Rising Through the Ranks: Flavor Hierarchies from a Gauged SU(2) Symmetry

TL;DR

This paper introduces a simple, renormalizable model with a gauged SU(2) flavor symmetry to explain quark and lepton mass hierarchies, predicting observable effects in meson physics and aligning with recent Belle II results.

Contribution

It presents a minimal, renormalizable model with a gauged SU(2) flavor symmetry that naturally generates fermion mass hierarchies through three independent contributions.

Findings

Model explains fermion mass hierarchies with minimal new fields.

Predicts distinctive signatures in K and B meson processes.

Aligns with recent Belle II measurements of B+ to K+ nu nu

Abstract

We propose an economical model to address the mass hierarchies of quarks and charged leptons. The light generations of the left-handed fermions form doublets under an $ \mathrm{SU}(2) $ flavor symmetry, which is gauged. The generational hierarchies emerge from three independent rank-one contributions to the Yukawa matrices: one is a renormalizable contribution, the second is suppressed by a mass ratio, and the last by an additional loop factor. The model is renormalizable and features only a handful of new fields and is remarkably simple compared to typical completions of gauged flavor symmetries or Froggatt-Nielsen. The model has a rich phenomenology, and we highlight promising signatures, especially in the context of $K$ and $B$ meson physics. This includes an interpretation of the latest $B^+ \to K^+ \nu \bar \nu$ measurement from Belle II.