Abstract
We consider a flavor model based on the ${A}_{4}$ modular group to account for both lepton and quark parameters (masses and mixing). The inverse seesaw mechanism is considered to produce the light neutrino masses. Lepton masses and mixing are obtained in terms of Yukawa coupling ratios and values of the modulus $\ensuremath{\tau}$ nearby some fixed points for inverted neutrino mass hierarchy. The quark masses and mixing are arisen at the same $\ensuremath{\tau}$ values used in inverted neutrino mass hierarchy and are in agreement with the recent data.
Highlights
The smallness of the neutrino mass is usually explained via the type-I seesaw mechanism [1] which is the common scenario used to account for neutrino masses and mixing
We introduce a model based on modular A4 symmetry to account for masses and mixing for leptons and quarks
We built an A4 modular invariance model to account for both lepton and quark masses and mixing
Summary
The smallness of the neutrino mass is usually explained via the type-I seesaw mechanism [1] which is the common scenario used to account for neutrino masses and mixing. The flavor symmetry was proposed to account for many aspects such as the differences in mixing and mass hierarchy for lepton and quark sectors. Several models based on discrete symmetries were proposed to account for fermion masses and mixing (see [6]) Most of these models suffer from considerations of a large number of scalars (flavons), considering extra ZN symmetries and/or finetuning to account for experimental data. We introduce a model based on modular A4 symmetry to account for masses and mixing for leptons and quarks. We give an introduction to the modular groups and how to use them as flavor symmetries, we explain our A4 model in the lepton sector, and we study the quark masses and mixing
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