Electroweak absorptive parts in the matching conditions of nonrelativistic QCD

Electroweak corrections associated with the instability of the top quark to the next-to-next-to-leading logarithmic (NNLL) total top pair threshold cross section in $e^{+}{e}^{-}$ annihilation are determined. Our method is based on absorptive parts in electroweak matching conditions of the operators of nonrelativistic QCD and the optical theorem. The corrections lead to ultraviolet phase space divergences that have to be renormalized and lead to NLL mixing effects. Numerically, the corrections can amount to several percent and are comparable to the known NNLL QCD corrections.