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1.1     ! uid12904    1: 
        !             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: