A 3-3-1 model with right-handed neutrinos based on the $\Delta\left(27\right)$ family symmetry

TL;DR

This paper introduces a novel extension of the 3-3-1 model with right-handed neutrinos, incorporating a $ ext{Delta}(27)$ family symmetry and additional discrete groups, successfully fitting fermion masses and mixing angles, especially for the inverted neutrino hierarchy.

Contribution

It presents the first multiscalar singlet extension of the 3-3-1 model with $ ext{Delta}(27)$ symmetry, achieving a minimal parameter fit to fermion data and exploring neutrino mass hierarchies.

Findings

Model fits 18 observables with only 14 parameters.

Predicted neutrinoless double beta decay effective mass: 22 meV.

Inverted hierarchy fits data well; normal hierarchy is disfavored.

Abstract

We present the first multiscalar singlet extension of the 3-3-1 model with right-handed neutrinos, based on the $\Delta \left( 27\right) $ family symmetry, supplemented by the $Z_{4}\otimes Z_{8}\otimes Z_{14}$ flavor group, consistent with current low energy fermion flavor data. In the model under consideration, the light active neutrino masses are generated from a double seesaw mechanism and the observed pattern of charged fermion masses and quark mixing angles is caused by the breaking of the $\Delta \left( 27\right) \otimes Z_{4}\otimes Z_{8}\otimes Z_{14}$ discrete group at very high energy. Our model has only 14 effective free parameters, which are fitted to reproduce the experimental values of the 18 physical observables in the quark and lepton sectors. The obtained physical observables for the quark sector agree with their experimental values, whereas those ones for the lepton sector also do, only for the inverted neutrino mass hierarchy. The normal neutrino mass hierarchy scenario of the model is disfavored by the neutrino oscillation experimental data. We find an effective Majorana neutrino mass parameter of neutrinoless double beta decay of $m_{\beta \beta }=$ 22 meV, a leptonic Dirac CP violating phase of $34^{\circ }$ and a Jarlskog invariant of about $10^{-2}$ for the inverted neutrino mass spectrum.