Electroweak Bubble Wall Speed Limit

TL;DR

The paper revisits the possibility of runaway electroweak bubble walls in extensions with extra scalars and demonstrates that transition radiation from particles crossing the wall provides a γ-dependent friction that stops true runaway behavior. While the leading 1→1 friction saturates at large γ, the dominant 1→2 transition-radiation processes yield a friction that grows linearly with γ, yielding a practical speed limit around γ ~ 1/α (or parametrically γ ~ m/(g^2 T) in runaway scenarios). Consequently, walls can approach the speed of light but carry only a vanishing fraction of the plasma energy, affecting predictions for baryogenesis and gravitational waves. The analysis also notes potential nonperturbative occupancies of soft gauge bosons and outlines infrared and wall-thickness effects that regulate the emission, highlighting areas for future work. Together, these findings refine the understanding of bubble-wall dynamics during a strong electroweak phase transition and its observational implications.

Abstract

In extensions of the Standard Model with extra scalars, the electroweak phase transition can be very strong, and the bubble walls can be highly relativistic. We revisit our previous argument that electroweak bubble walls can "run away," that is, achieve extreme ultrarelativistic velocities $γ\sim 10^{14}$. We show that, when particles cross the bubble wall, they can emit transition radiation. Wall-frame soft processes, though suppressed by a power of the coupling $α$, have a significance enhanced by the $γ$-factor of the wall, limiting wall velocities to $γ\sim 1/α$. Though the bubble walls can move at almost the speed of light, they carry an infinitesimal share of the plasma's energy.

Figures (1)

• Figure 1: Bubble wall geometry, and particle trajectories depending on energy and direction.