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 ($12\ensuremath{\pi}/e$) of magnetic charge, independent of the electroweak mixing angle ${\ensuremath{\theta}}_{w}$. 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 $4\ensuremath{\pi}/e$ is also described. Finally, there exists a configuration with an EM charge of $8\ensuremath{\pi}/e$ as well as screened color magnetic charge.
Highlights
It is widely recognized that the Standard Model (SM)based on the gauge group SUð3Þc × SUð2ÞL × Uð1ÞY=Z3 × Z2 does not contain topologically stable finite-energy monopoles
We have explored how purely EM monopole configurations may arise in the SM
We do not expect such configurations to have well-defined energy because of the singular nature of the Dirac monopole associated with the Uð1ÞY sector of the electroweak model
Summary
Based on the gauge group SUð3Þc × SUð2ÞL × Uð1ÞY=Z3 × Z2 does not contain topologically stable finite-energy monopoles. The EM and Z magnetic flux carried by the monopole are found to be ð4π=eÞsin2θw and ð4π=eÞ sin θw cos θw, respectively, where θw is the electroweak mixing angle with sin2θw 1⁄4 0.23. Motivated by these considerations, it seems appropriate to enquire whether a purely electromagnetic monopole configuration can be realized in the SM. Ignoring the singular nature of a Dirac monopole [9] for a moment, it turns out that a purely electromagnetic monopole can be realized by combining via Z strings a single Y monopole of appropriate magnetic charge with three Nambu monopoles This composite monopole structure carries a magnetic charge of (12π=e) in order to satisfy the Dirac quantization conditions in the presence of quarks and charged leptons. Two additional examples are provided of configurations that carry EM charges of 4π=e and 8π=e as well as screened color magnetic charge
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