Neutral Bound States in Kink-like Theories

TL;DR

This paper derives the semi-classical spectrum of neutral particles in kink-like field theories, showing stability conditions, decay rates, and symmetry properties, with applications to various models.

Contribution

It provides an elementary derivation of neutral particle spectra and analyzes stability and decay in non-integrable kink theories, including phase space estimates and form factor properties.

Findings

Each vacuum supports at most two stable neutral particles.

Higher mass particles can be more stable than lower mass ones in certain coupling ranges.

Neutral excitations are mostly resonances that decay over time.

Abstract

In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than two stable particles, since all other neutral exitations are resonances, which will eventually decay. A phase space estimate of these decay rates is also given. This shows that there may be a window of values of the coupling constant where a particle with higher mass is more stable than the one with lower mass. We also discuss the crossing symmetry properties of the semiclassical form factors and the possibility of extracting the elastic part of the kink $S$-matrix below their inelastic threshold. We present the analysis of theories with symmetric and asymmetric wells, as well as of those with symmetric or asymmetric kinks. Illustrative examples of such theories are provided, among others, by the Tricritical Ising Ising, the Double Sine Gordon model and by a class of potentials recently introduced by Bazeira et al.