Static solutions in the U(1) gauged Skyrme model

TL;DR

This paper investigates static solutions in a U(1) gauged Skyrme model, finding axially symmetric solutions with reduced energy compared to the ungauged case, and analyzing the magnetic moment perturbatively.

Contribution

It introduces a gauged Skyrme model with a U(1) field and demonstrates the existence of axially symmetric solutions with specific properties, extending the understanding of gauged Skyrmions.

Findings

Gauged Skyrmions have lower energy than ungauged ones.

Solutions include electrically charged and uncharged axially symmetric configurations.

The U(1) field's impact is minimal at physical parameters, allowing perturbative analysis.

Abstract

We use a prescription to gauge the su(2) Skyrme model with a U(1) field, characterised by a conserved Baryonic current. This model reverts to the usual Skyrme model in the limit of the gauge coupling constant vanishing. We show that there exist axially symmetric static solutions with zero magnetic charge, which can be electrically either charged or uncharged. The energies of the (uncharged) gauged Skyrmions are less than the energy of the (usual) ungauged Skyrmion. For physical values of the parameters the impact of the U(1) field is very small, so that it can be treated as a perturbation to the (ungauged) spherically symmetric Hedgehog. This allows the perturbative calculation of the magnetic moment.