Gauge-independent treatment of electroweak phase transition

TL;DR

This paper establishes a gauge-independent method for calculating bubble nucleation rates during the electroweak phase transition within the standard model effective field theory, with implications for gravitational wave predictions.

Contribution

It provides the first rigorous proof of gauge independence of bubble nucleation rates at two-loop order using thermal effective field theory.

Findings

Bubble nucleation rate is gauge-independent up to two-loop order.

Phase transition parameters influence gauge parameter dependence.

Implications for gravitational wave signals from electroweak phase transitions.

Abstract

We provide the first certificate of the gauge-independent bubble nucleation at the electroweak phase transition with the standard model effective field theory. Taking advantage of the thermal effective field theory framework, with the power counting $\lambda \sim g^3$, we rigorously demonstrate the gauge independence of the bubble nucleation rate up to two-loop order. Furthermore, we analyze the influence of relevant phase transition parameters on the gauge parameter and investigate its implications for gravitational waves generated by the electroweak phase transitions.