  To understand the mass spectra of charged lepton and neutrino $A_4$ symmetry
has been proposed in addition with the Standard $SU(2)_L\times U(1)_Y$ model.
We break $A_4$ symmetry softly and the deviation from the tri-bimaximal mixing
arises due to Zee mechanism. In the present work, we express two mixing angles
$\theta_{13}$ and $\theta_{23}$ in terms of a single model parameter and
experimental observables, such as, mixing angle $\theta_{12}$, mass squared
differences $\Delta m^2_{21}$ and $\Delta m^2_{32}$. Using the experimental
values of $\theta_{23}$, $\theta_{12}$, $\Delta m^2_{21}$ and $\Delta m^2_{32}$
we restrict the model parameter and we predict $\theta_{13}$. This model gives
rise to $\theta_{13}\simeq 11^\circ$ if we allow $1\sigma$ deviation of
$\theta_{23}$ and $2^\circ$ deviation of $\theta_{12}$ from their best fit
values. Utilizing all those constraints, we explore the extent of CP violation
parameter $J_{\rm CP}$ in the present model and found a value of $J_{\rm
CP}\approx 2.65\times 10^{-3}$ (for $1\sigma$ deviation of $\theta_{23}$ and
$2^\circ$ deviation of $\theta_{12}$) consistent with the other neutrino
experimental results. We have studied the mass pattern of neutrino and
neutrinoless double beta decay $(\beta\beta_{0\nu})$ parameter $|(M_\nu)_{ee}|$
in this model.

High Energy Physics - Phenomenology