$A_4$ model of Magic neutrino mass matrix 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. In general, 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 coupling $y_{\Delta_1}$ at dimension-four is responsible for the breaking of $\mu-\tau$ symmetry. We, also, study the implication of the model for successful leptogenesis using approximated solution of the Boltzmann equations. We find that the observed baryon asymmetry of the universe requires the lightest right-handed neutrino mass to be $(2.36-2.40)\times 10^{9} $GeV for NH ($(2.15-2.17)\times10^{9}$GeV for IH) which is consistent with the Davidson-Ibarra bound of $10^{9}$GeV.