Gauge-invariant Slavnov-Taylor Decomposition for Trilinear Vertices

TL;DR

This paper develops a gauge-invariant decomposition for trilinear vertices in spontaneously broken gauge theories, enabling better understanding of cancellations and aiding in the determination of counter-terms without invariant regularization.

Contribution

It introduces a method to decompose amplitudes into gauge-invariant sectors for chiral Abelian theories, valid to all orders in perturbation theory.

Findings

Separately gauge-invariant subsectors are characterized for trilinear vertices.

The approach simplifies the analysis of unphysical degree cancellations.

Provides a new strategy for determining counter-terms in chiral gauge theories.

Abstract

We continue the analysis of the gauge-invariant decomposition of amplitudes in spontaneously broken massive gauge theories by providing a characterization of separately gauge-invariant subsectors for amplitudes involving trilinear interaction vertices for an Abelian theory with chiral fermions. We show that the use of Frohlich-Morchio-Strocchi gauge-invariant dynamical (i.e. propagating inside loops) fields yields a very powerful handle on the cancellations among unphysical degrees of freedom (the longitudinal mode of the massive gauge field, the Goldstone scalar and the ghosts). The resulting cancellations are encoded into separately Slavnov-Taylor invariant sectors for 1-PI amplitudes. The construction works to all orders in perturbation theory. This decomposition suggests a novel strategy for the determination of finite counter-terms required to restore the Slavnov-Taylor identities in chiral theories in the absence of an invariant regularization scheme.