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.
