Abstract
We study UV-complete Froggatt-Nielsen-like models for the generation of mass and mixing hierarchies, assuming that the integrated heavy fields are chiral with respect to an abelian Froggatt-Nielsen symmetry. It modifies the mixed anomalies with respect to the Standard Model gauge group, which opens up the possibility to gauge the Froggatt-Nielsen symmetry without the need to introduce additional spectator fermions, while keeping mass matrices usually associated to anomalous flavour symmetries. We give specific examples where this happens, and we study the flavourful axion which arises from an accidental Peccei-Quinn symmetry in some of those models. Such an axion is typically more coupled to matter than in models with spectator fermions.
Highlights
It modifies the mixed anomalies with respect to the Standard Model gauge group, which opens up the possibility to gauge the Froggatt-Nielsen symmetry without the need to introduce additional spectator fermions, while keeping mass matrices usually associated to anomalous flavour symmetries
We give specific examples where this happens, and we study the flavourful axion which arises from an accidental Peccei-Quinn symmetry in some of those models
We studied the gauging of a horizontal abelian symmetry generating the Froggatt-Nielsen mechanism, when the heavy fields in the UV completion of the mechanism are chiral with respect to this family symmetry
Summary
The flavour structure of the SM is a consequence of the number of families and of the structure of the Yukawa sector:. Where the hXij are order one numbers, M is a high scale of new physics, for instance the mass scale of heavy fields which mix with the standard model ones (see section 3.1 for explicit examples) or the Planck mass if those higher-dimensional operators are generated by supergravity, and the nXij are the U(1)FN charges of the MSSM Yukawa couplings in units of the charge of φ. We understand that (2.5) introduces a U(1)FN which has mixed anomalies with the SM gauge group GSM This enables one to interpret the phase of φ as a flavourful QCD axion when U(1)FN is global [6,7,8,9], with couplings to gauge fields and SM fermions which are fully determined by the mass matrices. Let us point out in passing that, due to the phenomenological interest in additional abelian factors to the SM gauge group, there are recent works about anomaly cancellation in such models with a general focus, see e.g. [67,68,69,70]
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