Modular $A_4$ invariance and neutrino mixing

TL;DR

This paper explores how modular $A_4$ symmetry constrains neutrino mass models without flavons, predicting specific ranges for mixing angles and CP phases, and analyzing their compatibility with experimental data.

Contribution

It introduces a modular symmetry-based approach to neutrino mass modeling, avoiding flavons, and classifies models under different neutrino mass hierarchies with testable predictions.

Findings

Normal hierarchy models fit oscillation and cosmological data.

Predicted neutrinoless double beta decay effective mass is around 22 meV.

Inverted hierarchy favors Dirac neutrino models.

Abstract

We study the phenomenological implications of the modular symmetry $\Gamma(3) \simeq A_4$ of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus $\tau$, which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with $A_4$ symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted $\sin^2\theta_{23}$ is restricted to be larger than $0.54$ and $\delta_{CP}=\pm (50^{\circ}\mbox{--}180^{\circ})$. Since the correlation of $\sin^2\theta_{23}$ and $\delta_{CP}$ is sharp, the prediction is testable in the future. It is remarkable that the effective mass $m_{ee}$ of the neutrinoless double beta decay is around $22$\,meV while the sum of neutrino masses is predicted to be $145$\,meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.