Summing up My New Semi-Empirical

                                         Neutrino Physics Ideas from 2016 Year


                                                    E. M. Lipmanov, Brighton


1) As in case of light at the dawn of quantum physics, neutrino special empirical features probably suggest new fundamental physics, in particular flavor one. Semi-empirical neutrino mixing angle phenomenology is described by one primary equation

                  cos^2 (2θ12) + cos^2 (2θ23) + cos^2 (2θ13) = 1+ sin^2 (2θ13),      (1)

                                cos(4θ13) = 1 – [cos^2 (2θ12) + cos^2 (2θ23)],                (1`)

which predicts the magnitude of finite small reactor angle θ13 = ~ 8.5o and suggests deeper physical meaning by accurate quantitative description of small neutrino mixing deviation, (right side term sin^2 (2θ13) of Eq. (1)) from geometric SO(3)-symmetry (left side of Eq. (1)). Again, in analogy with particle-wave duality in case of light, Eq. (1) indicates new fundamental physics flavor-geometric duality: congruence of flavor neutrino leading approximation bimaximal mixing angle hierarchy and flavor neutrino momentum vector leading approximation direction angle hierarchy -- both at presentations without free parameters.

That quantum-geometric congruence fact may be also interesting as an empirical example of relation between neutrino mass state superposition quantum mechanics and outer Euclidean geometry -- particular evidence of the discussed in the literature general theoretical ideas of connection between quantum physics and geometry. 


2) There is a principal question – Why is Geometric SO(3)-symmetry of the realistic neutrino mixing violated? In the framework of Standard Model there is only one answer: the violation of neutrino mixing geometric symmetry is caused by the necessary CP-violation of neutrino weak interactions. CP-violation is the only possible cause of geometric symmetry violation that is absent in 3-space Euclidean geometry and therefore is absent in the mentioned flavor-geometric duality.


3) Suggested connection between violation of neutrino mixing geometric symmetry and CP-violation in the neutrino Pontecorvo-Maki-Nakagava-Sokata mixing matrix means that θ13-angle is tied to the Dirac CP-phase ‘d’ in that mixing matrix

                                                           |d| = (90^o - 2 θ13).                                    (2)

Indeed, in combination with (1) the complementary relation (2) shows possible primary cause of neutrino mixing geometric symmetry violation as phenomenon of CP-symmetry violation in the neutrino weak interactions as described by equation

                           Cos^2 (2θ12) + cos^2 (2θ23) + cos^2 (2θ13) = 1 + cos^2 d.    (3)

From that equation, the CP-violating Dirac phase |d| is maximal |d| = 90^o at leading bimaximal neutrino mixing approximation θ12 = θ23 = 90^o, θ13 = 0.

It should be underlined that despite maximal CP-phase the factual CP-violation effect at leading bimaximal approximation is zero since θ13 = 0. But at realistic neutrino mixing θ13 = ~ 8.5^o a prediction follows,

                                             d = + - (90^o - 2 θ13) = ~ + - (72 – 74)^o,                 (4)

and so, a physically observable CP-violation effect in neutrino physics appears

                                         [sin θ13 exp(-id)] = ~ [0.15(0.3 + - 0.96i)],                (5)

which is testable and falsifiable in coming neutrino experiments. If confirmed, those semi-empirical results of weakly violated neutrino mixing symmetry and CP-violation may influence general fundamentally new particle physics.

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