A different perspective on the vev insertion approximation for electroweak baryogenesis

TL;DR

This paper offers a new perspective on the vev insertion approximation for electroweak baryogenesis, demonstrating the equivalence of different calculation methods and analyzing the validity of derivative expansions.

Contribution

It introduces a first-order expansion approach that clarifies the relation between different formalisms in the vev insertion approximation.

Findings

The first-order expansion yields the same results as second-order self-energy calculations.

The approach explicitly shows the equivalence of including mass in free or interaction Lagrangian.

A derivative expansion cutoff is estimated for large bubble widths.

Abstract

In the vev insertion approximation (VIA) the spacetime dependent part of the mass matrix is treated as a perturbation. We calculate the source terms for baryogenesis expanding both the self-energy and propagator to first order in mass insertions, which gives the same results as the usual approach of calculating the self-energy at second order and using zeroth order propagators. This procedure shows explicitly the equivalence between including the mass in the free or in the interaction Lagrangian. The VIA source then originates from the same term in the kinetic equation as the semi-classical source, but at leading order in the derivative expansion (the expansion in diamond operators). On top, another type of derivative expansion is done, which we estimate to be valid for a bubble width larger than the inverse thermal width. This cuts off the divergence in the VIA source in the limit that the thermal width vanishes.