Convergence of the nucleation rate for first-order phase transitions

TL;DR

This paper analyzes the impact of radiative corrections on the bubble-nucleation rate in first-order phase transitions, emphasizing gauge invariance and the significance of sub-leading corrections, using effective theories and multiple models.

Contribution

It provides a consistent, gauge-invariant calculation framework for nucleation rates, incorporating higher-order thermal effects and analyzing their significance across different models.

Findings

Sub-leading corrections can be large and significant.

Radiative corrections are enhanced for large bubbles.

Effective three-dimensional theory captures higher-order thermal masses.

Abstract

This paper investigates the importance of radiative corrections for first-order phase transitions, with particular focus on the bubble-nucleation rate. All calculations are done with a strict power-counting, and observables are consistently calculated at every order. This ensures that physical quantities are gauge and renormalization-scale invariant. Furthermore, to avoid large logarithms at high-temperatures, an effective three-dimensional theory is used. This effective theory automatically incorporates higher-order thermal masses. The results of this paper indicate that sub-leading corrections to the rate can be large. This is partly because radiative corrections are enhanced for large bubbles. To illustrate the calculations, three models are considered: a real-scalar model, a radiative-barrier model, and a model with an effective dimension $6$ operator. Relevant observables are calculated for each model, and the reliability of perturbation theory is discussed.