Abstract
We consider a direct approach to quark mixing based on the discrete family symmetry Δ(6N2) in which the Cabibbo angle is determined by a residual Z2×Z2 subgroup to be |Vus|=0.222521, for N being a multiple of 7. We propose a particular model in which unequal smaller quark mixing angles and CP phases may occur without breaking the residual Z2×Z2 symmetry. We perform a numerical analysis of the model for N=14, where small Z2×Z2 breaking effects of order 3% are allowed by model, allowing perfect agreement within the uncertainties of the experimentally determined best fit quark mixing values.
Highlights
Non-Abelian discrete groups have been extensively used as family symmetries in the lepton sector, in order to account for the large leptonic mixing angles [1] In the direct approach, a non-Abelian family symmetry in the lepton sector is assumed
Following the determination of a Cabibbo-sized reactor angle, the only viable class appears to be ∆(6N2) for large N values [6, 7, 8, 9]. Such a symmetry is broken to Z2 × Z2 in the neutrino sector and Z3 in the charged lepton sector, with the mixing angles determined from symmetry
Some authors have speculated that both the lepton mixing angles and the Cabibbo angle may arise from some common discrete family symmetry group [17, 18]
Summary
Non-Abelian discrete groups have been extensively used as family symmetries in the lepton sector, in order to account for the large leptonic mixing angles [1] (for reviews see e.g. [2, 3, 4, 5].) In the direct approach, a non-Abelian family symmetry in the lepton sector is assumed. Non-Abelian discrete groups have been extensively used as family symmetries in the lepton sector, in order to account for the large leptonic mixing angles [1] A complementary approach to deriving the Cabibbo angle of θC ≈ 1/4 at leading order was recently considered in an indirect model based on a vacuum alignment (1, 4, 2) without any residual symmetry [19].
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