Radiative generation of realistic neutrino mixing with $A4$

Radiative generation of realistic mixing in neutrino sector is studied at one-loop level in a scotogenic $A4\times Z_2$ symmetric framework. A scheme of obtaining non-zero $\theta_{13}$ through small mass splitting in right-handed neutrino sector is proposed. The model consists of three right-handed neutrinos, two of which were required to be degenerate in masses to yield the common structure of the left-handed neutrino mass matrix that corresponds to $\theta_{13}=0$, $\theta_{23}=\pi/4$ and any $\theta_{12}^0$ in particular the choices specific to the Tribimaximal (TBM), Bimaximal (BM) and Golden Ratio (GR) mixings. Non-zero $\theta_{13}$, deviations of $\theta_{23}$ from maximality and small corrections to the solar mixing angle $\theta_{12}$ can be generated in one stroke by shifting from this degeneracy in the right-handed neutrino sector by a small amount. The lightest among the three $Z_2$ odd inert $SU(2)_L$ doublet scalars present in the model can be a potential dark matter candidate.