The tunneling decay rate in QFT beyond the thin wall approximation

TL;DR

This paper develops a variational method to estimate quantum tunneling decay rates in quantum field theory beyond the thin-wall approximation, providing a practical alternative to complex numerical solutions.

Contribution

It introduces a simple variational approach to compute bounce solutions and decay rates without relying on the thin-wall approximation, improving applicability.

Findings

Good agreement with full numerical calculations

Effective estimation of decay rates beyond thin-wall limit

Provides a practical method for complex tunneling problems

Abstract

The tunneling decay rate per unit volume in Quantum Field Theory (QFT), at order $\hbar$, is given by $\Gamma/V = Ae^{-B}$, 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 $\Gamma/V$, 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.