On the Decay of Soliton Excitations

TL;DR

This paper introduces a method to incorporate collective excitations arising from symmetry breaking in soliton scattering, enabling calculation of their decay widths, with applications to the Skyrme model and the Yukawa problem.

Contribution

It presents a novel approach to include collective modes in scattering calculations, addressing a longstanding issue in chiral soliton models.

Findings

Method allows computation of decay widths of collective excitations.

Application to the Skyrme model demonstrates solving the Yukawa problem.

Enhances understanding of symmetry-breaking modes in soliton scattering.

Abstract

In field theory the scattering about spatially extended objects, such as solitons, is commonly described by small amplitude fluctuations. Since soliton configurations often break internal symmetries, excitations exist that arise from quantizing the modes that are introduced to restore these symmetries. These modes represent collective distortions and cannot be treated as small amplitude fluctuations. Here we present a method to embrace their contribution to the scattering matrix. In essence this allows us to compute the decay widths of such collective excitations. As an example we consider the Skyrme model for baryons and explain that the method helps to solve the long--standing Yukawa problem in chiral soliton models.