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\section{Objective}


\subsection{Standard Model}

The presented analysis involves measurement of the cross-section of
top quark pair production using the $\tau+jets$ final state (Figure
\ref{diagram}).%
\begin{figure}
\includegraphics[scale=0.7]{plots/feynman}


\caption{The dominant Feynman diagram for the $t\bar{t}\rightarrow\tau+jets$
process.}

\begin{centering}\label{diagram}\par\end{centering}
\end{figure}


Theoretical computation of $\sigma(p\bar{p}\rightarrow t\bar{t})$
is constantly improving. The latest published NNLO cross section is
6.8$\pm$0.4 pb \cite{NNLO}. The decay mode to $\tau+jets$ has branching
fraction of 0.15 (Figure \ref{pie}), the sane as $e+jets$ and $\mu+jets$
channels.

%
\begin{figure}
\includegraphics[bb=15bp 26bp 597bp 777bp,clip,scale=0.7]{plots/pie}


\caption{\char`\"{}Pie chart\char`\"{}, displaying the branching fractions
of different final states of top quark pair decay.}

\begin{centering}\label{pie}\par\end{centering}
\end{figure}


No cross section measurement in the $\tau$ + X channels has yet been
performed. This is largely due to the challenges of $\tau$ reconstruction.
Unlike electrons and muons, $\tau$ leptons decay before reaching
the detector volume and need to be reconstructed from their decay
products. Also, unlike other $l+jets$ channels, where the only source
of $\not\!\! E_{T}$ is $W$ decay, $\tau$ lepton produces neutrinos
in its own subsequent decay.

The D0 $\tau$ - ID algorithm only reconstructs $\tau$ which undergo
hadronic decay, which happens only 65 \% of the time. This leads to
an additional efficiency hit, compared to $e$ and $\mu$ channels.

Still, as can be seen from Figure \ref{pie}, $\tau+X$ constitute
24\% of the total $t\bar{t}$ decay width. Thus, a large fraction
of $t\bar{t}$ events would be missed totally if we ignore the taus.

Furthermore, in order to thoroughly test the Standard Model it is
important to study top physics in all possible decay modes. If there
are any flavor or mass dependent coupling (beyond SM) present in $t\bar{t}$
decay, it may show up preferentially in the $\tau+X$ final states
(due to the relatively large mass of $\tau$).


\subsection{Beyond the Standard Model}

In fact - $\tau$ lepton modes become especially useful to look for
signs of new phenomena. Many theoretical models predict violation
of SM flavor universality. If such processes exist they can very well
favor $\tau$ over other leptons, enhancing the branching fraction
of our channel.

An interesting example is the charged Higgs boson, which appears in
extensions of the SM Higgs sector to 2HDMs (Two-Higgs Doublet Models)
and is required in MSSM \cite{Charged Higgs Theory}. Since Higgs
coupling is proportional to mass it favor sheavy $\tau$ to light
$e$ and $\mu.$ This prompts us to search for $H^{+}$to $\tau$s.
D0 and CDF had performed such search in Run I (\cite{CDF Charged Higgs,D0 Charged Higgs}).

Table 1 shows all possible decay modes of $t\bar{t}\rightarrow\tau+X$
available if $H^{+}$ exists. D0 \cite{D0 Charged Higgs} had optimized
their selection criteria for the states 2, 4 and 5 ($\tau+jets$ channel).
CDF \cite{CDF Charged Higgs} had chosen 1, 3 and 5 ($\tau+e$ and
$\tau+\mu$ channels). Both analysis had to take into account the
ditau channel. The measurement described here establishes the foundation
for undertaking such search at Run II.

%
\begin{table}
\begin{tabular}{|c|c|c|c|}
\hline 
{\small Final state}&
{\small First decay}&
{\small Secondary decays}&
{\small B for secondary decays at large $\tan\beta$}\tabularnewline
\hline
\hline 
{\small 1}&
{\small $t\overline{t}$$\rightarrow W^{\mp}W^{\pm}b\bar{b}$}&
{\small $W^{\mp}\rightarrow$$\tau^{\mp}\nu$, $W^{\pm}\rightarrow l\nu$}&
{\small 0.012}\tabularnewline
\hline 
{\small 2}&
{\small $t\overline{t}$$\rightarrow W^{\mp}W^{\pm}b\bar{b}$}&
{\small $W^{\mp}\rightarrow$$\tau^{\mp}\nu$, $W^{\pm}\rightarrow jets$}&
{\small 0.074}\tabularnewline
\hline 
{\small 3}&
{\small $t\overline{t}$$\rightarrow W^{\mp}H^{\pm}b\bar{b}$}&
{\small $W^{\mp}\rightarrow$$l\nu$, $H^{\pm}\rightarrow\tau^{\pm}\nu$}&
{\small 0.11}\tabularnewline
\hline 
{\small 4}&
{\small $t\overline{t}$$\rightarrow W^{\mp}H^{\pm}b\bar{b}$}&
{\small $W^{\mp}\rightarrow$$jets$, $H^{\pm}\rightarrow\tau^{\pm}\nu$}&
{\small 0.64}\tabularnewline
\hline 
{\small 5}&
{\small $t\overline{t}$$\rightarrow H^{\mp}H^{\pm}b\bar{b}$}&
{\small $H^{\mp}\rightarrow$$\tau^{\mp}\nu$, $H^{\pm}\rightarrow\tau^{\pm}\nu$}&
{\small 0.92}\tabularnewline
\hline
\end{tabular}


\caption{Decay modes and their branching ratios, for $\tau+jets$, assuming
large $\tan\beta$. The $l$ refers to any single lepton channel}
\end{table}