Oscillating monopole-antimonopole pair in the Weinberg-Salam model

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 $\frac{4π}{e}\sin^2θ_{\scalebox{.5} {W}}$, 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.

A corrected, rewritten and up-to-date version is separately submitted to arXiv:2207.06768