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 θ23 ≤ 45°, corrected by the quark mixing angle θ23CKM ≈ 2.4°, with the correction controlled by an undetermined phase in the quark sector. The solar angle is predicted by the tri-bimaximal complementarity relation: θ12+(1/2 1/2)(θC/3)cos (δ-π) ≈ 35.26°, where θC is the Cabibbo angle and δ is the neutrino oscillation phase. The reactor angle is predicted to be θ13 ≈ (1/2 1/2)(θC/3) ≈ 3.06°. The MNS neutrino oscillation phase δ is predicted in terms of the solar angle to be cos (δ-π) ≈ (35.26°-θ12°)/3.06°. These predictions can all be tested by future high precision neutrino oscillation experiments, thereby probing the nature of high energy quark-lepton unification. © SISSA 2005.