Bubble Wall Velocity at the Electroweak Phase Transition

TL;DR

Problem: determine bubble wall velocity and thickness at a first-order electroweak transition in the Minimal Standard Model. Approach: semiclassical Higgs evolution with a two-loop finite-temperature potential, augmented by a Boltzmann-fluid treatment of non-equilibrium particle populations that captures transport and friction. Contributions: dynamically determined wall thickness, explicit friction calculations, and identification of top-quark dominance; findings include a fast, thick wall and sensitivity to nonperturbative symmetric-phase effects. Significance: provides quantitative constraints for electroweak baryogenesis and informs extensions to multi-Higgs sectors and nonperturbative dynamics.

Abstract

We calculate the velocity and thickness of a bubble wall at the electroweak phase transition in the Minimal Standard Model. We model the wall with semiclassical equations of motion and show that friction arises from the deviation of massive particle populations from thermal equilibrium. We treat these with Boltzmann equations in a fluid approximation in the background of the wall. Our analysis improves on the previous work by using the two loop effective potential, accounting for particle transport, and determining the wall thickness dynamically. We find that the wall is significantly thicker than at phase equilibrium, and that the velocity is fairly high, $v_w \simeq 0.7c$, and quite weakly dependent on the Higgs mass.