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\newpage
\section{\label{sec:intro}\boldmath{Introduction}}

\noindent Since its discovery at the Fermilab TEVATRON collider in 1995, the top quark has been one 
of the most important topics in High Energy Physics. The study of its production rate and
properties allows us to perform precision tests of standard model (SM) predictions as well as
represents a chance of observing possible deviations from such predictions. 
Amongst all subsequent top decays, the process $t \rightarrow Wb \rightarrow \tau \nu_{\tau} b$
represents one of the most important tools for probing beyond-SM physics. For instance, 
the MSSM (Minimal Supersymmetric Standard Model) \cite{Charged Higgs Theory} predicts 
the existence of the decay $t \rightarrow H^{+}b$ if $m_{H_{-}^{+}} < m_{t} - m_{b}$.
As the Higgs-fermion coupling is proportional to the latter's 
mass, the subsequent decay of a charged Higgs boson into a $\tau$ lepton
is much more favored than its decays into $e$'s and $\mu$'s.
Therefore, for high values of tan $\beta$ (the ratio of the vacuum expectation values
of the two Higgs doublets) the charged Higgs preferentially decays to $\tau \nu_{\tau}$,
which increases the branching ratio (BR) of $t \rightarrow \tau \nu_{\tau} b$ relative
to the SM prediction. Thus, any non-standard flavor- and
mass-dependent could produce a significant effect on the $\tau$ production channel. In this
respect, the work presented here represents an important test of the SM predictions as well as
one step further on the investigation of non-SM processes.


In this analysis we study the process when the $W$ boson from one of the top quarks decays into a 
$\tau$ lepton and its associated neutrino, while the other $W$ boson decays into 
a quark-antiquark pair. The $\tau$ is the heaviest lepton and its prompt decay into other
particles and the probability of being faked by electrons, muons and jets
makes its reconstruction and identification much more difficult than other top decays.

Here we focus on events where the $\tau$ decays hadronically, 
meaning to one or three charged hadrons, zero or more neutral hadrons and a tau neutrino.
This implies that our signal consists of a final state with four or more jets. 
Figures \ref{fig:feynman} and \ref{fig:pie} show respectively the Feynman diagram that decribes
the process $t\bar{t} \rightarrow \tau + jets$ and the pie chart of top decay.
In Section \ref{sec:dataset} we discuss or signal and main backgrounds.

\begin{figure}[h]
\includegraphics[scale=0.50]{plots/feynman}
\caption{Feynman diagram for $t\bar{t} \rightarrow \tau + jets$ .}
\label{fig:feynman}
\end{figure}

\newpage

\begin{figure}[t]
\includegraphics[scale=0.40]{plots/pie}
\caption{Top quark decay pie chart.}
\label{fig:pie}
\end{figure}

%\clearpage

The present work is the third measurement of the $t\bar{t}$ cross section in the $\tau + jets$ 
channel performed with the D\O\ detector. Previous results \cite{p14_note,p17_note} used using p14 RunI
and p17 RunIIa Data and are summarized in Table \ref{previous} (only statistical uncertainties are shown).

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c|r|} \hline
Data set ($pb^{-1}$)  & cross section ($pb$)        \\ \hline

\hline

p14 (349.0) & \multicolumn{1}{c|}{$5.05\;\;_{-3.46}^{+4.31}$}\\ \hline

p17 (974.2) & \multicolumn{1}{c|}{$6.90\;\;_{-1.20}^{+1.20}$}\\ \hline

\end{tabular}
\caption{Previous $t\bar{t}$ cross section measurements in the $\tau + jets$ channel}
\end{center}
\label{previous} 
\end{table}

 
The main improvements upon previous p17 analysis are listed below:

\begin{itemize}
\item 5 times more data (RunIIb1, RunIIb2 and RunIIb3). 
\item Trigger used: we use a new set of multijet triggers that represents a gaim of ~ 10\% in the final efficiency.
\item Use of vertex confirmed jets.
\item Tau energy scale added to the analysis.
\item Improved neural net (NN) optimization.
\item New set of p20 b-tag TRF's.
\end{itemize}