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

Abstract

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