The neutron CP problem is a disparity between the Standard Model view of particle physics, and theoretical aspects of QCD (Quantum Chromo Dynamics).
The neutron (as the name implies) has a neutral electrical 'charge', because the three quarks from which it is formed have fractional positive and negative charges which add to exactly zero. No experimental measurements to-date have shown anything other than a non-zero charge. This is in conflict with the highly-robust QCD theory, which insists that Charge and Parity (CP) would not be zero under all conditions.
A theoretical particle the Axion, is proposed to resolve the problem. It has never been detected.
Further reading MIT
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