the form $$\begin{aligned}
{\cal O}_{V,{\mbox{\scriptsize\boldmath $p$}}} & = & 
\big[\,\bar e\,\gamma_j\,e\,\big]\,{\cal O}_{{\mbox{\scriptsize\boldmath $p$}},1}^j
\,,
\\[2mm]
{\cal O}_{A,{\mbox{\scriptsize\boldmath $p$}}} & = &
\big[\,\bar e\,\gamma_j\,\gamma_5\,e\,\big]\,{\cal O}_{{\mbox{\scriptsize\boldmath $p$}},1}^j
\,,\end{aligned}$$ where $$\begin{aligned}
{\cal O}_{{\mbox{\scriptsize\boldmath $p$}},1}^j & = &
\Big[\,\psi_{{\mbox{\scriptsize\boldmath $p$}}}^\dagger\, \sigma_j (i\sigma_2)
  \chi_{-{\mbox{\scriptsize\boldmath $p$}}}^*\,\Big]
\,.\end{aligned}$$ They give the contribution $\Delta {\cal L} = \sum_{{\mbox{\scriptsize\boldmath $p$}}} \left(C_V {\cal O}_{V,{\mbox{\scriptsize\boldmath $p$}}} +  C_A
{\cal O}_{A,{\mbox{\scriptsize\boldmath $p$}}} \right) + \mbox{h.c.}$ to the effective theory Lagrangian where the hermitian conjugation is referring to the operators only. The index $j=1,2,3$ is summed. The corresponding operators describing $t\bar t$ annihilation are obtained by the hermitian conjugation. Since in this work we only focus on the electroweak effects related to the top quark decay and, in particular, neglect QED radiative corrections (including QED binding and the beam effects mentioned above) the electron and positron fields act like classic fields in the effective theory.[^5] In a more complete treatment of electroweak effects, however, their interactions with photons have to be accounted for [@Beneke1]. The leading order matching conditions of the operators ${\cal O}_{V/A,{\mbox{\scriptsize\boldmath $p$}}}$ obtained from the full theory Born diagrams with photon and Z exchange are of order $g^2$ and read $$\begin{aligned}
C_V^{\rm born}(\nu=1) & = & 
\frac{\alpha\pi}{m_t^2(4c_w^2-x)}\,\bigg[\,
Q_e Q_t(4-x) + 