Anomaly free Froggatt-Nielsen models of flavor

We introduce two anomaly free versions of Froggatt-Nielsen (FN) models, based on either GFN = U(1)3 or GFN = U(1) horizontal symmetries, that generate the SM quark and lepton flavor structures. The structure of these “inverted” FN models is motivated by the clockwork mechanism: the chiral fields, singlets under GFN, are supplemented by chains of vector-like fermions charged under GFN. Unlike the traditional FN models the hierarchy of quark and lepton masses is obtained as an expansion in M/〈ϕ〉, where M is the typical vector-like fermion mass, and 〈ϕ〉 the flavon vacuum expectation value. The models can be searched for through deviations in flavor observables such as K−K¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K-\overline{K} $$\end{document} mixing, μ → e conversion, etc., where the present bounds restrict the masses of vector-like fermions to be above O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(107 GeV). If GFN is gauged, the models can also be probed by searching for the flavorful Z′ gauge bosons. In principle, the Z′s can be very light, and can be searched for using precision flavor, astrophysics, and beam dump experiments.