I Unitarity Triangle CP Violation Angle β & θ

[Ranku]

Unitarity Triangle containing angle β describes CP violation in the weak interaction. If there is CP violation in the strong interaction, is it also described by a Unitarity Triangle containing the CP violating angle θ?

 

[vanhees71]

In the weak interaction the CP violation is due to the quark-mixing matrix. In case of the strong interaction you have two terms, the socalled $\Theta$-term and in the mass term of the quarks, related to chiral symmetry. To explain, why there is no CP violation observed in the strong interaction is still a challenge of contemporary particle theory. The most promising solution is the idea of another non-standard-model particle, called "the axion". The Wikipedia article is a good start:

https://en.wikipedia.org/wiki/Strong_CP_problem

 

[Orodruin]

In case of the strong interaction you have two terms, the socalled Θ-term and in the mass term of the quarks, related to chiral symmetry.

I guess that this depends a bit on how one counts, but you can put either of those contributions to zero by a chiral transformation - but generally not both simultaneously (or rather, the strong CP problem is that it does seem possible to do so). In some sense similar to how you can get rid of the Majorana phases in the CKM but not the Dirac phase - you do end up with a physical phase and thus CP violation. Exactly where the phase enters will depend on how one chooses to parameteise the theory.

 

[vanhees71]

That's true. You can as well only write down the $\Theta$. The point is to explain, why also this term must vanish. It's explained in the above quoted Wikipedia article.

 

[Ranku]

So the methodology of CP violation in weak interaction and strong interaction is quite different, in that CP violation angle β and θ have quite different meanings.

 

[Orodruin]

Indeed. They are both phases that break CP but the origin is quite different.

Now here’s a little brain teaser for you: What happened to the theta terms of the electroweak interactions?

 

[Ranku]

Now here’s a little brain teaser for you: What happened to the theta terms of the electroweak interactions?

My familiarity is only with the graphical unitary triangle, and they contain the β, α, and γ angles.

 

[Orodruin]

My familiarity is only with the graphical unitary triangle, and they contain the β, α, and γ angles.

Save it for later. It is an interesting puzzle that tends to confuse people.

 

[ohwilleke]

Unitarity Triangle containing angle β describes CP violation in the weak interaction. If there is CP violation in the strong interaction, is it also described by a Unitarity Triangle containing the CP violating angle θ?

Standard Model QCD assumes as an axiom that the CP violating angle θ of the strong force is zero, and there is no experimental evidence that disagrees in a statistically significant way with this conclusion.

Background:

Possible Resolutions

There are a couple of ways that people concerned about the "strong CP problem" (I'm not one of them) imagine could resolve it. One is that the issue would disappear if the up quark had a mass of zero, although experimental data fairly conclusively establish that up quarks have a non-zero mass. Another is to add a beyond the Standard Model particle called "the axion" which is very, very low in mass (a tiny fraction of an electron-volt).

A January 2022 preprint uses lattice QCD methods to suggest another reason that there is no CP violation in the strong force, without a need to resort to axions, and that such axions should not exist.

It suggests that if theta were non-zero and there was CP violation in the strong force, that confinement wouldn't happen. Therefore, the theta term in the strong force equations must be zero, and the hypothetical axion cannot exist.

Three hard problems!

In this talk I investigate the long-distance properties of quantum chromodynamics in the presence of a topological theta term. This is done on the lattice, using the gradient flow to isolate the long-distance modes in the functional integral measure and tracing it over successive length scales.

It turns out that the color fields produced by quarks and gluons are screened, and confinement is lost, for vacuum angles theta > 0, thus providing a natural solution of the strong CP problem. This solution is compatible with recent lattice calculations of the electric dipole moment of the neutron, while it excludes the axion extension of the Standard Model.

Gerrit Schierholz, "Strong CP problem, electric dipole moment, and fate of the axion" arXiv:2201.12875 (January 30, 2022) (invited talk at XXXIII International Workshop on High Energy Physics "Hard Problems of Hadron Physics: Non-Perturbative QCD and Related Quests", November 2021).

My "go to" heuristic explanation, in contrast, has been that since gluons are massless (i.e. have zero rest mass) that they don't experience the passage of time. Thus, the strong force shouldn't have a parameter that is sensitive to the direction of time that its carrier boson does not experience, because CP violation is equivalent to saying that a process behaves differently going forward and backward in time.