Relations Between Standard Model Parameters from $T^{'}$ Flavor Symmetry
Spontaneously broken flavor symmetry involving the binary tetrahedral group $T^{'}$ relates parameters in the standard model. In one example the CP violating Pontecorvo-Maki-Nakagawa-Sakata phase $\delta_{PMNS}$ and atmospheric mixing angle $\theta_{23}$ of neutrinos are related to the Cabibbo mixing angle $\Theta_C$ for quarks. A second formula relates a ratio of neutrino mass eigenvalues to the Cabibbo angle.
Neutrino mixing from the double tetrahedral group T
It is shown that it is possible to create successful models of flavor for both quarks and leptons using the discrete non-Abelian group T{sup '} by itself. Two simple realizations are presented that can be used as the starting point for more general scenarios. In addition to the minimal supersymmetric standard model particle content, the models include three generations of right-handed neutrinos and four scalar flavon fields. Three of the flavons are needed in the quark and charged lepton sector of the models, and the fourth flavon participates only in the neutrino sector.
Quark masses and mixing with A4 family symmetry
Abstract The successful A 4 family symmetry for leptons is applied to quarks, motivated by the quark–lepton assignments of SU ( 5 ) . Realistic quark masses and mixing angles are obtained, in good agreement with data. In particular, we find a strong correlation between | V u b | and the CP phase β , thus allowing for a decisive future test of this model.