An Effective Sphaleron Awakens

TL;DR

This paper develops a gauge-invariant, perturbative framework using 3D effective field theory to accurately compute the sphaleron rate during the electroweak phase transition, with implications for baryon number preservation.

Contribution

It introduces a self-consistent, higher-order corrected method for calculating the sphaleron rate in the Higgs phase using 3D EFT, applicable to models like the triplet-extended Standard Model.

Findings

No strong one-step electroweak phase transitions in the considered parameter space.

Provides compact formulas for sphaleron rate and baryon washout factor.

Connects sphaleron rate calculations with bubble nucleation results.

Abstract

Using thermal effective field theory, we present a self-consistent perturbative formulation of the Higgs phase sphaleron rate after a radiatively-induced first-order phase transition. This gauge-invariant formulation is based on dimensionally reduced effective field theory (3D EFT) at high temperatures and paves a way for including higher order corrections within the 3D EFT perturbation theory without double counting. Concretely, we compute the Higgs phase sphaleron rate in a semi-classical approximation within the two-loop resummed 3D EFT. We find compact results for the sphaleron rate and the baryon washout factor as well as criteria for the baryon number preservation by providing a clear connection to the results obtained using a similar 3D EFT description for the bubble nucleation. We demonstrate these calculations for the real triplet-extended Standard Model, and conclude that when all two-loop thermal effects for the matching are accounted, no sufficiently strong one-step electroweak phase transitions exist within the parameter space regime that can be mapped onto the 3D EFT we have considered.