Nonlinear rigid-body quantization of Skyrmions

We consider rigid-body quantization of the Skyrmion in the most general four-derivative generalization of the Skyrme model with a potential giving pions a mass, as well as in a class of higher-order Skyrme models. We quantize the spin and isospin zero modes following the results of Pottinger and Rathske. Although one could hope that a one-parameter family of theories could provide a smaller spin contribution to the energy at some point in theory space—which would be welcome for Bogomol’nyi-Prasad-Sommerfield-type models, we find that the standard Skyrme model limit, with two time derivatives, gives rise to the smallest spin contribution to the energy. We speculate whether this tuning of the spin energy could be useful in the larger picture of quantizing vibrational and light massive modes of the Skyrmions. Finally, we establish a topological energy bound for the Pottinger-Rathske model with potential terms as well as new bounds for higher-order Skyrme models, with and without a potential.