Magic neutrino mass model with broken $\mu-\tau$ symmetry and Leptogenesis

We investigate baryogenesis via leptogenesis in $A_4$ flavor model within the paradigm of type-I and II seesaw mechanism resulting in magic neutrino mass matrix with broken $\mu-\tau$ symmetry in a minimal scenario with two right-handed neutrinos(2RHN). Additional $Z_3$ cyclic symmetry is employed to constrain the Yukawa structure of model. The type-II seesaw terms play crucial role in generating non-degenerate neutrino masses and non-zero $\theta_{13}$ and contribute in baryogenesis. In particular, after the spontaneous symmetry breaking, the Yukawa couplings $y_{\Delta_1}$ and $y_{\Delta_3}$ are responsible for the breaking of $\mu-\tau$ symmetry. The effective Majorana neutrino mass $|M_{ee}|$ is found to be well within the sensitivity reach of the $0\nu\beta\beta$ experiments, in particular, for inverted hierarchy. The model has imperative implication for inverted hierarchy, for example, the non-observation of this process at nEXO will rule out IH. The predicted baryon asymmetry is in good agreement with the observed baryon asymmetry for NH whereas IH is disallowed at 2.5$\sigma$ C.L..