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

TL;DR

This paper revisits the $A_4$ lepton model incorporating a new flavon to better fit recent neutrino oscillation data, predicting specific CP phases and neutrino mass sums testable by future experiments.

Contribution

It introduces a new flavon $ exteta$ in the $A_4$ model, providing improved predictions for neutrino mixing angles and CP phases consistent with NuFIT 3.2 data.

Findings

Predicts $ heta_{12}$ around NuFIT 3.2 best fit

Forecasts Dirac CP phase $| extdelta_{CP}|=50^ extdegree-120^ extdegree$

Neutrino mass sum > 90 meV for best fit $ heta_{23}$

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.