Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification

Abstract

We show how the neutrino mixing angles and oscillation phase can be predicted from tri-bimaximal neutrino mixing, corrected by charged lepton mixing angles which are related to quark mixing angles via quark-lepton unification. The tri-bimaximal neutrino mixing can naturally originate from the see-saw mechanism via constrained sequential dominance (CSD), where CSD can result from the vacuum alignment of a non-Abelian family symmetry such as SO(3). We construct a realistic model of quark and lepton masses and mixings based on SO(3) family symmetry with quark-lepton unification based on the Pati-Salam gauge group. The atmospheric angle is predicted to be approximately maximal ${\theta }_{23}=45^{\circ }$, corrected by the quark mixing angle ${\theta }_{23}^{\mathrm{CKM}}\approx 2.4^{\circ }$, with the correction controlled by an undetermined phase in the quark sector. The solar angle is predicted by the tri-bimaximal complementarity relation: ${\theta }_{12}+\frac{1}{\sqrt{2}}\frac{{\theta }_{\mathrm{C}}}{3}\cos (\delta -\pi )\approx 35.26^{\circ }$, where ${\theta }_{\mathrm{C}}$ is the Cabibbo angle and $\delta$ is the neutrino oscillation phase. The reactor angle is predicted to be ${\theta }_{13}\approx \frac{1}{\sqrt{2}}\frac{{\theta }_{\mathrm{C}}}{3}\approx 3.06^{\circ }$. The MNS neutrino oscillation phase $\delta$ is predicted in terms of the solar angle to be $\cos (\delta -\pi )\approx (35.26^{\circ }-{\theta }_{12}^{\circ })/3.06^{\circ }$. These predictions can all be tested by future high precision neutrino oscillation experiments, thereby probing the nature of high energy quark-lepton unification.

Comments: 24 pages; references modified, footnote extended, version to appear in JHEP