Predictive neutrino spectrum in minimal SO(10) grand unification

We show that in minimal SO(10) models where the fermions have Yukawa couplings to only one (complex) 10 and one 126 of Higgs scalars the standard model doublet contained in the 126 receives an induced vacuum expectation value at tree level. In addition to correcting the bad asymptotic mass relations ${\mathit{m}}_{\mathit{d}}$=${\mathit{m}}_{\mathit{e}}$ and ${\mathit{m}}_{\mathit{s}}$=${\mathit{m}}_{\mathrm{\ensuremath{\mu}}}$, this also leads to a predictive neutrino spectrum. We find that (i) the ${\ensuremath{\nu}}_{\mathit{e}\mathrm{\ensuremath{-}}}$${\ensuremath{\nu}}_{\mathrm{\ensuremath{\mu}}}$ mixing angle lies in the range sin${\mathrm{\ensuremath{\theta}}}_{\mathit{e}\mathrm{\ensuremath{\mu}}}$=0--0.3, (ii) sin${\mathrm{\ensuremath{\theta}}}_{\mathit{e}\mathrm{\ensuremath{\tau}}}$\ensuremath{\simeq}3\ensuremath{\Vert}${\mathit{V}}_{\mathit{t}\mathit{d}}$\ensuremath{\Vert}\ensuremath{\simeq}0.05, (iii) sin${\mathrm{\ensuremath{\theta}}}_{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{\tau}}}$\ensuremath{\simeq}3\ensuremath{\Vert}${\mathit{V}}_{\mathit{c}\mathit{b}}$\ensuremath{\Vert}=0.12--0.16, and (iv) ${\mathit{m}}_{\ensuremath{\nu}\mathrm{\ensuremath{\tau}}}$/${\mathit{m}}_{\ensuremath{\nu}\mathrm{\ensuremath{\mu}}}$\ensuremath{\ge}${10}^{3}$, implying that ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{-}}}$${\ensuremath{\nu}}_{\mathrm{\ensuremath{\tau}}}$ oscillations should be accessible to forthcoming experiments.