HEP In the literature: open

Why is the QCD $\theta$ angle smaller than $1e-10$?

In plain words

The strong-force angle $\theta$ could have any value up to about 3, yet the neutron's electric dipole moment shows it is below $1e-10$. No reason for this is known.

Precise statement

The physical parameter $\theta_{\mathrm{bar}} = \theta - \arg \det(M_{q})$ induces $d_{n} \sim 1e-16\ \theta_{\mathrm{bar}}\ e\ \mathrm{cm}$; the PSI bound $\mid d_{n}\mid < 1.8e-26\ e\ \mathrm{cm}$ (90 percent CL, 2020) gives $\mid\theta_{\mathrm{bar}}\mid < \sim 1e-10$. An answer is a mechanism (Peccei-Quinn axion, massless up quark, spontaneous CP or P violation such as Nelson-Barr) consistent with lattice QCD and flavor data.

What would settle it

Detection of the QCD axion with the predicted mass-coupling relation, or a confirmed alternative such as a nonzero measured $d_n$ with the pattern predicted by a Nelson-Barr model.

Status in the literature

Lattice QCD (2010s to 2020s) excludes $m_{u} = 0$, removing the massless up quark solution.