Flavour from the grand unification scale to the electroweak scale

Abstract

The flavour puzzle, the origin of the three families of quarks and leptons, with their observed pattern of masses and mixing, persist as one of the deepest enigmas unanswered by the Standard Model. The discovery of neutrino masses makes the flavour puzzle even more acute, but also provides new features like small neutrino masses and large lepton mixing. The smallness of neutrino masses may be explained with a type-I seesaw mechanism, which introduces at least two right-handed neutrinos, while a large lepton mixing may be an indication of an underlying non-Abelian family symmetry.

We extend these ideas into unified models of flavour based on S₄ × SO(10) and A₄ × SU(5), which are spontaneously broken to the minimal supersymmetric Standard Model. We give a dynamical origin to Yukawa couplings, leading to predictive mass matrix structures for both quarks and leptons and giving a natural understanding for the hierarchies between fermion masses. We also address the doublet-triplet splitting and the µ problem, proton decay and GUT breaking. We perform a χ² fit to available data in each of the models and we also find that in one of the S₄ × SO(10) models, the correct baryon asymmetry of the Universe can be reproduced through N₂ thermal leptogenesis. In the case of the A₄ × SU(5) model, we include extra dimensions whose orbifold geometry leads to the discrete symmetry. We also introduce the modular symmetry, which is used as a family symmetry, meaning that the Yukawa couplings in this model become modular forms.

Lastly, we present an extension of the Standard Model with a U(1)' symmetry and an additional fourth family of vector-like fermions to give a possible explanation for the recent R_K and R_K∗ anomalies. The Z ' gets induced couplings to the second family of left-handed lepton doublets and to the third family of left-handed quark doublets, accounting for the measured B-meson decay ratios while consistent with existing experimental constraints.

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