Rising through the ranks: flavor hierarchies from a gauged $${\varvec{\mathrm {SU(2)}}}$$ 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 $$ \textrm{SU}(2) $$ 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, 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 $$B^+ \rightarrow K^+ \nu \bar{\nu }$$ B + → K + ν ν ¯ measurement from Belle II.