Electrically charged one-and-a-half monopole solution

Abstract

Recently, we have discussed the coexistence of a finite energy one-half monopole and a ’t Hooft–Polyakov monopole of opposite magnetic charges. In this paper, we would like to introduce electric charge into this new monopoles configuration, thus creating a one-and-a-half dyon. This new dyon possesses finite energy, magnetic dipole moment, and angular momentum and is able to precess in the presence of an external magnetic field. Similar to the other dyon solutions, when the Higgs self-coupling constant, \(\lambda \), is nonvanishing, this new dyon solution possesses critical electric charge, total energy, magnetic dipole moment, and dipole separation as the electric charge parameter, \(\eta \), approaches 1. The electric charge and total energy increase with \(\eta \) to maximum critical values as \(\eta \rightarrow 1\) for all nonvanishing \(\lambda \). However, the magnetic dipole moment decreases with \(\eta \) when \(\lambda \ge 0.1\) and the dipole separation decreases with \(\eta \) when \(\lambda \ge 1\) to minimum critical values as \(\eta \rightarrow 1\).