Beyond the thin-wall approximation : precise numerical computation of prefactors in false vacuum decay

TL;DR

This paper introduces a numerical method to accurately compute the false vacuum decay rate and its quantum fluctuation prefactor in scalar field theories without relying on the thin-wall approximation, enhancing precision in nucleation modeling.

Contribution

The authors develop a general numerical approach using the Gelfand-Yaglom method extended to higher dimensions, allowing precise calculation of decay rates beyond the thin-wall approximation.

Findings

The method accurately computes decay rates including quantum fluctuations.

Comparison with thin-wall approximation shows improved precision.

Derived a new formula for zero mode contributions based on bounce asymptotics.

Abstract

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a self-interacting scalar field theory modeling the process of nucleation in four dimensional spacetime. This technique does not rely on the thin-wall approximation. The method is based on the Gelfand-Yaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation. We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution.