A consistent approach to bubble-nucleation theory

TL;DR

This paper presents a unified method for calculating bubble-nucleation rates in phase transitions, addressing previous issues with potential convexity, fluctuation effects, and divergences, and applies it to Higgs vacuum stability and electroweak transitions.

Contribution

It introduces a consistent framework based on a coarse-grained potential and saddle-point expansion, resolving key theoretical problems in bubble-nucleation rate calculations.

Findings

Identifies the limits of the saddle-point expansion near the spinodal line.

Provides bounds on Higgs-boson mass from vacuum metastability.

Analyzes the electroweak phase transition using the new method.

Abstract

We summarize recent work on the consistent calculation of bubble-nucleation rates. Our approach is based on the notion of a real coarse-grained potential. The bubble-nucleation rate is calculated through an expansion around the semiclassical saddle point associated with tunnelling. We resolve outstanding problems related to the convexity of the potential, the double-counting of the effect of fluctuations and the inherent ultraviolet divergences. We determine the region of validity of the expansion around the saddle point. We find that this expansion fails near the spinodal line, and for weak or radiatively-induced first-order phase transitions. We apply our method to the bound on the Higgs-boson mass from vacuum metastability and the electroweak phase transition.