and $\bar b W^-$ intermediate states. Only the $bW^+$ cut is drawn explicitly. \[figcuts\] ](figures/fig1.ps){width="14cm"}

The results for the cuts in the full theory amplitude have the form $$\begin{aligned}
{\cal A} & = &
i\,\Big[\,\bar v_{e^+}(k^\prime)\,\gamma^\mu
 (i C_V^{\rm bW,abs}+i C_A^{\rm bW,abs}\,\gamma_5)\, u_{e^-}(k)\,\Big]\,
\Big[\,\bar u_t(p)\,\gamma_\mu\,v_{\bar t}(p)\,\Big]
\,,
\label{eett}\end{aligned}$$ where $k+k^\prime=2p=(2m_t,0)$ and $$\begin{aligned}
i C_V^{\rm bW,abs} & = & 
-i\,\frac{\alpha^2 \pi |V_{tb}|^2}{12 m_t^2 s_w^2 x(4c_w^2-x)(1+x)}\,
\bigg[\,
\frac{3x(1+x)}{(1-x)}\bigg(1+\frac{x-4}{4s_w^2}\bigg)\,\ln\Big(\frac{2-x}{x}\Big)
\nonumber\\[2mm] & &
+\,Q_e Q_t (1-x)(4-x)(1+2x)(1+x+x^2)
\nonumber\\[3mm] & & 
+\, Q_e(x-1)(1+4x+2x^2+2x^3)
\, +\,  Q_t(1-x)(1+2x)(1+x+x^2)
\nonumber\\[2mm] & &
-\,\frac{1}{2}(1+12x+9x^2+2x^3)
\,+\,\frac{1}{8s_w^2}(2+41x+28x^2-x^3+2x^4)
\,\bigg]
\,,
\nonumber\\[3mm]
i C_A^{\rm bW,abs} & = &
i\,\frac{\alpha^2 \pi |V_{tb}|^2}{12 m_t^2 s_w^2 x(4c_w^2-x)(1+x)}\,
\bigg[\,
\frac{3x(1+x)}{(1-x)}\bigg(1+\frac{x-4}{4s_w^2}\bigg)\,\ln\Big(\frac{2-x}{x}\Big)
\nonumber\\[3mm] & &
+\, Q_t(1-x)(1+2x)(1+x+x^2)
\nonumber\\[2mm] & &
-\, \frac{1}{2}(1+12x+9x^2+2x^3)
\,+\,\frac{1}{8s_w^2}(2+41x+28x^2-x^3+2x^4)
\,\bigg]
\,.\end{aligned}$$ The results for the charge conjugated process describing top pair annihilation, on the other hand, read $$\begin{aligned}
\bar{\cal A} & = &
i\,\Big[\,\bar u_{e^-}(k)\,\gamma^\mu
 (i C_V^{\rm bW,abs}+i C_A^{\rm bW,abs}\,\gamma_5)\, v_{e^+}(k^\prime)\,\Big]\,
\Big[\,\bar v_{\bar t}(p)\,\gamma_\mu\,u_t(p)\,\Big]
\,.
\label{eettadj}\end{aligned}$$ We used the cutting equations to obtain the result and checked electroweak gauge invariance by carrying out the computation in unitary and Feynman gauge. In both cases we computed the cut $W$ lines with physical polarizations as well as with unphysical ones including also the charged Goldstone exchange. We note that 