Light neutrino masses and mixing angles in SO(10) from the flavor structure of quarks, and the solar neutrino problem

Abstract

The light neutrino masses and their mixing angles are investigated in a class of SO(10) models with the GRSY seesaw mechanism. The models are motivated by a recent proposal on the structure of the Yukawa couplings postulated from the observed KM angles and the strong- CP problem. The scale of the seesaw mechanism is found to be bounded from above by the invisible axion scale, leading to a lower bound on the light neutrino masses. The main results are: 0.18 eV⩽m v3 ⩽100 eV, m v1 m v2 = O( m u m c ) , and m v2 m v3 = O(( m c m t )( m u m c m t )) for the non-hierarchical structure of the right-handed neutrino mass matrix ( M N), and m v2 m v3 = O( m c m t ) for the hierarchical structure of M N , θ eμ ≅| m e m μ + exp( iη l′ ) O( m u m c )|, θ μt≅| m μ m t - exp( iη 2) O( m c m t )| , and θ e/ m t θ μt , where η 1′ and η 2 are some phases. With present experimental constraints on the mixing angles, ν μ − ν τ and ν e − ν μ oscillations may be observable in the next generation of experiments. Regarding the solution to the solar neutrino problem with the MSW amplification mechanism, we find that the relevant neutrino oscillation in the sun should be in the ν e − ν μ channel, instead of the ν e − ν t channel which the “naive seesaw” model at the GUT scale predicts. Moreover, we also find that, for the structure of M N similar to those of quarks, the existence of a light fourth generation neutrino is inevitable, if the cosmological mass density bound is to be saturated by the light neutrino masses and the solar neutrino problem is solved by the MSW mechanism.