Abstract
The flavour problem of the Standard Model can be addressed through the Froggatt-Nielsen (FN) mechanism. In this work, we develop an approach to the study of FN textures building a direct link between FN-charge assignments and the measured masses and mixing angles via unitary transformations in flavour space. We specifically focus on the quark sector to identify the most economic FN models able to provide a dynamical and natural understanding of the flavour puzzle. Remarkably, we find viable FN textures, involving charges under the horizontal symmetry that do not exceed one in absolute value (in units of the flavon charge). Within our approach, we also explore the degree of tuning of FN models in solving the flavour problem via a measure analogous to the Barbieri-Giudice one. We find that most of the solutions do not involve peculiar cancellations in flavour space.
Highlights
Fields whose vacuum expectation value (VEV) yields spontaneous symmetry breaking of a large enough symmetry group, subgroup of GF, responsible of the low-energy fermion mass spectrum and the mixing-angle patterns
According to the FN mechanism, the SM flavour puzzle is addressed by the introduction of an Abelian flavour symmetry U(1)X, spontaneously broken by the VEV vφ of a single flavon field φ; the flavour structure observed at low energy arises once heavy new degrees of freedom — the FN messengers [50] — properly charged under the horizontal symmetry broken by the flavon, have been integrated out at the high-energy scale Λ > vφ
We will work within an effective field theory (EFT) approach, and as such we will leave unspecified the details of the UV dynamics that will cure any gauge anomaly naively present in the X charge assignments considered at low energy [73]
Summary
Fields whose vacuum expectation value (VEV) yields spontaneous symmetry breaking of a large enough (discrete or continuous) symmetry group, subgroup of GF , responsible of the low-energy fermion mass spectrum and the mixing-angle patterns. According to the FN mechanism, the SM flavour puzzle is addressed by the introduction of an Abelian flavour symmetry U(1)X , spontaneously broken by the VEV vφ of a single flavon field φ; the flavour structure observed at low energy arises once heavy new degrees of freedom — the FN messengers [50] — properly charged under the horizontal symmetry broken by the flavon, have been integrated out at the high-energy scale Λ > vφ Such a simple setup has recently gained particular attention in the context of a possible flavour window on the QCD axion and on axion-like particles [51,52,53,54,55]; for collider programs dedicated to the flavour problem [56]; for the vacuum stability of the Higgs potential [57]; in connection to the present tensions in B physics [58,59,60]; in relation to the clockwork mechanism [61, 62] for flavour via an inverted FN construction [63,64,65]; as an unorthodox bridge to the fundamental questions in the physics of the Early Universe [66,67,68,69,70,71,72]. The novelty is to start from a basis where inputs are the precise measurements of fermion masses and mixing angles, an exploit unitary rotations in GF to map SM fields into eigenstates of the new FN interactions;
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