Octahedral Symmetry with Geometrical Breaking: New Prediction for Neutrino Mixing Angle theta_{13} and CP Violation

Abstract

We propose octahedral group O_h as the family symmetry of neutrino-lepton sector. We find that O_h contains subgroups Z_2(mu-tau) x Z_2(solar) and Z_4^l for realizing the bimaximal (BM) mixings, theta_{23} = theta_{12} = 45^o and theta_{13}=0^o, where Z_2(mu-tau) x Z_2(solar) and Z_4^l serve as the residual symmetries of neutrinos and charged leptons, respectively. We present geometric interpretations of BM mixing in the octahedron, and construct natural geometrical breaking of Z_4^l, leading to nontrivial deviations from the BM mixings. Our theory makes truly simple predictions of a relatively large reactor angle, theta_{13} = 45^o - theta_{12} = 7.5^o - 13.7^o (3 sigma), the nearly maximal atmospheric angle and the approximate maximal Dirac CP violation. These agree well with the current neutrino data, and will be further probed by the on-going and upcoming oscillation experiments.