Relations Between Standard Model Parameters from $T^{{}^{\mathrm{\prime }}}$ Flavor Symmetry

Spontaneously broken flavor symmetry involving the binary tetrahedral group $T^{{}^{\mathrm{\prime }}}$ 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 ${\mathrm{\Theta }}_C$ for quarks. A second formula relates a ratio of neutrino mass eigenvalues to the Cabibbo angle.