# Electroweak Bubble Wall Speed Limit

## TL;DR

This paper investigates the maximum achievable velocity of electroweak bubble walls in models with extra scalars, revealing that transition radiation limits their ultrarelativistic speeds despite their near-light velocities.

## Contribution

It demonstrates that transition radiation from particles crossing the wall constrains bubble wall velocities to gamma factors around 1/alpha, revising previous ultrarelativistic limits.

## Key findings

- Transition radiation limits bubble wall velocities to gamma ~ 1/alpha.
- Bubble walls can approach light speed but carry negligible plasma energy.
- Ultrarelativistic bubble walls are constrained by soft processes despite high gamma.

## 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 $\gamma \sim 10^{14}$. 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 $\alpha$, have a significance enhanced by the $\gamma$-factor of the wall, limiting wall velocities to $\gamma \sim 1/\alpha$. Though the bubble walls can move at almost the speed of light, they carry an infinitesimal share of the plasma's energy.