On the width of collective excitations in chiral soliton models

Lint ∼ g ψ̄B′ φψB , (1.1) where B′ is the resonance that decays into baryon B and meson φ and g is a coupling constant. It is crucial that this interaction Lagrangian is linear in the meson field. If φ is a pseudoscalar meson this interaction yields the decay width Γ (B′ → Bφ) ∝ g2|~ pφ|, with ~pφ being the momentum of the outgoing meson. The situation is significantly different in soliton models that are based on action functionals of only meson degrees of freedom, Γ = Γ [Φ]. These action functionals contain classical (static) soliton solutions, Φsol, that are identified as baryons. The interaction of these baryons with mesons is described by the (small) meson fluctuations about the soliton: Φ = Φsol + φ. By pure definition we have