Towards an all-orders calculation of the electroweak bubble wall velocity

TL;DR

This paper develops an all-orders resummation method for calculating the velocity of electroweak bubble walls during a phase transition, revealing a slower terminal velocity than previously thought due to enhanced thermal pressure.

Contribution

It introduces a combined analytical and numerical resummation approach for soft gauge boson emissions affecting bubble wall velocity in the electroweak phase transition.

Findings

Resummation shows thermal pressure scales as γ^2 T^4 for fast walls.

Numerical and analytical methods agree within 10%.

Terminal velocity is slower than earlier estimates.

Abstract

We analyze Higgs condensate bubble expansion during a first-order electroweak phase transition in the early Universe. The interaction of particles with the bubble wall can be accompanied by the emission of multiple soft gauge bosons. When computed at fixed order in perturbation theory, this process exhibits large logarithmic enhancements which must be resummed to all orders when the wall velocity is large. We perform this resummation both analytically and numerically at leading logarithmic accuracy. The numerical simulation is achieved by means of a particle shower in the broken phase of the electroweak theory. The two approaches agree to the 10\% level. For fast-moving walls, we find the scaling of the thermal pressure exerted against the wall to be $P\sim \gamma^2T^4$, independent of the particle masses, implying a significantly slower terminal velocity than previously suggested.