Fermion masses and mixings in a $U(1)_X$ model based on the $\Sigma(18)$ discrete symmetry

TL;DR

This paper presents a renormalizable $U(1)_X$ model incorporating the $oldsymbol{ ext{Sigma}(18)}$ discrete symmetry, successfully explaining fermion masses, mixings, and neutrino properties consistent with experimental data.

Contribution

It is the first to implement the $ ext{Sigma}(18)$ flavor symmetry in a renormalizable $U(1)_X$ model for fermion mass and mixing explanations.

Findings

Model fits fermion masses and mixing angles successfully.

Predicted neutrino effective mass parameters align with experimental limits.

Results are consistent with observed CP phases and mixing angles.

Abstract

We have built a renormalizable $U(1)_X$ model with a $\Sigma (18)\times Z_4$ symmetry, whose spontaneous breaking yields the observed SM fermion masses and fermionic mixing parameters. The tiny masses of the light active neutrinos are produced by the type I seesaw mechanism mediated by very heavy right handed Majorana neutrinos. To the best of our knowledge, this model is the first implementation of the $\Sigma (18)$ flavor symmetry in a renormalizable $U(1)_X$ model. Our model allows a successful fit for the SM fermion masses, fermionic mixing angles and CP phases for both quark and lepton sectors. The obtained values for the physical observables of both quark and lepton sectors are in accordance with the experimental data. We obtain an effective neutrino mass parameter of $\langle m_{ee}\rangle=1.51\times 10^{-3}\, \mathrm{eV}$ for normal ordering and $\langle m_{ee}\rangle =4.88\times 10^{-2} \, \mathrm{eV}$ for inverted ordering which are well consistent with the recent experimental limits on neutrinoless double beta decay.