Predictive Neutrino Spectrum in Minimal $SO(10)$ Grand Unification

Abstract

We show that minimal SO(10) Grand Unification models where the fermions have Yukawa couplings to only one (complex) {\bf 10} and one {\bf 126} of Higgs scalars lead to a very predictive neutrino spectrum. This comes about since the standard model doublet contained in the {\bf 126} of Higgs (needed for the see--saw mechanism) receives an induced vacuum expectation value at tree--level, which, in addition to correcting the bad asymptotic mass relations $m_d=m_e$ and $m_s=m_{\mu }$, also relates the Majorana neutrino mass matrix to observables in the charged fermion sectors. We find that (i) the ${\nu }_e-{\nu }_{\mu }$ mixing angle relevant for the solar neutrinos can be considerably smaller than the Cabibbo angle and lies in the range $\sin {\theta }_{e\mu }=0-0.3$, (ii) ${\nu }_e-{\nu }_{\tau }$ mixing is sin${\theta }_{e\tau }\simeq 3|V_{td}|\simeq 0.05$, (iii) the ${\nu }_{\mu }-{\nu }_{\tau }$ mixing angle is large, $\sin {\theta }_{\mu \tau }\simeq 3|V_{cb}|=0.12-0.16$, and (iv) $m_{{\nu }_{\tau }}/m_{{\nu }_{\mu }}\ge 10^3$, implying that ${\nu }_{\mu }-{\nu }_{\tau }$ oscillations should be accessible to forthcoming experiments.

14 pages, Latex

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