One-loop corrections to the metastable vacuum decay

TL;DR

This paper calculates the one-loop quantum corrections to the decay rate of a metastable vacuum in a scalar field theory, using numerical methods to handle functional determinants, zero modes, and renormalization.

Contribution

It introduces a numerical approach to evaluate the one-loop prefactor in vacuum decay, connecting thin-wall and gradient expansion results.

Findings

Quantum corrections decrease away from the thin-wall limit.

Numerical results agree with gradient expansion in the thin-wall limit.

Proper treatment of zero modes and renormalization is essential.

Abstract

We evaluate the one-loop prefactor in the false vacuum decay rate in a theory of a self interacting scalar field in 3+1 dimensions. We use a numerical method, established some time ago, which is based on a well-known theorem on functional determinants. The proper handling of zero modes and of renormalization is discussed. The numerical results in particular show that quantum corrections become smaller away from the thin-wall case. In the thin-wall limit the numerical results are found to join into those obtained by a gradient expansion.