Semiclassical force for electroweak baryogenesis: three-dimensional derivation

TL;DR

This work derives a first-principles semiclassical transport framework for fermions interacting with a CP-violating planar electroweak bubble wall in a 3+1D setting. By performing a gradient (ħ) expansion of the Kadanoff–Baym equations and exploiting a boost to eliminate parallel momentum, the authors obtain on-shell kinetic equations with a CP-violating force enhanced by the wall's boost, and they show the results are equivalent to those obtained via the WKB method. The formalism is extended to mixing fermions and MSSM chargino transport, providing explicit expressions for CP-violating sources that feed baryogenesis in the charge-transport picture. Limitations include the collisionless approximation and the neglect of gauge-field dynamics, with future work aimed at incorporating collisions and self-consistent gauge fields for a more complete EWBG treatment.

Abstract

We derive a semiclassical transport equation for fermions propagating in the presence of a CP-violating planar bubble wall at a first order electroweak phase transition. Starting from the Kadanoff-Baym (KB) equation for the two-point (Wightman) function we perform an expansion in gradients, or equivalently in the Planck constant h-bar. We show that to first order in h-bar the KB equations have a spectral solution, which allows for an on-shell description of the plasma excitations. The CP-violating force acting on these excitations is found to be enhanced by a boost factor in comparison with the 1+1-dimensional case studied in a former paper. We find that an identical semiclassical force can be obtained by the WKB method. Applications to the MSSM are also mentioned.