Half-Monopole in the Weinberg-Salam Model

TL;DR

This paper introduces a new axially symmetric half-monopole solution in the Weinberg-Salam model, featuring finite energy, a net magnetic charge of half a monopole, and a magnetic dipole moment that diminishes with increasing Higgs self-coupling.

Contribution

The paper presents the first explicit construction of an axially symmetric half-monopole configuration in the Weinberg-Salam model with finite energy and distinctive magnetic properties.

Findings

Finite total energy that grows logarithmically with Higgs self-coupling.

Half-monopole has a net magnetic charge of 2π/e.

Magnetic dipole moment decreases exponentially with Higgs self-coupling.

Abstract

We present new axially symmetric half-monopole configuration of the SU(2)$\times$U(1) Weinberg-Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge $2\pi/e$ which is half the magnetic charge of a Cho-Maison monopole. The electromagnetic gauge potential is singular along the negative $z$-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant $\lambda^{1/2}$ at $\sin^2\theta_W=0.2312$. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin $r=0$ and lying along the negative $z$-axis. In the SU(2) 't Hooft magnetic field, it is a point magnetic charge located at $r=0$. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant $\lambda^{1/2}$ at $\sin^2\theta_W=0.2312$.