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.
T ′ predictions of PMNS and CKM angles
Abstract Generalizing a previous model to accommodate the third quark family and CP violation, we present a T ′ model which predicts tribimaximal neutrino (PMNS) mixings while the central predictions for quark mixings are | V t d / V t s | = 0.245 and | V u b / V c b | = 0.237 with a predicted CP violating KM phase δ KM = 65.8 ° . All these are acceptably close to experiment, including the KM phase for which the allowed values are 63 ° δ KM 72 ° , and depend only on use of symmetry T ′ × Z 2 to define the model and no additional parameters.
Charged lepton corrections to neutrino mixing angles and CP phases revisited
Abstract We re-analyze charged lepton corrections to neutrino mixing angles and CP phases, carefully including CP phases from the charged lepton sector. We present simple analytical formulae for including the charged lepton corrections and derive compact new results for small neutrino and charged lepton mixings θ 13 ν and θ 13 e . We find a generic relation θ 12 + 1 2 θ 12 e cos ( δ − π ) ≈ θ 12 ν , which relates the prediction from the neutrino sector θ 12 ν to the charged lepton mixing θ 12 e and to the MNS neutrino oscillation phase δ. We apply our formula to the examples of bimaximal or tri-bimaximal neutrino mixing. One implication is that the so-called quark–lepton complementarity relation θ 12 + θ C = 45 ° can only hold for δ = π and it gets modified in the presence of leptonic CP violation. On the other hand, the lepton mixing θ 13 generated from the charged lepton correction θ 12 e is independent of CP phases and given by θ 13 = 1 2 θ 12 e . Combining these results leads to a model-independent sum rule: θ 12 + θ 13 cos ( δ − π ) ≈ θ 12 ν where θ 12 ν = ( 35.26 ° ) 45 ° in the case of (tri-)bimaximal neutrino mixing, for example.