Abstract
We analyze the structure of a recently proposed effective field theory (EFT) for the generation of quark and lepton mass ratios and mixing angles, based on the spontaneous breaking of an $SU(3)$ family gauge symmetry at a high scale $F$. We classify the Yukawa operators necessary to seed the masses, making use of the continuous global symmetries that they preserve. One global $U(1)$, in addition to baryon number and electroweak hypercharge, remains unbroken after the inclusion of all operators required by standard model fermion phenomenology. An associated vacuum symmetry insures the vanishing of the first-family quark and charged-lepton masses in the absence of the family gauge interaction. If this $U(1)$ symmetry is taken to be exact in the EFT, broken explicitly by only the QCD-induced anomaly, and if the breaking scale $F$ is taken to lie in the range ${10}^{9}--{10}^{12}\text{ }\text{ }\mathrm{GeV}$, then the associated Nambu-Goldstone boson is a potential QCD axion.
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