Natural seesaw mechanism, eV-keV-MeV-type neutrino spectrum, and cosmology

We show that in left-right-symmetric models one can have ${\mathit{m}}_{\mathit{v}\mathit{e}}$:${\mathit{m}}_{\mathit{v}\mathrm{\mu }}$:${\mathit{m}}_{\mathit{v}\mathrm{\tau }}$≃eV:KeV:MeV without any fine-tuning of parameters. The ${\nu }_{\mu }$ and ${\nu }_{\tau }$ decay via Majoron emission with lifetimes short enough to avoid cosmological constraints. The key ingredient of the model is the breaking of D parity, present in SO(10), at a scale much higher than the scale of SU(2${)}_R$ breaking. Using the Fritzsch ansatz for up-quark mass matrices and a diagonal form for the heavy neutrino masses, we predict &<10 TeV, and &≥0.2 eV.