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 $1'$ 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 $\Delta m_{\rm atm}^2$ and $\Delta m_{\rm sol}^2$. 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.