Revisiting $A_4$ model for leptons in light of NuFIT 3.2

Abstract

We revisit the $A_4$ model for leptons in light of new result of NuFIT 3.2. We introduce a new flavon $\eta$ transforming as $A_4$ singlet $1^{\prime }$ or $1"$ which couples to both charged leptons and neutrinos in next-leading order operators. The model consists of the five parameters: the lightest neutrino mass $m_1$, the vacuum expectation value of $\eta$ and three CP violating phases after inputting the experimental values of $\Delta m_{\mathrm{atm}}^2$ and $\Delta m_{\mathrm{sol}}^2$. The model with the $1"$ singlet flavon gives the prediction of ${\sin }^2{\theta }_{12}$ around the best fit of NuFIT 3.2 while keeping near the maximal mixing of ${\theta }_{23}$. Inputting the experimental mixing angles with the $1\sigma$ error-bar, the Dirac CP violating phase is clearly predicted to be $|{\delta }_{\text{CP}}|=50^{\circ }-120^{\circ }$, which will be tested by the precise observed value in the future. In order to get the best fit value ${\sin }^2{\theta }_{23}=0.538$, the sum of three neutrino masses is predicted to be larger than $90$meV. The cosmological observation for the sum of neutrino masses will also provide a crucial test of our predictions. It is remarked that the model is consistent with the experimental data only for the normal hierarchy of neutrino masses.

Comments: 21 pages, 14 figures