Basic Connection Between Neutrino Flavor and Geometry: Absolute Masses and CP-Violation Model
The true physics approach means that independent of how clever you are and what known expert you are and how beautiful your theory is, it should be rejected if disagrees with experimental data. The opposite is also true. Supported by data solid semi-empirical research (beyond mainstream) of less known author must have the preference of full attention. In Standard Model the electroweak interactions are weak and treated by perturbation approach. And so, the clearly supported by data bimaximal neutrino mixing leading approximation with no free external parameters must be the zero EW one. Where does it come from? The only model-independed answer is – from Euclidean 3-space geometry implicitly present in the low energy SM. Well known in 3-space geometry are 3-vector direction angle bimaximal hierarchies (in geometric singled out coordinate system with Z axis parallel to the vector). In accordance, zero electroweak approximation of neutrino mixing angles likely originate from bimaximal hierarchy of 3-vector direction angles in Euclidean geometry. The supported by data relation between leading approximation symmetry of neutrino flavor mixing quantum superposition effect and the metric symmetry of outer Euclidean 3-space may be a semi-empirical evidence in favor of discussed in the literature theoretical idea of possible basic connection between quantum mechanics and geometry. If the symmetric equation (22) for neutrino mixing angles is considered without empirical free parameters, it has two extreme equally grounded formal solutions, bimaximal and biminimal ones. On the other hand, by considering solar and atmospheric mixing angles as data parameters, only the bimaximal solution with geometric symmetry is the pertinent one for the neutrino mixing leading approximation. Hence the experimental data for neutrino mixing angles clearly favor weakly violated geometric symmetry. It cannot be disregarded. We discuss a new pertinent form of relations between neutrino mass ratios and mixing angles Eq. (11). Unexpectedly, it describes many basic quantitative features of the neutrino flavor phenomenology such as a) predicts weak violation of neutrino mixing geometric SO(3) symmetry, b) together with neutrino mass squared differences, predicts small absolute neutrino masses, c) predicts realistic values of solar and reactor mixing angles, d) suggests a testable and falsifiable in coming neutrino experiments phenomenological model of large Dirac CP-violating phase and not zero CP-violating observation results in the neutrino PMNS matrix based on two equations (22) and (25). The considered neutrino mixing geometric symmetry presents an interesting new basic connection of neutrino mixing quantum mechanics (neutrino mass eigenstate superposition) and classical Euclidean geometry of 3-spece obtained in the present research on grounds of semi-empirical data analysis independent of any theoretical model. The new phenomenological model of CP-violation in the observable neutrino Pontecorvo-Maki-Nakagava-Sakata mixing matrix quantitatively predicts large, but importantly not maximal, value of Dirac CP-phase. Hence, it predicts observable CP-violation effect in the realistic neutrino PMNS mixing matrix because of the definitely not zero combination Im[sinθ13) exp(id-CP)] ≠ 0.