Can electroweak bubble walls run away?

TL;DR

The paper investigates whether electroweak bubble walls can run away in extensions of the Standard Model that include a real SU(2) singlet scalar. It develops a simple one-loop framework where friction in the ultra-relativistic wall limit is governed by a mean-field thermal potential tilde V, enabling a clear criterion to distinguish runaway from finite-velocity walls. Applying this to a real-singlet extension with parameter scans, the authors find that strong mean-field transitions generally lead to runaway walls, though a subset with flat inter-minimum potentials can end up with finite wall velocities; the presence of light scalar states can also influence the outcome. The work has implications for baryogenesis viability and gravitational wave production, and provides a practical diagnostic tool for model builders.

Abstract

In extensions of the Standard Model with SU(2) singlet scalar fields, there can be regions of parameter space for which the electroweak phase transition is first order already at the mean-field level of analysis. We show that in this case the phase interface (bubble wall) can become ultra-relativistic, with the relativistic gamma factor gamma = (1-v_{wall}^2)^{-1/2} growing linearly with the wall's propagation distance. We provide a simple criterion for determining whether the bubble wall "runs away" in this way or if gamma approaches a terminal value.

Figures (3)

• Figure 1: Example of the potential $V={V_{\rm vac}}+V_{ T}$ in our toy model, for parameters which give a first order transition. The curves are $V(h)$ at a series of temperatures from high (top) to low (bottom); the dotted curves are the potential when the $h=0$ phase becomes spinodally unstable ($T_0$) and where the $h\neq 0$ phase becomes unstable ($T_1$). The solid curve is the potential at the equilibrium temperature ($T_c$) where both phases have the same minimum value.
• Figure 2: Cartoon of a bubble wall: the scalar field $h$ as a function of position $h(z)$. Particles "hit" the wall from either side, inducing net forces.
• Figure 4: Scatter-plots of $h/T$ versus the free energy available in the transition (left) and versus the lighter physical vacuum scalar mass (right). In both figures, red dots are parameter values which give runaway bubble wall velocities, while black values give finite bubble wall velocities. For the transition to provide a large free energy or to arise from relatively heavy scalars, the bubble wall must generally be of the runaway type.