A model of a neutrino mixing with an $A_4\times Z_3\times Z_4$ flavor symmetry is suggested. In addition to the standard model fields, the present model contains six new fields that transform under different representations of $A_4\times Z_3\times Z_4$. The model is constructed to slightly deviate from a tribimaximal model in agreement with the current experimental data; thus, all analysis can be done in the base of the perturbation method. Within this model, as an application, a relation between the mixing angles (${\theta }_{12}$, ${\theta }_{23}$, ${\theta }_{13}$) and the Dirac $CP$-violation phase (${\delta }_{CP}$) is established. This relation allows a prediction of ${\delta }_{CP}$ and the Jarlskog parameter ($J_{CP}$). The predicted value ${\delta }_{CP}$ is in the $1\sigma$ region of the global fit for both the normal and inverse neutrino mass ordering and gives $J_{CP}$ to be within the bound $\left|J_{CP}\right|\le 0.04$. For an illustration, the model is checked numerically and gives values of the neutrino masses (of the order of 0.1 eV) and the mixing angle ${\theta }_{13}$ (about 9°) very close to the current experimental data.

• Received 2 July 2016

DOI:https://doi.org/10.1103/PhysRevD.94.095009

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