Does chiral perturbation theory rule out QCD-based solutions to the strong CP problem?

Understand

The conventional view is that a solution of the strong CP problem lies beyond QCD.

• A strong argument supporting this view is that the chiral expansion shows that observables depend on theta (unless a quark mass is zero); this eliminates the possibility that theta is physically irrelevant and appears to necessitate an explanation beyond the standard model.
• However, scenarios that solve the strong CP problem exist that are consistent with known chiral behavior; in these, QCD becomes nonviable as a theory for nonzero theta.
• Such scenarios appear to be compatible with lattice studies of the topological susceptibility.