We derive analytic formulas for mass scales and the GUT coupling constant in SO(10) with ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\times {\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}_R\times {\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}}_C$ ($\equiv G_{214}$) intermediate breaking including two-loops and threshold effects. We find that the mass-scale predictions are in agreement with the CERN LEP data and proton-lifetime limit provided threshold effects due to heavy Higgs scalars are included. In one case the predicted proton lifetime is close to the experimental limit, while the ${\nu }_e$ mass is small, the ${\nu }_{\mu }$ mass is accessible to laboratory experiments, and the ${\nu }_{\tau }$ mass is consistent with the 17 keV neutrino. In the most interesting case the predicted proton lifetime is accessible to the Superkamiokande experiments and the ${\nu }_e$ and ${\nu }_{\mu }$ masses have the right values needed for understanding the solar neutrino problem using the Mikheyev-Smirnov-Wolfenstein mechanism. The ${\nu }_{\tau }$ mass is found to be consistent with the requirement for the dark matter of the Universe.

• Received 21 May 1993

DOI:https://doi.org/10.1103/PhysRevD.49.3704