Guesswork for Dirac and Majorana neutrino mass matrices

Abstract

In the framework of seesaw mechanism with three neutrino flavors, we propose tentatively an efficient parametrization for the spectra of Dirac and righthanded Majorana neutrino mass matrices in terms of three free parameters. Two of them are related to (and determined by) the corresponding parameters introduced previously for the mass spectra of charged leptons and up and down quarks. The third is determined from the experimental estimate of solar $\Delta m^2_{21}$. Then, the atmospheric $\Delta m^2_{32}$ is {\it predicted} close to its experimental estimation. With the use of these three parameters all light active-neutrino masses $ m_1 < m_2 < m_3$ and heavy sterile-neutrino masses $ M_1 < M_2 < M_3$ are readily evaluated. The latter turn out much more {\it hierarchical} than the former. The lightest heavy mass $ M_1$ comes out to be of the order $O(10^6 {\rm GeV})$ so, it is too light to imply that the mechanism of baryogenesis through thermal leptogenesis might work.