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Level C · Reviewed Hard Theoretical physics P-strong-cp-problem

The strong CP problem

Explain why the CP-violating θ parameter of QCD is experimentally smaller than about 10^-10 when nothing in the Standard Model requires it to be small.

Status (as of 2026-10-03): Open. The neutron EDM bound implies θ̄ ≲ 10⁻¹⁰; the axion and other solutions remain unconfirmed.
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Cite 
@misc{cairn-strong-cp-problem,
  title        = {The strong CP problem},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/strong-cp-problem}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-11-12}
}

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What a result looks like: C-16, a newcomer working with an AI model found C(85,24,3) ≤ 76 (previous best 77), and a computer verified it within minutes. A documented dead end counts too.

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The problem

The question. QCD admits a CP-violating term with angle θ̄ that could take any value between 0 and 2π. Its only known effect at low energy, a neutron electric dipole moment, is not observed. Why is θ̄ so small?

Known status. The PSI nEDM collaboration (Abel et al., PRL 2020) measured d_n = (0.0 ± 1.1_stat ± 0.2_sys) × 10^-26 e·cm, giving the limit |d_n| < 1.8 × 10^-26 e·cm, which translates into θ̄ below roughly 10^-10. Proposed explanations include the Peccei–Quinn mechanism with an axion, a massless up quark (disfavoured by lattice determinations of the quark masses), and Nelson–Barr-type models with spontaneous CP violation. Hook's TASI lectures (2018) review these options and their difficulties (e.g. the axion quality problem).

What counts as progress

  • Syntheses that list the solution classes with their assumptions, their open theoretical issues and the experimental observables that would confirm or rule out each one.
  • Careful calculations of specific model consequences (e.g. radiative corrections to θ̄ in a Nelson–Barr model, quality requirements for a Peccei–Quinn symmetry) with explicit assumptions; symbolic or numerical parts should be reproducible.
  • Documented negative results: "model class X regenerates θ̄ above 10^-10 at loop order Y unless Z".

How it is checked. Expert and agent review of the arguments against the cited literature; calculations are re-derived or re-run from supplied notebooks.