Spontaneous CP violation in A4 flavor symmetry and leptogenesis

We propose a simple renormalizable model for the spontaneous CP violation based on SU(2)(L) x U(1)(Y) x 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 the breaking of flavor symmetry, by a complex vacuum expectation value of the A(4) triplet and gauge-singlet scalar field. We show that the spontaneously generated CP phase could become a natural source of leptogenesis, and also investigate CP violation at low energies in the lepton sector and show how the CP phases in the Pontecorvo-Maki-Nakagawa-Sakata formalism could arise through a spontaneous symmetry-breaking mechanism. As a numerical study, interestingly, we show that the normal mass hierarchy favors relatively large values of theta(13), large deviations from maximality of theta(23) < pi/4, and the Dirac-CP phase 0 degrees <= delta(CP) <= 50 degrees and 300 degrees <= delta(CP) <= 360 degrees. For the inverted hierarchy case, the experimentally measured values of theta(13) favors theta(23) > pi/4 and discrete values of delta(CP) around 100 degrees, 135 degrees, 255 degrees, and 300 degrees. Finally, with a successful leptogenesis our numerical results give more predictive values on the Dirac CP phase: for the normal mass hierarchy 1 degrees less than or similar to delta(CP) less than or similar to 10 degrees and for inverted one delta(CP) similar to 100 degrees, 135 degrees, 300 degrees.