Geometrical Model for Non-Zero theta_13

Abstract

Based on Friedberg and Lee's geometric picture by which the tribimaximal Pontecorvo-Maki-Nakawaga-Sakata leptonic mixing matrix is constructed, namely, corresponding mixing angles correspond to the geometric angles among the sides of a cube. We suggest that the three realistic mixing angles, which slightly deviate from the values determined for the cube, are due to a viable deformation from the perfectly cubic shape. Taking the best-fitted results of ${\theta }_{12}$ and ${\theta }_{23}$ as inputs, we determine the central value of ${\sin }^{2}2{\theta }_{13}$ should be 0.0238, with a relatively large error tolerance; this value lies in the range of measurement precision of the Daya Bay experiment and is consistent with recent results from the T2K Collaboration.

Comments: 14 pages, 7 figures. Published version in Phys. Rev. D