Bounded System of Monopole and Half-monopole in the Weinberg-Salam Model

TL;DR

This paper investigates a bound state of monopole and half-monopole in the Weinberg-Salam model, revealing flux tube formation, magnetic dipole moments, and differences from SU(2) Yang-Mills-Higgs theory.

Contribution

It introduces a novel monopole-half-monopole configuration in the Weinberg-Salam model with detailed analysis of its properties and differences from related theories.

Findings

Flux tube creates bound state between monopole and half-monopole.

System has non-zero magnetic dipole moment without circulating current loop.

Total energy remains finite despite singular gauge potentials.

Abstract

In this work, we study the one plus half-monopole configuration in Weinberg-Salam model, covering $\phi$-winding number $n$ = 1. We observed that while the finite separation between the one-monopole and the half-monopole becomes larger as compared to the same configuration in SU(2) Yang-Mills-Higgs theory, a flux tube is established, creating a bound-state of one-monopole and half-monopole in Weinberg-Salam model. There is no electromagnetic current loop circulating the pair of one-monopole and half-monopole, but the system possesses non-vanishing magnetic dipole moment. The non-Abelian gauge potential and the electromagnetic gauge potential are singular along the negative $z$-axis, but the total energy is finite. The solutions are investigated by fixing the Weinberg angle while varying the Higgs self-coupling constant and vice versa. It is shown that this configuration in Weinberg-Salam model possesses different behaviours than its counterpart in SU(2) Yang-Mills-Higgs theory.