$Q_{6}$ As The Flavour Symmetry in a Non-minimal SUSY $SU(5)$ Model

TL;DR

This paper introduces a non-minimal SUSY SU(5) model with a $Q_6$ flavour symmetry, successfully reproducing quark and lepton mixing data, including neutrino oscillation parameters, with specific predictions for neutrino mass hierarchies.

Contribution

The paper develops a novel SUSY SU(5) model incorporating $Q_6$ symmetry, extended Higgs sector, and right-handed neutrinos, providing detailed mass matrices and mixing predictions.

Findings

Reproduces CKM mixing consistent with current data.

Achieves good agreement with neutrino mixing angles for both hierarchies.

Predicts a lower bound for the reactor angle $ heta_{13}$ around 3.38 degrees.

Abstract

We present a non-minimal renormalizable SUSY $SU(5)$~model, with extended Higgs sector and right-handed neutrinos, where the flavour sector exhibits a $Q_{6}$ flavour symmetry. We analysed the simplest version of this model, in which R-parity is conserved and the right-handed neutrino masses in the flavour doublet are considered with and without degeneration. We find the generic form of the mass matrices both in the quark and lepton sectors. We reproduce, according to current data, the mixing in the CKM matrix. In the leptonic sector, in the general case where the right-handed neutrino masses are not degenerate, we find that the values for the solar, atmospheric, and reactor mixing angles are in very good agreement with the experimental data, both for a normal and an inverted hierarchy. In the particular case where the right handed neutrinos masses are degenerate, the model predicts a strong inverted hierarchy spectrum and a sum rule among the neutrino masses. In this case the atmospheric and solar angles are in very good agreement with experimental data, and the reactor one is different from zero, albeit too small ($\theta^{\ell^{th}}_{13} \sim 3.38 $). This value constitues a lower bound for $\theta_{13}$ in the general case. We also find the range of values for the neutrino masses in each case.