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

We show how the neutrino mixing angles and oscillation phase can be predictedfrom tri-bimaximal neutrino mixing, corrected by charged lepton mixing angleswhich are related to quark mixing angles via quark-lepton unification. Thetri-bimaximal neutrino mixing can naturally originate from the see-sawmechanism via constrained sequential dominance (CSD), where CSD can result fromthe vacuum alignment of a non-Abelian family symmetry such as SO(3). Weconstruct a realistic model of quark and lepton masses and mixings based onSO(3) family symmetry with quark-lepton unification based on the Pati-Salamgauge 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 controlledby an undetermined phase in the quark sector. The solar angle is predicted bythe tri-bimaximal complementarity relation: $\theta_{12}+\frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3} \cos (\delta - \pi) \approx35.26^\circ $, where $\theta_{\mathrm{C}}$ is the Cabibbo angle and $\delta$ isthe neutrino oscillation phase. The reactor angle is predicted to be$\theta_{13} \approx \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3}\approx3.06^\circ$. The MNS neutrino oscillation phase $\delta$ is predicted in termsof 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 futurehigh precision neutrino oscillation experiments, thereby probing the nature ofhigh energy quark-lepton unification.Comment: 24 pages; references modified, footnote extended, version to appear in JHE