Why is the QCD $\theta$ angle smaller than $10^{-10}$?
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 $10^{-10}$. No reason for this is known.
Precise statement
The physical parameter $\theta_{\mathrm{bar}} = \theta - \arg \det(M_{q})$ induces $d_{n} \sim 10^{-16}\ \theta_{\mathrm{bar}}\ e\ \mathrm{cm}$; the PSI bound $\mid d_{n}\mid < 1.8 \times 10^{-26}\ e\ \mathrm{cm}$ (90 percent CL, 2020) gives $\mid\theta_{\mathrm{bar}}\mid < \sim 10^{-10}$. 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.
Problems built on this one
Special cases
- How is the Peccei-Quinn symmetry protected from gravitational breaking? · open
- Does the QCD axion exist? · open
Results
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