Instantons: thick-wall approximation

TL;DR

This paper introduces a new thick-wall approximation method for estimating false vacuum decay probabilities via instantons, especially when the thin-wall approximation fails due to unbounded potentials or deep true vacua.

Contribution

The authors develop a novel approximation technique that simplifies instanton calculations in complex potentials where traditional thin-wall methods are invalid.

Findings

The approximation accurately reproduces known exact solutions.

It effectively estimates decay probabilities in unbounded and deep potential scenarios.

Applicable to scalar fields in any number of dimensions.

Abstract

We develop a new method for estimating the decay probability of the false vacuum via regularized instantons. Namely, we consider the case where the potential is either unbounded from below or the second minimum corresponding to the true vacuum has a depth exceeding the height of the potential barrier. In this case, the materialized bubbles dominating the vacuum decay naturally have a thick wall and the thin-wall approximation is not applicable. We prove that in such a case the main contribution to the action determining the decay probability comes from the part of the solution for which the potential term in the equation for instantons can be neglected compared to the friction term. We show that the developed approximation exactly reproduces the leading order results for the few known exactly solvable potentials. The proposed method is applied to generic scalar field potentials in an arbitrary number of dimensions.