Dirac plus Nambu Monopoles in the Standard Model

TL;DR

This paper explores how monopoles in the Standard Model can merge into composite monopoles with specific magnetic charges, and discusses their regularization within grand unified theories.

Contribution

It introduces new composite monopole configurations in the Standard Model and discusses their properties and regularization via grand unified theories.

Findings

Composite monopoles can carry quantized magnetic flux consistent with Dirac's condition.

Embedding in grand unified theories can resolve singularities of monopole solutions.

Multiple monopole configurations with different magnetic charges are possible.

Abstract

We show how in the standard electroweak model three $SU(2)_L$ Nambu monopoles, each carrying electromagnetic (EM) and Z- magnetic fluxes, can merge (through Z-strings) with a single $U(1)_Y$ Dirac monopole to yield a composite monopole that only carries EM magnetic flux. Compatibility with the Dirac quantization condition requires this composite monopole to carry six quanta ($12 \pi /e$) of magnetic charge, independent of the electroweak mixing angle $\theta_w$. The Dirac monopole is not regular at the origin and the energy of the composite monopole is therefore divergent. We discuss how this problem is cured by embedding $U(1)_Y$ in a grand unified group such as $SU(5)$. A second composite configuration with only one Nambu monopole and a colored $U(1)_Y$ Dirac monopole that has minimal EM charge of $4\pi/e$ is also described. Finally, there exists a configuration with an EM charge of $8\pi/e$ as well as screened color magnetic charge.