Realization of the minimal extended seesaw mechanism and $TM_2$ type neutrino mixing in the light of $A_4\times C_4$ symmetry group

We study the phenomenology of an $A_4\times C_4$ based neutrino mass model accommodating a light sterile neutrino in the minimal extended seesaw scheme. Mass terms consisting of the Standard Model neutrinos, the right-handed heavy neutrinos and the sterile neutrinos are obtained in terms of the vacuum alignments of a set of flavons transforming under $A_4\times C_4$. The corresponding mass matrices when incorporated into the MES formula, give rise to the $\text{TM}_2$ mixing pattern having non-zero reactor angle. We express all the active and the sterile oscillation observables in terms of only four real model parameters. Using this highly constrained scenario we predict $\sin^2 \theta_{23} =0.545^{+0.003}_{-0.004}$, $\sin \delta = -0.911^{+0.006}_{-0.005}$, $|U_{e4}|^2 = 0.029^{+0.009}_{-0.008}$, $|U_{\mu4}|^2 = 0.010^{+0.003}_{-0.003}$ and $|U_{\tau4}|^2 = 0.006^{+0.002}_{-0.002}$ which are consistent with the current data.