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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
4   In this Section we discuss the systematic uncertainty on the BG
5   prediction.  This prediction is assembled from the event
6   counts in the peak region of the transverse mass distribution as
# Line 22 | Line 14 | The calculation is done for each signal
14   region,
15   for electrons and muons separately.
16  
17 < The choice to normalizing to the peak region of $M_T$ has the
17 > The choice to normalize to the peak region of $M_T$ has the
18   advantage that some uncertainties, e.g., luminosity, cancel.
19   It does however introduce complications because it couples
20   some of the uncertainties in non-trivial ways.  For example,
# Line 33 | Line 25 | for example,
25   the $t\bar{t} \to$ dilepton BG estimate because it changes the
26   $t\bar{t}$ normalization to the peak region (because some of the
27   events in the peak region are from rare processes).  These effects
28 < are carefully accounted for.  The contribution to the overall
29 < uncertainty from each BG source is tabulated in
28 > are carefully accounted for. The contribution to the overall
29 > uncertainty from each background source is tabulated in
30   Section~\ref{sec:bgunc-bottomline}.
31 < First, however, we discuss the uncertainties one-by-one and we comment
31 > Here we discuss the uncertainties one-by-one and comment
32   on their impact on the overall result, at least to first order.
33   Second order effects, such as the one described, are also included.
34  
35   \subsection{Statistical uncertainties on the event counts in the $M_T$
36   peak regions}
37 < These vary between XX and XX \%, depending on the signal region
37 > These vary between 2\% and 20\%, depending on the signal region
38   (different
39   signal regions have different \met\ requirements, thus they also have
40 < different $M_T$ regions used as control.
40 > different $M_T$ regions used as control).
41   Since
42 < the major BG, eg, $t\bar{t}$ are normalized to the peak regions, this
42 > the major backgrounds, eg, $t\bar{t}$ are normalized to the peak regions, this
43   fractional uncertainty is pretty much carried through all the way to
44   the end.  There is also an uncertainty from the finite MC event counts
45   in the $M_T$ peak regions.  This is also included, but it is smaller.
46  
47 + Normalizing to the $M_T$ peak has the distinct advantages that
48 + uncertainties on luminosity, cross-sections, trigger efficiency,
49 + lepton ID, cancel out.
50 + For the low statistics regions with high \met\ requirements, the
51 + price to pay in terms of event count is that statistical uncertainties start
52 + to become significant.  In the future we may consider a different
53 + normalization startegy in the low statistics regions.
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
56  
57 < \subsection{Uncertainty on the Wjets cross-section and the rare MC cross-sections}
57 > This choice affects the scale factors of Table~\ref{tab:mtpeaksf}.  
58 > If the $M_T$ peak region is not well modelled, this would introduce an
59 > uncertainty.
60 >
61 > We have tested this possibility by recalculating the post-veto scale factors for a different
62 > choice
63 > of $M_T$ peak region ($40 < M_T < 100$ GeV instead of the default
64 > $50 < M_T < 80$ GeV).  This is shown in Table~\ref{tab:mtpeaksf2}.  
65 > The two results for the scale factors are very compatible.
66 > We do not take any systematic uncertainty for this possible effect.
67 >
68 > \begin{table}[!h]
69 > \begin{center}
70 > {\footnotesize
71 > \begin{tabular}{l||c|c|c|c|c|c|c}
72 > \hline
73 > Sample              & SRA & SRB & SRC & SRD & SRE & SRF & SRG\\
74 > \hline
75 > \hline
76 > \multicolumn{8}{c}{$50 \leq \mt \leq 80$} \\
77 > \hline
78 > $\mu$ pre-veto \mt-SF      & $1.02 \pm 0.02$ & $0.95 \pm 0.03$ & $0.90 \pm 0.05$ & $0.98 \pm 0.08$ & $0.97 \pm 0.13$ & $0.85 \pm 0.18$ & $0.92 \pm 0.31$ \\
79 > $\mu$ post-veto \mt-SF     & $1.00 \pm 0.02$ & $0.95 \pm 0.03$ & $0.91 \pm 0.05$ & $1.00 \pm 0.09$ & $0.99 \pm 0.13$ & $0.85 \pm 0.18$ & $0.96 \pm 0.31$ \\
80 > \hline
81 > $\mu$ veto \mt-SF          & $0.98 \pm 0.01$ & $0.99 \pm 0.01$ & $1.01 \pm 0.02$ & $1.02 \pm 0.04$ & $1.02 \pm 0.06$ & $1.00 \pm 0.09$ & $1.04 \pm 0.11$ \\
82 > \hline
83 > \hline
84 > e pre-veto \mt-SF          & $0.95 \pm 0.02$ & $0.95 \pm 0.03$ & $0.94 \pm 0.06$ & $0.85 \pm 0.09$ & $0.84 \pm 0.13$ & $1.05 \pm 0.23$ & $1.04 \pm 0.33$ \\
85 > e post-veto \mt-SF         & $0.92 \pm 0.02$ & $0.91 \pm 0.03$ & $0.91 \pm 0.06$ & $0.74 \pm 0.08$ & $0.75 \pm 0.13$ & $0.91 \pm 0.22$ & $1.01 \pm 0.33$ \\
86 > \hline
87 > e veto \mt-SF      & $0.97 \pm 0.01$ & $0.96 \pm 0.02$ & $0.97 \pm 0.03$ & $0.87 \pm 0.05$ & $0.89 \pm 0.08$ & $0.86 \pm 0.11$ & $0.97 \pm 0.14$ \\
88 > \hline
89 > \hline
90 > \multicolumn{8}{c}{$40 \leq \mt \leq 100$} \\
91 > \hline
92 > $\mu$ pre-veto \mt-SF      & $1.02 \pm 0.01$ & $0.97 \pm 0.02$ & $0.91 \pm 0.05$ & $0.95 \pm 0.06$ & $0.97 \pm 0.10$ & $0.80 \pm 0.14$ & $0.74 \pm 0.22$ \\
93 > $\mu$ post-veto \mt-SF     & $1.00 \pm 0.01$ & $0.96 \pm 0.02$ & $0.90 \pm 0.04$ & $0.98 \pm 0.07$ & $1.00 \pm 0.11$ & $0.80 \pm 0.15$ & $0.81 \pm 0.24$ \\
94 > \hline
95 > $\mu$ veto \mt-SF          & $0.98 \pm 0.01$ & $0.99 \pm 0.01$ & $0.99 \pm 0.02$ & $1.03 \pm 0.03$ & $1.03 \pm 0.05$ & $1.01 \pm 0.08$ & $1.09 \pm 0.09$ \\
96 > \hline
97 > \hline
98 > e pre-veto \mt-SF          & $0.97 \pm 0.01$ & $0.93 \pm 0.02$ & $0.94 \pm 0.04$ & $0.81 \pm 0.06$ & $0.86 \pm 0.10$ & $0.95 \pm 0.17$ & $1.06 \pm 0.26$ \\
99 > e post-veto \mt-SF         & $0.94 \pm 0.01$ & $0.91 \pm 0.02$ & $0.91 \pm 0.04$ & $0.71 \pm 0.06$ & $0.82 \pm 0.10$ & $0.93 \pm 0.17$ & $1.09 \pm 0.27$ \\
100 > \hline
101 > e veto \mt-SF      & $0.97 \pm 0.01$ & $0.98 \pm 0.01$ & $0.97 \pm 0.02$ & $0.88 \pm 0.04$ & $0.95 \pm 0.06$ & $0.98 \pm 0.08$ & $1.03 \pm 0.09$ \\
102 > \hline
103 > \end{tabular}}
104 > \caption{ \mt\ peak Data/MC scale factors. The pre-veto SFs are applied to the
105 >  \ttdl\ sample, while the post-veto SFs are applied to the single
106 >  lepton samples. The veto SF is shown for comparison across channels.
107 >  The raw MC is used for backgrounds from rare processes.
108 >  The uncertainties are statistical only.
109 > \label{tab:mtpeaksf2}}
110 > \end{center}
111 > \end{table}
112 >
113 >
114 > \subsection{Uncertainty on the \wjets\ cross-section and the rare MC cross-sections}
115   These are taken as 50\%, uncorrelated.  
116   The primary effect is to introduce a 50\%
117   uncertainty
# Line 71 | Line 125 | attributed to $t\bar{t}$ goes down, and
125   scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$
126   BG goes down.  
127  
128 < \subsection{Scale factors for the tail-to-peak ratios for lepton +
128 > \subsection{Tail-to-peak ratios for lepton +
129    jets top and W events}
130 < These tail-to-peak ratios are described in Section~\ref{sec:ttp}.
131 < They are studied in CR1 and CR2.  The studies are described
132 < in Sections~\ref{sec:cr1} and~\ref{sec:cr2}), respectively, where
133 < we also give the uncertainty on the scale factors.
130 > The tail-to-peak ratios $R_{top}$ and $R_{wjet}$ are described in Section~\ref{sec:ttp}.
131 > The data/MC scale factors are studied in CR1 and CR2 (Sections~\ref{sec:cr1} and~\ref{sec:cr2}).
132 > Only the scale factor for \wjets, $SFR_{wjet}$, is used, and its
133 > uncertainty is given in Table~\ref{tab:cr1yields}.
134 > This uncertainty affects both $R_{wjet}$ and $R_{top}$.
135 > The additional systematic uncertainty on $R_{top}$ from the variation between optimistic and pessimistic scenarios is given in Section~\ref{sec:ttp}.
136 >
137  
138   \subsection{Uncertainty on extra jet radiation for dilepton
139    background}
# Line 84 | Line 141 | As discussed in Section~\ref{sec:jetmult
141   jet distribution in
142   $t\bar{t} \to$
143   dilepton MC is rescaled by the factors $K_3$ and $K_4$ to make
144 < it agree with the data.  The XX\% uncertainties on $K_3$ and $K_4$
144 > it agree with the data.  The 3\% uncertainties on $K_3$ and $K_4$
145   comes from data/MC statistics.  This  
146 < result directly in a XX\% uncertainty on the dilepton BG, which is by far
146 > results directly in a 3\% uncertainty on the dilepton background, which is by far
147   the most important one.
148  
149 + \subsection{Uncertainty from MC statistics}
150 + This affects mostly the \ttll\ background estimate, which is taken
151 + from
152 + Monte Carlo with appropriate correction factors.  This uncertainty
153 + is negligible in the low \met\ signal regions, and grows to about
154 + 15\% in SRG.
155  
93 \subsection{Uncertainty on the \ttll\ Acceptance}
156  
157 + \subsection{Uncertainty on the \ttll\ Background}
158 + \label{sec:ttdilbkgunc}
159   The \ttbar\ background prediction is obtained from MC, with corrections
160   derived from control samples in data. The uncertainty associated with
161 < the theoretical modeling of the \ttbar\ production and decay is
162 < estimated by comparing the background predictions obtained using
161 > the \ttbar\ background is derived from the level of closure of the
162 > background prediction in CR4 (Table~\ref{tab:cr4yields}) and
163 > CR5 (Table~\ref{tab:cr5yields}). The results from these control region
164 > checks are shown in Figure~\ref{fig:ttdlunc}. The uncertainties assigned
165 > to the \ttdl\ background prediction based on these tests are
166 > 5\% (SRA), 10\% (SRB), 15\% (SRC), 25\% (SRD), 40\% (SRE-G).
167 >
168 > \begin{figure}[hbt]
169 >  \begin{center}
170 >        \includegraphics[width=0.6\linewidth]{plots/ttdilepton_uncertainty.pdf}
171 >        \caption{
172 >          \label{fig:ttdlunc}%\protect
173 >          Results of the comparison of yields in the \mt\ tail comparing the MC prediction (after
174 >          applying SFs) to data for CR4 and CR5 for all the signal
175 >          region requirements considered (A-G). The bands indicate the
176 >          systematic uncertainties assigned based on these tests,
177 >          ranging from $5\%$ for SRA to $40\%$ for SRE-G.}
178 >      \end{center}
179 > \end{figure}
180 >
181 >
182 > \subsubsection{Check of the uncertainty on the \ttll\ Background}
183 >
184 > We check that the systematic uncertainty assigned to the \ttll\ background prediction
185 > covers the uncertainty associated with
186 > the theoretical modeling of the \ttbar\ production and decay
187 > by comparing the background predictions obtained using
188   alternative MC samples. It should be noted that the full analysis is
189   performed with the alternative samples under consideration,
190   including the derivation of the various data-to-MC scale factors.
# Line 103 | Line 192 | The variations considered are
192  
193   \begin{itemize}
194   \item Top mass: The alternative values for the top mass differ
195 <  from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}}
195 >  from the central value by $6~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}}
196    = 166.5~\GeV$.
197   \item Jet-parton matching scale: This corresponds to variations in the
198    scale at which the Matrix Element partons from Madgraph are matched
# Line 115 | Line 204 | The variations considered are
204    value for the scale used is $Q^2 = m_{\mathrm{top}}^2 +
205    \sum_{\mathrm{jets}} \pt^2$.
206   \item Alternative generators: Samples produced with different
207 <  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.
207 >  generators, Powheg (our default) and Madgraph.
208   \item Modeling of taus: The alternative sample does not include
209    Tauola and is otherwise identical to the Powheg sample.
210    This effect was studied earlier using 7~TeV samples and found to be negligible.
211   \item The PDF uncertainty is estimated following the PDF4LHC
212 <  recommendations[CITE]. The events are reweighted using alternative
212 >  recommendations. The events are reweighted using alternative
213    PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the
214 <  alternative eigenvector variations and the ``master equation''. In
215 <  addition, the NNPDF2.1 set with 100 replicas. The central value is
214 >  alternative eigenvector variations and the ``master equation''.
215 >  The NNPDF2.1 set with 100 replicas is also used. The central value is
216    determined from the mean and the uncertainty is derived from the
217    $1\sigma$ range. The overall uncertainty is derived from the envelope of the
218    alternative predictions and their uncertainties.
219    This effect was studied earlier using 7~TeV samples and found to be negligible.
220    \end{itemize}
221  
135
222   \begin{figure}[hbt]
223    \begin{center}
224 <        \includegraphics[width=0.8\linewidth]{plots/n_dl_syst_comp.png}
224 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRA.pdf}%
225 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf}
226 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}%
227 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf}
228 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf}
229          \caption{
230 <          \label{fig:ttllsyst}%\protect
230 >          \label{fig:ttllsyst}\protect
231            Comparison of the \ttll\ central prediction with those using
232            alternative MC samples. The blue band corresponds to the
233            total statistical error for all data and MC samples. The
234            alternative sample predictions are indicated by the
235            datapoints. The uncertainties on the alternative predictions
236            correspond to the uncorrelated statistical uncertainty from
237 <          the size of the alternative sample only.
238 <        [TO BE UPDATED WITH THE LATEST SELECTION AND SFS]}
237 >          the size of the alternative sample only.  Note the
238 >          suppressed vertical scales.}
239        \end{center}
240      \end{figure}
241  
242 +
243 + \begin{table}[!h]
244 + \begin{center}
245 + {\footnotesize
246 + \begin{tabular}{l||c|c|c|c|c|c|c}
247 + \hline
248 + $\Delta/N$  [\%] & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
249 + Match Up & Match Down \\
250 + \hline
251 + \hline
252 + SRA      & $2$ & $2$ & $5$ & $12$ & $7$ & $0$ & $2$  \\
253 + \hline
254 + SRB      & $6$ & $0$ & $6$ & $5$ & $12$ & $5$ & $6$  \\
255 + \hline
256 + % SRC    & $10$ & $3$ & $2$ & $12$ & $14$ & $16$ & $4$  \\
257 + % \hline
258 + % SRD    & $10$ & $6$ & $6$ & $21$ & $15$ & $19$ & $0$  \\
259 + % \hline
260 + % SRE    & $6$ & $17$ & $15$ & $2$ & $12$ & $17$ & $8$  \\
261 + \hline
262 + \end{tabular}}
263 + \caption{ Relative difference in \ttdl\ predictions for alternative MC
264 +  samples in
265 + the higher statistics regions SRA and SRB.  These differences
266 + are based on the central values of the predictions.  For a fuller
267 + picture
268 + of the situation, including statistical uncertainites, see Fig.~\ref{fig:ttllsyst}.
269 + \label{tab:fracdiff}}
270 + \end{center}
271 + \end{table}
272 +
273 +
274 + In Fig.~\ref{fig:ttllsyst} we compare the alternate MC \ttll\ background predictions
275 + for regions A through E.  We can make the following observations based
276 + on this Figure.
277 +
278 + \begin{itemize}
279 + \item In the tighter signal regions we are running out of
280 +  statistics.    
281 + \item Within the limited statistics, there is no evidence that the
282 +  situation changes as we go from signal region A to signal region E.
283 + %Therefore, we assess a systematic based on the relatively high
284 + %statistics
285 + %test in signal region A, and apply the same systematic uncertainty
286 + %to all other regions.
287 + \item In signal regions B and above, the uncertainties assigned in Section~\ref{sec:ttdilbkgunc}
288 + fully cover the alternative MC variations.
289 + \item In order to fully (as opposed as 1$\sigma$) cover the
290 + alternative MC variations in region A we would have to take a
291 + systematic
292 + uncertainty of $\approx 10\%$ instead of $5\%$.  This would be driven by the
293 + scale up/scale down variations, see Table~\ref{tab:fracdiff}.
294 + \end{itemize}
295 +
296 + \begin{table}[!ht]
297 + \begin{center}
298 + \begin{tabular}{l|c|c}
299 + \hline
300 +            Sample
301 +            &                K3   & K4\\
302 + \hline
303 + \hline
304 + Powheg     & $1.01 \pm 0.03$ & $0.93 \pm 0.04$ \\
305 + Madgraph  & $1.01 \pm 0.04$ & $0.92 \pm 0.04$ \\
306 + Mass Up    & $1.00 \pm 0.04$ & $0.92 \pm 0.04$ \\
307 + Mass Down    & $1.06 \pm 0.04$ & $0.99 \pm 0.05$ \\
308 + Scale Up    & $1.14 \pm 0.04$ & $1.23 \pm 0.06$ \\
309 + Scale Down    & $0.89 \pm 0.03$ & $0.74 \pm 0.03$ \\
310 + Match Up    & $1.02 \pm 0.04$ & $0.97 \pm 0.04$ \\
311 + Match Down    & $1.02 \pm 0.04$ & $0.91 \pm 0.04$ \\
312 + \hline
313 + \end{tabular}
314 + \caption{$\met>100$ GeV: Data/MC scale factors used to account for differences in the
315 +  fraction of events with additional hard jets from radiation in
316 +  \ttll\ events. \label{tab:njetskfactors_met100}}
317 + \end{center}
318 + \end{table}
319 +
320 +
321 + However, we have two pieces of information indicating that the
322 + scale up/scale down variations are inconsistent with the data.
323 + These are described below.
324 +
325 + The first piece of information is that the jet multiplicity in the scale
326 + up/scale down sample is the most inconsistent with the data.  This is shown
327 + in Table~\ref{tab:njetskfactors_met100}, where we tabulate the
328 + $K_3$ and $K_4$ factors of Section~\ref{sec:jetmultiplicity} for
329 + different \ttbar\ MC samples.  The data/MC disagreement in the $N_{jets}$
330 + distribution
331 + for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup}
332 + and~\ref{fig:dileptonnjets_scaledw}.  This should be compared with the
333 + equivalent $N_{jets}$ plots for the default Powheg MC, see
334 + Fig.~\ref{fig:dileptonnjets}, which agrees much better with data.
335 +
336 + \begin{figure}[hbt]
337 +  \begin{center}
338 +        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaleup.pdf}
339 +        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaleup.pdf}%
340 +        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaleup.pdf}
341 +        \caption{
342 +          \label{fig:dileptonnjets_scaleup}%\protect
343 +          SCALE UP: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
344 +          (top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}  
345 +      \end{center}
346 + \end{figure}
347 +
348 + \begin{figure}[hbt]
349 +  \begin{center}
350 +        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaledw.pdf}
351 +        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaledw.pdf}%
352 +        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaledw.pdf}
353 +        \caption{
354 +          \label{fig:dileptonnjets_scaledw}%\protect
355 +          SCALE DOWN: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
356 +          (top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}  
357 +      \end{center}
358 + \end{figure}
359 +
360 +
361 + \clearpage
362 +
363 + The second piece of information is that we have performed closure
364 + tests in CR5 using the alternative MC samples.  These are exactly
365 + the same tests as the one performed in Section~\ref{sec:CR5} on the
366 + Powheg sample.  As we argued previously, this is a very powerful
367 + test of the background calculation.
368 + The results of this test are summarized in Table~\ref{tab:hugecr5yields}.
369 + Concentrating on the relatively high statistics CR5A region, we see
370 + for all \ttbar\ MC samples except scale up/scale down we obtain
371 + closure within 1$\sigma$.  The scale up/scale down tests closes
372 + worse, only within 2$\sigma$.  This again is evidence that the
373 + scale up/scale down variations are in disagreement with the data.
374 +
375 + \input{hugeCR5Table.tex}
376 +
377 + Based on the two observations above, we argue that the MC
378 + scale up/scale down variations are too extreme.  We feel that
379 + a reasonable choice would be to take one-half of the scale up/scale
380 + down variations in our MC.  This factor of 1/2 would then bring
381 + the discrepancy in the closure test of
382 + Table~\ref{tab:hugecr5yields} for the scale up/scale down variations
383 + from about 2$\sigma$ to about 1$\sigma$.
384 +
385 + Then, going back to Table~\ref{tab:fracdiff}, and reducing the scale
386 + up/scale
387 + down variations by a factor 2, we can see that a systematic
388 + uncertainty
389 + of 5\% covers the range of reasonable variations from different MC
390 + models in SRA and SRB.
391 + %The alternative MC models indicate that a 6\% systematic uncertainty
392 + %covers the range of reasonable variations.
393 + Note that this 5\% is also consistent with the level at which we are
394 + able to test the closure of the method with alternative samples in CR5 for the high statistics
395 + regions (Table~\ref{tab:hugecr5yields}).
396 + The range of reasonable variations obtained with the alternative
397 + samples are consistent with the uncertainties assigned for
398 + the \ttll\ background based on the closure of the background
399 + predictions and data in CR4 and CR5.
400 +
401 +
402 +
403 +
404 +
405 + %\begin{table}[!h]
406 + %\begin{center}
407 + %{\footnotesize
408 + %\begin{tabular}{l||c||c|c|c|c|c|c|c}
409 + %\hline
410 + %Sample              & Powheg & Madgraph & Mass Up & Mass Down & Scale
411 + %Up & Scale Down &
412 + %Match Up & Match Down \\
413 + %\hline
414 + %\hline
415 + %SRA     & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$  \\
416 + %\hline
417 + %SRB     & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$  \\
418 + %\hline
419 + %SRC     & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$  \\
420 + %\hline
421 + %SRD     & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$  \\
422 + %\hline
423 + %SRE     & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$  \\
424 + %\hline
425 + %\end{tabular}}
426 + %\caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only.
427 + %\label{tab:ttdlalt}}
428 + %\end{center}
429 + %\end{table}
430 +
431 +
432 +
433 +
434 + %\begin{table}[!h]
435 + %\begin{center}
436 + %{\footnotesize
437 + %\begin{tabular}{l||c|c|c|c|c|c|c}
438 + %\hline
439 + %$N \sigma$     & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
440 + %Match Up & Match Down \\
441 + %\hline
442 + %\hline
443 + %SRA     & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$  \\
444 + %\hline
445 + %SRB     & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$  \\
446 + %\hline
447 + %SRC     & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$  \\
448 + %\hline
449 + %SRD     & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$  \\
450 + %\hline
451 + %SRE     & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$  \\
452 + %\hline
453 + %\end{tabular}}
454 + %\caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples.
455 + %\label{tab:nsig}}
456 + %\end{center}
457 + %\end{table}
458 +
459 +
460 + %\begin{table}[!h]
461 + %\begin{center}
462 + %\begin{tabular}{l||c|c|c|c}
463 + %\hline
464 + %Av. $\Delta$ Evt.     & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale
465 + %& $\Delta$ Match \\
466 + %\hline
467 + %\hline
468 + %SRA     & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$)  \\
469 + %\hline
470 + %SRB     & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$)  \\
471 + %\hline
472 + %SRC     & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$)  \\
473 + %\hline
474 + %SRD     & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$)  \\
475 + %\hline
476 + %SRE     & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$)  \\
477 + %\hline
478 + %\end{tabular}
479 + %\caption{ Av. difference in \ttdl\ events for alternative sample pairs.
480 + %\label{tab:devt}}
481 + %\end{center}
482 + %\end{table}
483 +
484 +
485 +
486   \clearpage
487  
488   %
# Line 290 | Line 624 | This is the uncertainty associated with
624   veto performance is modeled by the Monte Carlo.  This uncertainty
625   only applies to the fraction of dilepton BG events that have
626   a second e/$\mu$ or a one prong $\tau \to h$, with
627 < $P_T > 10$ GeV in $|\eta| < 2.4$.  This fraction is 1/3 (THIS WAS THE
628 < 7 TEV NUMBER, CHECK).  The uncertainty for these events
629 < is XX\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto}
627 > $P_T > 10$ GeV in $|\eta| < 2.4$.  This fraction is about 1/3, see
628 > Table~\ref{tab:trueisotrk}.
629 > The uncertainty for these events
630 > is 6\% and is obtained from tag-and-probe studies, see Section~\ref{sec:trkveto}.
631 >
632 > \begin{table}[!h]
633 > \begin{center}
634 > {\footnotesize
635 > \begin{tabular}{l||c|c|c|c|c|c|c}
636 > \hline
637 > Sample              & SRA & SRB & SRC & SRD & SRE & SRF & SRG \\
638 > \hline
639 > \hline
640 > $\mu$ Frac. \ttdl\ with true iso. trk.   & $0.32 \pm 0.03$ & $0.30 \pm 0.03$ & $0.32 \pm 0.06$ & $0.34 \pm 0.10$ & $0.35 \pm 0.16$ & $0.40 \pm 0.24$ & $0.50 \pm 0.32$  \\
641 > \hline
642 > \hline
643 > e Frac. \ttdl\ with true iso. trk.       & $0.32 \pm 0.03$ & $0.31 \pm 0.04$ & $0.33 \pm 0.06$ & $0.38 \pm 0.11$ & $0.38 \pm 0.19$ & $0.60 \pm 0.31$ & $0.61 \pm 0.45$  \\
644 > \hline
645 > \end{tabular}}
646 > \caption{ Fraction of \ttdl\ events with a true isolated track.
647 > \label{tab:trueisotrk}}
648 > \end{center}
649 > \end{table}
650  
651   \subsubsection{Isolated Track Veto: Tag and Probe Studies}
652   \label{sec:trkveto}
653  
300 [EVERYTHING IS 7TEV HERE, UPDATE WITH NEW RESULTS \\
301 ADD TABLE WITH FRACTION OF EVENTS THAT HAVE A TRUE ISOLATED TRACK]
654  
655   In this section we compare the performance of the isolated track veto in data and MC using tag-and-probe studies
656   with samples of Z$\to$ee and Z$\to\mu\mu$. The purpose of these studies is to demonstrate that the efficiency
657   to satisfy the isolated track veto requirements is well-reproduced in the MC, since if this were not the case
658 < we would need to apply a data-to-MC scale factor in order to correctly predict the \ttll\ background. This study
658 > we would need to apply a data-to-MC scale factor in order to correctly
659 > predict the \ttll\ background.
660 >
661 > This study
662   addresses possible data vs. MC discrepancies for the {\bf efficiency} to identify (and reject) events with a
663   second {\bf genuine} lepton (e, $\mu$, or $\tau\to$1-prong). It does not address possible data vs. MC discrepancies
664   in the fake rate for rejecting events without a second genuine lepton; this is handled separately in the top normalization
665   procedure by scaling the \ttlj\ contribution to match the data in the \mt\ peak after applying the isolated track veto.
666 +
667   Furthermore, we test the data and MC
668   isolated track veto efficiencies for electrons and muons since we are using a Z tag-and-probe technique, but we do not
669   directly test the performance for hadronic tracks from $\tau$ decays. The performance for hadronic $\tau$ decay products
# Line 320 | Line 676 | decays are well-understood, we currently
676   Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed.
677   As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%,
678   leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background
679 < due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as neglgigible.
679 > due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as negligible.
680  
681 < The tag-and-probe studies are performed in the full 2011 data sample, and compared with the DYJets madgraph sample.
681 > The tag-and-probe studies are performed in the full data sample, and compared with the DYJets madgraph sample.
682   All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV.
683   We compare the distributions of absolute track isolation for probe electrons/muons in data vs. MC. The contributions to
684   this isolation sum are from ambient energy in the event from underlying event, pile-up and jet activitiy, and hence do
# Line 344 | Line 700 | The specific criteria for tags and probe
700  
701        \begin{itemize}
702        \item Electron passes full analysis ID/iso selection
703 <      \item \pt\ $>$ 30 GeV, $|\eta|<2.5$
704 <
349 <      \item Matched to 1 of the 2 electron tag-and-probe triggers
350 <        \begin{itemize}
351 <        \item \verb=HLT_Ele17_CaloIdVT_CaloIsoVT_TrkIdT_TrkIsoVT_SC8_Mass30_v*=
352 <        \item \verb=HLT_Ele17_CaloIdVT_CaloIsoVT_TrkIdT_TrkIsoVT_Ele8_Mass30_v*=
353 <        \end{itemize}
703 >      \item \pt\ $>$ 30 GeV, $|\eta|<2.1$
704 >      \item Matched to the single electron trigger \verb=HLT_Ele27_WP80_v*=
705        \end{itemize}
706  
707      \item{Probe criteria}
# Line 365 | Line 716 | The specific criteria for tags and probe
716        \begin{itemize}
717        \item Muon passes full analysis ID/iso selection
718        \item \pt\ $>$ 30 GeV, $|\eta|<2.1$
719 <      \item Matched to 1 of the 2 electron tag-and-probe triggers
719 >      \item Matched to 1 of the 2 single muon triggers
720          \begin{itemize}
721          \item \verb=HLT_IsoMu30_v*=
722          \item \verb=HLT_IsoMu30_eta2p1_v*=
# Line 382 | Line 733 | The specific criteria for tags and probe
733   The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe
734   good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy
735   absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}.
736 < In the $\geq$0 and $\geq$1 jet bins where the efficiencies can be tested with statistical precision, the data and MC
737 < efficiencies agree within 7\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency.
736 > In the $\geq 0$ and $\geq 1$ jet bins where the efficiencies can be tested with statistical precision, the data and MC
737 > efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency.
738   For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for
739   a data vs. MC discrepancy in the isolated track veto efficiency.
740  
# Line 394 | Line 745 | a data vs. MC discrepancy in the isolate
745  
746   \begin{figure}[hbt]
747    \begin{center}
748 <        %\includegraphics[width=0.3\linewidth]{plots/el_tkiso_0j.pdf}%
749 <        %\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_0j.pdf}
750 <        %\includegraphics[width=0.3\linewidth]{plots/el_tkiso_1j.pdf}%
751 <        %\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_1j.pdf}
752 <        %\includegraphics[width=0.3\linewidth]{plots/el_tkiso_2j.pdf}%
753 <        %\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_2j.pdf}
754 <        %\includegraphics[width=0.3\linewidth]{plots/el_tkiso_3j.pdf}%
755 <        %\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_3j.pdf}
756 <        %\includegraphics[width=0.3\linewidth]{plots/el_tkiso_4j.pdf}%
757 <        %\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_4j.pdf}
748 >        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_0j.pdf}%
749 >        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_0j.pdf}
750 >        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_1j.pdf}%
751 >        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_1j.pdf}
752 >        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_2j.pdf}%
753 >        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_2j.pdf}
754 >        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_3j.pdf}%
755 >        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_3j.pdf}
756 >        \includegraphics[width=0.3\linewidth]{plots/el_tkiso_4j.pdf}%
757 >        \includegraphics[width=0.3\linewidth]{plots/mu_tkiso_4j.pdf}
758          \caption{
759            \label{fig:tnp} Comparison of the absolute track isolation in data vs. MC for electrons (left) and muons (right)
760   for events with the \njets\ requirement varied from \njets\ $\geq$ 0 to \njets\ $\geq$ 4.
# Line 415 | Line 766 | for events with the \njets\ requirement
766  
767   \begin{table}[!ht]
768   \begin{center}
769 < \caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements
770 < on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various
771 < jet multiplicity requirements.}
772 < \begin{tabular}{l|l|c|c|c|c|c}
769 > \begin{tabular}{l|c|c|c|c|c}
770 >
771 > %Electrons:
772 > %Selection            : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&1)==1))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_Ele27_WP80_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&8)==8))&&(probe->pt()>30))&&(drprobe<0.05)
773 > %Total MC yields        : 2497277
774 > %Total DATA yields      : 2649453
775 > %Muons:
776 > %Selection            : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&2)==2))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_IsoMu24_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&65536)==65536))&&(probe->pt()>30))&&(drprobe<0.05)
777 > %Total MC yields        : 3749863
778 > %Total DATA yields      : 4210022
779 > %Info in <TCanvas::MakeDefCanvas>:  created default TCanvas with name c1
780 > %Info in <TCanvas::Print>: pdf file plots/nvtx.pdf has been created
781 >
782   \hline
783   \hline
784 < e + $\geq$0 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
784 > e + $\geq$0 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
785   \hline
786 <      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  \\
787 <        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  \\
788 <   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  \\
786 >      data   &  0.098 $\pm$ 0.0002   &  0.036 $\pm$ 0.0001   &  0.016 $\pm$ 0.0001   &  0.009 $\pm$ 0.0001   &  0.006 $\pm$ 0.0000  \\
787 >        mc   &  0.097 $\pm$ 0.0002   &  0.034 $\pm$ 0.0001   &  0.016 $\pm$ 0.0001   &  0.009 $\pm$ 0.0001   &  0.005 $\pm$ 0.0000  \\
788 >   data/mc   &     1.00 $\pm$ 0.00   &     1.04 $\pm$ 0.00   &     1.04 $\pm$ 0.01   &     1.03 $\pm$ 0.01   &     1.02 $\pm$ 0.01  \\
789 >
790   \hline
791   \hline
792 < $\mu$ + $\geq$0 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
792 > $\mu$ + $\geq$0 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
793   \hline
794 <      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  \\
795 <        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  \\
796 <   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  \\
794 >      data   &  0.094 $\pm$ 0.0001   &  0.034 $\pm$ 0.0001   &  0.016 $\pm$ 0.0001   &  0.009 $\pm$ 0.0000   &  0.006 $\pm$ 0.0000  \\
795 >        mc   &  0.093 $\pm$ 0.0001   &  0.033 $\pm$ 0.0001   &  0.015 $\pm$ 0.0001   &  0.009 $\pm$ 0.0000   &  0.006 $\pm$ 0.0000  \\
796 >   data/mc   &     1.01 $\pm$ 0.00   &     1.03 $\pm$ 0.00   &     1.03 $\pm$ 0.01   &     1.03 $\pm$ 0.01   &     1.02 $\pm$ 0.01  \\
797 >
798   \hline
437 \hline
438 e + $\geq$1 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
799   \hline
800 <      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  \\
441 <        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  \\
442 <   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  \\
800 > e + $\geq$1 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
801   \hline
802 +      data   &  0.110 $\pm$ 0.0005   &  0.044 $\pm$ 0.0003   &  0.022 $\pm$ 0.0002   &  0.014 $\pm$ 0.0002   &  0.009 $\pm$ 0.0002  \\
803 +        mc   &  0.110 $\pm$ 0.0005   &  0.042 $\pm$ 0.0003   &  0.021 $\pm$ 0.0002   &  0.013 $\pm$ 0.0002   &  0.009 $\pm$ 0.0001  \\
804 +   data/mc   &     1.00 $\pm$ 0.01   &     1.04 $\pm$ 0.01   &     1.06 $\pm$ 0.02   &     1.08 $\pm$ 0.02   &     1.06 $\pm$ 0.03  \\
805 +
806   \hline
445 $\mu$ + $\geq$1 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
807   \hline
808 <      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  \\
448 <        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  \\
449 <   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  \\
808 > $\mu$ + $\geq$1 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
809   \hline
810 +      data   &  0.106 $\pm$ 0.0004   &  0.043 $\pm$ 0.0003   &  0.023 $\pm$ 0.0002   &  0.014 $\pm$ 0.0002   &  0.010 $\pm$ 0.0001  \\
811 +        mc   &  0.106 $\pm$ 0.0004   &  0.042 $\pm$ 0.0003   &  0.021 $\pm$ 0.0002   &  0.013 $\pm$ 0.0002   &  0.009 $\pm$ 0.0001  \\
812 +   data/mc   &     1.00 $\pm$ 0.01   &     1.04 $\pm$ 0.01   &     1.06 $\pm$ 0.01   &     1.08 $\pm$ 0.02   &     1.07 $\pm$ 0.02  \\
813 +
814   \hline
452 e + $\geq$2 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
815   \hline
816 <      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  \\
455 <        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  \\
456 <   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  \\
816 > e + $\geq$2 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
817   \hline
818 +      data   &  0.117 $\pm$ 0.0012   &  0.050 $\pm$ 0.0008   &  0.026 $\pm$ 0.0006   &  0.017 $\pm$ 0.0005   &  0.012 $\pm$ 0.0004  \\
819 +        mc   &  0.120 $\pm$ 0.0012   &  0.048 $\pm$ 0.0008   &  0.025 $\pm$ 0.0006   &  0.016 $\pm$ 0.0005   &  0.011 $\pm$ 0.0004  \\
820 +   data/mc   &     0.97 $\pm$ 0.01   &     1.05 $\pm$ 0.02   &     1.05 $\pm$ 0.03   &     1.07 $\pm$ 0.04   &     1.07 $\pm$ 0.05  \\
821 +
822   \hline
459 $\mu$ + $\geq$2 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
823   \hline
824 <      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  \\
462 <        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  \\
463 <   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  \\
824 > $\mu$ + $\geq$2 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
825   \hline
826 +      data   &  0.111 $\pm$ 0.0010   &  0.048 $\pm$ 0.0007   &  0.026 $\pm$ 0.0005   &  0.018 $\pm$ 0.0004   &  0.013 $\pm$ 0.0004  \\
827 +        mc   &  0.115 $\pm$ 0.0010   &  0.048 $\pm$ 0.0006   &  0.025 $\pm$ 0.0005   &  0.016 $\pm$ 0.0004   &  0.012 $\pm$ 0.0003  \\
828 +   data/mc   &     0.97 $\pm$ 0.01   &     1.01 $\pm$ 0.02   &     1.04 $\pm$ 0.03   &     1.09 $\pm$ 0.04   &     1.09 $\pm$ 0.04  \\
829 +
830   \hline
466 e + $\geq$3 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
831   \hline
832 <      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  \\
833 <        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  \\
834 <   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  \\
832 > e + $\geq$3 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
833 > \hline
834 >      data   &  0.123 $\pm$ 0.0031   &  0.058 $\pm$ 0.0022   &  0.034 $\pm$ 0.0017   &  0.023 $\pm$ 0.0014   &  0.017 $\pm$ 0.0012  \\
835 >        mc   &  0.131 $\pm$ 0.0030   &  0.055 $\pm$ 0.0020   &  0.030 $\pm$ 0.0015   &  0.020 $\pm$ 0.0013   &  0.015 $\pm$ 0.0011  \\
836 >   data/mc   &     0.94 $\pm$ 0.03   &     1.06 $\pm$ 0.06   &     1.14 $\pm$ 0.08   &     1.16 $\pm$ 0.10   &     1.17 $\pm$ 0.12  \\
837 >
838   \hline
839   \hline
840 < $\mu$ + $\geq$3 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
840 > $\mu$ + $\geq$3 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
841   \hline
842 <      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  \\
843 <        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  \\
844 <   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  \\
842 >      data   &  0.121 $\pm$ 0.0025   &  0.055 $\pm$ 0.0018   &  0.033 $\pm$ 0.0014   &  0.022 $\pm$ 0.0011   &  0.017 $\pm$ 0.0010  \\
843 >        mc   &  0.120 $\pm$ 0.0024   &  0.052 $\pm$ 0.0016   &  0.029 $\pm$ 0.0012   &  0.019 $\pm$ 0.0010   &  0.014 $\pm$ 0.0009  \\
844 >   data/mc   &     1.01 $\pm$ 0.03   &     1.06 $\pm$ 0.05   &     1.14 $\pm$ 0.07   &     1.14 $\pm$ 0.08   &     1.16 $\pm$ 0.10  \\
845 >
846   \hline
847   \hline
848 < e + $\geq$4 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
848 > e + $\geq$4 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
849   \hline
850 <      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  \\
851 <        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  \\
852 <   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  \\
850 >      data   &  0.129 $\pm$ 0.0080   &  0.070 $\pm$ 0.0061   &  0.044 $\pm$ 0.0049   &  0.031 $\pm$ 0.0042   &  0.021 $\pm$ 0.0034  \\
851 >        mc   &  0.132 $\pm$ 0.0075   &  0.059 $\pm$ 0.0053   &  0.035 $\pm$ 0.0041   &  0.025 $\pm$ 0.0035   &  0.017 $\pm$ 0.0029  \\
852 >   data/mc   &     0.98 $\pm$ 0.08   &     1.18 $\pm$ 0.15   &     1.26 $\pm$ 0.20   &     1.24 $\pm$ 0.24   &     1.18 $\pm$ 0.28  \\
853 >
854   \hline
855   \hline
856 < $\mu$ + $\geq$4 jets            &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
856 > $\mu$ + $\geq$4 jets   &           $>$ 1 GeV   &           $>$ 2 GeV   &           $>$ 3 GeV   &           $>$ 4 GeV   &           $>$ 5 GeV  \\
857   \hline
858 <      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  \\
859 <        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  \\
860 <   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  \\
858 >      data   &  0.136 $\pm$ 0.0067   &  0.064 $\pm$ 0.0048   &  0.041 $\pm$ 0.0039   &  0.029 $\pm$ 0.0033   &  0.024 $\pm$ 0.0030  \\
859 >        mc   &  0.130 $\pm$ 0.0063   &  0.065 $\pm$ 0.0046   &  0.035 $\pm$ 0.0034   &  0.020 $\pm$ 0.0026   &  0.013 $\pm$ 0.0022  \\
860 >   data/mc   &     1.04 $\pm$ 0.07   &     0.99 $\pm$ 0.10   &     1.19 $\pm$ 0.16   &     1.47 $\pm$ 0.25   &     1.81 $\pm$ 0.37  \\
861 >
862   \hline
863   \hline
864  
865   \end{tabular}
866 + \caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements
867 + on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various
868 + jet multiplicity requirements.}
869   \end{center}
870   \end{table}
871  
872 + \clearpage
873 + \subsection{Summary of uncertainties}
874 + \label{sec:bgunc-bottomline}
875 +
876 + The contribution from each source to the total uncertainty on the background yield is given in Tables~\ref{tab:relativeuncertaintycomponents} and~\ref{tab:uncertaintycomponents} for the relative and absolute uncertainties, respectively. In the low-\met\ regions the dominant uncertainty comes from the top tail-to-peak ratio, $R_{top}$ (Section~\ref{sec:ttp}), while in the high-\met\ regions the \ttll\ systematic uncertainty dominates (Section~\ref{sec:ttdilbkgunc}).
877 +
878 + \input{uncertainties_table.tex}
879 +
880 +
881 +
882  
883  
884   %Figure.~\ref{fig:reliso} compares the relative track isolation
# Line 548 | Line 931 | jet multiplicity requirements.}
931   %END SECTION TO WRITE OUT
932  
933  
934 < {\bf fix me: What you have written in the next paragraph does not explain how $\epsilon_{fake}$ is measured.
935 < Why not measure $\epsilon_{fake}$ in the b-veto region?}
934 > %{\bf fix me: What you have written in the next paragraph does not
935 > %explain how $\epsilon_{fake}$ is measured.
936 > %Why not measure $\epsilon_{fake}$ in the b-veto region?}
937  
938   %A measurement of the $\epsilon_{fake}$ in data is non-trivial. However, it is
939   %possible to correct for differences in the $\epsilon_{fake}$ between data and MC by
# Line 577 | Line 961 | Why not measure $\epsilon_{fake}$ in the
961   %      \end{center}
962   %\end{figure}
963  
580 \subsection{Summary of uncertainties}
581 \label{sec:bgunc-bottomline}.
964  
965 < THIS NEEDS TO BE WRITTEN
965 >
966 > % THIS NEEDS TO BE WRITTEN

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