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.

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

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