On the Existence of Tunneling Bounce Solutions in Piecewise Linear Potentials

DESY, Notkestrasse 85, 22607 Hamburg, Germany(Dated: February 14, 2012)Coleman tunneling in a general scalar potential with two non-degenerate minima is known tohave 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 ofthe bounce solution needs the scalar eld to ’wait’ for some amount of Euclidean time at one ofthe ’kinks’. We discuss under which circumstances the correct bounce action can be consistentlyobtained as the limiting case of a regular scalar potential where ’kinks’ are resolved as locally smooth’cap’ regions.I. INTRODUCTION