Patrick Janot edited Theory.tex  about 9 years ago

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The ${\rm t\bar t}$ couplings to the photon and the Z can be parameterized in several ways. In Ref.~\cite{Baer_2013}, for example, the following $F_i$ parameterization is used:  \begin{equation}  \Gamma_\mu^{ttX} = -ie \left\{ \gamma_\mu \left( F_{1V}^X +\gamma_5 F_{1A}^X \right) + {\sigma_{\mu\nu} \over 2 m_{\rm t}} (p_t + p_{\bar t})_\mu \left( i F_{2V}^X + \gamma_5 F_{2A}^X \right)\right\} \right)\right\},  \end{equation}  with, in the standard model, vanishing $F_2$s and  \begin{equation} 

On the other hand, the optimal-observable statistical analysis presented in Section~\ref{sec:optimal} is based on Ref.~\cite{Grzadkowski_2000}, which uses the following $A,B,C,D$ parameterization:   \begin{equation}  \Gamma^\mu_{ttv} = {g\over 2} \left[ \gamma^\mu \left\{ (A_v+\delta A_v) +\gamma_5 (B_v+\delta B_v) \right\} + {(p_t -p_{\bar t})^\mu\over 2 m_{\rm t}} \left( \delta C_v + \delta D_v \gamma_5 \right) \right] \right],  \end{equation}  and which easily relates to the previous parameterization with  \begin{equation}  A_v+\delta A_v = - 2\sin\theta_W \left( F_{1V}^X + F_{2V}^X \right), \ \ B_v+\delta B_v = - 2\sin\theta_W F_{1A}^X, \ \ \delta C_v = 2\sin\theta_W F_{2V}^X  \end{equation}