# Peccei–Quinn theory

This Peccei–Quinn symmetry is inexact because it is anomalously broken by QCD instantons. If there is a compensatory term canceling the QCD anomaly breaking term, the axion becomes an exactly massless Goldstone boson and θ is no longer fixed. The effective potential of the axion is the summed potential above the QCD scale; with the potential term induced by nonperturbative QCD effects. If the axion is fundamental, or emerges at a scale far higher than the QCD scale, then the dimension 5 axion coupling term $a \mathrm{Tr}[ F \wedge F ]$ is suppressed by $1/\Lambda$ where $\Lambda$ is the scale of the axion. Because of this, in order for θ to be so small at the minimum of the effective potential, the bare potential has to be many orders of magnitude smaller than the instanton induced potential, compounded by the $\Lambda$ factor. This requires quite a bit of reconciliation with an approximate global symmetry, for which there is no current explanation.