Oscillating monopole-antimonopole pair in the Weinberg-Salam model

TL;DR

This paper studies axially symmetric monopole-antimonopole pairs in the Weinberg-Salam model, revealing their energy range, time-dependent oscillations, and magnetic charge distribution, which differ from simpler theories.

Contribution

It provides the first detailed numerical analysis of monopole-antimonopole pairs in the Weinberg-Salam model, including their energy, oscillatory behavior, and magnetic charge distribution.

Findings

Energy range: 13.17 - 21.02 TeV

Evidence of time-dependent oscillations

Magnetic charge spread along the string

Abstract

We investigate further the properties of axially symmetrical monopole-antimonopole pair in the standard Weinberg-Salam theory. These numerical solutions behave quite differently from their counterparts in the SU(2) Yang-Mills-Higgs theory as the poles are now bounded by a flux string. Our results confirm that the energy of these solutions resides in a range of 13.17 - 21.02 TeV. In addition, we found strong evidence suggesting this configuration is time-dependent and discovered an energy oscillation phenomenon between the monopole and anti-monopole, which is associated with the symmetry of the solution. Finally, we calculate numerically the magnetic charge of the solution and confirm that its value is indeed $\frac{4\pi}{e}\sin^2\theta_{\scalebox{.5} {W}}$, as predicted by Y. Nambu in the 1970s. Counterintuitively, the magnetic charge is spread out and distributed along the string instead of concentrated near the poles.