Multi-Skyrmion Solutions for the 6th order Skyrme Model

TL;DR

This paper extends the Skyrme model by adding a sixth order term, analyzes classical multi-Skyrmion solutions numerically up to B=5, and validates the rational map ansatz for the generalized model.

Contribution

It introduces a sixth order term to the Skyrme model and demonstrates that the rational map ansatz remains effective for the extended model.

Findings

Multi-Skyrmion solutions have same symmetries as in the original model.

Rational map ansatz accurately estimates energies and radii for the extended model.

Numerical solutions up to B=5 show consistent properties with the classical Skyrme solutions.

Abstract

Following Marleau, we study an extended version of the Skyrme model to which a sixth order term has been added to the Lagrangian and we analyse some of its classical properties. We compute the multi-Skyrmion solutions numerically for up to B=5 and show that they have the same symmetries as the usual Skyrmion solutions. We use the rational map ansatz introduced by Houghton et al. to evaluate the energy and the radius for multi-skyrmion solutions of up to B=6 for both the SU(2) and SU(3) models and compare these results to the ones obtained numerically. We show that the rational map ansatz works as well for the generalised model as for the pure Skyrme model.