Abstract
A non-Abelian finite flavor group G⊂SO(3) can have double covering G′⊂SU(2) such that G⊄G′. This situation is not contradictory, but quite natural, and we give explicit examples such as G=Dn, G′=Q2n and G=T, G′=T′. This observation can be crucial in particle theory model building.
Highlights
One promising direction for extending the standard model of particle theory lies in using a flavor symmetry GF which commutes with the gauge group
The flavor symmetry can lead to predictions for the quarks and lepton mixing angles
The standard model gauge group GSM is comprised of the direct product of continuous groups GSM ≡ SU(3) × SU(2) × U(1)
Summary
One promising direction for extending the standard model of particle theory lies in using a flavor symmetry GF which commutes with the gauge group. First we will set the stage by considering a few explicit examples, including an infinite series of SU(2) subgroups, after a brief and self-contained survey of the small nonabelian groups.
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