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Description
The Peccei–Quinn (PQ) mechanism is a prominent solution to the strong CP problem. However, it faces the axion quality problem: higher-dimensional, Planck-suppressed operators which explicitly break PQ symmetry can reintroduce the effective QCD theta angle. In composite axion models, where strong dynamics at high energies break PQ symmetry at a dynamically generated scale, the Peccei–Quinn scale arises naturally through dimensional transmutation, and certain constructions also address this quality problem. This setup, however, raises a further question: hidden interactions distinct from QCD may also generate instanton effects, which could appear to give additional contributions to the axion mass. We demonstrate that while these small instantons enhance the axion mass in a toy model, they do not contribute to the axion mass in a more complete explicit composite axion model.