Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models

To explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine-tuning of prefactors. Fitting with quark and lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic $CP$ violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.

Figure 1

Scatter plots of the $CP$ $\delta$ vs ${\sin }^2{\theta }_{23}$ for the NH models in (a) and for the IH models in (b). The symbols label the sets of models listed in Table 2 for both normal and inverted hierarchy.

Figure 2

Effective mass for neutrinoless double beta decay vs the lightest neutrino mass for both NH and IH models. The symbols for the models are the same as in Fig. 1.