Dirac plus Nambu Monopoles in the Standard Model

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.

arXiv comment4 pages, 2 figures; published (PRD) version

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