Baryonic torii: Toroidal baryons in a generalized Skyrme model

TL;DR

This paper explores toroidal baryons in a generalized Skyrme model inspired by Bose-Einstein condensates, revealing stable configurations, instability patterns, and a phase transition related to the potential's mass parameter.

Contribution

It introduces a BEC-motivated potential in a Skyrme-type model and analyzes the stability and structure of toroidal Skyrmions with various winding numbers.

Findings

Stable Skyrmions for P=1 to 5 with Q=1

Higher Q configurations are unstable and split into Q=1 states

Identified a possible first-order phase transition in the mass parameter

Abstract

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.