Radiative corrections and uncertainties in seesaw formulas for neutrino masses

Evaluation of radiative corrections and uncertainties in the coefficients Cνi(q) (Cνi(l)) when the Dirac mass of the upquark (charged lepton) occurs in the quadratic seesaw formula, reveals that Cντ(q) which is nearly 65% more than the earlier value, is stable against uncertainties in the input parameters, but Cνe(q) and Cνμ(q) have larger uncertainties dominating over their central values. The leptonic coefficients Cνi(l) (i = e, μ, τ) estimated here for the first time show that Cντ(l) is renormalized by 20–40% while Cνμ(l) and Cνe(l) are reduced by 60–80% from their canonical value. All the leptonic coefficients are found to possess smaller uncertainties. These results are generally valid in two-step breakings of SO(10) and other grand unified theories.