--- ttbar/p20_taujets_note/Summary.tex 2011/05/18 21:30:40 1.1 +++ ttbar/p20_taujets_note/Summary.tex 2011/06/01 01:20:54 1.2 @@ -1,7 +1,7 @@ \section{\label{sub:xsect}Cross section} Having presented the preselection yelds on Section \ref{sub:Preselection} we now show the results of the -efficiencies for $\tau$ ID, b-tagging and trigger for all $t\bar{t}$ channels +efficiencies for $\tau$ ID, b-tagging and trigger for all $t\bar{t}$ channels (only statistical uncertainties are shown). \begin{table}[h] @@ -14,7 +14,7 @@ Trigger & $ 84.54 \pm 0.55 \ $ & $ 18 b-tagging & $ 61.82 \pm 0.55 \ $ & $ 11.61 \pm 0.16\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow\tau+jets$ final cut flow for taus types 1 and 2} +\caption{$t\overline{t}\rightarrow\tau+jets$ cut flow for taus of Types 1 and 2.} %\end{center} \label{taujets_final12} \end{table} @@ -30,7 +30,7 @@ Trigger & $ 84.79 \pm 0.75 \ $ & $ 10 b-tagging & $ 59.63 \pm 0.75 \ $ & $ 6.26 \pm 0.13\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow\tau+jets$ final cut flow for taus type 3} +\caption{$t\overline{t}\rightarrow\tau+jets$ cut flow for taus of Type 3} %\end{center} \label{taujets_final3} \end{table} @@ -46,7 +46,7 @@ Trigger & $ 83.40 \pm 0.81 \ $ & $ 9. b-tagging & $ 61.30 \pm 0.82 \ $ & $ 5.52 \pm 0.12\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow e+jets$ final cut flow for taus types 1 and 2} +\caption{$t\overline{t}\rightarrow e+jets$ cut flow for taus of Types 1 and 2} %\end{center} \label{elecjets_final12} \end{table} @@ -61,7 +61,7 @@ Trigger & $ 83.62 \pm 1.77 \ $ & $ 1. b-tagging & $ 58.26 \pm 1.76 \ $ & $ 1.10 \pm 0.06\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow e+jets$ final cut flow for taus type 3} +\caption{$t\overline{t}\rightarrow e+jets$ cut flow for taus of Type 3} %\end{center} \label{elecjets_final3} \end{table} @@ -79,7 +79,7 @@ Trigger & $ 84.44 \pm 2.13 \ $ & $ 2. b-tagging & $ 61.25 \pm 2.16 \ $ & $ 1.75 \pm 0.11\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow \mu +jets$ final cut flow for taus types 1 and 2.} +\caption{$t\overline{t}\rightarrow \mu +jets$ cut flow for taus of Types 1 and 2.} %\end{center} \label{muonjets_final12} \end{table} @@ -95,7 +95,7 @@ Trigger & $ 82.79 \pm 2.04 \ $ & $ 3. b-tagging & $ 58.11 \pm 2.05 \ $ & $ 1.87 \pm 0.11\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow \mu +jets$ final cut flow for taus type 3} +\caption{$t\overline{t}\rightarrow \mu +jets$ cut flow for taus of Type 3.} %\end{center} \label{muonjets_final3} \end{table} @@ -111,7 +111,7 @@ Trigger & $ 79.56 \pm 0.90 \ $ & $ 16 b-tagging & $ 62.83 \pm 0.92 \ $ & $ 10.59 \pm 0.25\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow dilepton$ final cut flow for taus types 1 and 2} +\caption{$t\overline{t}\rightarrow dilepton$ cut flow for taus of Types 1 and 2.} %\end{center} \label{dilep_final12} \end{table} @@ -129,7 +129,7 @@ Trigger & $ 78.78 \pm 1.08 \ $ & $ 11 b-tagging & $ 63.62 \pm 1.11 \ $ & $ 7.38 \pm 0.22\ $ \\ \hline \end{tabular} -\caption{$t\overline{t}\rightarrow dilepton$ final cut flow for taus type 3.} +\caption{$t\overline{t}\rightarrow dilepton$ cut flow for taus of Type 3.} %\end{center} \label{dilep_final3} \end{table} @@ -150,7 +150,7 @@ $t\overline{t}\rightarrow e+jets$ & $ $t\overline{t}\rightarrow \mu +jets$ & $ 1.67 \pm 0.01 $ & $ 3.38 \pm 0.19 $ & $ 2.86 \pm 0.17 $ & $ 1.75 \pm 0.11 $\\ $t\overline{t}\rightarrow dilepton$ & $ 1.36 \pm 0.01 $ & $ 21.18 \pm 0.37 $ & $ 16.85 \pm 0.34 $ & $ 10.59 \pm 0.25 $\\ \hline \end{tabular} -\caption{Summary of all selections for taus type 1 \& 2.} +\caption{Summary of all selections for taus of Types 1 and 2.} %\end{center} \label{summary12} \end{table} @@ -166,14 +166,14 @@ $t\overline{t}\rightarrow e+jets$ & $ $t\overline{t}\rightarrow \mu +jets$ & $ 1.67 \pm 0.01 $ & $ 3.88 \pm 0.21 $ & $ 3.21 \pm 0.18 $ & $ 1.87 \pm 0.11 $\\ $t\overline{t}\rightarrow dilepton$ & $ 1.36 \pm 0.01 $ & $ 14.73 \pm 0.34 $ & $ 11.60 \pm 0.30 $ & $ 7.38 \pm 0.22 $\\ \hline \end{tabular} -\caption{Summary of all selections for taus type 3.} +\caption{Summary of all selections for taus of Type 3.} %\end{center} \label{summary3} \end{table} %\clearpage -Table below summarizes the number of events in each channel after final selection. +Table \ref{event yeild summary1} summarizes the number of events in each channel after the final selection. \begin{table}[h] @@ -248,7 +248,7 @@ S/B ratio& 0.08\\ \end{tabular} %\end{ruledtabular} -\label{event yeild summary} +\label{event yeild summary1} \end{table} % @@ -257,21 +257,22 @@ S/B ratio& %The cross section is defined as %$\sigma=\frac{Number\, of\, signal\, events}{\varepsilon(t\bar{t})\cdot BR(t\bar{t}\rightarrow \tau+jets)\cdot Luminosity}$. %However, we are not simply doing a `counting experiment`, but want to utilize the entire range of NN output. -The cross section was measured by minimizing the sum of -the negative log-likelihood functions for each bin of both the types 1 and 2 channel and the type 3 $\tau$ channel. +The cross section is measured by minimizing the sum of +the negative log-likelihood functions for each bin of both the Types 1 and 2 channel and the Type 3 $\tau$ channel. These are functions used by MINUIT to perform fits shown in Figs \ref{fig:nnout_type2} and \ref{fig:nnout_type3} 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 section, so we must express it in terms of $\sigma(\ttbar)$: \begin{center} \begin{equation} -L(\sigma, \tilde{N}_{i}, N^{obs}_{i}) \equiv -log(\prod_{i} \frac{\tilde{N}^{N^{obs}_{i}}_{i}}{N^{obs}_{i}!} e^{-\tilde{N}_{i}}) +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}}) +\label{log_xsec} \end{equation} \end{center} \noindent where \(\tilde{N}_{i} = \sigma \times BR \times \mathcal{L} \times \epsilon(t\bar{t})_{i} + N_{bkg}\) is number -events predicted in bin i of the data NN distribution and \(N^{obs}_{i}\) is the actual count observed in that bin. -The cross-section is then the minimum value of each function. But, as stressed out in Section \ref{sub:Results-of-the}, -we have to take +events predicted in bin $i$ of the data NN distribution and \(N^{obs}_{i}\) is the actual count observed in that bin. +The minimum value of the graph of the function in Eq \ref{log_xsec} is the cross section. +But, as stressed out in Section \ref{sub:Results-of-the}, we have to take into account both signal ($\ttbar$) and electroweak contamination in the loose-tight sample we use to model QCD in the high NN region used for the measurement. The electroweak component is small and therefore it is kept fixed during the fit and @@ -282,10 +283,10 @@ when we assumed a $t\bar{t}$ cross secti events for taus types 1 and 2 are actually $\ttbar$ events and 3.0\% (12.37 events) of 412.22 QCD events for taus type 3 are actually $\ttbar$ 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 -and type 3 respectively. However this is not the final measurement yet since the cross-section -measurement only makes sense if the cross-section we measure in the and is the same as the one we have assumed +and type 3 respectively. However this is not the final measurement yet since the cross section +measurement only makes sense if the cross section we measure in the and is the same as the one we have assumed to normalize $t\bar{t}$ MC samples. This means that we had to iterate back -by normalizing the signal samples until we found a convergence of the cross-section. Table XXIII summarizes +by normalizing the signal samples until we found a convergence of the cross section. Table 33 summarizes the iteration process. \begin{table}[htbp] @@ -309,34 +310,35 @@ Assumed $\sigma(\ttbar)$ (pb) & signal \multicolumn{1}{|c|}{8.46} & \multicolumn{1}{c|}{6.2} & \multicolumn{1}{c|}{3.4} & \multicolumn{1}{c|}{8.46} \\ \hline \end{tabular} -\caption{Cross-section iteration process.} +\caption{Cross section iteration process.} \end{center} \label{iteration1} \end{table} -Table above 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 +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 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. This represents an increase in the number of signal events of 10.82\% for types 1 and 2 and 42.33\% for type 3. -By considering such events as part of the signal $\ttbar$ sample we measure for the cross-sections: +By considering such events as part of the signal $\ttbar$ sample we measure for the cross sections: %\newpage \begin{center}$\tau$+jets types 1 and 2 cross section: \[\sigma (t\overline{t}) = -8.83\;\;_{-1.12}^{+1.14}\;\;({\textrm{stat}})\;\;_{-0.94}^{+0.89}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\] +8.83\;\;_{-1.12}^{+1.14}\;\;({\textrm{stat}})\;\;_{-0.79}^{+0.84}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\] \par\end{center} \begin{center}$\tau$+jets type 3 cross section: \[\sigma (t\overline{t}) = -6.06\;\;_{-2.62}^{+2.77}\;\;({\textrm{stat}})\;\;_{-0.99}^{+0.94}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\] +6.06\;\;_{-2.62}^{+2.77}\;\;({\textrm{stat}})\;\;_{-0.82}^{+0.88}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb,}\] \par\end{center} \begin{center}Combined cross section: \[\sigma (t\overline{t}) = -8.46\;\;_{-1.04}^{+1.06}\;\;({\textrm{stat}})\;\;_{-0.88}^{+0.92}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb.}\] +8.46\;\;_{-1.04}^{+1.06}\;\;({\textrm{stat}})\;\;_{-0.78}^{+0.84}\;\;({\textrm{syst}})\;\;\pm 0.3\;\;({\textrm{lumi}})\;\; \rm{pb.}\] \par\end{center} -\noindent The correspondent likelihoods of these measurements are shown in Figures \ref{fig:type2_llhood}, \ref{fig:type3_llhood} +\noindent The correspondent negative log likelihoods of these measurements are shown in +Figures \ref{fig:type2_llhood}, \ref{fig:type3_llhood} and \ref{fig:type123_llhood}. Figures \ref{fig:xsec_pres2_llhood}, \ref{fig:xsec_pres3_llhood} and \ref{fig:xsec_pres123_llhood} show zoomed in graphs of the same likelihood functions described above. @@ -399,7 +401,7 @@ Further investigation showed that the cu discrepancy. Below we show the same measurement as done above but now with no NNelec cut applied. -Table below summarizes the number of events in each channel after final selection. +Table \ref{event yeild summary2} summarizes the number of events in each channel after final selection. \begin{table}[h] @@ -474,7 +476,7 @@ S/B ratio& 0.08\\ \end{tabular} %\end{ruledtabular} -\label{event yeild summary} +\label{event yeild summary2} \end{table} % @@ -501,9 +503,9 @@ Assumed $\sigma(\ttbar)$ (pb) & signal \multicolumn{1}{|c|}{6.92} & \multicolumn{1}{c|}{5.5} & \multicolumn{1}{c|}{2.8} & \multicolumn{1}{c|}{6.92} \\ \hline \end{tabular} -\caption{Cross-section iteration process.} +\caption{Cross section iteration process.} \end{center} -\label{iteration} +\label{iteration2} \end{table} @@ -525,7 +527,7 @@ Assumed $\sigma(\ttbar)$ (pb) & signal \par\end{center} -As we can see the statistical uncertainty decreases to 0.54 pb which is in a good agreement to what we would expect if compared -to 1.2 pb measured in p17. Appendix \ref{app:xsec_nocont} shows cross sections measurements when signal contamination is not -taken into account for both NNelec $>$ 0.9 and no NNelec cut applied. Once again we observed a discrepancy when NNelec is applied -and the expected value when NNelec is not applied. +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 +to the 1.2 pb measured in p17. Appendix \ref{app:xsec_nocont} shows cross section measurements when signal contamination is not +taken into account for both NNelec $>$ 0.9 and no NNelec cut applied. Once again, we observed the difference caused by the +NNelec requirement.