Electroweak instantons at non-zero Weinberg angle

Previous calculations of instanton effects in electroweak theory have concentrated on the case of zero Weinberg angle ${\theta }_w$, where the U(1) hypercharge field decouples. In this paper we extend the instanton calculation to non-zero ${\theta }_w$, by constructing a perturbation expansion. This allows for the first time the study of photon production at B and L number violating verticies. We find that the orientation of the instanton solution in isospin space has to be carefully considered to avoid unphysical results.