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                      2: \section{Objective}
                      3: 
                      4: 
                      5: \subsection{Standard Model}
                      6: 
                      7: The presented analysis involves measurement of the cross-section of
                      8: top quark pair production using the $\tau+jets$ final state (Figure
                      9: \ref{diagram}).%
                     10: \begin{figure}
                     11: \includegraphics[scale=0.7]{plots/feynman}
                     12: 
                     13: 
                     14: \caption{The dominant Feynman diagram for the $t\bar{t}\rightarrow\tau+jets$
                     15: process.}
                     16: 
                     17: \begin{centering}\label{diagram}\par\end{centering}
                     18: \end{figure}
                     19: 
                     20: 
                     21: Theoretical computation of $\sigma(p\bar{p}\rightarrow t\bar{t})$
                     22: is constantly improving. The latest published NNLO cross section is
                     23: 6.8$\pm$0.4 pb \cite{NNLO}. The decay mode to $\tau+jets$ has branching
                     24: fraction of 0.15 (Figure \ref{pie}), the sane as $e+jets$ and $\mu+jets$
                     25: channels.
                     26: 
                     27: %
                     28: \begin{figure}
                     29: \includegraphics[bb=15bp 26bp 597bp 777bp,clip,scale=0.7]{plots/pie}
                     30: 
                     31: 
                     32: \caption{\char`\"{}Pie chart\char`\"{}, displaying the branching fractions
                     33: of different final states of top quark pair decay.}
                     34: 
                     35: \begin{centering}\label{pie}\par\end{centering}
                     36: \end{figure}
                     37: 
                     38: 
                     39: No cross section measurement in the $\tau$ + X channels has yet been
                     40: performed. This is largely due to the challenges of $\tau$ reconstruction.
                     41: Unlike electrons and muons, $\tau$ leptons decay before reaching
                     42: the detector volume and need to be reconstructed from their decay
                     43: products. Also, unlike other $l+jets$ channels, where the only source
                     44: of $\not\!\! E_{T}$ is $W$ decay, $\tau$ lepton produces neutrinos
                     45: in its own subsequent decay.
                     46: 
                     47: The D0 $\tau$ - ID algorithm only reconstructs $\tau$ which undergo
                     48: hadronic decay, which happens only 65 \% of the time. This leads to
                     49: an additional efficiency hit, compared to $e$ and $\mu$ channels.
                     50: 
                     51: Still, as can be seen from Figure \ref{pie}, $\tau+X$ constitute
                     52: 24\% of the total $t\bar{t}$ decay width. Thus, a large fraction
                     53: of $t\bar{t}$ events would be missed totally if we ignore the taus.
                     54: 
                     55: Furthermore, in order to thoroughly test the Standard Model it is
                     56: important to study top physics in all possible decay modes. If there
                     57: are any flavor or mass dependent coupling (beyond SM) present in $t\bar{t}$
                     58: decay, it may show up preferentially in the $\tau+X$ final states
                     59: (due to the relatively large mass of $\tau$).
                     60: 
                     61: 
                     62: \subsection{Beyond the Standard Model}
                     63: 
                     64: In fact - $\tau$ lepton modes become especially useful to look for
                     65: signs of new phenomena. Many theoretical models predict violation
                     66: of SM flavor universality. If such processes exist they can very well
                     67: favor $\tau$ over other leptons, enhancing the branching fraction
                     68: of our channel.
                     69: 
                     70: An interesting example is the charged Higgs boson, which appears in
                     71: extensions of the SM Higgs sector to 2HDMs (Two-Higgs Doublet Models)
                     72: and is required in MSSM \cite{Charged Higgs Theory}. Since Higgs
                     73: coupling is proportional to mass it favor sheavy $\tau$ to light
                     74: $e$ and $\mu.$ This prompts us to search for $H^{+}$to $\tau$s.
                     75: D0 and CDF had performed such search in Run I (\cite{CDF Charged Higgs,D0 Charged Higgs}).
                     76: 
                     77: Table 1 shows all possible decay modes of $t\bar{t}\rightarrow\tau+X$
                     78: available if $H^{+}$ exists. D0 \cite{D0 Charged Higgs} had optimized
                     79: their selection criteria for the states 2, 4 and 5 ($\tau+jets$ channel).
                     80: CDF \cite{CDF Charged Higgs} had chosen 1, 3 and 5 ($\tau+e$ and
                     81: $\tau+\mu$ channels). Both analysis had to take into account the
                     82: ditau channel. The measurement described here establishes the foundation
                     83: for undertaking such search at Run II.
                     84: 
                     85: %
                     86: \begin{table}
                     87: \begin{tabular}{|c|c|c|c|}
                     88: \hline 
                     89: {\small Final state}&
                     90: {\small First decay}&
                     91: {\small Secondary decays}&
                     92: {\small B for secondary decays at large $\tan\beta$}\tabularnewline
                     93: \hline
                     94: \hline 
                     95: {\small 1}&
                     96: {\small $t\overline{t}$$\rightarrow W^{\mp}W^{\pm}b\bar{b}$}&
                     97: {\small $W^{\mp}\rightarrow$$\tau^{\mp}\nu$, $W^{\pm}\rightarrow l\nu$}&
                     98: {\small 0.012}\tabularnewline
                     99: \hline 
                    100: {\small 2}&
                    101: {\small $t\overline{t}$$\rightarrow W^{\mp}W^{\pm}b\bar{b}$}&
                    102: {\small $W^{\mp}\rightarrow$$\tau^{\mp}\nu$, $W^{\pm}\rightarrow jets$}&
                    103: {\small 0.074}\tabularnewline
                    104: \hline 
                    105: {\small 3}&
                    106: {\small $t\overline{t}$$\rightarrow W^{\mp}H^{\pm}b\bar{b}$}&
                    107: {\small $W^{\mp}\rightarrow$$l\nu$, $H^{\pm}\rightarrow\tau^{\pm}\nu$}&
                    108: {\small 0.11}\tabularnewline
                    109: \hline 
                    110: {\small 4}&
                    111: {\small $t\overline{t}$$\rightarrow W^{\mp}H^{\pm}b\bar{b}$}&
                    112: {\small $W^{\mp}\rightarrow$$jets$, $H^{\pm}\rightarrow\tau^{\pm}\nu$}&
                    113: {\small 0.64}\tabularnewline
                    114: \hline 
                    115: {\small 5}&
                    116: {\small $t\overline{t}$$\rightarrow H^{\mp}H^{\pm}b\bar{b}$}&
                    117: {\small $H^{\mp}\rightarrow$$\tau^{\mp}\nu$, $H^{\pm}\rightarrow\tau^{\pm}\nu$}&
                    118: {\small 0.92}\tabularnewline
                    119: \hline
                    120: \end{tabular}
                    121: 
                    122: 
                    123: \caption{Decay modes and their branching ratios, for $\tau+jets$, assuming
                    124: large $\tan\beta$. The $l$ refers to any single lepton channel}
                    125: \end{table}
                    126: