Static solutions in the U(1) gauged Skyrme model

We use a prescription to gauge the SU(2) Skyrme model with a U(1) field, characterized 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.