A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry

Abstract: A model of a neutrino mixing with an $A_4\times Z_3\times Z_4$ flavour symmetry is suggested. In addition to the standard model fields, the present model contains six new fields which transform under different representations of $A_4\times Z_3\times Z_4$. The model is constructed to slightly deviate from a tri-bi-maximal 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 $|J_{CP}|\leq 0.04$. 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 $9^\circ$) very close to the current experimental data.