CP-violating transport theory for Electroweak Baryogenesis with thermal corrections

TL;DR

This paper derives and compares CP-violating transport equations for electroweak baryogenesis, highlighting issues with the VEV-insertion approximation and establishing a consistent semiclassical formalism including thermal corrections.

Contribution

It provides a rigorous derivation of semiclassical transport equations with thermal effects and clarifies the invalidity of the VEV-insertion approximation's source term.

Findings

VIA-source term is ill-defined and non-existent.

Semiclassical formalism with thermal corrections is consistent.

Spurious collisional source terms vanish in proper calculations.

Abstract

We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an {\em assumption} that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences. We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current $\partial_\mu j^\mu = 0$. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanishes in a consistent calculation.