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Leptogenesis and $CP$ violation in $SU(5)$ models with lepton flavor mixing originating from the right-handed sector

We discuss neutrino masses and mixing in the context of seesaw type I models with three right-handed Majorana neutrinos and an approximately diagonal Dirac sector. This ansatz is motivated by the idea that the flavor structure in the right-handed Majorana masses is responsible for the large mixing angles, whereas the small mixing angle $θ_{13}$ originates from the Dirac Yukawa couplings in analogy to the quark sector. To obtain $θ_{13} \approx 0.15$ we study a possible $SU(5)$ grand unified theory realization with a $U(1) \times \mathbb{Z}'_2 \times \mathbb{Z}''_2 \times \mathbb{Z}'''_2$ flavor symmetry and include a complex perturbation parameter in the Dirac mass matrix. The consequences for $CP$ violating phases and effects on leptogenesis are investigated.