Predictive minimal model for neutrino masses and mixings

A model is considered in which the scale of the heavy singlet neutrinos is a few orders of magnitude below the grand unification scale and where right-handed vector bosons still play a negligible role. In a basis with diagonal up-quark and Dirac-neutrino mass matrices it is assumed that the heavy neutrino mass matrix has only zero elements in its diagonal, in analogy with the light neutrino mass matrix in the Zee model. Connecting then the remaining matrix elements with the small parameter describing the hierarchy of quark masses and mixings and by assuming commutativity of the charged lepton with the down-quark mass matrix, the calculation of all neutrino properties can be performed in terms of the two mass differences relevant for atmospheric and solar neutrino oscillations. CP violation is directly related to CP violation in the quark sector.