Rising through the ranks: flavor hierarchies from a gauged SU(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varv
We propose an economical model to address the mass hierarchies of quarks and charged leptons. The light generations of the left-handed fermions form doublets under an SU(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{SU}(2) $$\end{document} flavor symmetry, which is gauged. The generational hierarchies emerge from three independent rank-one contributions to the Yukawa matrices: one is a renormalizable contribution, the second is suppressed by a mass ratio, and the last by an additional loop factor. The model is renormalizable, features only a handful of new fields, and is remarkably simple compared to typical completions of gauged flavor symmetries or Froggatt–Nielsen. The model has a rich phenomenology, and we highlight promising signatures, especially in the context of K and B meson physics. This includes an interpretation of the latest B+→K+νν¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B^+ \rightarrow K^+ \nu \bar{\nu }$$\end{document} measurement from Belle II.