Unstable Particles and Non-Conserved Currents: a Generalization of the Fermion-Loop Scheme

A generalization of the Fermion-Loop scheme is introduced to account for external, non-conserved, currents. Complete Dyson re-summed transitions are introduced, including the contributions from the Higgs-Kibble ghosts in the 't Hooft-Feynman gauge. Running vector boson masses are introduced and their relation with the corresponding complex poles are investigated. It is shown that any S-matrix element takes a very simple form when written in terms of these running masses. A special example of Ward identity, the U(1) Ward identity for single-W, is derived in a situation where all currents are non-conserved and where the top quark mass is not neglected inside loops.