Prediction of leptonic $CP$ phase in $A_4$ symmetric model

We consider minimal modifications to the tribimaximal (TBM) mixing matrix which accommodate nonzero mixing angle ${\theta }_{13}$ and $CP$ violation. We derive four possible forms for the minimal modifications to TBM mixing in a model with $A_4$ flavor symmetry by incorporating symmetry breaking terms appropriately. We show how possible values of the Dirac-type $CP$ phase ${\delta }_D$ can be predicted with regards to two neutrino mixing angles in the standard parametrization of the neutrino mixing matrix. Carrying out a numerical analysis based on the recent updated experimental results for neutrino mixing angles, we predict the values of the $CP$ phase for all possible cases. We also confront our predictions for the $CP$ phase with the updated fit.

Figure 1

Prediction of ${\delta }_D$ in terms of $s_{12}^2$ for C based on the $1\sigma$ experimental data.

Figure 2

Prediction for ${\delta }_D$ in terms of (a) $s_{23}^2$ for s A and B, and (b) $s_{12}^2$ for s C and D, based on $3\sigma$ experimental data. Regions surrounded by blue (green) lines correspond to s (A, C) and (B, D). These are almost equally predicted for both neutrino mass orderings. The small regions surrounded by the red line corresponding to $s_{23}^2\le 0.41$.