The Peccei-Quinn symmetry, $U(1)_{PQ}$, is proposed as a flavor symmetry, whereby the mass hierarchies
of the fermions can be explained through the Froggatt-Nielsen mechanism, while at the same time solving the strong CP problem.
At leading order, the quark mass matrices obtain a Nearest-Neighbor-Interaction structure, whereas the neutrino mass matrix has an $A_2$ structure.
Phenomenological a
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