The tunneling decay rate in QFT beyond the thin-wall approximation

Instituto de Física e Química, Universidade Federal de Itajubá - 37500-903, MG, Brazil

Received: 12 September 2025
Accepted: 31 October 2025

Abstract

The tunneling decay rate per unit volume in Quantum Field Theory (QFT), at order ℏ, is given by , where B is the Euclidean action evaluated at the so-called bounce, and A is proportional to the determinant of a second-order differential operator. The dominant contribution comes from the exponential factor. To estimate , one must determine the bounce configuration, which satisfies a highly nonlinear equation. A common approach in the literature is the thin-wall approximation. In this work, we extend the formalism to cases where the thin-wall approximation is not valid. We employ a simple variational method to estimate both the bounce and the decay rate, and we find good agreement between our results and full numerical calculations.