\newpage \section{\label{sub:Results-of-the}\boldmath$b$ and \boldmath$\tau$ selections} In the next step we applied the requirements of tight $\tau$- and $b$-tagging. Table \ref{cap:btaggingandtau} shows the selection criteria that we applied to data and MC. The b-tag operating point used was TIGHT, which corresponds to NNbtag $>$ 0.775. We chose the $\tau$ with the highest $NN_{\tau}$ as \textit{the} $\tau$ candidate. At this stage of the analysis we separated the events dataset we deal with into parts, according to which type of $\tau$ the candidate with highest NN belongs. This was done primarily to separate the type 3 tau events (which are expected to have much higher fake rate and thus weaker $\ttbar$ cross section result) from the type 2 events. The separate measurement channels were later combined to get the final result (Section \ref{sub:xsect}). In principle, types 1 and 2 should be separated as well but as there exists a considerable cross-migration between them \cite{tau-id} and type 1 is a small fraction of the total (10\% of type 1, 54.5\% of type 2 and 35.5\% of type 3), they were taken togetther in this analysis. The topological NN used to enhance the signal content is described in section \ref{sub:NN-variables} . %Table \ref{b and tau type 3} shows the same efficiencies for %type 3. We see that for type 3 $\tau$ candidates (which are more jet-like then other types) twice more %candidate events are selected due to high $\tau$ fake rate. At this point, we used these ID algorithms to define 3 mutually exclusive and exhastive subsamples out of the original preselected data sample: \begin{itemize} \item The {}``non-$b$ veto'' or {}``signal'' sample - the $\tau$ candidate has $NN_{\tau}>0.90$ ($NN_{\tau}$ denotes the NN cut commonly applied to all taus) for taus types 1 and 2 and $NN(\tau)>0.95$ for taus type 3, and at least one NN b-tag (as in Table \ref{cap:btaggingandtau}). These $NN(\tau)$ cuts were chosen based on previous studies involving hadronic decays of taus \cite{tes,higgs_tau}. This is the sample used to extract the cross section. Jets matched to $\tau$ candidates are not $b$-tagged, althought they still count as jets. \item The {}``$\tau$ veto sample'' or ``loose-tight $\tau$ sample'' - Same selection, but with $0.3$ 0.9 only to type 2 taus since these are more likely to be faked by electrons. The cut NNelec $>$ 0.9 was chosen in order to match the lowest cut of $NN_{\tau}$ $>$ 0.9 applied to type 2 taus (Section \ref{sub:Results-of-the}). As both b and $\tau$ ID is the step immediately after the preselection, the number of events available is 2800000 million events. As explained above 1400000 events were used for taus type 1 and 2 NN training and 600000 for type 3 taus NN training. Thus, there are 1400000 events available in each sample for the measurement in the case of types 1 and 2 and 2200000 in the case of type 3. Details on NN training are given in Section \ref{sub:NN-variables}. The QCD modelling method used here is the same as used in p17 and is described in Section IXA of \cite{p17_note}. The final number of events in each channel for both signal and $b$ veto samples is shown on Tables \ref{b_and_tau_type1_2}, \ref{b_and_tau_type_3}, \ref{bveto_type1_2} and \ref{b_veto_type_3} (only statistical uncertainties are shown). As important as determining the subsamples to be used in this analysis, a determination as precise as possible of both signal and electroweak contamination in the ``loose-tight $\tau$ sample'' had be done in order to know whether this sample is totally QCD dominated or not. Numbers showing the composition of such sample are shown on Tables \ref{loosetight1_2} and \ref{loosetight_3} with their respective statistical uncertainties. From the $t\bar{t}$ content in each case we are able estimate the signal contamination in the loose-tight sample. Such contaminations are 5.4\% and 3.0\% for taus type 1 and 2 and type 3 respectively when a cross section of 7.46 pb is assumed (Section \ref{sub:mcsample}). Likewise we see that electroweak contaminations are 2.2\% and 0.9\%. As this is the sample used to model the QCD background both signal and electroweak contaminations were taken into account when measuring the cross section in Section \ref{sub:xsect}. \begin{table}[h] \begin{tabular}{ccc} \hline & {\scriptsize data}& {\scriptsize taggingMC}\\ & {\scriptsize $\geq1$ $\tau$ with $|\eta|<2.5$ and $p_{T}>20$ GeV}& {\scriptsize $\geq1$ $\tau$ with $|\eta|<2.5$ and $p_{T}>20$ GeV}\\ & {\scriptsize $\geq1$ NN b-tag}& {\scriptsize $mcweight \cdot TrigWeight \cdot bTagProb \cdot lumiReWeight \cdot PVzReWeight \cdot bFragWeight$ }\\ & {\scriptsize }& %{\scriptsize $\cdot WZPtReweight \cdot tau$\_$nnout$\_$corr$\_$p20 \cdot tau$\_$track$\_$corr$\_$p20$ }\\ {\scriptsize $\cdot WZPtReweight $ }\\ & {\scriptsize $\geq4$ jets with $|\eta|<2.5$ and $p_{T}>20$ GeV}& {\scriptsize $\geq4$ jets with $|\eta|<2.5$ and $p_{T}>20$ GeV}\\ \end{tabular} \caption{$b$-tagging and $\tau$ ID. In the MC, we use the $b$-tagging certified parameterization rather than actual $b$-tagging, that is, we applied the $b$-tagging weight. We also used the triggering weight as computed by the trigger efficiency parameterization as well as luminosity profile and $PV_Z$ reweighting weights. $ mcweight$ is the MC normalization factors (to luminosity), which are different for MC samples with different parton multiplicities in ALPGEN MC samples.}%\end{ruledtabular} \label{cap:btaggingandtau} \end{table} % \begin{table}[h] %\begin{ruledtabular} \begin{tabular}{cccc} \hline Sample & & \# events\\ \hline data& & 386\\ $t\overline{t}\rightarrow\tau+jets$& & 48.03 $\pm$ 0.53&\\ $t\overline{t}\rightarrow e+jets$& & 25.57 $\pm$ 0.36&\\ $t\overline{t}\rightarrow\mu+jets$& & 3.21 $\pm$ 0.14&\\ $t\overline{t}\rightarrow l+l$& & 4.01 $\pm$ 0.07&\\ $Wbb+jets\rightarrow$ $l\nu+bb+jets$& & 7.48 $\pm$ 0.30\\ $Wcc+jets\rightarrow$ $l\nu+cc+jets$& & 4.68 $\pm$ 0.17\\ $Wjj+jets\rightarrow$ $l\nu+jj+jets$& & 5.66 $\pm$ 0.11 \\ $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$& & 0.93 $\pm$ 0.08\\ $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$& & 0.51 $\pm$ 0.04\\ $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$& & 1.07 $\pm$ 0.10 \\ $Zbb+jets\rightarrow$ $ee+bb+jets$& & 0.03 $\pm$ 0.01\\ $Zcc+jets\rightarrow$ $ee+cc+jets$& & 0.00 $\pm$ 0.00\\ $Zjj+jets\rightarrow$ $ee+jj+jets$& & 0.02 $\pm$ 0.01 \\ $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$& & 0.07 $\pm$ 0.02\\ $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$& & 0.02 $\pm$ 0.01\\ $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$& & 0.01 $\pm$ 0.01 \\ $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$& & 0.08 $\pm$ 0.03\\ $Zcc+jets\rightarrow$ $\nu\nu+cc+jets$& & 0.00 $\pm$ 0.00\\ $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& & 0.04 $\pm$ 0.01\\ \hline \end{tabular} \caption{Final number of events in each channel for taus types 1 and 2 $\tau$ after b-tagging, $\tau$ ID and trigger in the signal sample when the assumed cross section is 7.46 pb. An estimate of QCD background is not included.} %\end{ruledtabular} \label{b_and_tau_type1_2} \end{table} % %\clearpage \begin{table}[t] %\begin{ruledtabular} \begin{tabular}{cccc} \hline Sample & & \# of events\\ \hline data& & 459\\ $t\overline{t}\rightarrow\tau+jets$& & 25.88 $\pm$ 0.39&\\ $t\overline{t}\rightarrow e+jets$& & 4.35 $\pm$ 0.16&\\ $t\overline{t}\rightarrow\mu+jets$& & 3.43 $\pm$ 0.14&\\ $t\overline{t}\rightarrow l+l$& & 2.80 $\pm$ 0.06&\\ $Wbb+jets\rightarrow$ $l\nu+bb+jets$& & 3.92 $\pm$ 0.17\\ $Wcc+jets\rightarrow$ $l\nu+cc+jets$& & 3.26 $\pm$ 0.15\\ $Wjj+jets\rightarrow$ $l\nu+jj+jets$& & 4.08 $\pm$ 0.11\\ $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$& & 0.74 $\pm$ 0.07\\ $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$& & 0.41 $\pm$ 0.03\\ $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$& & 0.80 $\pm$ 0.10 \\ $Zbb+jets\rightarrow$ $ee+bb+jets$& & 0.00 $\pm$ 0.00\\ $Zcc+jets\rightarrow$ $ee+cc+jets$& & 0.01 $\pm$ 0.01\\ $Zjj+jets\rightarrow$ $ee+jj+jets$& & 0.01 $\pm$ 0.01 \\ $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$& & 0.04 $\pm$ 0.02\\ $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$& & 0.01 $\pm$ 0.01\\ $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$& & 0.00 $\pm$ 0.00 \\ $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$& & 0.12 $\pm$ 0.04\\ $Zcc+jets\rightarrow$ $\nu\nu+cc+jets$& & 0.19 $\pm$ 0.04\\ $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& & 0.06 $\pm$ 0.01 \\ \hline \end{tabular} \caption{Final number of events in each channel for taus type 3 $\tau$ After b-tagging, $\tau$ ID and trigger in the signal sample when the assumed cross section is 7.46 pb. An estimate of QCD background is not included.}%\end{ruledtabular} \label{b_and_tau_type_3} \end{table} \newpage \begin{table}[t] %\begin{ruledtabular} \begin{tabular}{cccc} \hline Sample & & \# of events\\ \hline data& & 2494 \\ $t\overline{t}\rightarrow\tau+jets$& & 33.57 $\pm$ 0.34\\ $t\overline{t}\rightarrow e+jets$& & 15.67 $\pm$ 0.23&\\ $t\overline{t}\rightarrow\mu+jets$& & 2.30 $\pm$ 0.09&\\ $t\overline{t}\rightarrow l+l$& & 2.69 $\pm$ 0.04&\\ $Wbb+jets\rightarrow$ $l\nu+bb+jets$& & 9.29 $\pm$ 0.27\\ $Wcc+jets\rightarrow$ $l\nu+cc+jets$& & 31.63 $\pm$ 0.90\\ $Wjj+jets\rightarrow$ $l\nu+jj+jets$& & 169.95 $\pm$ 2.68\\ $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$& & 1.30 $\pm$ 0.11\\ $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$& & 3.15 $\pm$ 0.20\\ $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$& & 16.86 $\pm$ 1.14 \\ $Zbb+jets\rightarrow$ $ee+bb+jets$& & 0.02 $\pm$ 0.01\\ $Zcc+jets\rightarrow$ $ee+cc+jets$& & 0.00 $\pm$ 0.00\\ $Zjj+jets\rightarrow$ $ee+jj+jets$& & 0.74 $\pm$ 0.33 \\ $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$& & 0.08 $\pm$ 0.02\\ $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$& & 0.07 $\pm$ 0.03\\ $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$& & 0.38 $\pm$ 0.22 \\ $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$& & 0.10 $\pm$ 0.03\\ $Zcc+jets\rightarrow$ $\nu\nu+cc+jets$& & 0.00 $\pm$ 0.00\\ $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& & 1.36 $\pm$ 0.49 \\ \hline \end{tabular} \caption{$b$-veto data set composition for types 1 and 2 $\tau$ when the assumed cross section is 7.46 pb.}%\end{ruledtabular} \label{bveto_type1_2} \end{table} %\clearpage \begin{table}[t] %\begin{ruledtabular} \begin{tabular}{cccc} \hline Sample & & \# of events\\ \hline data& & 3688 \\ $t\overline{t}\rightarrow\tau+jets$& & 19.85 $\pm$ 0.27\\ $t\overline{t}\rightarrow e+jets$& & 3.53 $\pm$ 0.13\\ $t\overline{t}\rightarrow\mu+jets$& & 2.80 $\pm$ 0.10\\ $t\overline{t}\rightarrow l+l$& & 1.81 $\pm$ 0.03\\ $Wbb+jets\rightarrow$ $l\nu+bb+jets$& & 5.26 $\pm$ 0.19\\ $Wcc+jets\rightarrow$ $l\nu+cc+jets$& & 22.43 $\pm$ 0.80\\ $Wjj+jets\rightarrow$ $l\nu+jj+jets$& & 126.41 $\pm$ 2.60 \\ $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$& & 0.92 $\pm$ 0.09\\ $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$& & 2.86 $\pm$ 0.20\\ $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$& & 14.53 $\pm$ 1.15 \\ $Zbb+jets\rightarrow$ $ee+bb+jets$& & 0.00 $\pm$ 0.00\\ $Zcc+jets\rightarrow$ $ee+cc+jets$& & 0.08 $\pm$ 0.04\\ $Zjj+jets\rightarrow$ $ee+jj+jets$& & 0.31 $\pm$ 0.18 \\ $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$& & 0.04 $\pm$ 0.02\\ $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$& & 0.05 $\pm$ 0.02\\ $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$& & 0.05 $\pm$ 0.04 \\ $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$& & 0.16 $\pm$ 0.05\\ $Zcc+jets\rightarrow$ $\nu\nu+cc+jets$& & 0.83 $\pm$ 0.15\\ $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& & 2.31 $\pm$ 0.46 \\ \hline \end{tabular} %\end{ruledtabular} \caption{$b$-veto data set composition for type 3 $\tau$ when the assumed cross section is 7.46 pb.} \label{b_veto_type_3} \end{table} \begin{table}[t] %\begin{ruledtabular} \begin{tabular}{cccc} \hline Sample & & \# of events\\ \hline data& & 1217 \\ $t\overline{t}\rightarrow\tau+jets$& & 32.94 $\pm$ 0.48\\ $t\overline{t}\rightarrow e+jets$& & 17.02 $\pm$ 0.34&\\ $t\overline{t}\rightarrow\mu+jets$& & 14.37 $\pm$ 0.32&\\ $t\overline{t}\rightarrow l+l$& & 2.43 $\pm$ 0.06&\\ $Wbb+jets\rightarrow$ $l\nu+bb+jets$& & 6.33 $\pm$ 0.23\\ $Wcc+jets\rightarrow$ $l\nu+cc+jets$& & 4.63 $\pm$ 0.19\\ $Wjj+jets\rightarrow$ $l\nu+jj+jets$& & 11.34 $\pm$ 0.26\\ $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$& & 0.50 $\pm$ 0.06\\ $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$& & 0.58 $\pm$ 0.06\\ $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$& & 1.10 $\pm$ 0.13 \\ $Zbb+jets\rightarrow$ $ee+bb+jets$& & 0.01 $\pm$ 0.01\\ $Zcc+jets\rightarrow$ $ee+cc+jets$& & 0.01 $\pm$ 0.01\\ $Zjj+jets\rightarrow$ $ee+jj+jets$& & 0.00 $\pm$ 0.00 \\ $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$& & 0.03 $\pm$ 0.01\\ $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$& & 0.04 $\pm$ 0.01\\ $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$& & 0.02 $\pm$ 0.01 \\ $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$& & 1.07 $\pm$ 0.17\\ $Zcc+jets\rightarrow$ $\nu\nu+cc+jets$& & 0.57 $\pm$ 0.10\\ $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& & 0.36 $\pm$ 0.04 \\ \hline \end{tabular} \caption{loose-tight data set composition for types 1 and 2 $\tau$ when the assumed cross section is 7.46 pb.}%\end{ruledtabular} \label{loosetight1_2} \end{table} \begin{table}[t] %\begin{ruledtabular} \begin{tabular}{cccc} \hline Sample & & \# of events\\ \hline data& & 4733\\ $t\overline{t}\rightarrow\tau+jets$& & 51.16 $\pm$ 0.57\\ $t\overline{t}\rightarrow e+jets$& & 40.02 $\pm$ 0.50\\ $t\overline{t}\rightarrow\mu+jets$& & 48.00 $\pm$ 0.56\\ $t\overline{t}\rightarrow l+l$& & 2.16 $\pm$ 0.05\\ $Wbb+jets\rightarrow$ $l\nu+bb+jets$& & 8.95 $\pm$ 0.27\\ $Wcc+jets\rightarrow$ $l\nu+cc+jets$& & 7.80 $\pm$ 0.23\\ $Wjj+jets\rightarrow$ $l\nu+jj+jets$& & 16.32 $\pm$ 0.30 \\ $Zbb+jets\rightarrow$ $\tau\tau+bb+jets$& & 0.52 $\pm$ 0.05\\ $Zcc+jets\rightarrow$ $\tau\tau+cc+jets$& & 0.46 $\pm$ 0.04\\ $Zjj+jets\rightarrow$ $\tau\tau+jj+jets$& & 1.16 $\pm$ 0.12 \\ $Zbb+jets\rightarrow$ $ee+bb+jets$& & 0.00 $\pm$ 0.00\\ $Zcc+jets\rightarrow$ $ee+cc+jets$& & 0.00 $\pm$ 0.00\\ $Zjj+jets\rightarrow$ $ee+jj+jets$& & 0.01 $\pm$ 0.01 \\ $Zbb+jets\rightarrow$ $\mu\mu+bb+jets$& & 0.06 $\pm$ 0.01\\ $Zcc+jets\rightarrow$ $\mu\mu+cc+jets$& & 0.07 $\pm$ 0.01\\ $Zjj+jets\rightarrow$ $\mu\mu+jj+jets$& & 0.11 $\pm$ 0.02 \\ $Zbb+jets\rightarrow$ $\nu\nu+bb+jets$& & 2.49 $\pm$ 0.24\\ $Zcc+jets\rightarrow$ $\nu\nu+cc+jets$& & 1.90 $\pm$ 0.14\\ $Zjj+jets\rightarrow$ $\nu\nu+jj+jets$& & 1.28 $\pm$ 0.08 \\ \hline \end{tabular} %\end{ruledtabular} \caption{loose-tight data set composition for type 3 $\tau$ when the assumed cross section is 7.46 pb.} \label{loosetight_3} \end{table} \clearpage