Electrically charged finite energy solutions of an SO(5) and an SU(3) Higgs-Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions

We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons-Yang-Mills-Higgs (HCS-YMH) models in 3 + 1 dimensions, one with gauge group SO(5) and the other with SU(3). The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so that they do not vanish. The solutions of the SO(5) model carry only electric charge and zero magnetic charge, while the solutions of the SU(3) model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter, however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HCS-YMH models can be smaller than their electrically neutral counterparts in some parts of the parameter space. To establish this is the main task of this work, which is performed by constructing the HCS-YMH solutions numerically. In the case of the SU(3) HCS-YMH, we have considered the question of angular momentum and it turns out that it vanishes.