Editing Strong CP problem (section)

==Proposed solutions==

The strong CP problem is solved automatically if one of the quarks is massless.<ref>{{cite journal|last1=Hook|first1=A.|date=2019-07-22|title=TASI Lectures on the Strong CP Problem and Axions|url=https://pos.sissa.it/333/004/pdf|journal=Proceedings of Science|volume=333|page=004 |doi=10.22323/1.333.0004|arxiv=1812.02669|s2cid=119073163 |access-date=2021-12-02 |doi-access=free }}</ref> In that case one can perform a set of chiral transformations on all the massive quark fields to get rid of their complex mass phases and then perform another chiral transformation on the massless quark field to eliminate the residual θ-term without also introducing a complex mass term for that field. This then gets rid of all CP violating terms in the theory. The problem with this solution is that all quarks are known to be massive from experimental matching with [[lattice QCD|lattice calculations]]. Even if one of the quarks was essentially massless to solve the problem, this would in itself just be another fine-tuning problem since there is nothing requiring a quark mass to take on such a small value.

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.