A hidden hierarchy of neutrino masses

Abstract

The Dirac masses of neutrinos can exhibit a strong hierarchy even if the Majorana masses of the right-handed neutrinos are degenerate and the hierarchy of the mass scales governing the oscillations of solar and atmospheric neutrinos is rather small. This phenomenon results from the see-saw mechanism and the algebraic structure of the effective mass operator for the active neutrinos. The large hierarchy of the Dirac masses is drastically modified by a symmetric unitary matrix $R$ acting in the flavor space. A realistic pattern of neutrino masses and mixing is obtained. Maximal mixing for atmospheric neutrinos is attributed to the charged lepton sector. Large mixing in solar neutrino oscillations is due to the neutrino sector. Small $U_{e3}$ is a natural consequence of the model. The masses of the active neutrinos are given by $μ_3\approx\sqrt{Δm_{@}^2}$ and $μ_1/μ_2\approx \tan^2θ_\odot$.