Seesaw Neutrino Mass Ratios with Radiative Corrections

Unlike neutrino masses, the ratios of neutrino masses can be predicted by up-quark seesaw models using the known quark masses and including radiative corrections, with some restrictive assumptions. The uncertainties in these ratios can be reduced to three: the type of seesaw (quadratic, linear, etc.), the top quark mass, and the Landau-triviality value of the top quark mass. The inconclusive but suggestive results of recent solar and atmospheric neutrino and beta decay experiments [1] lead to the possibility of neutrino masses, which additionally may have important application to cosmology, astrophysics and laboratory searches for neutrino oscillations. The most economical model of light neutrinos is the so-called " seesaw " of the grand-unified type, which requires a superheavy right-handed neutrino for each ordinary neutrino and arises naturally in partially or completely unified theories with left-right symmetry, such as SO(10) [2,3,4]. These grand unified seesaw models predict small but non-zero Majorana masses for the ordinary neutrinos in terms of the Dirac masses of the up-type quarks (u, c, t) and the superheavy right-handed Majorana masses. These predictions are made uncertain, however, by the unknown right-handed masses and by ra-diative corrections. But the ratios of neutrino masses are more definite in seesaw models, under some neccesary and minimal assumptions (printed below in italics) about the physics underlying the seesaw [5]. The uncertainties in the mass ratios can then be narrowed to a handful. The general tree-level form of the seesaw model mass matrix for three families is: 0 m D m T D M N , (1) in the left-and right-handed neutrino basis, where each entry is a 3×3 matrix. We assume that the upper left corner is zero, as a non-zero Majorana mass for left-handed ν generally requires an SU(2) L Higgs triplet, an unnatural addition to the Standard Model in light of known electroweak neutral-current properties [6].