Anomaly free Froggatt-Nielsen models of flavor

Abstract

We introduce two anomaly free versions of Froggatt-Nielsen (FN) models, based on either $G_{\mathrm{FN}}=U(1{)}^3$ or $G_{\mathrm{FN}}=U(1)$ 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 $G_{\mathrm{FN}}$, are supplemented by chains of vector-like fermions charged under $G_{\mathrm{FN}}$. Unlike the traditional FN models the hierarchy of quark and lepton masses is obtained as an expansion in $M/⟨\varphi ⟩$, where $M$ is the typical vector-like fermion mass, and $⟨\varphi ⟩$ the flavon vacuum expectation value. The models can be searched for through deviations in flavor observables such as $K-\bar{K}$ mixing, $\mu \to e$ conversion, etc., where the present bounds restrict the masses of vector-like fermions to be above $\mathcal{O}(10^7\mathrm{GeV})$. If $G_{\mathrm{FN}}$ is gauged, the models can also be probed by searching for the flavorful $Z^{\prime }$ gauge bosons. In principle, the $Z^{\prime }$s can be very light, and can be searched for using precision flavor, astrophysics, and beam dump experiments.

Comments: 50 pages, 20 figures, discussion of rare meson decay bounds amended, Figs. 13, 14 and 18 updated