\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. In there are more than 1 tau candidate in the event then we
choose the one with the highets $NN_{\tau}$ as the only one. Also we apply a tau-jet matching
condition. A tau candidate is only used in the measurement if the separation between it
and a jet is $\Delta R = \sqrt{{(\Delta \eta})^{2} + {(\Delta \phi})^{2}} > 0.5$.
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 $NN_{\tau}$ 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 together 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 preselected data sample:

\begin{itemize}
\item The {}``non-$b$-tag'' 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
$0.3<NN_{\tau}<0.7$ for all taus. $\tau$ NN lower cut of 0.3 
instead of 0.0 was chosen to bias their jet properties closer to those of tight tau candidates, 
in particular, so they have narrow showers. The upper cut is at 0.7 and not 0.95 or 0.90 to reduce signal contamination. 
In this sample, 1400000 events were used for NN training for taus of Type 1 and 2 and 600000 events were used 
in the case of Type 3 taus. In both cases, the rest of the samples served as QCD template.
\item The {}``$b$ veto'' sample - Require exactly 0 tight $b$-tags. This is 
the control sample used to validate of the QCD modelling method. The b veto requirement
implies this sample is almost purely background.
\end{itemize}
%

One extra cut applied along with the $NN_{\tau}$ 
cut described above was the so called NNelec cut. It is meant to be applied to Type 2 taus only in order
to reduce the probability of having these being faked by electrons. We chose a non-optimized cut of NNelec $>$ 0.9.

As both b and $\tau$ ID is the step immediately after the preselection, the number of events available is 
2800000 events. As explained above 1400000 events were used for taus of 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 of 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 of Type 1 and 2 and Type 3 respectively when $\sigma_{t\bar{t}}$ = 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, $PV_Z$ reweighting
and $WZPt$ reweighting weights. $mcweight$ is the MC normalization factor (to luminosity), which is 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 \\
$\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
&
0.93 $\pm$ 0.08\\
$\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
&
0.51 $\pm$ 0.04\\
$\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
&
1.07 $\pm$ 0.10 \\
$\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
&
0.03 $\pm$ 0.01\\
$\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
&
0.00 $\pm$ 0.00\\
$\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
&
0.02 $\pm$ 0.01 \\
$\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
&
0.07 $\pm$ 0.02\\
$\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
&
0.02 $\pm$ 0.01\\
$\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
&
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 of Types 1 and 2 $\tau$ after b-tagging, $\tau$ ID and trigger
in the signal sample when $\sigma_{t\bar{t}}$ = 7.46 pb is assumed. 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\\
$\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
&
0.74 $\pm$ 0.07\\
$\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
&
0.41 $\pm$ 0.03\\
$\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
&
0.80 $\pm$ 0.10	\\
$\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
&
0.00 $\pm$ 0.00\\
$\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
&
0.01 $\pm$ 0.01\\
$\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
&
0.01 $\pm$ 0.01 \\
$\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
&
0.04 $\pm$ 0.02\\
$\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
&
0.01 $\pm$ 0.01\\
$\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
&
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 $\sigma_{t\bar{t}}$ = 7.46 pb is assumed. 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\\
$\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
&
1.30 $\pm$ 0.11\\
$\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
&
3.15 $\pm$ 0.20\\
$\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
&
16.86 $\pm$ 1.14 \\
$\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
&
0.02 $\pm$ 0.01\\
$\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
&
0.00 $\pm$ 0.00\\
$\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
&
0.74 $\pm$ 0.33 \\
$\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
&
0.08 $\pm$ 0.02\\
$\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
&
0.07 $\pm$ 0.03\\
$\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
&
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 $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}%\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 \\
$\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
&
0.92 $\pm$ 0.09\\
$\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
&
2.86 $\pm$ 0.20\\
$\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
&
14.53 $\pm$ 1.15 \\
$\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
&
0.00 $\pm$ 0.00\\
$\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
&
0.08 $\pm$ 0.04\\
$\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
&
0.31 $\pm$ 0.18 \\
$\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
&
0.04 $\pm$ 0.02\\
$\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
&
0.05 $\pm$ 0.02\\
$\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
&
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 $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}
\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\\
$\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
&
0.50 $\pm$ 0.06\\
$\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
&
0.58 $\pm$ 0.06\\
$\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
&
1.10 $\pm$ 0.13 \\
$\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
&
0.01 $\pm$ 0.01\\
$\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
&
0.01 $\pm$ 0.01\\
$\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
&
0.00 $\pm$ 0.00 \\
$\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
&
0.03 $\pm$ 0.01\\
$\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
&
0.04	 $\pm$ 0.01\\
$\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
&
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 $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}%\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 \\
$\gamma Zbb+jets\rightarrow$ $\tau\tau+bb+jets$&
&
0.52 $\pm$ 0.05\\
$\gamma Zcc+jets\rightarrow$ $\tau\tau+cc+jets$&
&
0.46 $\pm$ 0.04\\
$\gamma Zjj+jets\rightarrow$ $\tau\tau+jj+jets$&
&
1.16 $\pm$ 0.12 \\
$\gamma Zbb+jets\rightarrow$ $ee+bb+jets$&
&
0.00 $\pm$ 0.00\\
$\gamma Zcc+jets\rightarrow$ $ee+cc+jets$&
&
0.00 $\pm$ 0.00\\
$\gamma Zjj+jets\rightarrow$ $ee+jj+jets$&
&
0.01 $\pm$ 0.01 \\
$\gamma Zbb+jets\rightarrow$ $\mu\mu+bb+jets$&
&
0.06 $\pm$ 0.01\\
$\gamma Zcc+jets\rightarrow$ $\mu\mu+cc+jets$&
&
0.07 $\pm$ 0.01\\
$\gamma Zjj+jets\rightarrow$ $\mu\mu+jj+jets$&
&
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 $\sigma_{t\bar{t}}$ = 7.46 pb is assumed.}
\label{loosetight_3} 
\end{table}

\clearpage
