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 that are consistent with known chiral behavior exist; in these, QCD becomes nonviable as a theory for nonzero theta. Such scenarios appear to be compatible with lattice studies of the topological susceptibility.

• Received 26 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.094007

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Published by the American Physical Society