Resummation and cancellation of the VIA source in electroweak baryogenesis

TL;DR

This paper re-derives the vev-insertion approximation source in electroweak baryogenesis using self-energy diagrams, finding it vanishes due to cancellations, which clarifies its theoretical consistency.

Contribution

It provides a new derivation of the VIA source relying solely on 1PI diagrams and demonstrates its vanishing through both perturbative and resummed approaches.

Findings

VIA source vanishes for bosons and fermions

Cancellation causes the vanishing, not a pathology in the approximation

Resummed and perturbative approaches agree on the vanishing result

Abstract

We re-derive the vev-insertion approximation (VIA) source in electroweak baryogenesis. In contrast to the original derivation, we rely solely on 1-particle-irreducible self-energy diagrams. We solve the Green's function equations both perturbatively and resummed over all vev-insertions. The VIA source corresponds to the leading order contribution in the gradient expansion of the Kadanoff-Baym (KB) equations. We find that it vanishes both for bosons and fermions, both in the perturbative and in the resummed approach. Interestingly, the non-existence of the source is a result of a cancellation between different terms in the KB equations, and not of a pathology in the vev-insertion approximation itself.