Generalized eikonal identities for charged currents

We discuss QED radiative corrections to contact operators coupling two heavy fields and one light field. New eikonal identities are derived in the static limit that demonstrate the equivalence of a class of ladder graphs to an equivalent theory with a single heavy-light vertex and a background Coulomb field which communicates exclusively with the light field. We apply these new identities to nuclear beta decays and demonstrates that the "independent particle model" used by Jaus, Rasche, Sirlin \& Zucchini is closely related, though not identical, to a model independent EFT calculation.