Patrick Janot edited Theory.tex  about 9 years ago

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\section{Theoretical framework}  \label{sec:theory}  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: used (with $X = \gamma, Z$):  \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\},  \end{equation} 

F_{1V}^{\gamma} = -{2\over3}, \ \ F_{1A}^{\gamma} = 0, \ \ F_{1V}^Z = {1\over 4\sin\theta_W\cos\theta_W} \left(1-{8\over3}\sin^2\theta_W\right) {\rm \ and \ \ }F_{1A}^Z = {1 \over 4\sin\theta_W\cos\theta_W}.  \end{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: parameterization (with $v = \gamma, Z$):  \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],