Validity of the kink approximation to the tunneling action

TL;DR

This paper investigates the accuracy of the kink approximation in Coleman tunneling, analyzing when a simplified potential with sharp kinks can reliably estimate the tunneling action in scalar fields.

Contribution

It provides criteria for when the kink approximation accurately estimates the bounce action in scalar potentials with smooth regions.

Findings

Kink approximation is valid under specific conditions related to potential shape.

The paper identifies regimes where the approximation overestimates or underestimates the tunneling action.

Conditions for the approximation's applicability are clarified.

Abstract

Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima. This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'. We discuss under which conditions a kink approximation of locally smooth 'cap' regions provides a good estimate for the bounce action.