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The most popular solution to the problem is through the Peccei–Quinn mechanism.<ref>{{Cite book|author=Peccei, R. D. |year=2008 |chapter=The Strong CP Problem and Axions |title=Axions: Theory, Cosmology, and Experimental Searches |editor1-last=Kuster |editor1-first=M. |editor2-last=Raffelt |editor2-first=G. |editor3-last=Beltrán |editor3-first=B. |series=Lecture Notes in Physics |volume=741 |pages=3–17 |arxiv=hep-ph/0607268 |doi=10.1007/978-3-540-73518-2_1 |isbn=978-3-540-73517-5|s2cid=119482294 }}</ref> This introduces a new global [[anomaly (physics)|anomalous]] symmetry which is then [[spontaneous symmetry breaking|spontaneously broken]] at low energies, giving rise to a [[Goldstone boson|pseudo-Goldstone]] boson called an axion. The axion ground state dynamically forces the theory to be CP-symmetric by setting <math>\bar \theta = 0</math>. Axions are also considered viable candidates for [[dark matter]] and axion-like particles are also predicted by [[string theory]].
Other less popular proposed solutions exist such as Nelson–Barr models.<ref>{{cite journal|last=Nelson|first=A.|date=1984-03-15|title=Naturally weak CP violation|url=https://dx.doi.org/10.1016/0370-2693%2884%2992025-2|journal=Physics Letters B|volume=136|issue=5,6|pages=387–391|doi=10.1016/0370-2693(84)92025-2|pmid=|arxiv=|bibcode=1984PhLB..136..387N |s2cid=|access-date=2021-12-02|url-access=subscription}}</ref><ref>{{cite journal|last=Barr|first=S. M.|date=1984-04-18|title=Solving the Strong CP Problem without the Peccei–Quinn Symmetry|url=https://link.aps.org/doi/10.1103/PhysRevLett.53.329|journal=Phys. Rev. Lett.|volume=53|issue=4|pages=329–332|doi=10.1103/PhysRevLett.53.329|pmid=|arxiv=|bibcode=1984PhRvL..53..329B |s2cid=|access-date=2021-12-02|url-access=subscription}}</ref> These set <math>\bar \theta = 0</math> at some high energy scale where CP-symmetry is exact but the symmetry is then spontaneously broken. The Nelson–Barr mechanism is a way of explaining why <math>\bar \theta</math> remains small at low energies while the CP breaking phase in the [[Cabibbo–Kobayashi–Maskawa matrix|CKM matrix]] is large.
==See also==
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