Annotation of ttbar/p20_taujets_note/Objective.tex, revision 1.1.1.1
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:
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