Abstract
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-overline{K} mixing, μ → e conversion, etc., where the present bounds restrict the masses of vector-like fermions to be above mathcal{O} (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.
Highlights
U(1)FN, spontaneously broken by the vacuum expectation value of the flavon field, φ
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
How can one uncover experimentally whether any of the above anomaly free FN models is realized in Nature? The immediate answer is to search for new contributions to Flavor Changing Neutral Currents (FCNCs), e.g., B − B, K − K, mixing, μ → eγ, etc
Summary
We discuss the coupled FN chains, which are obtained in the case of a single horizontal U(1)FN, see figure 4. In the coupled case the zero mode overlaps with the zero node are described by 3 × 3 matrices, V0d(Rj),,u0R(i), due to the inter-generational mixing in the chains. Due to additional flavour mixing on each node the parametric relations are even more approximate compared to the case of decoupled of FN chains. We show this by performing a numerical scan. Since the expressions for SM quark masses effectively involve multiplications of a number of random matrices, eq (3.6), part of the hierarchy comes from the properties of random matrix multiplications [30] (see section 4)
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