Axion Quality from Exact Proton Stability

A discrete, anomaly-free Z 9 gauge symmetry may persist to the deep infrared, exactly forbidding proton decay. This Z 9 can emerge from Higgsing a lepton-flavour non-universal U(1) X that generates realistic neutrino masses and mixings through a high-scale seesaw and predicts an additional light Goldstone. Adding an anomaly-free chiral heavy-quark sector turns this mode into the QCD axion. The same selection rules that ban proton decay also forbid PQ-violating operators below a suitably high dimension, d PQ 10, including operators involving the heavy quarks that radiatively match onto the scalar potential. We construct explicit models viable when PQ breaking occurs before or after inflation; in the latter case, avoiding stable heavy relics and eliminating the string-wall network tightly constrain the heavy-quark spectrum. We identify restricted regions of parameter space where thermal leptogenesis remains viable and, for d PQ at least13, can coexist with a high-quality axion constituting all of the dark matter.