Abstract
We consider an extension of the Standard Model that was proposed recently by one of the current authors (PQH), which admits magnetic monopoles with a mass of order of a few TeV. We impose, in addition to topological quantization in the SU(2) sector of the model, the Dirac Quantization Condition (DQC) required for consistency of the quantum theory of a charged electron in the presence of the monopole. This leads to the prediction sin2θW=1/4, where θW is the weak mixing angle at the energy scale set by the monopole mass. A leading-order renormalization-group analysis yields the value of sin2θW≃0.231 at the Z-boson mass, as measured by experiment, under suitable conditions on the spectrum of the extra particles in the model.
Highlights
The electroweak mixing angle θW is a free parameter within the Standard Model (SM) of particle physics
It becomes possible to predict its value within extensions of the SM, e.g., by embedding the SM in a Grand Unified Theory (GUT), where the magnitude of θW is controlled by the details of unification [1,2,3], or in string theory [4]
We show that this condition is not sufficient by itself to guarantee satisfaction of the Dirac Quantization Condition (DQC), gM
Summary
The electroweak mixing angle θW is a free parameter within the Standard Model (SM) of particle physics. In this article we make a different prediction for sin2θW in an extension of the SM that is not a high-scale GUT, but rather a theory, proposed by one of the current authors (PQH) in [7], that includes a topologically nontrivial magnetic monopole with a mass of a few TeV This magnetic monopole is associated with a real scalar triplet of the SU(2) group, in a spirit similar to the GeorgiGlashow model [8], and obeys a topological quantization condition that stems from the known non-trivial homotopy properties of the SU(2) group. The EW-νR model makes an interesting connection between the light neutrino masses and the existence of magnetic monopole solutions It was noted in [7] that, since S2 is associated with the vacuum manifold of the real triplet ξ, topological quantization would involve the SU(2) coupling g, rather than the electromagnetic coupling e, leading to the following quantization condition for the magnetic charge gof the monopole: ggc n, n ∈ Z. One obtains the topological quantization condition (6)
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