On Neutrino CP-Violation Idea
Primarysuggestive qualitative ideas are especially important in basic frontierphysics. As examples, Einstein’s thought experiment on space-time connection inspecial relativity, equivalence principle in General relativity and others.
Themodern Standard Model is in need of a reliable flavor theory with CP-violation.An appropriate suggestive qualitative idea for CP-violating flavor degree offreedom is welcome. It seems that such idea exists, it can be outlined here.
In theSM, there is a universal leading by data bimaximalapproximation for all Dirac elementary particle (charged leptons and quarks) masshierarchy and neutrino mixing hierarchy quantities. We concentrate on neutrinomixing and likely needed here CP-violation.
Bimaximalapproximation is a distinguished one, especially by its two exact symmetries –geometric type SO(3) mixing symmetry and CP symmetry. But if CP symmetry isviolated in Nature, there must be already a related first stage quantity in theneutrino bimaximal approximation. In the SM, neutrino CP-violation is describedby nonzero imaginary part of the product Im [sinθ13 exp(i dCP)] = (sinθ13sindCP) inthe Pontecorvo-Maki-Nakagava-Sakata mixing matrix. That first stage quantity inthe bimaximal approximation may be maximal CP-phase dCP = 90o at θ13 = 0, and vacuumfluctuations of the angle θ13 would produce vacuum CP-violating fluctuations.Since the empirical reactor angle θ13 = ~8.5o is not zero but small, the necessary condition for observable CP-violationis that Dirac CP-phase dCP should not be small. Because bimaximal neutrinomixing is the leading approximation of the realistic one, the requirement oflarge realistic Dirac phase follows from a feasible requirement of maximal firststage phase value dCP at bimaximal approximation. It does not produce observableCP effects at this approximation, but it calls for large realistic Dirac phase dCP< ~ 90o and nonzero reactor angle θ13 > 0. Boththose conditions together produce observable CP-violation - (sinθ13sindCP) ≠0.