Electroweak Bubble Wall Friction: Analytic Results

TL;DR

This work provides an analytic, leading-log determination of the friction on an electroweak bubble wall during a first-order phase transition, arguing that infrared gauge-field physics, dominated by Landau damping and the Debye mass, sets the friction primarily through overdamped W-bosons. Within a perturbative regime $g^3 \ll \lambda \ll g^2/\log(1/g)$, the authors derive a closed-form expression for the friction coefficient $\eta$ that scales as $\eta \propto \alpha_w^2 T^4$ with a calculable logarithmic enhancement, and present two parametric results depending on the effective-theory regime considered. In the standard regime, $\eta = \frac{3 m_D^2 T}{16 \pi L} [\log(m_W L)+O(1)]$, yielding wall velocities of order $v_w \sim \alpha_w$, while Bödeker’s theory gives a closely related but differently parametrized result with a small extra log suppression. By coupling this friction to a simple driving-pressure estimate, the paper concludes that $v_w$ is typically much less than unity (often $\lesssim 0.1$), with the friction significantly larger than some prior numerical estimates, carrying important implications for electroweak baryogenesis and bubble-hydrodynamics in the early universe.

Abstract

We present an entirely analytic, leading log order determination of the friction an electroweak bubble wall feels during a first order electroweak phase transition. The friction is dominated by W bosons, and gives a wall velocity parametrically ~ alpha_w, and numerically small, ~ .01 -- 0.1 depending on the Higgs mass.