## CP Violation

Here are two more open questions about physics. I have a question of my own at the end!

Why are the laws of physics not symmetrical when we switch left and right, or future and past, or matter and antimatter? Why do the laws of nature even violate “CP symmetry”? That is: why are the laws not symmetrical under the operation where we simultaneously switch matter and antimatter and switch left and right?

Violation of P symmetry, meaning the symmetry between left and right, is strongly visible in the Standard Model: for example, all directly observed neutrinos are “left-handed”. But violation of CP symmetry is subtler: in the Standard Model it appears solely in interactions between the Higgs boson and quarks or leptons. Technically, it occurs because the numbers in the Cabibbo–Kobayashi–Maskawa matrix and Pontecorvo–Maki–Nakagawa–Sakata matrix (discussed in the previous question) are not all real numbers. Interestingly, this is only possible when there are 3 or more generations of quarks and/or leptons: with 2 or fewer generations the matrix can always be made real.

Does the strong force violate CP symmetry? In the Standard Model it would be very natural to add a CP-violating term to the equations describing the strong force, proportional to a constant called the “θ angle”. But experiments say the magnitude of the θ angle is less than 2 × 10-10. Is this angle zero or not? Nobody knows. Why is it so small? This is called the “strong CP problem”. One possible solution, called the Peccei–Quinn mechanism, involves positing a new very light particle called the axion, which might also be a form of dark matter. But despite searches, nobody has found any axions.

• Wikipedia, CP Violation.

• Wikpedia, Strong CP Problem.

• Michael Beyer, editor, CP Violation in Particle, Nuclear, and Astrophysics, Springer, Berlin, 2008.

It’s a theorem that quantum field theories are symmetrical under CPT: the combination of switching matter and antimatter, left and right, and future and past. Thus, a violation of CP implies a violation of time reversal symmetry. For more on this, see:

• R. G. Sachs, The Physics of Time Reversal, University of Chicago Press, Chicago, 1987.

What are the electric dipole moments of the electron and the neutron?

As of 2020, experiments show the electric dipole moment of the electron is less than 1.1 × 10-29 electron charge centimeters. According to the Standard Model it should have a very small nonzero value due to CP violation by virtual quarks, but various extensions of the Standard Model predict a larger dipole moment.

Also as of 2020, experiments show the neutron’s electric dipole is less than 1.8 × 10-26 e·cm. The Standard Model predicts a moment of about 10-31 e·cm, again due to CP violation by
virtual quarks, and again various other theories predict a larger moment.

Measuring these moments could give new information on physics beyond the Standard Model.

• Wikipedia, Electron Electric Dipole Moment.

• Wikipedia, Neutron Electric Dipole Moment.

• Maxim Pospelov and Adam Ritz, Electric Dipole Moments as Probes of New Physics.

Here’s my question. Do you know papers that actually calculate what the Standard Model predicts for the electric dipole moments of the electron and neutron?

### 7 Responses to CP Violation

1. I’d be curious to hear your thought on the possibility of CPT violation. Would it break physics as we know it? Lorentz invariance, spin-statistic? Could we survive it?

• John Baez says:

CPT violation would break quantum field theory on Minkowski spacetime as we know it, since CPT symmetry is a theorem in all decent axiomatizations of that sort of quantum field theory.

Quantum gravity also probably breaks quantum field theory on Minkowski spacetime. So it’s perhaps not completely surprising that Hawking gave an argument that quantum gravity could violate CPT invariance, as well as the unitarity of time evolution:

• Stephen Hawking, The unpredictability of quantum gravity., Communications in Mathematical Physics 87 (1982): 395–415.

I don’t know what the AdS-CFT crowd thinks, but since they believe quantum gravity can be described by a quantum field theory “on the boundary”, they probably also believe it’s CPT invariant.

• mitchellporter says:

The status of CPT in string theory is unclear. But one of Hawking’s last papers (1401.5761) used CPT and AdS/CFT to argue that there are no true event horizons, only temporary apparent horizons.

2. But experiments say the magnitude of the θ angle is less than $2 \times 10^{-10}.$ Is this angle zero or not? Nobody knows. Why is it so small?

It seems to be one of the examples of fine-tuning which, as far as I know, has no convincing weak-anthropic explanation.

• John Baez says:

I think it’s a fascinating puzzle. There is a certain amount of philosophy involved, which I find frustrating: namely, do you really need to provide an argument that each term that one could add to the Lagrangian, consistent with renormalizability and the gauge symmetries, is not actually there (or has an extremely low coupling constant)? Endless ink has been spilt on this subject, so let’s not talk about it more. But if someone can use this sort of reasoning to find new physics—like an axion—then more power to them!

3. Of course there are lattice computations of the neutron electric dipole moment, but maybe not yet enough to establish a stable result. Here is the most recent:

• C. Alexandrou, A. Athenodorou, K. Hadjiyiannakou and A. Todaro, Neutron electric dipole moment using lattice QCD simulations at the physical point.

• John Baez says:

Thanks, I didn’t know about these computations! I’ll check this out.

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