Does a nonzero $\theta$ produce observable CP violation in QCD?
In plain words
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 statement
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.
What would settle it
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 $\theta$.
Status in the literature
Unverified 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.