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version 1.1, 2011/05/18 21:30:40
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version 1.2, 2011/06/01 01:20:54
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Line 1
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Line 1
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| \section{\label{sub:xsect}Cross section} |
\section{\label{sub:xsect}Cross section} |
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| Having presented the preselection yelds on Section \ref{sub:Preselection} we now show the results of the |
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). |
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| \begin{table}[h] |
\begin{table}[h] |
|
Line 14 Trigger & $ 84.54 \pm 0.55 \ $ & $ 18
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Line 14 Trigger & $ 84.54 \pm 0.55 \ $ & $ 18
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| b-tagging & $ 61.82 \pm 0.55 \ $ & $ 11.61 \pm 0.16\ $ \\ \hline |
b-tagging & $ 61.82 \pm 0.55 \ $ & $ 11.61 \pm 0.16\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{taujets_final12} |
\label{taujets_final12} |
| \end{table} |
\end{table} |
|
Line 30 Trigger & $ 84.79 \pm 0.75 \ $ & $ 10
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Line 30 Trigger & $ 84.79 \pm 0.75 \ $ & $ 10
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| b-tagging & $ 59.63 \pm 0.75 \ $ & $ 6.26 \pm 0.13\ $ \\ \hline |
b-tagging & $ 59.63 \pm 0.75 \ $ & $ 6.26 \pm 0.13\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{taujets_final3} |
\label{taujets_final3} |
| \end{table} |
\end{table} |
|
Line 46 Trigger & $ 83.40 \pm 0.81 \ $ & $ 9.
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Line 46 Trigger & $ 83.40 \pm 0.81 \ $ & $ 9.
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| b-tagging & $ 61.30 \pm 0.82 \ $ & $ 5.52 \pm 0.12\ $ \\ \hline |
b-tagging & $ 61.30 \pm 0.82 \ $ & $ 5.52 \pm 0.12\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{elecjets_final12} |
\label{elecjets_final12} |
| \end{table} |
\end{table} |
|
Line 61 Trigger & $ 83.62 \pm 1.77 \ $ & $ 1.
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Line 61 Trigger & $ 83.62 \pm 1.77 \ $ & $ 1.
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| b-tagging & $ 58.26 \pm 1.76 \ $ & $ 1.10 \pm 0.06\ $ \\ \hline |
b-tagging & $ 58.26 \pm 1.76 \ $ & $ 1.10 \pm 0.06\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{elecjets_final3} |
\label{elecjets_final3} |
| \end{table} |
\end{table} |
|
Line 79 Trigger & $ 84.44 \pm 2.13 \ $ & $ 2.
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Line 79 Trigger & $ 84.44 \pm 2.13 \ $ & $ 2.
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| b-tagging & $ 61.25 \pm 2.16 \ $ & $ 1.75 \pm 0.11\ $ \\ \hline |
b-tagging & $ 61.25 \pm 2.16 \ $ & $ 1.75 \pm 0.11\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{muonjets_final12} |
\label{muonjets_final12} |
| \end{table} |
\end{table} |
|
Line 95 Trigger & $ 82.79 \pm 2.04 \ $ & $ 3.
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Line 95 Trigger & $ 82.79 \pm 2.04 \ $ & $ 3.
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| b-tagging & $ 58.11 \pm 2.05 \ $ & $ 1.87 \pm 0.11\ $ \\ \hline |
b-tagging & $ 58.11 \pm 2.05 \ $ & $ 1.87 \pm 0.11\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{muonjets_final3} |
\label{muonjets_final3} |
| \end{table} |
\end{table} |
|
Line 111 Trigger & $ 79.56 \pm 0.90 \ $ & $ 16
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Line 111 Trigger & $ 79.56 \pm 0.90 \ $ & $ 16
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| b-tagging & $ 62.83 \pm 0.92 \ $ & $ 10.59 \pm 0.25\ $ \\ \hline |
b-tagging & $ 62.83 \pm 0.92 \ $ & $ 10.59 \pm 0.25\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{dilep_final12} |
\label{dilep_final12} |
| \end{table} |
\end{table} |
|
Line 129 Trigger & $ 78.78 \pm 1.08 \ $ & $ 11
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Line 129 Trigger & $ 78.78 \pm 1.08 \ $ & $ 11
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| b-tagging & $ 63.62 \pm 1.11 \ $ & $ 7.38 \pm 0.22\ $ \\ \hline |
b-tagging & $ 63.62 \pm 1.11 \ $ & $ 7.38 \pm 0.22\ $ \\ \hline |
| |
|
| \end{tabular} |
\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} |
%\end{center} |
| \label{dilep_final3} |
\label{dilep_final3} |
| \end{table} |
\end{table} |
|
Line 150 $t\overline{t}\rightarrow e+jets$ & $
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Line 150 $t\overline{t}\rightarrow e+jets$ & $
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| $t\overline{t}\rightarrow \mu +jets$ & $ 1.67 \pm 0.01 $ & $ 3.38 \pm 0.19 $ & $ 2.86 \pm 0.17 $ & $ 1.75 \pm 0.11 $\\ |
$t\overline{t}\rightarrow \mu +jets$ & $ 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 |
$t\overline{t}\rightarrow dilepton$ & $ 1.36 \pm 0.01 $ & $ 21.18 \pm 0.37 $ & $ 16.85 \pm 0.34 $ & $ 10.59 \pm 0.25 $\\ \hline |
| \end{tabular} |
\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} |
%\end{center} |
| \label{summary12} |
\label{summary12} |
| \end{table} |
\end{table} |
|
Line 166 $t\overline{t}\rightarrow e+jets$ & $
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Line 166 $t\overline{t}\rightarrow e+jets$ & $
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| $t\overline{t}\rightarrow \mu +jets$ & $ 1.67 \pm 0.01 $ & $ 3.88 \pm 0.21 $ & $ 3.21 \pm 0.18 $ & $ 1.87 \pm 0.11 $\\ |
$t\overline{t}\rightarrow \mu +jets$ & $ 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 |
$t\overline{t}\rightarrow dilepton$ & $ 1.36 \pm 0.01 $ & $ 14.73 \pm 0.34 $ & $ 11.60 \pm 0.30 $ & $ 7.38 \pm 0.22 $\\ \hline |
| \end{tabular} |
\end{tabular} |
| \caption{Summary of all selections for taus type 3.} |
\caption{Summary of all selections for taus of Type 3.} |
| %\end{center} |
%\end{center} |
| \label{summary3} |
\label{summary3} |
| \end{table} |
\end{table} |
| |
|
| %\clearpage |
%\clearpage |
| |
|
| Table below summarizes the number of events in each channel after final selection. |
Table \ref{event yeild summary1} summarizes the number of events in each channel after the final selection. |
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| \begin{table}[h] |
\begin{table}[h] |
|
Line 248 S/B ratio&
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Line 248 S/B ratio&
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| 0.08\\ |
0.08\\ |
| \end{tabular} |
\end{tabular} |
| %\end{ruledtabular} |
%\end{ruledtabular} |
| \label{event yeild summary} |
\label{event yeild summary1} |
| \end{table} |
\end{table} |
| % |
% |
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|
Line 257 S/B ratio&
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Line 257 S/B ratio&
|
| %The cross section is defined as |
%The cross section is defined as |
| %$\sigma=\frac{Number\, of\, signal\, events}{\varepsilon(t\bar{t})\cdot BR(t\bar{t}\rightarrow \tau+jets)\cdot Luminosity}$. |
%$\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. |
%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 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. |
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} |
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 |
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 $\sigma(\ttbar)$: |
section, so we must express it in terms of $\sigma(\ttbar)$: |
| \begin{center} |
\begin{center} |
| \begin{equation} |
\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{equation} |
| \end{center} |
\end{center} |
| |
|
| \noindent where \(\tilde{N}_{i} = \sigma \times BR \times \mathcal{L} \times \epsilon(t\bar{t})_{i} + N_{bkg}\) is number |
\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. |
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}, |
The minimum value of the graph of the function in Eq \ref{log_xsec} is the cross section. |
| we have to take |
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 |
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 |
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 |
the measurement. The electroweak component is small and therefore it is kept fixed during the fit and |
|
Line 282 when we assumed a $t\bar{t}$ cross secti
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Line 283 when we assumed a $t\bar{t}$ cross secti
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| events for taus types 1 and 2 are actually $\ttbar$ events and 3.0\% (12.37 events) of 412.22 QCD events |
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 $\ttbar$ |
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 |
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 |
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 |
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 |
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. |
the iteration process. |
| |
|
| \begin{table}[htbp] |
\begin{table}[htbp] |
|
Line 309 Assumed $\sigma(\ttbar)$ (pb) & signal
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Line 310 Assumed $\sigma(\ttbar)$ (pb) & signal
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| \multicolumn{1}{|c|}{8.46} & \multicolumn{1}{c|}{6.2} & \multicolumn{1}{c|}{3.4} & \multicolumn{1}{c|}{8.46} \\ \hline |
\multicolumn{1}{|c|}{8.46} & \multicolumn{1}{c|}{6.2} & \multicolumn{1}{c|}{3.4} & \multicolumn{1}{c|}{8.46} \\ \hline |
| |
|
| \end{tabular} |
\end{tabular} |
| \caption{Cross-section iteration process.} |
\caption{Cross section iteration process.} |
| \end{center} |
\end{center} |
| \label{iteration1} |
\label{iteration1} |
| \end{table} |
\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. |
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. |
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 |
%\newpage |
| |
|
| |
|
| \begin{center}$\tau$+jets types 1 and 2 cross section: \[\sigma (t\overline{t}) = |
\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} |
\par\end{center} |
| |
|
| \begin{center}$\tau$+jets type 3 cross section: \[\sigma (t\overline{t}) = |
\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} |
\par\end{center} |
| |
|
| |
|
| |
|
| \begin{center}Combined cross section: \[\sigma (t\overline{t}) = |
\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} |
\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: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. |
and \ref{fig:xsec_pres123_llhood} show zoomed in graphs of the same likelihood functions described above. |
| |
|
|
Line 399 Further investigation showed that the cu
|
Line 401 Further investigation showed that the cu
|
| discrepancy. Below we show the same measurement as done above but now with no NNelec cut applied. |
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] |
\begin{table}[h] |
|
Line 474 S/B ratio&
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Line 476 S/B ratio&
|
| 0.08\\ |
0.08\\ |
| \end{tabular} |
\end{tabular} |
| %\end{ruledtabular} |
%\end{ruledtabular} |
| \label{event yeild summary} |
\label{event yeild summary2} |
| \end{table} |
\end{table} |
| % |
% |
| |
|
|
Line 501 Assumed $\sigma(\ttbar)$ (pb) & signal
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Line 503 Assumed $\sigma(\ttbar)$ (pb) & signal
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| \multicolumn{1}{|c|}{6.92} & \multicolumn{1}{c|}{5.5} & \multicolumn{1}{c|}{2.8} & \multicolumn{1}{c|}{6.92} \\ \hline |
\multicolumn{1}{|c|}{6.92} & \multicolumn{1}{c|}{5.5} & \multicolumn{1}{c|}{2.8} & \multicolumn{1}{c|}{6.92} \\ \hline |
| |
|
| \end{tabular} |
\end{tabular} |
| \caption{Cross-section iteration process.} |
\caption{Cross section iteration process.} |
| \end{center} |
\end{center} |
| \label{iteration} |
\label{iteration2} |
| \end{table} |
\end{table} |
| |
|
| |
|
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Line 525 Assumed $\sigma(\ttbar)$ (pb) & signal
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Line 527 Assumed $\sigma(\ttbar)$ (pb) & signal
|
| \par\end{center} |
\par\end{center} |
| |
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| |
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| 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 |
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 1.2 pb measured in p17. Appendix \ref{app:xsec_nocont} shows cross sections measurements when signal contamination is not |
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 a discrepancy when NNelec is applied |
taken into account for both NNelec $>$ 0.9 and no NNelec cut applied. Once again, we observed the difference caused by the |
| and the expected value when NNelec is not applied. |
NNelec requirement. |
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