Electroweak Monopole-antimonopole Pair in the Standard Model

TL;DR

This paper presents the first numerical solutions of a finite-separated monopole-antimonopole pair in the Standard Model's Weinberg-Salam theory, analyzing their properties despite infinite total energy due to singularities.

Contribution

It provides the first numerical monopole-antimonopole solutions in the Standard Model, detailing their magnetic charges, separation, and dependence on model parameters.

Findings

Monopole and antimonopole carry magnetic charges of ±4π/e.

Solutions exist for a range of Weinberg angles and Higgs self-couplings.

Total energy is infinite due to point singularities at monopole locations.

Abstract

We present the first numerical solution that corresponds to a pair of Cho-Maison monopole and antimonopole (MAP) in the SU(2)$\times$U(1) Weinberg-Salam (WS) theory. The monopoles are finitely separated, while each pole carries magnetic charge $\pm 4\pi/e$. The positive pole is situated in the upper hemisphere, whereas the negative pole is in the lower hemisphere. The Cho-Maison MAP was investigated for a range of Weinberg angle, $0.4675\leq\tan\theta_W\leq10$, and Higgs self-coupling, $0\leq\beta\leq1.7704$. Magnetic dipole moment ($\mu_m$) and pole separation ($d_z$) of the numerical solutions are calculated and analyzed. Total energy of the system, however, is infinite due to point singularities at the locations of monopoles.