Paper detail

A dynamical CP source for CKM, PMNS and Leptogenesis

We propose a simple model for the spontaneous CP violation based on $SU(2)_{L}\times U(1)_{Y}\times A_{4}\times CP\times Z_{2}$ 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 $A_{4}$-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 $θ_{13}\simeq9^{\circ}$ and two large mixing angles $θ_{12}, θ_{23}$. 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 $ξ\simeq120^{\circ}$, the quarks lead to the correct CKM CP-phase corresponding to $δ^{q}_{CP}\simeq67^{\circ}$, while the leptons with the measured value of $θ_{13}$ favor $δ_{CP}=$, $|θ_{23}-45^{\circ}|\rightarrow0$ for normal mass hierarchy and $δ_{CP}=$, $|θ_{23}-45^{\circ}|\rightarrow5^{\circ}$ 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.