Radiative corrections and uncertainties in seesaw formulas for neutrino masses

Evaluation of radiative corrections and uncertainties in the coefficients C-nu i(q) (C-nu i((l))) when the Dirac mass of the upquark (charged lepton) occurs in the quadratic seesaw formula, reveals that C-nu tau((q)) which is nearly 65% more than the earlier value, is stable against uncertainties in the input parameters, but C-nu e((q)) and C-nu mu((q)) have larger uncertainties dominating over their central values. The leptonic coefficients C-nu i((l)) (i = e, mu, tau) estimated here for the first time show that C-nu tau((l)) is renormalized by 20-40% while C-nu mu((l)) and C-nu e((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.