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# Line 148 | Line 148 | the most important one.
148  
149   \subsection{Uncertainty on the \ttll\ Acceptance}
150  
151 [CLAUDIO: WE NEED TO DISCUSS THIS A LITTLE MORE -- THEN I CAN PUT THE
152 WORDS IN]
153
151   The \ttbar\ background prediction is obtained from MC, with corrections
152   derived from control samples in data. The uncertainty associated with
153   the theoretical modeling of the \ttbar\ production and decay is
# Line 189 | Line 186 | The variations considered are
186    This effect was studied earlier using 7~TeV samples and found to be negligible.
187    \end{itemize}
188  
189 <
190 < \begin{table}[!h]
191 < \begin{center}
192 < {\footnotesize
193 < \begin{tabular}{l||c||c|c|c|c|c|c|c}
194 < \hline
195 < Sample              & Powheg & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
196 < Match Up & Match Down \\
197 < \hline
198 < \hline
199 < SRA      & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$  \\
200 < \hline
201 < SRB      & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$  \\
202 < \hline
203 < SRC      & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$  \\
204 < \hline
205 < SRD      & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$  \\
206 < \hline
207 < SRE      & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$  \\
211 < \hline
212 < \end{tabular}}
213 < \caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only.
214 < \label{tab:ttdlalt}}
215 < \end{center}
216 < \end{table}
189 > \begin{figure}[hbt]
190 >  \begin{center}
191 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRA.pdf}%
192 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf}
193 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}%
194 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf}
195 >        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf}
196 >        \caption{
197 >          \label{fig:ttllsyst}\protect
198 >          Comparison of the \ttll\ central prediction with those using
199 >          alternative MC samples. The blue band corresponds to the
200 >          total statistical error for all data and MC samples. The
201 >          alternative sample predictions are indicated by the
202 >          datapoints. The uncertainties on the alternative predictions
203 >          correspond to the uncorrelated statistical uncertainty from
204 >          the size of the alternative sample only.  Note the
205 >          suppressed vertical scales.}
206 >      \end{center}
207 >    \end{figure}
208  
209  
210   \begin{table}[!h]
# Line 229 | Line 220 | SRA     & $2$ & $2$ & $5$ & $12$ & $7$ & $
220   \hline
221   SRB      & $6$ & $0$ & $6$ & $5$ & $12$ & $5$ & $6$  \\
222   \hline
223 < SRC      & $10$ & $3$ & $2$ & $12$ & $14$ & $16$ & $4$  \\
224 < \hline
225 < SRD      & $10$ & $6$ & $6$ & $21$ & $15$ & $19$ & $0$  \\
226 < \hline
227 < SRE      & $6$ & $17$ & $15$ & $2$ & $12$ & $17$ & $8$  \\
223 > % SRC    & $10$ & $3$ & $2$ & $12$ & $14$ & $16$ & $4$  \\
224 > % \hline
225 > % SRD    & $10$ & $6$ & $6$ & $21$ & $15$ & $19$ & $0$  \\
226 > % \hline
227 > % SRE    & $6$ & $17$ & $15$ & $2$ & $12$ & $17$ & $8$  \\
228   \hline
229   \end{tabular}}
230 < \caption{ Relative difference in \ttdl\ predictions for alternative MC samples.
230 > \caption{ Relative difference in \ttdl\ predictions for alternative MC
231 >  samples in
232 > the higher statistics regions SRA and SRB.  These differences
233 > are based on the central values of the predictions.  For a fuller
234 > picture
235 > of the situation, including statistical uncertainites, see Fig.~\ref{fig:ttllsyst}.
236   \label{tab:fracdiff}}
237   \end{center}
238   \end{table}
239  
240  
241 < \begin{table}[!h]
242 < \begin{center}
243 < {\footnotesize
248 < \begin{tabular}{l||c|c|c|c|c|c|c}
249 < \hline
250 < $N \sigma$     & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
251 < Match Up & Match Down \\
252 < \hline
253 < \hline
254 < SRA      & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$  \\
255 < \hline
256 < SRB      & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$  \\
257 < \hline
258 < SRC      & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$  \\
259 < \hline
260 < SRD      & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$  \\
261 < \hline
262 < SRE      & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$  \\
263 < \hline
264 < \end{tabular}}
265 < \caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples.
266 < \label{tab:nsig}}
267 < \end{center}
268 < \end{table}
241 > In Fig.~\ref{fig:ttllsyst} we compare the alternate MC \ttll\ background predictions
242 > for regions A through E.  We can make the following observations based
243 > on this Figure.
244  
245 + \begin{itemize}
246 + \item In the tighter signal regions we are running out of
247 +  statistics.    
248 + \item Within the limited statistics, there is no evidence that the
249 +  situation changes as we go from signal region A to signal region E.
250 + Therefore, we assess a systematic based on the relatively high
251 + statistics
252 + test in signal region A, and apply the same systematic uncertainty
253 + to all other regions.
254 + \item In order to fully (as opposed as 1$\sigma$) cover the
255 + alternative MC variations in region A we would have to take a
256 + systematic
257 + uncertainty of $\approx 10\%$.  This would be driven by the
258 + scale up/scale down variations, see Table~\ref{tab:fracdiff}.
259 + \end{itemize}
260  
261 < \begin{table}[!h]
261 > \begin{table}[!ht]
262   \begin{center}
263 < \begin{tabular}{l||c|c|c|c}
274 < \hline
275 < Av. $\Delta$ Evt.     & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale
276 < & $\Delta$ Match \\
277 < \hline
263 > \begin{tabular}{l|c|c}
264   \hline
265 < SRA      & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$)  \\
265 >            Sample
266 >            &                K3   & K4\\
267   \hline
281 SRB      & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$)  \\
268   \hline
269 < SRC      & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$)  \\
270 < \hline
271 < SRD      & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$)  \\
272 < \hline
273 < SRE      & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$)  \\
269 > Powheg     & $1.01 \pm 0.03$ & $0.93 \pm 0.04$ \\
270 > Madgraph  & $1.01 \pm 0.04$ & $0.92 \pm 0.04$ \\
271 > Mass Up    & $1.00 \pm 0.04$ & $0.92 \pm 0.04$ \\
272 > Mass Down    & $1.06 \pm 0.04$ & $0.99 \pm 0.05$ \\
273 > Scale Up    & $1.14 \pm 0.04$ & $1.23 \pm 0.06$ \\
274 > Scale Down    & $0.89 \pm 0.03$ & $0.74 \pm 0.03$ \\
275 > Match Up    & $1.02 \pm 0.04$ & $0.97 \pm 0.04$ \\
276 > Match Down    & $1.02 \pm 0.04$ & $0.91 \pm 0.04$ \\
277   \hline
278   \end{tabular}
279 < \caption{ Av. difference in \ttdl\ events for alternative sample pairs.
280 < \label{tab:devt}}
279 > \caption{$\met>100$ GeV: Data/MC scale factors used to account for differences in the
280 >  fraction of events with additional hard jets from radiation in
281 >  \ttll\ events. \label{tab:njetskfactors_met100}}
282   \end{center}
283   \end{table}
284  
285  
286 + However, we have two pieces of information indicating that the
287 + scale up/scale down variations are inconsistent with the data.
288 + These are described below.
289 +
290 + The first piece of information is that the jet multiplicity in the scale
291 + up/scale down sample is the most inconsistent with the data.  This can be shown
292 + in Table~\ref{tab:njetskfactors_met100}, where we tabulate the
293 + $K_3$ and $K_4$ factors of Section~\ref{tab:njetskfactors_met100} for
294 + different \ttbar\ MC samples.  The data/MC disagreement in the $N_{jets}$
295 + distribution
296 + for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup}
297 + and~\ref{fig:dileptonnjets_scaledw}.  This should be compared with the
298 + equivalent $N_{jets}$ plots for the default Powheg MC, see
299 + Fig.~\ref{fig:dileptonnjets}, which agrees much better with data.
300 +
301   \begin{figure}[hbt]
302    \begin{center}
303 <        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRA.pdf}%
304 <        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf}
305 <        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}%
306 <        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf}
307 <        \includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf}
308 <        \caption{
309 <          \label{fig:ttllsyst}\protect
305 <          Comparison of the \ttll\ central prediction with those using
306 <          alternative MC samples. The blue band corresponds to the
307 <          total statistical error for all data and MC samples. The
308 <          alternative sample predictions are indicated by the
309 <          datapoints. The uncertainties on the alternative predictions
310 <          correspond to the uncorrelated statistical uncertainty from
311 <          the size of the alternative sample only.
312 <        [TO BE UPDATED WITH THE LATEST SELECTION AND SFS]}
303 >        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaleup.pdf}
304 >        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaleup.pdf}%
305 >        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaleup.pdf}
306 >        \caption{
307 >          \label{fig:dileptonnjets_scaleup}%\protect
308 >          SCALE UP: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
309 >          (top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}  
310        \end{center}
311 <    \end{figure}
311 > \end{figure}
312 >
313 > \begin{figure}[hbt]
314 >  \begin{center}
315 >        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaledw.pdf}
316 >        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaledw.pdf}%
317 >        \includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaledw.pdf}
318 >        \caption{
319 >          \label{fig:dileptonnjets_scaledw}%\protect
320 >          SCALE DOWN: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\
321 >          (top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.}  
322 >      \end{center}
323 > \end{figure}
324 >
325 >
326 > \clearpage
327 >
328 > The second piece of information is that we have performed closure
329 > tests in CR5 using the alternative MC samples.  These are exactly
330 > the same tests as the one performed in Section~\ref{sec:CR5} on the
331 > Powheg sample.  As we argued previously, this is a very powerful
332 > test of the background calculation.
333 > The results of this test are summarized in Table~\ref{tab:hugecr5yields}.
334 > Concentrating on the relatively high statistics CR5A region, we see
335 > for all \ttbar\ MC samples except scale up/scale down we obtain
336 > closure within 1$\sigma$.  The scale up/scale down tests closes
337 > worse, only within 2$\sigma$.  This again is evidence that the
338 > scale up/scale down variations are in disagreement with the data.
339 >
340 > \input{hugeCR5Table.tex}
341 >
342 > Based on the two observations above, we argue that the MC
343 > scale up/scale down variations are too extreme.  We feel that
344 > a reasonable choice would be to take one-half of the scale up/scale
345 > down variations in our MC.  This factor of 1/2 would then bring
346 > the discrepancy in the closure test of
347 > Table~\ref{tab:hugecr5yields} for the scale up/scale down variations
348 > from about 2$\sigma$ to about 1$\sigma$.
349 >
350 > Then, going back to Table~\ref{tab:fracdiff}, and reducing the scale
351 > up/scale
352 > down variations by a factor 2, we can see that a systematic
353 > uncertainty
354 > of 6\% would fully cover all of the variations from different MC
355 > samples in SRA and SRB.
356 > {\bf Thus, we take a 6\% systematic uncertainty,  constant as a
357 > function of signal region, as the systematic due to alternative MC
358 > models.}.
359 > Note that this 6\% is also consistent with the level at which we are
360 > able
361 > to test the closure of the method in CR5 for the high statistics
362 > regions
363 > (Table~\ref{tab:hugecr5yields}).
364 >
365 >
366 >
367 >
368 >
369 >
370 > %\begin{table}[!h]
371 > %\begin{center}
372 > %{\footnotesize
373 > %\begin{tabular}{l||c||c|c|c|c|c|c|c}
374 > %\hline
375 > %Sample              & Powheg & Madgraph & Mass Up & Mass Down & Scale
376 > %Up & Scale Down &
377 > %Match Up & Match Down \\
378 > %\hline
379 > %\hline
380 > %SRA     & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$  \\
381 > %\hline
382 > %SRB     & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$  \\
383 > %\hline
384 > %SRC     & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$  \\
385 > %\hline
386 > %SRD     & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$  \\
387 > %\hline
388 > %SRE     & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$  \\
389 > %\hline
390 > %\end{tabular}}
391 > %\caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only.
392 > %\label{tab:ttdlalt}}
393 > %\end{center}
394 > %\end{table}
395 >
396 >
397 >
398 >
399 > %\begin{table}[!h]
400 > %\begin{center}
401 > %{\footnotesize
402 > %\begin{tabular}{l||c|c|c|c|c|c|c}
403 > %\hline
404 > %$N \sigma$     & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down &
405 > %Match Up & Match Down \\
406 > %\hline
407 > %\hline
408 > %SRA     & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$  \\
409 > %\hline
410 > %SRB     & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$  \\
411 > %\hline
412 > %SRC     & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$  \\
413 > %\hline
414 > %SRD     & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$  \\
415 > %\hline
416 > %SRE     & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$  \\
417 > %\hline
418 > %\end{tabular}}
419 > %\caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples.
420 > %\label{tab:nsig}}
421 > %\end{center}
422 > %\end{table}
423 >
424 >
425 > %\begin{table}[!h]
426 > %\begin{center}
427 > %\begin{tabular}{l||c|c|c|c}
428 > %\hline
429 > %Av. $\Delta$ Evt.     & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale
430 > %& $\Delta$ Match \\
431 > %\hline
432 > %\hline
433 > %SRA     & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$)  \\
434 > %\hline
435 > %SRB     & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$)  \\
436 > %\hline
437 > %SRC     & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$)  \\
438 > %\hline
439 > %SRD     & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$)  \\
440 > %\hline
441 > %SRE     & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$)  \\
442 > %\hline
443 > %\end{tabular}
444 > %\caption{ Av. difference in \ttdl\ events for alternative sample pairs.
445 > %\label{tab:devt}}
446 > %\end{center}
447 > %\end{table}
448 >
449 >
450  
451   \clearpage
452  

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