Strong CP problem: Difference between revisions

Revision as of 20:18, 2 December 2021

Revision as of 08:40, 3 December 2021

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CP-symmetry states that physics should be unchanged if particles were swapped with their antiparticles and then left-handed and right-handed particles were also interchanged. This corresponds to performing a charge conjugation transformation and then a parity transformation. The symmetry is known to be broken in the [[Standard Model]] through [[weak interaction|weak interactions]], but it is generically also expect it to be broken through [[strong interaction|strong interactions]] which govern [[quantum chromodynamics]] (QCD), something that has not been found.

To illustrate how the CP violation can come about in QCD, consider a [[Yang-Mills theory]] with a single massive [[quark]].<ref>{{cite conference|url=https://www.osti.gov/servlets/purl/6260191|title=A Brief Introduction to the Strong CP Problem|last1=Wu|first1=Dan-di|date=1991|publisher=|___location=Austin, Texas, United States|id=SSCL-548}}</ref> The most general mass term possible for the quark is a complex mass written as <math>m e^{i\theta' \gamma_5}</math> for some arbitrary phase <math>\theta'</math>. In that case the [[Lagrangian]]{{dn|date=December 2021}} describing the theory consists of four terms

:<math>

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The strong CP problem is solved automatically if one of the quarks is massless.<ref>{{cite journal|last1=Hook|first1=Anson|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|doi=10.22323/1.333.0004|arxiv=1812.02669|access-date=2021-12-02}}</ref> In that case one can perform a set of chiral transformations on all the massive quark field 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 quark masses 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=Markus |editor2-last=Raffelt |editor2-first=Georg |editor3-last=Beltrán |editor3-first=Berta |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]]{{dn|date=December 2021}} [[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 [[string theory]].

Other less popular proposed solutions exist such as Nelson-Barr models.<ref>{{cite journal|last=Nelson|first=Ann|date=1984-03-15|title=Naturally weak CP violation|url=https://www.sciencedirect.com/science/article/pii/0370269384920252|journal=Physics Letters B|volume=136|issue=5,6|pages=387-391|doi=10.1016/0370-2693(84)92025-2|pmid=|arxiv=|s2cid=|access-date=2021-12-02}}</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=|s2cid=|access-date=2021-12-02}}</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 at low energies. The tricky part of the models is to account for why <math>\bar \theta</math> remains small at low energies while the CP breaking phase in the [[Cabibbo–Kobayashi–Maskawa matrix|CKM matrix]] becomes large.