An $A_4$ realization of inverse seesaw: neutrino masses, $\theta_{13}$ and leptonic non-unitarity

We provide an $A_4$ based flavor symmetric scenario to accommodate the inverse seesaw mechanism for explaining light neutrino masses and mixing. We find that the lepton mixing, in particular the tri-bimaximal mixing pattern and its deviation through nonzero $\theta_{13}$, is originated solely from the flavor structure of the lepton number violating contribution of the neutral lepton mass matrix. Here we discuss in detail how a nonzero value of $\theta_{13}$ is correlated with the other parameters in the framework and its impact on the Dirac CP phase $\delta$. We also analyze the non-unitarity effects on lepton mixing matrix and its implication in terms of the lepton flavor violating decays, etc..