$$Q_{6}$$ Q 6 as the flavor symmetry in a non-minimal SUSY $$SU(5)$$ S U ( 5 ) model

Abstract

We present a non-minimal renormalizable SUSY $$SU(5)$$ model, with extended Higgs sector and right-handed neutrinos, where the flavor sector exhibits a $$Q_{6}$$ flavor symmetry. We analyzed the simplest version of this model, in which R-parity is conserved and the right-handed neutrino masses in the flavor doublet are considered with and without degeneracy. 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 ( $$\theta ^{\ell ^{\mathrm{th}}}_{13} \sim 3.38^{\circ } $$ ). This value constitutes a lower bound for $$\theta _{13}$$ in the general case. We also find the range of the values for the neutrino masses in each case.