Annotation of ttbar/p20_taujets_note/Summary.tex, revision 1.2
1.1 uid12904 1: \section{\label{sub:xsect}Cross section}
2:
3: Having presented the preselection yelds on Section \ref{sub:Preselection} we now show the results of the
1.2 ! uid12904 4: efficiencies for $\tau$ ID, b-tagging and trigger for all $t\bar{t}$ channels (only statistical uncertainties are shown).
1.1 uid12904 5:
6:
7: \begin{table}[h]
8: %\begin{center}
9: \begin{tabular}{ccccc}
10: \hline
11: Selection & Relative(\%) & Cumulative(\%) \\ \hline
12: $\tau$ ID & $ 22.20 \pm 0.24 $ & $ 22.20 \pm 0.24 $ \\
13: Trigger & $ 84.54 \pm 0.55 \ $ & $ 18.77 \pm 0.22\ $ \\
14: b-tagging & $ 61.82 \pm 0.55 \ $ & $ 11.61 \pm 0.16\ $ \\ \hline
15:
16: \end{tabular}
1.2 ! uid12904 17: \caption{$t\overline{t}\rightarrow\tau+jets$ cut flow for taus of Types 1 and 2.}
1.1 uid12904 18: %\end{center}
19: \label{taujets_final12}
20: \end{table}
21:
22:
23: \begin{table}[h]
24: %\begin{center}
25: \begin{tabular}{ccccc}
26: \hline
27: Selection & Relative(\%) & Cumulative(\%) \\ \hline
28: $\tau$ ID & $ 12.37 \pm 0.21 $ & $ 12.37 \pm 0.21 $ \\
29: Trigger & $ 84.79 \pm 0.75 \ $ & $ 10.49 \pm 0.19\ $ \\
30: b-tagging & $ 59.63 \pm 0.75 \ $ & $ 6.26 \pm 0.13\ $ \\ \hline
31:
32: \end{tabular}
1.2 ! uid12904 33: \caption{$t\overline{t}\rightarrow\tau+jets$ cut flow for taus of Type 3}
1.1 uid12904 34: %\end{center}
35: \label{taujets_final3}
36: \end{table}
37:
38:
39: \begin{table}[h]
40: %\begin{center}
41: \begin{tabular}{ccccc}
42: \hline
43: Selection & Relative(\%) & Cumulative(\%) \\ \hline
44: $\tau$ ID & $ 10.81 \pm 0.20 $ & $ 10.81 \pm 0.20 $ \\
45: Trigger & $ 83.40 \pm 0.81 \ $ & $ 9.02 \pm 0.18\ $ \\
46: b-tagging & $ 61.30 \pm 0.82 \ $ & $ 5.52 \pm 0.12\ $ \\ \hline
47:
48: \end{tabular}
1.2 ! uid12904 49: \caption{$t\overline{t}\rightarrow e+jets$ cut flow for taus of Types 1 and 2}
1.1 uid12904 50: %\end{center}
51: \label{elecjets_final12}
52: \end{table}
53:
54: \begin{table}[b]
55: %\begin{center}
56: \begin{tabular}{ccccc}
57: \hline
58: Selection & Relative(\%) & Cumulative(\%) \\ \hline
59: $\tau$ ID & $ 2.25 \pm 0.11 $ & $ 2.25 \pm 0.11 $ \\
60: Trigger & $ 83.62 \pm 1.77 \ $ & $ 1.88 \pm 0.09 \ $ \\
61: b-tagging & $ 58.26 \pm 1.76 \ $ & $ 1.10 \pm 0.06\ $ \\ \hline
62:
63: \end{tabular}
1.2 ! uid12904 64: \caption{$t\overline{t}\rightarrow e+jets$ cut flow for taus of Type 3}
1.1 uid12904 65: %\end{center}
66: \label{elecjets_final3}
67: \end{table}
68:
69: %\newpage
70:
71:
72: \begin{table}[b]
73: %\begin{center}
74: \begin{tabular}{ccccc}
75: \hline
76: Selection & Relative(\%) & Cumulative(\%) \\ \hline
77: $\tau$ ID & $ 3.38 \pm 0.19 $ & $ 3.38 \pm 0.19 $ \\
78: Trigger & $ 84.44 \pm 2.13 \ $ & $ 2.86 \pm 0.17\ $ \\
79: b-tagging & $ 61.25 \pm 2.16 \ $ & $ 1.75 \pm 0.11\ $ \\ \hline
80:
81: \end{tabular}
1.2 ! uid12904 82: \caption{$t\overline{t}\rightarrow \mu +jets$ cut flow for taus of Types 1 and 2.}
1.1 uid12904 83: %\end{center}
84: \label{muonjets_final12}
85: \end{table}
86:
87:
88: \begin{table}[b]
89: %\begin{center}
90: \begin{tabular}{ccccc}
91: \hline
92: Selection & Relative(\%) & Cumulative(\%) \\ \hline
93: $\tau$ ID & $ 3.88 \pm 0.21 $ & $ 3.88 \pm 0.21 $ \\
94: Trigger & $ 82.79 \pm 2.04 \ $ & $ 3.21 \pm 0.18\ $ \\
95: b-tagging & $ 58.11 \pm 2.05 \ $ & $ 1.87 \pm 0.11\ $ \\ \hline
96:
97: \end{tabular}
1.2 ! uid12904 98: \caption{$t\overline{t}\rightarrow \mu +jets$ cut flow for taus of Type 3.}
1.1 uid12904 99: %\end{center}
100: \label{muonjets_final3}
101: \end{table}
102:
103:
104: \begin{table}[b]
105: %\begin{center}
106: \begin{tabular}{ccccc}
107: \hline
108: Selection & Relative(\%) & Cumulative(\%) \\ \hline
109: $\tau$ ID & $ 21.18 \pm 0.37 $ & $ 21.18 \pm 0.37 $ \\
110: Trigger & $ 79.56 \pm 0.90 \ $ & $ 16.85 \pm 0.34 \ $ \\
111: b-tagging & $ 62.83 \pm 0.92 \ $ & $ 10.59 \pm 0.25\ $ \\ \hline
112:
113: \end{tabular}
1.2 ! uid12904 114: \caption{$t\overline{t}\rightarrow dilepton$ cut flow for taus of Types 1 and 2.}
1.1 uid12904 115: %\end{center}
116: \label{dilep_final12}
117: \end{table}
118:
119:
120: \clearpage
121:
122: \begin{table}[t]
123: %\begin{center}
124: \begin{tabular}{ccccc}
125: \hline
126: Selection & Relative(\%) & Cumulative(\%) \\ \hline
127: $\tau$ ID & $ 14.73 \pm 0.34 $ & $ 14.73 \pm 0.34 $ \\
128: Trigger & $ 78.78 \pm 1.08 \ $ & $ 11.60 \pm 0.30\ $ \\
129: b-tagging & $ 63.62 \pm 1.11 \ $ & $ 7.38 \pm 0.22\ $ \\ \hline
130:
131: \end{tabular}
1.2 ! uid12904 132: \caption{$t\overline{t}\rightarrow dilepton$ cut flow for taus of Type 3.}
1.1 uid12904 133: %\end{center}
134: \label{dilep_final3}
135: \end{table}
136:
137: %\newpage
138:
139:
140:
141: After having computed all efficiencies it is worthy to summarize all of them (in \%) for the different tau types:
142:
143: \begin{table}[h]
144: %\begin{center}
145: \begin{tabular}{ccccc}
146: \hline
147: Channel &Preselection & $\tau$ ID & Trigger & b-tag \\ \hline
148: $t\overline{t}\rightarrow\tau+jets$ & $ 3.70 \pm 0.02 $ & $ 22.20 \pm 0.24 $ & $ 18.77 \pm 0.22 $ & $ 11.61 \pm 0.16 $\\
149: $t\overline{t}\rightarrow e+jets$ & $ 3.54 \pm 0.02 $ & $ 10.80 \pm 0.20 $ & $ 9.02 \pm 0.18 $ & $ 5.53 \pm 0.12 $\\
150: $t\overline{t}\rightarrow \mu +jets$ & $ 1.67 \pm 0.01 $ & $ 3.38 \pm 0.19 $ & $ 2.86 \pm 0.17 $ & $ 1.75 \pm 0.11 $\\
151: $t\overline{t}\rightarrow dilepton$ & $ 1.36 \pm 0.01 $ & $ 21.18 \pm 0.37 $ & $ 16.85 \pm 0.34 $ & $ 10.59 \pm 0.25 $\\ \hline
152: \end{tabular}
1.2 ! uid12904 153: \caption{Summary of all selections for taus of Types 1 and 2.}
1.1 uid12904 154: %\end{center}
155: \label{summary12}
156: \end{table}
157:
158:
159: \begin{table}[h]
160: %\begin{center}
161: \begin{tabular}{ccccc}
162: \hline
163: Channel &Preselection & $\tau$ ID & Trigger & b-tag \\ \hline
164: $t\overline{t}\rightarrow\tau+jets$ & $ 3.70 \pm 0.02 $ & $ 12.37 \pm 0.21 $ & $ 10.49 \pm 0.19 $ & $ 6.26 \pm 0.13 $\\
165: $t\overline{t}\rightarrow e+jets$ & $ 3.54 \pm 0.02 $ & $ 2.25 \pm 0.11 $ & $ 1.88 \pm 0.09 $ & $ 1.10 \pm 0.06 $\\
166: $t\overline{t}\rightarrow \mu +jets$ & $ 1.67 \pm 0.01 $ & $ 3.88 \pm 0.21 $ & $ 3.21 \pm 0.18 $ & $ 1.87 \pm 0.11 $\\
167: $t\overline{t}\rightarrow dilepton$ & $ 1.36 \pm 0.01 $ & $ 14.73 \pm 0.34 $ & $ 11.60 \pm 0.30 $ & $ 7.38 \pm 0.22 $\\ \hline
168: \end{tabular}
1.2 ! uid12904 169: \caption{Summary of all selections for taus of Type 3.}
1.1 uid12904 170: %\end{center}
171: \label{summary3}
172: \end{table}
173:
174: %\clearpage
175:
1.2 ! uid12904 176: Table \ref{event yeild summary1} summarizes the number of events in each channel after the final selection.
1.1 uid12904 177:
178:
179: \begin{table}[h]
180: \caption{Final number of events in the two analysis channels.}
181: %\begin{ruledtabular}
182: \begin{tabular}{cccccc}
183: \hline
184: &$\tau$ type I,II
185: &$\tau$ type I,II (fitted)
186: &$\tau$ type III
187: &$\tau$ type III (fitted)&\\
188: \hline
189: data&
190: 386 &
191: &
192: 459 &
193: &\\
194: $t\overline{t}\rightarrow\tau+jets$&
195: 72.04 $\pm$ 0.53&
196: &
197: 38.82 $\pm$ 0.39&\\
198: $t\overline{t}\rightarrow e+jets$&
199: 38.35 $\pm$ 0.36&
200: &
201: 6.52 $\pm$ 0.16&
202: &\\
203: $t\overline{t}\rightarrow\mu+jets$&
204: 4.81 $\pm$ 0.14&
205: &
206: 5.14 $\pm$ 0.14&
207: &\\
208: $t\overline{t}\rightarrow l+l$&
209: 6.02 $\pm$ 0.07&
210: &
211: 4.20 $\pm$ 0.06&
212: &\\
213: $t\overline{t}$ total MC&
214: &
215: 121.22 $\pm$ 0.43&
216: &
217: 54.68 $\pm$ 0.20&\\
218: $t\overline{t}$ total fitted&
219: &
220: 133.04 $\pm$ 17.09&
221: &
222: 33.12 $\pm$ 15.04&\\
223: $W$+jets&
224: 17.82 $\pm$ 0.33&
225: &
226: 11.26 $\pm$ 0.23&
227: &\\
228: $Z$+jets&
229: 2.78 $\pm$ 0.14&
230: &
231: 2.39 $\pm$ 0.12&
232: &\\
233: QCD&
234: &
235: 232.35 $\pm$ 17.09&
236: &
237: 412.22 $\pm$ 15.04\\
238: Signal significance&
239: &
240: 6.77&
241: &
242: 1.54
243: &\\
244: S/B ratio&
245: &
246: 0.52&
247: &
248: 0.08\\
249: \end{tabular}
250: %\end{ruledtabular}
1.2 ! uid12904 251: \label{event yeild summary1}
1.1 uid12904 252: \end{table}
253: %
254:
255: \clearpage
256:
257: %The cross section is defined as
258: %$\sigma=\frac{Number\, of\, signal\, events}{\varepsilon(t\bar{t})\cdot BR(t\bar{t}\rightarrow \tau+jets)\cdot Luminosity}$.
259: %However, we are not simply doing a `counting experiment`, but want to utilize the entire range of NN output.
1.2 ! uid12904 260: The cross section is measured by minimizing the sum of
! 261: the negative log-likelihood functions for each bin of both the Types 1 and 2 channel and the Type 3 $\tau$ channel.
1.1 uid12904 262: These are functions used by MINUIT to perform fits shown in Figs \ref{fig:nnout_type2} and \ref{fig:nnout_type3}
263: in Section \ref{sub:NN-variables}. But there $L$ was function of $f(QCD)$ and now we want to use it to measure the cross
264: section, so we must express it in terms of $\sigma(\ttbar)$:
265: \begin{center}
266: \begin{equation}
1.2 ! uid12904 267: L(\sigma, \tilde{N}_{i}, N^{obs}_{i}) \equiv -\ln(\prod_{i} \frac{\tilde{N}^{N^{obs}_{i}}_{i}}{N^{obs}_{i}!} e^{-\tilde{N}_{i}})
! 268: \label{log_xsec}
1.1 uid12904 269: \end{equation}
270: \end{center}
271:
272: \noindent where \(\tilde{N}_{i} = \sigma \times BR \times \mathcal{L} \times \epsilon(t\bar{t})_{i} + N_{bkg}\) is number
1.2 ! uid12904 273: events predicted in bin $i$ of the data NN distribution and \(N^{obs}_{i}\) is the actual count observed in that bin.
! 274: The minimum value of the graph of the function in Eq \ref{log_xsec} is the cross section.
! 275: But, as stressed out in Section \ref{sub:Results-of-the}, we have to take
1.1 uid12904 276: into account both signal ($\ttbar$) and electroweak contamination in the loose-tight sample we
277: use to model QCD in the high NN region used for
278: the measurement. The electroweak component is small and therefore it is kept fixed during the fit and
279: subtracted from the loose-tight sample.
280: However, as dicussed before, the numbers for signal contamination are 5.4\% and 3.0\% for taus types
281: 1 and 2 and type 3 respectively
282: when we assumed a $t\bar{t}$ cross section of 7.46 pb. This means that 5.4\% (12.55 events) of 232.35 QCD
283: events for taus types 1 and 2 are actually $\ttbar$ events and 3.0\% (12.37 events) of 412.22 QCD events
284: for taus type 3 are actually $\ttbar$
285: events. 12.55 and 12.37 events represent increases of 9.43\% and 37.35\% on the number of signal events for types 1 and 2
1.2 ! uid12904 286: and type 3 respectively. However this is not the final measurement yet since the cross section
! 287: measurement only makes sense if the cross section we measure in the and is the same as the one we have assumed
1.1 uid12904 288: to normalize $t\bar{t}$ MC samples. This means that we had to iterate back
1.2 ! uid12904 289: by normalizing the signal samples until we found a convergence of the cross section. Table 33 summarizes
1.1 uid12904 290: the iteration process.
291:
292: \begin{table}[htbp]
293: \label{est}
294: \begin{center}
295: \begin{tabular}{|c|r|r|r|} \hline
296: Assumed $\sigma(\ttbar)$ (pb) & signal contamination for types 1 \& 2 (\%) & signal contamination for type
297: 3 (\%) & measured $\sigma(\ttbar)$ (pb) \\ \hline
298:
299: \hline
300:
301: \multicolumn{1}{|c|}{7.46} & \multicolumn{1}{c|}{5.4} & \multicolumn{1}{c|}{3.0} & \multicolumn{1}{c|}{8.37} \\ \hline
302:
303: %$t\bar{t} \rightarrow \mbox{dilepton}$ & \multicolumn{1}{c|}{1.4} \\ \hline
304:
305: \multicolumn{1}{|c|}{8.37} & \multicolumn{1}{c|}{6.1} & \multicolumn{1}{c|}{3.3} & \multicolumn{1}{c|}{8.42} \\ \hline
306:
307: \multicolumn{1}{|c|}{8.42} & \multicolumn{1}{c|}{6.2} & \multicolumn{1}{c|}{3.4} & \multicolumn{1}{c|}{8.46} \\ \hline
308:
309:
310: \multicolumn{1}{|c|}{8.46} & \multicolumn{1}{c|}{6.2} & \multicolumn{1}{c|}{3.4} & \multicolumn{1}{c|}{8.46} \\ \hline
311:
312: \end{tabular}
1.2 ! uid12904 313: \caption{Cross section iteration process.}
1.1 uid12904 314: \end{center}
315: \label{iteration1}
316: \end{table}
317:
1.2 ! uid12904 318: Table \ref{iteration1} shows that when we assumed a cross section of 8.46 pb we measured the exact same value, which means that we had to take
1.1 uid12904 319: into account signal contaminations of 6.2\% (14.40 events) and 3.4\% (14.02 events) for taus types 1 and 2 and 3 respectively.
320: This represents an increase in the number of signal events of 10.82\% for types 1 and 2 and 42.33\% for type 3.
1.2 ! uid12904 321: By considering such events as part of the signal $\ttbar$ sample we measure for the cross sections:
1.1 uid12904 322:
323: %\newpage
324:
325:
326: \begin{center}$\tau$+jets types 1 and 2 cross section: \[\sigma (t\overline{t}) =
1.2 ! uid12904 327: 8.83\;\;_{-1.12}^{+1.14}\;\;({\textrm{stat}})\;\;_{-0.79}^{+0.84}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\]
1.1 uid12904 328: \par\end{center}
329:
330: \begin{center}$\tau$+jets type 3 cross section: \[\sigma (t\overline{t}) =
1.2 ! uid12904 331: 6.06\;\;_{-2.62}^{+2.77}\;\;({\textrm{stat}})\;\;_{-0.82}^{+0.88}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\]
1.1 uid12904 332: \par\end{center}
333:
334:
335:
336: \begin{center}Combined cross section: \[\sigma (t\overline{t}) =
1.2 ! uid12904 337: 8.46\;\;_{-1.04}^{+1.06}\;\;({\textrm{stat}})\;\;_{-0.78}^{+0.84}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb.}\]
1.1 uid12904 338: \par\end{center}
339:
1.2 ! uid12904 340: \noindent The correspondent negative log likelihoods of these measurements are shown in
! 341: Figures \ref{fig:type2_llhood}, \ref{fig:type3_llhood}
1.1 uid12904 342: and \ref{fig:type123_llhood}. Figures \ref{fig:xsec_pres2_llhood}, \ref{fig:xsec_pres3_llhood}
343: and \ref{fig:xsec_pres123_llhood} show zoomed in graphs of the same likelihood functions described above.
344:
345:
346: All associated systematics concerning this measurement can be seen in Table \ref{cap:Syst1}.
347:
348: %\newpage
349:
350: \begin{figure}[h]
351: \includegraphics[scale=0.38]{plots2/type2_llhood.eps}
352: \caption{The log likelihood function for type 1 and 2 $\tau$ channel}
353: \label{fig:type2_llhood}
354: \end{figure}
355:
356: %\newpage
357:
358: \begin{figure}[h]
359: \includegraphics[scale=0.38]{plots2/type3_llhood.eps}
360: \caption{The log likelihood function for type 3 $\tau$ channel}
361: \label{fig:type3_llhood}
362: \end{figure}
363:
364:
365: \begin{figure}[b]
366: \includegraphics[scale=0.38]{plots2/type123_llhood.eps}
367: \caption{The log likelihood function for all three types combined}
368: \label{fig:type123_llhood}
369: \end{figure}
370:
371: \clearpage
372:
373: \begin{figure}[h]
374: \includegraphics[scale=0.38]{plots2/xsec12_pres.eps}
375: \caption{Zoom in of the log likelihood function for type 1 and 2 $\tau$ channel}
376: \label{fig:xsec_pres2_llhood}
377: \end{figure}
378:
379: %\newpage
380:
381: \begin{figure}[h]
382: \includegraphics[scale=0.38]{plots2/xsec3_pres.eps}
383: \caption{Zoom in of the log likelihood function for type 3 $\tau$ channel}
384: \label{fig:xsec_pres3_llhood}
385: \end{figure}
386:
387:
388: \begin{figure}[b]
389: \includegraphics[scale=0.38]{plots2/xsecall_pres.eps}
390: \caption{Zoom in of the log likelihood function for all three types combined}
391: \label{fig:xsec_pres123_llhood}
392: \end{figure}
393:
394: \clearpage
395:
396:
397: After measuring the combined cross section we observed a significant higher statistical uncertainty value if
398: compared to the one we expected to see based on the fact that we have approximately 5 times more
399: data than in p17, where the signal contamination was not taken into account (see Appendix \ref{app:xsec_nocont}).
400: Further investigation showed that the cut NNelec $>$ 0.9 applied to taus type 2 only was responsible for such
401: discrepancy. Below we show the same measurement as done above but now with no NNelec cut applied.
402:
403:
1.2 ! uid12904 404: Table \ref{event yeild summary2} summarizes the number of events in each channel after final selection.
1.1 uid12904 405:
406:
407: \begin{table}[h]
408: \caption{Final number of events in the two analysis channels.}
409: %\begin{ruledtabular}
410: \begin{tabular}{cccccc}
411: \hline
412: &$\tau$ type I,II
413: &$\tau$ type I,II (fitted)
414: &$\tau$ type III
415: &$\tau$ type III (fitted)&\\
416: \hline
417: data&
418: 583 &
419: &
420: 459 &
421: &\\
422: $t\overline{t}\rightarrow\tau+jets$&
423: 85.46 $\pm$ 0.58&
424: &
425: 38.82 $\pm$ 0.39&\\
426: $t\overline{t}\rightarrow e+jets$&
427: 175.23 $\pm$ 0.85&
428: &
429: 6.52 $\pm$ 0.16&
430: &\\
431: $t\overline{t}\rightarrow\mu+jets$&
432: 8.98 $\pm$ 0.19&
433: &
434: 5.14 $\pm$ 0.14&
435: &\\
436: $t\overline{t}\rightarrow l+l$&
437: 12.62 $\pm$ 0.10&
438: &
439: 4.18 $\pm$ 0.06&
440: &\\
441: $t\overline{t}$ total MC&
442: &
443: 282.27 $\pm$ 1.05&
444: &
445: 54.67 $\pm$ 0.41&\\
446: $t\overline{t}$ total fitted&
447: &
448: 260.71 $\pm$ 20.74&
449: &
450: 35.73 $\pm$ 15.28&\\
451: $W$+jets&
452: 39.65 $\pm$ 0.50&
453: &
454: 11.26 $\pm$ 0.25&
455: &\\
456: $Z$+jets&
457: 4.56 $\pm$ 0.10&
458: &
459: 2.38 $\pm$ 0.11&
460: &\\
461: QCD&
462: &
463: 278.04 $\pm$ 20.74&
464: &
465: 409.62 $\pm$ 15.28\\
466: Signal significance&
467: &
468: 10.80&
469: &
470: 1.67
471: &\\
472: S/B ratio&
473: &
474: 0.80&
475: &
476: 0.08\\
477: \end{tabular}
478: %\end{ruledtabular}
1.2 ! uid12904 479: \label{event yeild summary2}
1.1 uid12904 480: \end{table}
481: %
482:
483: Table below shows the iteration process in this case and and the cross section measurement follows:
484:
485: \begin{table}[htbp]
486: \label{est}
487: \begin{center}
488: \begin{tabular}{|c|r|r|r|} \hline
489: Assumed $\sigma(\ttbar)$ (pb) & signal contamination for types 1 \& 2 (\%) & signal contamination for type
490: 3 (\%) & measured $\sigma(\ttbar)$ (pb) \\ \hline
491:
492: \hline
493:
494: \multicolumn{1}{|c|}{7.46} & \multicolumn{1}{c|}{6.0} & \multicolumn{1}{c|}{3.0} & \multicolumn{1}{c|}{6.84} \\ \hline
495:
496: %$t\bar{t} \rightarrow \mbox{dilepton}$ & \multicolumn{1}{c|}{1.4} \\ \hline
497:
498: \multicolumn{1}{|c|}{6.84} & \multicolumn{1}{c|}{5.4} & \multicolumn{1}{c|}{2.7} & \multicolumn{1}{c|}{6.91} \\ \hline
499:
500: \multicolumn{1}{|c|}{6.91} & \multicolumn{1}{c|}{5.5} & \multicolumn{1}{c|}{2.8} & \multicolumn{1}{c|}{6.92} \\ \hline
501:
502:
503: \multicolumn{1}{|c|}{6.92} & \multicolumn{1}{c|}{5.5} & \multicolumn{1}{c|}{2.8} & \multicolumn{1}{c|}{6.92} \\ \hline
504:
505: \end{tabular}
1.2 ! uid12904 506: \caption{Cross section iteration process.}
1.1 uid12904 507: \end{center}
1.2 ! uid12904 508: \label{iteration2}
1.1 uid12904 509: \end{table}
510:
511:
512: %\newpage
513:
514:
515: \begin{center}$\tau$+jets types 1 and 2 cross section: \[\sigma (t\overline{t}) =
516: 7.03\;\;_{-0.56}^{+0.54}\;\;({\textrm{stat}})\;\;_{-0.61}^{+0.65}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\]
517: \par\end{center}
518:
519: \begin{center}$\tau$+jets type 3 cross section: \[\sigma (t\overline{t}) =
520: 4.36\;\;_{-2.50}^{+2.62}\;\;({\textrm{stat}})\;\;_{-0.61}^{+0.62}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\]
521: \par\end{center}
522:
523:
524:
525: \begin{center}Combined cross section: \[\sigma (t\overline{t}) =
526: 6.92\;\;_{-0.54}^{+0.54}\;\;({\textrm{stat}})\;\;_{-0.60}^{+0.62}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\]
527: \par\end{center}
528:
529:
1.2 ! uid12904 530: As we can see the statistical uncertainty decreases to 0.54 pb, which is in a good agreement with what we would expect if compared
! 531: to the 1.2 pb measured in p17. Appendix \ref{app:xsec_nocont} shows cross section measurements when signal contamination is not
! 532: taken into account for both NNelec $>$ 0.9 and no NNelec cut applied. Once again, we observed the difference caused by the
! 533: NNelec requirement.
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