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

TL;DR

This paper extends the Fermion-Loop scheme to include non-conserved currents, introducing running masses and Dyson re-summation, simplifying S-matrix elements and deriving Ward identities in complex scenarios.

Contribution

It generalizes the Fermion-Loop scheme to non-conserved currents, incorporating running masses and Dyson resummation with ghost contributions.

Findings

S-matrix elements simplify with running masses.

Derived U(1) Ward identity for non-conserved currents.

Established relation between running masses and complex poles.

Abstract

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.