Stable and unstable classical solutions in an effective gauge theory for low energy mesons

Abstract

We study the stability of two related classical solutions in an effective gauge theory, which correctly describes the properties of π and ρ mesons at low energies. The first solution (sphaleron), which excites only the ρ field, with baryon numberB=0 and energyE≈1.5 GeV is unstable. The second (Skyrmion), which excites both the π and ρ fields, withB=1 andE≈1.0 GeV is perhaps stable locally. We show how to make this Skurmion absolutely stable without raising its energy too much, both of which properties are desirable for identification with the nucleon. We comment on the potential of heavy ion collision experiments to study configuration space. The Skyrmion solution may also have some relevance for the electroweak interactions (nowE≈10 TeV).