Rotating and vibrating Skyrmions

Abstract

The stability of rotating solitons is analyzed. It is found that both the linear σ-model and the chiral Skyrme Lagrangian (Skyrmion) yield unstable solutions with respect to pion emission. Introducing a symmetry breaking pion mass term stable solutions for the nucleon and the ▵(1232) are obtained in the Skyrme model. Furthermore with spherical symmetry, no parameter set is found which yields stable rotating solutions for both the nucleon and the delta, with correct masses. When parameters from earlier literature are used, the nucleon is stable but not the delta. To describe baryon excited states small amplitude fluctuations around the rotating solution are considered. The calculated P₁₁ phase shift to the “breathing mode” excitation of the nucleon is compared to earlier results neglecting rotations and it is found that rotation-vibration coupling leads to sizable changes.