SU(3) gauge family symmetry and prediction for the lepton-flavor mixing and neutrino masses with maximal spontaneous CP violation

Abstract

A model for the lepton-flavor mixing and CP violation is proposed based on the SUF(3) gauge family symmetry and the Majorana feature of neutrinos. A consistent prediction for the lepton-flavor mixing and masses is shown to be resulted from the appropriate vacuum structure of SUF(3) gauge symmetry breaking. By choosing the SUF(3) gauge fixing condition to possess a residual Z2 symmetry and requiring the vacuum structure of spontaneous symmetry breaking to have approximate global U(1) family symmetries, we obtain naturally the tri-bimaximal mixing matrix and largely degenerate neutrino masses in the neutrino sector and the small mixing matrix in the charged-lepton sector. With a simple ansatz that all the smallness due to the approximate global U(1) family symmetries is characterized by a single Wolfenstein parameter λ≃0.22, and the charged-lepton mixing matrix has a similar hierarchy structure as the CKM quark mixing matrix, we arrive at a consistent prediction for the MNSP lepton-flavor mixing with a maximal spontaneous CP violation: δ=π/2, sin2θ13≃12λ2≃0.024 (sin22θ13≃0.094), sin2θ12≃13(1−2λ3)≃0.326 and sin2θ23≃12(1−λ2)≃0.48, which agree well with the current experimental data. The CP-violating Jarlskog-invariant is obtained to be JCP≃16λ(1−λ2/2−λ3)sinδ≃0.035, which is detectable in next generation neutrino experiment. The small masses of the neutrinos and charged leptons are simply attributed to the standard seesaw mechanism. The largely degenerate neutrino masses with the normal hierarchy and inverse hierarchy are discussed and found to be at the order mνi≃O(λ2)≃0.04–0.06 eV with a total mass ∑mν∼0.15 eV, which is testable in future precision astrophysics and cosmology.