A Fresh Look at the Calculation of Tunneling Actions

TL;DR

This paper introduces a new method for calculating tunneling actions that avoids Euclidean bounces by using an auxiliary tunneling potential, enabling faster and more precise evaluations for metastable decay.

Contribution

It presents a novel approach using a tunneling potential to compute decay rates, generalizing the thin-wall approximation for arbitrary potentials.

Findings

Allows rapid numerical evaluation with sub-percent accuracy.

Generalizes thin-wall action to arbitrary potentials.

Can generate potentials with analytic tunneling solutions.

Abstract

An alternative approach to the calculation of tunneling actions, that control the exponential suppression of the decay of metastable phases, is presented. The new method circumvents the use of bounces in Euclidean space by introducing an auxiliary function, a tunneling potential $V_t$ that connects smoothly the metastable and stable phases of the field potential $V$. The tunneling action is obtained as the integral in field space of an action density that is a simple function of $V_t$ and $V$. This compact expression can be considered as a generalization of the thin-wall action to arbitrary potentials and allows a fast numerical evaluation with a precision below the percent level for typical potentials. The method can also be used to generate potentials with analytic tunneling solutions.