A viable axion from gauged flavor symmetries

We consider a string inspired non-supersymmetric extension of the standard model with gauged anomalous U(1) flavor symmetries. Consistency requires the Green-Schwarz mechanism to cancel mixed anomalies. The additional required scalars provide Stuckelberg masses for the $Z'$ particles associated to the gauged flavor symmetry, so they decouple at low energies. Our models also include a complex scalar field $\phi$ to generate Froggatt-Nielsen mass terms for light particles giving a partial solution to the fermion mass problem. A residual approximate (anomalous) global symmetry survives at low energies. The associated pseudo-Goldstone mode is the phase of the $\phi$ scalar field, and it becomes the dominant contribution to the physical axion. An effective field theory analysis that includes neutrino masses gives a prediction for the axion decay constant. We find a simple modeI where the axion decay constant is in the center of the allowed window.