order one we apply the same counting to the SU(2) and U(1) gauge couplings. The term $\delta m_t$ is a residual mass term of order $v^2$ that arises if a threshold mass scheme [@synopsis] is used. The LL order terms in Eq.(\[Lke\]) lead to the top/antitop propagator $$\begin{aligned}
  \frac{i}{p^0 - {\itbf{p}}^2/(2m_t) + i\Gamma_t/2 -\delta m_t} \,.
\label{toppropagator}\end{aligned}$$ Although the exchange of time-like ultrasoft $A^0$ gluons contributes at LL order according to the $v$-counting, their contribution at LL order can be removed from the particle-antiparticle sector of the theory by a redefinition of the top and antitop fields related to static Wilson lines [@Korchemsky1; @Bauer1].[^4] The time dilatation term $\propto
\Gamma_t({\mathbf p}^2/2m_t^2)$ originates from the momentum-dependence of the full theory spinors and contributes at NNLL order.

The $t\bar t$ pair is produced by an electroweak process. As long as electroweak effects are only treated at leading order in the $v$-expansion it is sufficient to describe $t\bar t$ production by a bilinear quark-antiquark current. However, as shown below it is necessary to include the initial-state $(e^+e^-)$ fields to ensure electroweak gauge invariance at subleading order in the $v$-expansion. The dominant operators that have to be used describing $t\bar t$ spin-triplet production have 