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 $\sin^22\theta_{13}$ 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.