\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 the Standard Model (SM) 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) predicts 
the existence of the decay $t \rightarrow H^{\pm}b$ if $m_{H^{\pm}} < m_{t} - m_{b}$ \cite{Charged Higgs Theory}.
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. As this
analyis is limited to SM only in consists of 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  more difficult than other leptonic decays of the top.

Here we focus on events where the $\tau$ decays hadronically, 
meaning to one or more charged hadrons, zero or more neutral hadrons and a tau neutrino. Thus
this analysis is sensitive to 65\% of all $\tau$ decays.
This particular $\tau$ decay mode plus 2 $b$ jets produce a final state with four or more jets. 
Therefore we look for signal events with ate least 4 high-$p_{T}$ jets including 2 $b$ jets
at least one $\tau$ and large $\not\!\! E_{T}$.
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 the 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/top_pair_branching_frac}
\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 D0 detector. Previous results using p14
and p17 data \cite{p14_note,p17_note} summarized in Table 1 (only statistical uncertainties are shown).

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c|r|} \hline
$\int \mathcal{L}\mbox{d}t$ ($\mbox{pb}^{-1}$)  & cross section ($\mbox{pb}$)        \\ \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 over the previous p17 analysis are listed below:

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