Nonzero θ13, CP-violation and neutrinoless double beta decay for neutrino mixing in the A4×Z2×Z3 flavor symmetry model

We study the modification of Altarelli-Feruglio $A_4$ flavor symmetry model by adding three singlet flavons $\xi'$, $\xi''$ and $\rho$ is augmented with extra $Z_2\times Z_2^ \prime$ to prevent unwanted terms in our study. The addition these lead two higher order corrections form perturbation parameters $\epsilon$ $\epsilon^\prime$. These yield deviation from exact tri-bimaximal (TBM) neutrino mixing pattern producing a non-zero $\theta_{13}$ other oscillation which are consistent latest experimental data. In both corrections, masses generated via Weinberg operator. analysis $\epsilon^\prime$, shows that normal hierarchy (NH) inverted (IH) for does not change much. However, as values $\epsilon^\prime$ increases, $\theta_{23}$ occupies lower octant NH case. further investigate neutrinoless double beta decay parmeter $m_{\beta\beta}$ using parameter space hierarchies masses.