Geometrical Model for Non-Zero theta_13

TL;DR

This paper proposes a geometric deformation model of a cube to explain the non-zero value of the neutrino mixing angle theta_13, aligning with recent experimental findings.

Contribution

It introduces a geometric deformation approach to account for the observed non-zero theta_13 in neutrino mixing, extending Friedberg and Lee's cube model.

Findings

Predicted sin^2(2theta_13) = 0.0238 with large error margin

Result consistent with Daya Bay and T2K experimental data

Provides a geometric interpretation for deviations from tribimaximal mixing

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.