Analytic Techniques for Solving the Transport Equations in Electroweak Baryogenesis

TL;DR

This paper introduces an analytical method for solving transport equations in electroweak baryogenesis, enabling efficient calculations of baryon asymmetry with applications to Standard Model effective theories.

Contribution

The authors develop a novel analytical approach that reduces complex second-order differential equations to first order, facilitating more accurate and efficient baryogenesis calculations.

Findings

The method accurately computes the baryon asymmetry in various parameter regimes.

It tests the validity of the thin-wall approximation in baryogenesis scenarios.

The approach provides insights into the sensitivity of BAU to model parameters.

Abstract

We develop an efficient method for solving transport equations, particularly in the context of electroweak baryogenesis. It provides fully-analytical results under mild approximations and can also test semi-analytical results, which are applicable in more general cases. Key elements of our method include the reduction of the second-order differential equations to first order, representing the set of coupled equations as a block matrix of the particle densities and their derivatives, identification of zero modes, and block decomposition of the matrix. We apply our method to calculate the baryon asymmetry of the Universe (BAU) in a Standard Model effective field theory framework of complex Yukawa couplings to determine the sensitivity of the resulting BAU to modifications of various model parameters and rates, and to estimate the effect of the commonly-used thin-wall approximation.