Taking Froggatt-Nielsen

Seriously

In the Froggatt-Nielsen solution to the flavor puzzle, a spontaneously broken global symmetry U(1)_H is postulated to distinguish between generations of fermions. The light Goldstone boson of this symmetry can be identified as a QCD axion, sometimes called the flaxion or axiflavon, solving the strong CP problem and the flavor puzzle at once. In this work, we consider UV completions in which U(1)_H is not imposed by hand, but arises either as an accidental symmetry of a gauged discrete Z_N, or as a gauge symmetry itself.

We study the properties of the axion in these contexts, in particular the extent to which the axion quality problem is alleviated by a symmetry that is already constrained by the flavor hierarchy, and how the low-energy axion couplings depend on the UV content. In the accidental symmetry case, we find that the U(1)_H charges needed to generate the observed mass hierarchy are already enough to forbid the lowest dimension symmetry-violating operators, so that a high-quality axion comes for free. In the gauge symmetry case, we invoke the Green-Schwarz mechanism to cancel gauge anomalies, which generally gives exponentially good quality to the axion. In addition, the physical axion in this scenario is generically no longer simply the CP-odd component of the flavon, but we find that the low-energy axion-photon coupling nonetheless retains the anomaly ratio of the flavon component.