Particles of One-Half Topological Charge

TL;DR

This paper demonstrates the existence of finite energy SU(2) Yang-Mills-Higgs particles with half-integer topological charge, featuring unique magnetic field configurations and two distinct energy states.

Contribution

It introduces novel solutions of SU(2) Yang-Mills-Higgs theory with half-integer topological charge and analyzes their properties.

Findings

Existence of finite energy solutions with half-integer topological charge.

Solutions have magnetic fields resembling a half monopole with a Dirac string.

Total energy increases with Higgs self-coupling constant.

Abstract

We would like to show the existence of finite energy SU(2) Yang-Mills-Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole located at the origin and a semi-infinite Dirac string which carries a magnetic flux of $\frac{2\pi}{g}$ going into the center of the sphere at infinity. Hence the net magnetic charge of the configuration is zero. The solutions possess gauge potentials that are singular along one-half of the z-axis, elsewhere they are regular. There are two distinct configurations of these particles with different total energies and magnetic dipole moments. Their total energies are found to increase with the strength of the Higgs field self-coupling constant $\lambda$.