\newpage

\section{\label{sub:Topo}Topological variables}

In this section we show plots of the topological variables used in this analysis in order to
check the agreement between data and Monte Carlo in all cases. Plots are separated in two kinds:
signal sample and b-veto control plots.

\subsection{\label{sub:signalplots}Signal sample plots}

As stated in Section \ref{sub:Results-of-the} the signal sample is the one we used to perform
the measurement. The cuts here consist of  $NN(\tau)>0.90$ for taus types 1 and 2,
$NN(\tau)>0.95$ for taus type 3, and at least one NN b-tag. This sample contains
a good amount of $t\bar{t}$ (19.7\% for types 1 and 2 and 8.6\% for type 3) as shown in Tables
\ref{b_and_tau_type1_2} and \ref{b_and_tau_type_3}. Next we show the plots of
the topological variables for this sample. The error bars represent the statistical uncertainties only.

\begin{figure}[h]
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/aplan}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/ht}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/cent}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/spher}

\caption{The topological variables in the signal sample
($\tau$ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating the level of agreement.}

%\label{fig:variables_type2_Std} 
\end{figure}

\newpage

\begin{figure}[t]
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/sqrts}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/costhetastar}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/metl}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeI_II/met}

\caption{The topological variables in the signal sample
($\tau$ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating the level of agreement.}
%\label{fig:variables_type2_Std} 
\end{figure}


\begin{figure}[b]
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/aplan}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/ht}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/cent}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/spher}

\caption{The topological variables in the signal sample
($\tau$ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating the level of agreement.}
%\label{fig:variables_type2_Std} 
\end{figure}

\begin{figure}[t]
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/sqrts}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/costhetastar}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/metl}
\includegraphics[scale=0.34]{CONTROLPLOTS/Std_TypeIII/met}

\caption{The topological variables in the signal sample
($\tau$ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating the level of agreement.}
%\label{fig:variables_type2_Std} 
\end{figure}

\clearpage

\subsection{\label{sub:signalplots}b-veto control sample plots}

The b-veto sample is the one used to test our QCD modelling \ref{sub:Results-of-the}. As it requires no
NN b-tags it is QCD-dominated and has a tiny amount of $t\bar{t}$ (1.9\% for types 1 and 2 and 0.7\% for type 3) 
as shown in Tables \ref{bveto_type1_2} and \ref{b_veto_type_3}. It consists of an ideal sample to make sure
that the QCD modelling works and can be used in the measurement. Next we show the plots of
the topological variables for this sample. The error bars represent the statistical uncertainties only.

\begin{figure}[h]
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/aplan}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/ht}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/cent}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/spher}

\caption{The topological variables in the b-veto control sample
($\tau$ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating how good the agreement is.}

%\label{fig:variables_type2_bveto} 
\end{figure}

\newpage

\begin{figure}[t]
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/sqrts}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/costhetastar}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/metl}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeI_II/met}

\caption{The topological variables in the b-veto control sample
($\tau$ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating how good the agreement is.}

%\label{fig:variables_type2_bveto} 
\end{figure}

\begin{figure}[b]
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/aplan}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/ht}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/cent}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/spher}

\caption{The topological variables in the b-veto control sample
($\tau$ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating how good the agreement is.}

%\label{fig:variables_type2_bveto} 
\end{figure}


\begin{figure}[t]
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/sqrts}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/costhetastar}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/metl}
\includegraphics[scale=0.34]{CONTROLPLOTS/bveto_TypeIII/met}

\caption{The topological variables in the b-veto control sample
($\tau$ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown,
indicating how good the agreement is.}

%\label{fig:variables_type2_bveto} 
\end{figure}

\clearpage