Flavour in supersymmetry: horizontal symmetries or wave function renormalisation

TL;DR

This paper compares two supersymmetric flavor models, showing they predict similar fermion masses but differ in FCNC suppression, and demonstrates how unification constraints align their anomaly conditions, with an extra-dimensional model for leptonic FCNC suppression.

Contribution

It reveals the equivalence of FN and extra-dimensional models in fermion mass predictions and clarifies the impact of unification constraints on their anomaly conditions.

Findings

Both models predict similar fermion mass matrices.

Extra-dimensional models provide stronger FCNC suppression.

Unification conditions align anomaly constraints in both models.

Abstract

We compare theoretical and experimental predictions of two main classes of models addressing fermion mass hierarchies and flavour changing neutral currents (FCNC) effects in supersymmetry: Froggatt-Nielsen (FN) U(1) gauged flavour models and Nelson-Strassler/extra dimensional models with hierarchical wave functions for the families. We show that whereas the two lead to identical predictions in the fermion mass matrices, the second class generates a stronger suppression of FCNC effects. We prove that, whereas at first sight the FN setup is more constrained due to anomaly cancelation conditions, imposing unification of gauge couplings in the second setup generates conditions which precisely match the mixed anomaly constraints in the FN setup. Finally, we provide an economical extra dimensional realisation of the hierarchical wave functions scenario in which the leptonic FCNC can be efficiently suppressed due to the strong coupling (CFT) origin of the electron mass.