Bound states of a fermion-dyon system

TL;DR

This paper investigates the bound states of fermions around an Abelian dyon, analyzing their energy levels, electric and magnetic dipole moments, and the effects of CP violation through analytical and numerical methods.

Contribution

It provides a detailed analysis of fermion-dyon bound states, highlighting the dependence of electric dipole moments on CP violation and the independence of magnetic moments.

Findings

Bound states exist due to the dyon's electric charge.

Electric dipole moments depend on CP violation parameter.

Magnetic dipole moments are largely independent of CP violation.

Abstract

The bound states of fermions in the external field of an Abelian dyon are studied here both analytically and numerically. Their existence is due to the dyon's electric charge resulting from a polarization of the fermionic vacuum. The configuration of the dyon's field is not invariant under $P$ or $CP$ transformations. The dependence of the energy levels of the fermion-dyon system on a parameter of $CP$ violation is investigated. The absence of $P$ invariance results in nonzero electric dipole moments of the bound fermionic states. These depend nontrivially on the parameter of $CP$ violation. The bound fermionic states also possess nonzero magnetic dipole moments. Unlike the electric dipole moments, the magnetic dipole moments are practically independent of the parameter of $CP$ violation. In addition, the magnitudes of the electric dipole moments significantly exceed those of the magnetic dipole moments.