An Electroweak Monopole, Dirac Quantization and the Weak Mixing Angle

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 <math altimg="si1.svg"><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mi>W</mi></mrow></msub><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>1</mn><mo stretchy="false">/</mo><mn>4</mn></math>, where <math altimg="si2.svg"><msub><mrow><mi>θ</mi></mrow><mrow><mi>W</mi></mrow></msub></math> is the weak mixing angle at the energy scale set by the monopole mass. A leading-order renormalization-group analysis yields the value of <math altimg="si3.svg"><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mi>W</mi></mrow></msub><mo>≃</mo><mn>0.231</mn></math> at the Z-boson mass, as measured by experiment, under suitable conditions on the spectrum of the extra particles in the model.