CP violations in a predictive A4 symmetry model

Abstract

Abstract We will investigate numerically a seesaw model with $A_4$ flavor symmetry to find allowed regions satisfying the current experimental neutrino oscillation data, then use them to predict physical consequences. Namely, the lightest active neutrino mass is of the order of $\mathcal{O}(10^{-2})$ eV. The effective neutrino mass $|\langle m\rangle|$ associated with neutrinoless double beta decay is in the range $[0.002 \,\mathrm{eV},0.038\,\mathrm{eV}]$ and $[0.048\,\mathrm{eV},0.058\,\mathrm{eV}]$, corresponding to the normal and the inverted hierarchy schemes, respectively. Other relations among relevant physical quantities are shown, so that they can be determined if some of them are confirmed experimentally. The recent data of the baryon asymmetry of the Universe ($\eta_B$) can be explained via leptogenesis caused by the effect of the renormalization group evolution on the Dirac Yukawa couplings, provided the right-handed neutrino mass scale $M_0$ ranges from $\mathcal{O}(10^8)$ GeV to $\mathcal{O}(10^{12})$ GeV for $\tan\beta =3$. This allowed $M_0$ range is different from the scale of $\mathcal{O}(10^{13})$ GeV for other effects that also generate a consistent $\eta_B$ from leptogenesis. The branching ratio of the decay $ \mu \rightarrow\,e\gamma$ may reach future experimental sensitivity for very light values of $M_0$. Hence, it will be inconsistent with the $M_0$ range predicted from the $\eta_B$ data whenever this decay is detected experimentally.