the $t \bar t$ vector and axial-vector currents. In the non-relativistic limit they reduce to the insertions of Coulomb potentials described by the higher order terms in Eq.(\[deltaGCoul\]). Due to the cancellation of the QCD interference effects caused by gluons with ultrasoft momenta there are no further QCD corrections in the non-relativistic limit.

An interesting new conceptual aspect of the corrections shown in Eq.(\[dsignaNNLL\]) is that they have UV $1/\epsilon$-divergences that arise from a logarithmic high energy behavior of the top-antitop effective theory phase space integration for matrix elements containing a single insertion of the Coulomb potential. In the forward scattering amplitude these UV divergences arise because the imaginary parts of the matching conditions of Eqs.(\[Cvaabs\]) lead to a dependence on the real part of $G^0$ (see Eq. (\[deltaGCoul\])). In the full theory this logarithmic behavior is regularized by the top quark mass. While phase space logarithms are known in the literature and can be resummed with renormalization group techniques [@Bauer2], the divergences here are specific since they would not exist if the top quark were approximated as being stable. In particular, the UV divergences from the time dilatation corrections arise from the Breit-Wigner-type high energy behavior of the effective 