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

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.

Comments: 18 pages, 7 figures, 3 tables