A dynamical CP source for CKM, PMNS and Leptogenesis

TL;DR

This paper introduces a unified model with spontaneous CP violation that explains quark and lepton mixing, CP phases, leptogenesis, and addresses the strong CP problem within a flavor symmetry framework.

Contribution

It presents a novel high-energy spontaneous CP violation model based on A4 symmetry, linking quark and lepton CP phases and providing solutions for leptogenesis and the strong CP problem.

Findings

Reproduces observed CKM CP phase around 67°

Predicts leptonic CP phase consistent with measurements

Links low-energy phenomenology with leptogenesis scenarios

Abstract

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 $\theta_{13}\simeq9^{\circ}$ and two large mixing angles $\theta_{12}, \theta_{23}$. We show that the spontaneously generated CP phase "$\xi$" 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 $\xi\simeq120^{\circ}$, the quarks lead to the correct CKM CP-phase corresponding to $\delta^{q}_{CP}\simeq67^{\circ}$, while the leptons with the measured value of $\theta_{13}$ favor $\delta_{CP}=$, $|\theta_{23}-45^{\circ}|\rightarrow0$ for normal mass hierarchy and $\delta_{CP}=$, $|\theta_{23}-45^{\circ}|\rightarrow5^{\circ}$ 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.