC8_Mass30_v*=
351	+	\item \verb=HLT_Ele17_CaloIdVT_CaloIsoVT_TrkIdT_TrkIsoVT_Ele8_Mass30_v*=
352	+	\end{itemize}
353	+	\end{itemize}
354	+
355	+	\item{Probe criteria}
356	+	\begin{itemize}
357	+	\item Electron passes full analysis ID selection
358	+	\item \pt\ $>$ 30 GeV
359	+	\end{itemize}
360	+	\end{itemize}
361	+	\item{Muons}
362	+	\begin{itemize}
363	+	\item{Tag criteria}
364	+	\begin{itemize}
365	+	\item Muon passes full analysis ID/iso selection
366	+	\item \pt\ $>$ 30 GeV, $|\eta|<2.1$
367	+	\item Matched to 1 of the 2 electron tag-and-probe triggers
368	+	\begin{itemize}
369	+	\item \verb=HLT_IsoMu30_v*=
370	+	\item \verb=HLT_IsoMu30_eta2p1_v*=
371	+	\end{itemize}
372	+	\end{itemize}
373	+	\item{Probe criteria}
374	+	\begin{itemize}
375	+	\item Muon passes full analysis ID selection
376	+	\item \pt\ $>$ 30 GeV
377	+	\end{itemize}
378	+	\end{itemize}
379	+	\end{itemize}
380	+
381	+	The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe
382	+	good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy
383	+	absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}.
384	+	In the $\geq$0 and $\geq$1 jet bins where the efficiencies can be tested with statistical precision, the data and MC
385	+	efficiencies agree within 7\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency.
386	+	For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for
387	+	a data vs. MC discrepancy in the isolated track veto efficiency.
388	+
389	+
390	+	%This is because our analysis requirement is relative track isolation $<$ 0.1, and m
391	+	%This requirement is chosen because most of the tracks rejected by the isolated
392	+	%track veto have a \pt\ near the 10 GeV threshold, and our analysis requirement is relative track isolation $<$ 1 GeV.
393
394		\begin{figure}[hbt]
395		\begin{center}
396	<	\includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf}
397	<	\includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf}
396	>	%\includegraphics[width=0.3\linewidth]{plots/el_tkiso_0j.pdf}%
397	>	%\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_0j.pdf}
398	>	%\includegraphics[width=0.3\linewidth]{plots/el_tkiso_1j.pdf}%
399	>	%\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_1j.pdf}
400	>	%\includegraphics[width=0.3\linewidth]{plots/el_tkiso_2j.pdf}%
401	>	%\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_2j.pdf}
402	>	%\includegraphics[width=0.3\linewidth]{plots/el_tkiso_3j.pdf}%
403	>	%\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_3j.pdf}
404	>	%\includegraphics[width=0.3\linewidth]{plots/el_tkiso_4j.pdf}%
405	>	%\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_4j.pdf}
406		\caption{
407	<	\label{fig:kvmet}\protect
408	<	The left plot shows
409	<	K as a function of \MET\ in MC (red) and data (black).
410	<	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}
407	>	\label{fig:tnp} Comparison of the absolute track isolation in data vs. MC for electrons (left) and muons (right)
408	>	for events with the \njets\ requirement varied from \njets\ $\geq$ 0 to \njets\ $\geq$ 4.
409	>	}
410	>	\end{center}
411		\end{figure}
412
413	+	\clearpage
414
415	<
111	<	\begin{table}[htb]
415	>	\begin{table}[!ht]
416		\begin{center}
417	<	\caption{\label{fig:kvmettable} The values of K used in the OF background prediction.
418	<	The uncertainties shown are the total relative systematic used for the OF prediction,
419	<	which is the systematic uncertainty from K added in quadrature with
420	<	a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the
421	<	inclusive analysis.
422	<	}
423	<	\begin{tabular}{lcc}
424	<	\hline
425	<	\MET\ Cut    &    K        &  Relative Systematic \\
426	<	\hline
427	<	%the met zero row is used only for normalization of the money plot.
428	<	%0    &  0.1   &        \\
429	<	30   &  0.12  &  20\%  \\
430	<	60   &  0.13  &  20\%  \\
431	<	80   &  0.12  &  20\%  \\
432	<	100  &  0.12  &  20\%  \\
433	<	150  &  0.09  &  25\%  \\
434	<	200  &  0.06  &  60\%  \\
417	>	\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements
418	>	on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various
419	>	jet multiplicity requirements.}
420	>	\begin{tabular}{l|l|c|c|c|c|c}
421	>	\hline
422	>	\hline
423	>	e + $\geq$0 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
424	>	\hline
425	>	data   &  0.088 $\pm$ 0.0003   &  0.030 $\pm$ 0.0002   &  0.013 $\pm$ 0.0001   &  0.007 $\pm$ 0.0001   &  0.005 $\pm$ 0.0001  \\
426	>	mc   &  0.087 $\pm$ 0.0001   &  0.030 $\pm$ 0.0001   &  0.014 $\pm$ 0.0001   &  0.008 $\pm$ 0.0000   &  0.005 $\pm$ 0.0000  \\
427	>	data/mc   &     1.01 $\pm$ 0.00   &     0.99 $\pm$ 0.01   &     0.97 $\pm$ 0.01   &     0.95 $\pm$ 0.01   &     0.93 $\pm$ 0.01  \\
428	>	\hline
429	>	\hline
430	>	$\mu$ + $\geq$0 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
431	>	\hline
432	>	data   &  0.087 $\pm$ 0.0002   &  0.031 $\pm$ 0.0001   &  0.015 $\pm$ 0.0001   &  0.008 $\pm$ 0.0001   &  0.005 $\pm$ 0.0001  \\
433	>	mc   &  0.085 $\pm$ 0.0001   &  0.030 $\pm$ 0.0001   &  0.014 $\pm$ 0.0000   &  0.008 $\pm$ 0.0000   &  0.005 $\pm$ 0.0000  \\
434	>	data/mc   &     1.02 $\pm$ 0.00   &     1.06 $\pm$ 0.00   &     1.06 $\pm$ 0.01   &     1.03 $\pm$ 0.01   &     1.02 $\pm$ 0.01  \\
435	>	\hline
436	>	\hline
437	>	e + $\geq$1 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
438	>	\hline
439	>	data   &  0.099 $\pm$ 0.0008   &  0.038 $\pm$ 0.0005   &  0.019 $\pm$ 0.0004   &  0.011 $\pm$ 0.0003   &  0.008 $\pm$ 0.0002  \\
440	>	mc   &  0.100 $\pm$ 0.0004   &  0.038 $\pm$ 0.0003   &  0.019 $\pm$ 0.0002   &  0.012 $\pm$ 0.0002   &  0.008 $\pm$ 0.0001  \\
441	>	data/mc   &     0.99 $\pm$ 0.01   &     1.00 $\pm$ 0.02   &     0.99 $\pm$ 0.02   &     0.98 $\pm$ 0.03   &     0.97 $\pm$ 0.03  \\
442	>	\hline
443	>	\hline
444	>	$\mu$ + $\geq$1 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
445	>	\hline
446	>	data   &  0.100 $\pm$ 0.0006   &  0.041 $\pm$ 0.0004   &  0.022 $\pm$ 0.0003   &  0.014 $\pm$ 0.0002   &  0.010 $\pm$ 0.0002  \\
447	>	mc   &  0.099 $\pm$ 0.0004   &  0.039 $\pm$ 0.0002   &  0.020 $\pm$ 0.0002   &  0.013 $\pm$ 0.0001   &  0.009 $\pm$ 0.0001  \\
448	>	data/mc   &     1.01 $\pm$ 0.01   &     1.05 $\pm$ 0.01   &     1.05 $\pm$ 0.02   &     1.06 $\pm$ 0.02   &     1.06 $\pm$ 0.03  \\
449	>	\hline
450	>	\hline
451	>	e + $\geq$2 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
452	>	\hline
453	>	data   &  0.105 $\pm$ 0.0020   &  0.042 $\pm$ 0.0013   &  0.021 $\pm$ 0.0009   &  0.013 $\pm$ 0.0007   &  0.009 $\pm$ 0.0006  \\
454	>	mc   &  0.109 $\pm$ 0.0011   &  0.043 $\pm$ 0.0007   &  0.021 $\pm$ 0.0005   &  0.013 $\pm$ 0.0004   &  0.009 $\pm$ 0.0003  \\
455	>	data/mc   &     0.96 $\pm$ 0.02   &     0.97 $\pm$ 0.03   &     1.00 $\pm$ 0.05   &     1.01 $\pm$ 0.06   &     0.97 $\pm$ 0.08  \\
456	>	\hline
457	>	\hline
458	>	$\mu$ + $\geq$2 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
459		\hline
460	+	data   &  0.106 $\pm$ 0.0016   &  0.045 $\pm$ 0.0011   &  0.025 $\pm$ 0.0008   &  0.016 $\pm$ 0.0007   &  0.012 $\pm$ 0.0006  \\
461	+	mc   &  0.108 $\pm$ 0.0009   &  0.044 $\pm$ 0.0006   &  0.024 $\pm$ 0.0004   &  0.016 $\pm$ 0.0004   &  0.011 $\pm$ 0.0003  \\
462	+	data/mc   &     0.98 $\pm$ 0.02   &     1.04 $\pm$ 0.03   &     1.04 $\pm$ 0.04   &     1.04 $\pm$ 0.05   &     1.06 $\pm$ 0.06  \\
463	+	\hline
464	+	\hline
465	+	e + $\geq$3 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
466	+	\hline
467	+	data   &  0.117 $\pm$ 0.0055   &  0.051 $\pm$ 0.0038   &  0.029 $\pm$ 0.0029   &  0.018 $\pm$ 0.0023   &  0.012 $\pm$ 0.0019  \\
468	+	mc   &  0.120 $\pm$ 0.0031   &  0.052 $\pm$ 0.0021   &  0.027 $\pm$ 0.0015   &  0.018 $\pm$ 0.0012   &  0.013 $\pm$ 0.0011  \\
469	+	data/mc   &     0.97 $\pm$ 0.05   &     0.99 $\pm$ 0.08   &     1.10 $\pm$ 0.13   &     1.03 $\pm$ 0.15   &     0.91 $\pm$ 0.16  \\
470	+	\hline
471	+	\hline
472	+	$\mu$ + $\geq$3 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
473	+	\hline
474	+	data   &  0.111 $\pm$ 0.0044   &  0.050 $\pm$ 0.0030   &  0.029 $\pm$ 0.0024   &  0.019 $\pm$ 0.0019   &  0.014 $\pm$ 0.0017  \\
475	+	mc   &  0.115 $\pm$ 0.0025   &  0.051 $\pm$ 0.0017   &  0.030 $\pm$ 0.0013   &  0.020 $\pm$ 0.0011   &  0.015 $\pm$ 0.0009  \\
476	+	data/mc   &     0.97 $\pm$ 0.04   &     0.97 $\pm$ 0.07   &     0.95 $\pm$ 0.09   &     0.97 $\pm$ 0.11   &     0.99 $\pm$ 0.13  \\
477	+	\hline
478	+	\hline
479	+	e + $\geq$4 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
480	+	\hline
481	+	data   &  0.113 $\pm$ 0.0148   &  0.048 $\pm$ 0.0100   &  0.033 $\pm$ 0.0083   &  0.020 $\pm$ 0.0065   &  0.017 $\pm$ 0.0062  \\
482	+	mc   &  0.146 $\pm$ 0.0092   &  0.064 $\pm$ 0.0064   &  0.034 $\pm$ 0.0048   &  0.024 $\pm$ 0.0040   &  0.021 $\pm$ 0.0037  \\
483	+	data/mc   &     0.78 $\pm$ 0.11   &     0.74 $\pm$ 0.17   &     0.96 $\pm$ 0.28   &     0.82 $\pm$ 0.30   &     0.85 $\pm$ 0.34  \\
484	+	\hline
485	+	\hline
486	+	$\mu$ + $\geq$4 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
487	+	\hline
488	+	data   &  0.130 $\pm$ 0.0128   &  0.052 $\pm$ 0.0085   &  0.028 $\pm$ 0.0063   &  0.019 $\pm$ 0.0052   &  0.019 $\pm$ 0.0052  \\
489	+	mc   &  0.105 $\pm$ 0.0064   &  0.045 $\pm$ 0.0043   &  0.027 $\pm$ 0.0034   &  0.019 $\pm$ 0.0028   &  0.014 $\pm$ 0.0024  \\
490	+	data/mc   &     1.23 $\pm$ 0.14   &     1.18 $\pm$ 0.22   &     1.03 $\pm$ 0.27   &     1.01 $\pm$ 0.32   &     1.37 $\pm$ 0.45  \\
491	+	\hline
492	+	\hline
493	+
494		\end{tabular}
495		\end{center}
496		\end{table}
497	+
498	+
499	+
500	+	%Figure.~\ref{fig:reliso} compares the relative track isolation
501	+	%for events with a track with $\pt > 10~\GeV$ in addition to a selected
502	+	%muon for $\Z+4$ jet events and various \ttll\ components. The
503	+	%isolation distributions show significant differences, particularly
504	+	%between the leptons from a \W\ or \Z\ decay and the tracks arising
505	+	%from $\tau$ decays. As can also be seen in the figure, the \pt\
506	+	%distribution for the various categories of tracks is different, where
507	+	%the decay products from $\tau$s are significantly softer. Since the
508	+	%\pt\ enters the denominator of the isolation definition and hence
509	+	%alters the isolation variable...
510	+
511	+	%\begin{figure}[hbt]
512	+	%  \begin{center}
513	+	%       \includegraphics[width=0.5\linewidth]{plots/pfiso_njets4_log.png}%
514	+	%       \includegraphics[width=0.5\linewidth]{plots/pfpt_njets4.png}
515	+	%       \caption{
516	+	%         \label{fig:reliso}%\protect
517	+	%          Comparison of relative track isolation variable for PF cand probe in Z+jets and ttbar
518	+	%          Z+Jets and ttbar dilepton have similar isolation distributions
519	+	%          ttbar with leptonic and single prong taus tend to be less
520	+	%          isolated. The difference in the isolation can be attributed
521	+	%          to the different \pt\ distribution of the samples, since
522	+	%          $\tau$ decay products tend to be softer than leptons arising
523	+	%          from \W\ or \Z\ decays.}
524	+	%      \end{center}
525	+	%\end{figure}
526	+
527	+	%       \includegraphics[width=0.5\linewidth]{plots/pfabsiso_njets4_log.png}
528	+
529	+
530	+	%BEGIN SECTION TO WRITE OUT
531	+	%In detail, the procedure to correct the dilepton background is:
532	+
533	+	%\begin{itemize}
534	+	%\item Using tag-and-probe studies, we plot the distribution of {\bf absolute} track isolation for identified probe electrons
535	+	%and muons {\bf TODO: need to compare the e vs. $\mu$ track iso distributions, they might differ due to e$\to$e$\gamma$}.
536	+	%\item We verify that the distribution of absolute track isolation does not depend on the \pt\ of the probe lepton.
537	+	%This is due to the fact that this isolation is from ambient PU and jet activity in the event, which is uncorrelated with
538	+	%the lepton \pt {\bf TODO: verify this in data and MC.}.
539	+	%\item Our requirement is {\bf relative} track isolation $<$ 0.1. For a given \ttll\ MC event, we determine the \pt of the 2nd
540	+	%lepton and translate this to find the corresponding requirement on the {\bf absolute} track isolation, which is simply $0.1\times$\pt.
541	+	%\item We measure the efficiency to satisfy this requirement in data and MC, and define a scale-factor $SF_{\epsilon(trk)}$ which
542	+	%is the ratio of the data-to-MC efficiencies. This scale-factor is applied to the \ttll\ MC event.
543	+	%\item {\bf THING 2 we are unsure about: we can measure this SF for electrons and for muons, but we can't measure it for hadronic
544	+	%tracks from $\tau$ decays. Verena has showed that the absolute track isolation distribution in hadronic $\tau$ tracks is harder due
545	+	%to $\pi^0\to\gamma\gamma$ with $\gamma\to e^+e^-$.}
546	+	%\end{itemize}
547	+	%END SECTION TO WRITE OUT
548	+
549	+
550	+	{\bf fix me: What you have written in the next paragraph does not explain how $\epsilon_{fake}$ is measured.
551	+	Why not measure $\epsilon_{fake}$ in the b-veto region?}
552	+
553	+	%A measurement of the $\epsilon_{fake}$ in data is non-trivial. However, it is
554	+	%possible to correct for differences in the $\epsilon_{fake}$ between data and MC by
555	+	%applying an additional scale factor for the single lepton background
556	+	%alone, using the sample in the \mt\ peak region. This scale factor is determined after applying the isolated track
557	+	%veto and after subtracting the \ttll\ component, corrected for the
558	+	%isolation efficiency derived previously.
559	+	%As shown in Figure~\ref{fig:vetoeffcomp}, the efficiency for selecting an
560	+	%isolated track in single lepton events is independent of \mt\, so the use of
561	+	%an overall scale factor is justified to estimate the contribution in
562	+	%the \mt\ tail.
563	+	%
564	+	%\begin{figure}[hbt]
565	+	%  \begin{center}
566	+	%       \includegraphics[width=0.5\linewidth]{plots/vetoeff_comp.png}
567	+	%       \caption{
568	+	%         \label{fig:vetoeffcomp}%\protect
569	+	%          Efficiency for selecting an isolated track comparing
570	+	%          single lepton \ttlj\ and dilepton \ttll\ events in MC and
571	+	%          data as a function of \mt. The
572	+	%          efficiencies in \ttlj\ and \ttll\ exhibit no dependence on
573	+	%          \mt\, while the data ranges between the two. This behavior
574	+	%          is expected since the low \mt\ region is predominantly \ttlj, while the
575	+	%          high \mt\ region contains mostly \ttll\ events.}
576	+	%      \end{center}
577	+	%\end{figure}
578	+
579	+	\subsection{Summary of uncertainties}
580	+	\label{sec:bgunc-bottomline}.
581	+
582	+	THIS NEEDS TO BE WRITTEN

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