Hints on the high-energy seesaw mechanism from the low-energy neutrino spectrum

Abstract

It is an experimental fact that the mass ratio for the two heavier neutrinos, h = m_3/m_2 < 6, is much smaller than the typical quark and lepton hierarchies, which are O(20-300). We have explored whether this peculiar pattern of neutrino masses can be a consequence of the peculiar way they are generated through a see-saw mechanism, determining 1) How the present experimental data restrict the structure of the high-energy seesaw parameters and 2) Which choices, among the allowed ones, produce more naturally the observed pattern of neutrino masses. We have studied in particular if starting with hierarchical neutrino Yukawa couplings, as for the other fermions, one can naturally get the observed h~ 6 ratio. To perform the analysis we have put forward a top-down parametrization of the see-saw mechanism in terms of (high-energy) basis-independent quantities. Among the main results, we find that in most cases m_2/m_1 >> m_3/m_2, so m_1 should be extremely tiny. Also, the V_R matrix associated to the neutrino Yukawa couplings has a far from random structure, naturally resembling V_CKM. In fact we show that identifying V_R and V_CKM, as well as neutrino and u-quark Yukawa couplings can reproduce $h^{\rm exp}$ in a highly non-trivial way, which is very suggestive. The physical implications of these results are also discussed.