top or antitop 2-point functions in the effective theory to those in the full electroweak and QCD theory. The result up to NNLL order reads $$\begin{aligned}
 \label{Lke}
 {\mathcal L}_{\rm bilinear}(x) &=& \sum_{{\mbox{\scriptsize\boldmath $p$}}}
   \psip{{\mbox{\scriptsize\boldmath $p$}}}^\dagger(x)   \biggl\{ i D^0 - {(\itbf{p}-i{\mathbf D})^2 \over 2 m_t} 
   +\frac{{\itbf{p}}^4}{8m_t^3}  
   + \frac{i}{2} \Gamma_t \bigg( 1 - \frac{{\itbf{p}}^2}{2 m_t^2} \bigg) 
   - \delta m_t \biggr\} \psip{{\mbox{\scriptsize\boldmath $p$}}}(x) 
\nonumber\\ & & \qquad
+ (\psip{{\mbox{\scriptsize\boldmath $p$}}} \to\chip{{\mbox{\scriptsize\boldmath $p$}}})\,, \end{aligned}$$ and includes the terms shown in Eq.(\[Gtop\]). Here, the fields $\psip{{\mbox{\scriptsize\boldmath $p$}}}$ and $\chip{{\mbox{\scriptsize\boldmath $p$}}}$ destroy top and antitop quarks with momentum ${\itbf{p}}$, $D^\mu=(D^0,-{\mathbf D})=\partial^\mu + i g A^\mu$ is the ultrasoft gauge covariant derivative and $\Gamma_t$ is the top quark width defined at the top quark pole. At order $g^2$, $g$ being the SU(2) gauge coupling, the width has the form $$\begin{aligned}
 \label{Gamma}
\Gamma_t & = &
\frac{\alpha |V_{tb}|^2 m_t}{16 s_w^2 x}\,(1-x)^2(1+2x)
\,,\end{aligned}$$ where $s_w$ ($c_w$) is the sine (cosine) of the weak mixing angle, $\alpha$ the fine structure constant and $$\begin{aligned}
x\equiv \frac{M_W^2}{m_t^2}
\,.\end{aligned}$$ We use the usual $v$-counting $D^0\sim m_t v^2\sim\Gamma_t\sim m_t g^2$, which leads to the scaling relation $$\begin{aligned}
v\,\sim\,\alpha_s\,\sim\,g\,\sim\,g^\prime\end{aligned}$$ for the SU(2) and U(1) gauge couplings $g$ and $g^\prime$. Because the weak mixing is of 