Controlled fermion mixing and FCNCs in a $\Delta(27)$ 3+1 Higgs Doublet Model

TL;DR

This paper introduces a 3+1 Higgs Doublet Model with $\Delta(27)$ symmetry that explains fermion masses, mixings, neutrino masses, and dark matter, while predicting observable flavor-changing processes.

Contribution

The paper develops a novel 3+1 Higgs Doublet Model with discrete symmetries that accounts for fermion hierarchies, neutrino oscillations, and dark matter, with testable flavor-changing predictions.

Findings

Predicts neutrino effective Majorana mass between 3 and 18 meV.

Forecasts flavor-changing neutral currents within experimental reach.

Provides a consistent framework for fermion masses, mixings, and dark matter.

Abstract

We propose a 3+1 Higgs Doublet Model based on the $\Delta(27)$ family symmetry supplemented by several auxiliary cyclic symmetries leading to viable Yukawa textures for the Standard Model fermions, consistent with the observed pattern of fermion masses and mixings. The charged fermion mass hierarchy and the quark mixing pattern is generated by the spontaneous breaking of the discrete symmetries due to flavons that act as Froggatt-Nielsen fields. The tiny neutrino masses arise from a radiative seesaw mechanism at one loop level, thanks to a preserved $Z_2^{\left( 1\right)}$ discrete symmetry, which also leads to stable scalar and fermionic dark matter candidates. The leptonic sector features the predictive cobimaximal mixing pattern, consistent with the experimental data from neutrino oscillations. For the scenario of normal neutrino mass hierarchy, the model predicts an effective Majorana neutrino mass parameter in the range $3$~meV$\lesssim m_{\beta\beta}\lesssim$ $18$ meV, which is within the declared range of sensitivity of modern experiments. The model predicts Flavour Changing Neutral Currents which constrain the model, for instance Kaon mixing and $\mu \to e$ nuclear conversion processes, the latter which are found to be within the reach of the forthcoming experiments.