Gauge-Invariant Slavnov–Taylor Decomposition for Trilinear Vertices

Abstract

We continue the analysis of the gauge-invariant decomposition of amplitudes in spontaneously broken massive gauge theories by performing the 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 separate 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.

Keywords

• renormalization
• spontaneously broken gauge theories