the contributions that arise from off-shell corrections in the top self-energy graphs are necessary for electroweak gauge invariance. Since the $b\bar b$ and $W^+W^-$ cuts lead to different distinct phase space factors, we found that it is possible to identify the results also from the formulae given in [@GuthKuehn].

It is an important fact that the sign of the imaginary part of the amplitude does not change in the charge conjugated amplitude. As for the quark field bilinear terms discussed before in Eq.(\[Lke\]) this is related to the unitarity of the underlying theory. It is straightforward to match the amplitudes for the operators ${\cal O}_{V/A,{\mbox{\scriptsize\boldmath $p$}}}$ and ${\cal O}^\dagger_{V/A,{\mbox{\scriptsize\boldmath $p$}}}$ to the full theory results in Eqs.(\[eett\]) and (\[eettadj\]). The resulting matching conditions at the hard scale read $$\begin{aligned}
C_V(\nu=1) & = & C_V^{\rm born} + i\,C_V^{\rm bW,abs}
\,,
\nonumber
\\
C_A(\nu=1) & = & C_A^{\rm born} + i\,C_A^{\rm bW,abs}
\,,
\label{Cvaabs}\end{aligned}$$ where we have included also the Born level contributions from Eqs.(\[Cvborn\]) and (\[Caborn\]). We emphasize again that these matching conditions are valid for the operators ${\cal O}_{V/A,{\mbox{\scriptsize\boldmath $p$}}}$ and ${\cal O}^\dagger_{V/A,{\mbox{\scriptsize\boldmath $p$}}}$. In a full treatment of electroweak and QCD effects the coefficients $C_{V/A}$ also include the real 