Light neutrino masses and mixing angles in SO(10) with realistic flavor structure, and the solar neutrino problem

Abstract

The light neutrino mass spectrum and their mixing angles are investigated in a class of SO(10) models with GRSY seesaw mechanism. The models are motivated by a recent proposal on the structure of the Yukawa couplings postulated from the observed KM angles and the strong CP problem. The scale of GRSY seesaw mechanism is found to be bounded from above by the invisible axion scale, leading to a lower bound on the light neutrino masses, if the strong CP problem is solved by the standard Peccei-Quinn mechanism with the invisible axion. The main results on the light neutrino masses are: 0.18 eV ⩽ m ν 3 ⩽ 100 eV, m ν 1 / m ν 2 = O( m u/ m c) , and m ν 2 /m ν 3 = 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 ν 2 / m ν 3 = O( m c/ m t) for the hierarchical structure of M N. The mixing angles are predicted to be: θ eμ ⋍ | m e /m μ + e iη' 1 O( m u /m c ) | , θ μ⊥ ⋍ | m μ /m ⊥ − e iη 2 O( m c /m t ) | and θ e⊥ ⋍ m e /m μθ μ⊥, where η' 1 and η/ 2 are some phases. Present experimental constraints on the mixing angles suggest that the phase structures of the lepton mass matrices are similar to those for the quarks if the sum of the light neutrino masses saturates the cosmological mass density bound of 100 eV, implying that ν μ − ν ⊥ and ν e− ν μ oscillations may be observable in the next generation of experiments. Regarding the solution to the solar neutrino problem with 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 ⊥ channel which the “naive seesaw” model at the GUT scale predicts. Moreover, for the structure of M N similar to those of quarks, the existence of the fourth generation light 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 MSW mechanism. The results obtained in this paper are quite different from and far more interesting than those of the “naive” seesaw model in which M N is assumed to be proportional to the identity matrix and/or the scale of seesaw mechanism is taken to be the GUT scale.