Revision 1

Accepted · first revision · record

Title: Does a nonzero $\theta$ produce observable CP violation in QCD?
Plain: A few theorists argue that, done carefully, the strong-force theory never produces the forbidden effects, so there is no puzzle. Most others say the standard reasoning holds, and the disagreement has not been settled.
Precise: Determine whether CP-odd observables in QCD ($d_{n}$, the $\theta$ dependence of the vacuum energy and of hadron matrix elements) depend on $\theta_{\mathrm{bar}}$ when the infinite-volume limit and the sum over topological sectors are taken in the order argued by Ai, Cruz, Garbrecht and Tamarit (arXiv:2001.07152). An answer is a proof or a lattice computation showing $d_{n}$ proportional to $\theta_{\mathrm{bar}}$, or the opposite.
Settled by: A rigorous treatment of the $\theta$-dependence of CP-odd correlators in QCD, cross-checked by lattice computations of $d_n$ at imaginary or small real $\theta$.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: contested
Status note: Benabou, Hook, Manzari, Murayama and Safdi (arXiv:2510.18951, 2025) and Khoze (arXiv:2512.06827, 2025) argue $\theta$ is physical; Ai, Garbrecht and Tamarit replied (arXiv:2511.04216, 2025) and the exchange continues in 2026 (arXiv:2601.18248); the majority view keeps the strong CP problem.
Posed since: 2020