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 |
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] |
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 |
|
|