Classical Field Dynamics of the Electroweak Phase Transition
Guy D. Moore, Neil G. Turok
TL;DR
This work demonstrates that classical Yang–Mills–Higgs theory on a lattice can regulate the infrared dynamics of the electroweak phase transition, providing nonperturbative access to the thermodynamics and bubble dynamics while reproducing the leading infrared behavior of the quantum theory up to $O(\alpha)$ corrections. It delivers quantitative estimates for the order-parameter jump $\delta\phi \approx 1.5\,gT$, bubble-wall surface tension $\sigma \approx 0.07\,g^4T^3$, and friction on the moving wall $\eta \approx (0.03 \pm 0.004)\,g^6T^4$ for $m_H$ near $50$ GeV, and clarifies that infrared Chern–Simons-number dynamics near Walls are suppressed inside the wall. The study further confirms a robust connection between the thermodynamics of the infrared sector and dimensionally reduced theories, while highlighting finite-$a$ effects and hydrodynamic considerations as avenues for refinement and extension to richer Higgs sectors.
Abstract
We investigate the thermodynamics and dynamics of the electroweak phase transition by modelling the infrared physics with classical Yang-Mills Higgs theory. We discuss the accuracy of this approach and conclude that, for quantities whose determination is dominated by the infrared, the classical method should be correct up to parametrically suppressed (ie O(alpha)) corrections. For a Higgs self-coupling which at tree level corresponds to m_H ~ 50 GeV, we determine the jump in the order parameter to be delta phi = 1.5 gT, the surface tension to be sigma = 0.07 g^4 T^3, and the friction coefficient on the moving bubble wall due to infrared bosons to be η= P/v_w = 0.03 \pm .004 g^6 T^4. We also investigate the response of Chern-Simons number to a spatially uniform chemical potential and find that it falls off a short distance inside the bubble wall, both in equilibrium and below the equilibrium temperature.