The Flavor Physics in Unified Gauge Theory from an S3 × P Discrete Symmetry

Abstract

We investigate the phenomenological implication of the discrete symmetry S3 × P on flavor physics in SO(10) unified theory. We construct a minimal renormalizable model which reproduce all the masses and mixing angle of both quarks and leptons. As usually the SO(10) symmetry gives up to relations between the down sector and the charged lepton masses. The underlining discrete symmetry gives a contribution (from the charged lepton sector) to the PMNS mixing matrix which is bimaximal. This gives a strong correlation between the down quark and charged lepton masses, and the lepton mixing angles. We obtain that the small entries V ub, V cb, V td, and V ts in the CKM matrix are related to the small value of the ratio δ m2 solΔ m2 atm: they come from both the S3×P structure of our model and the small ratio of the other quark masses with respect to m t. Wonderfully, with our model, we fit 17 experimental data %with only 13 free relevant combinations of vevs.