Threshold effects on the mass-scale predictions in SO(10) models and solar-neutrino puzzle

We compute the threshold uncertainties due to unknown masses of the Higgs bosons on the predictions for the intermediate and unification scales, ${\mathit{M}}_{\mathit{I}}$ and ${\mathit{M}}_{\mathit{U}}$, respectively, in SO(10) models. We focus on models with separate breaking scales for parity and SU(2${)}_{\mathit{R}}$ symmetries since they provide a natural realization of the seesaw mechanism for neutrino masses. For the two-step symmetry-breaking chains, where left-right-symmetric gauge groups appear at the intermediate scale, we find that parity invariance of the theory at the unification scale drastically reduces the grand-unification-theory (GUT) threshold effects in some cases. Including the effects of the intermediate-scale thresholds, we compute the uncertainty in the above mass scales and study their implications for proton lifetime and neutrino masses. An important outcome of our analysis is that if the Mikheyev-Smirnov-Wolfenstein (MSW) solution to the solar-neutrino puzzle is accepted at the 1σ level, it rules out SU(2${)}_{\mathit{L}}$×SU(2${)}_{\mathit{R}}$×U(1${)}_{\mathit{B}\mathrm{-}\mathit{L}}$×SU(3${)}_{\mathit{c}}$ as an intermediate symmetry for SO(10) breaking whereas the intermediate symmetry SU(2${)}_{\mathit{L}}$×SU(2${)}_{\mathit{R}}$×SU(4${)}_{\mathit{c}}$ is quite consistent with it.