A dynamical CP source for CKM, PMNS and Leptogenesis

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We propose a simple model for the spontaneous CP violation based on SU(2)ₗ× U(1)Y× A₄× CP× Z₂ symmetry for quarks and leptons in a seesaw framework. In our model CP is spontaneously broken at high energies, after breaking of flavor symmetry, by a complex vacuum expectation value of A₄-triplet and gauge singlet scalar field. And, certain effective dimension-5 operators are introduced in the quark Lagrangian as an equal footing, which lead the quark mixing matrix to the Cabibbo-Kobayashi-Maskawa (CKM) one in the form, while the lepton Lagrangian is renormalizable, which gives rise to a non-degenerate Dirac neutrino Yukawa matrix and an unique CP-phase, and which in turn explains the non-zero value of θ₁₃≃9∘ and two large mixing angles θ₁₂, θ₂₃. We show that the spontaneously generated CP phase "ξ" could become a natural source of leptogenesis as well as CP violations in the CKM and Pontecorvo-Maki-Nakagawa-Sakata (PMNS). Moreover, we provide a solution for the strong CP problem. Interestingly enough, we show that, for around ξ≃120∘, the quarks lead to the correct CKM CP-phase corresponding to δqCP≃67∘, while the leptons with the measured value of θ₁₃ favor δCP=, |θ₂₃-45∘|→0 for normal mass hierarchy and δCP=, |θ₂₃-45∘|→5∘ for inverted one. As a numerical study in the lepton sector, we show low-energy phenomenologies and leptogenesis for the normal and inverted case, respectively, and a link between them.