Spontaneous CP Violation in $A_4$ Flavor Symmetry and Leptogenesis

Understand

We propose a simple renormalizable model for the spontaneous CP violation based on $SU(2)_{L}\times U(1)_{Y}\times A_{4}$ symmetry in a radiative seesaw mechanism, which can be guaranteed by an extra $Z_{2}$ symmetry.

• 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.
• We show that the spontaneously generated CP phase could become a natural source of leptogenesis, %CP violation for neutrino oscillation and leptogenesis, respectively.
• Then, and also investigate CP violation at low energies in the lepton sector and show how the CP phases in PMNS could be arisen through spontaneous symmetry breaking mechanism.