Baryonic torii: Toroidal baryons in a generalized Skyrme model

We study a Skyrme-type model with a potential term motivated by Bose-Einstein condensates (BECs), which we call the BEC Skyrme model. We consider two flavors of the model: the first is the Skyrme model, and the second has a sixth-order derivative term instead of the Skyrme term, both with the added BEC-motivated potential. The model contains toroidally shaped Skyrmions, and they are characterized by two integers P and Q, representing the winding numbers of two complex scalar fields along the toroidal and poloidal cycles of the torus, respectively. The baryon number is B = PQ. We find stable Skyrmion solutions for P = 1, 2, 3, 4, 5 with Q = 1, while for P = 6 and Q = 1, it is only metastable. We further find that configurations with higher Q > 1 are all unstable and split into Q configurations with Q = 1. Finally we discover a phase transition, possibly of first order, in the mass parameter of the potential under study.