Before we talk about axions, have a look at @chanda’s piece in @newscientist from a few years ago!

https://www.newscientist.com/article/mg24232302-100-axions-may-or-may-not-exist-but-were-not-just-making-things-up/

So what is the "strong CP problem,” why does it need a solution, and what did Quinn and her collaborator Roberto Peccei propose?

In particle physics, and in physics in general, we are always looking for symmetries of nature.

A symmetry is a way you can transform a physical system (like rotating an object, or shifting its position) or your description of a physical system (swapping out the particles in your model for different combinations of those particles) that leaves the physics unchanged.

Some rules of physics don't work the same way if we apply one or two of these discrete transformations. But the framework of particle physics, quantum field theory, MUST work the same way if we simultaneously make all three changes (CPT).

The Weak Interaction — one of the three interactions appearing at low energies in the Standard Model of particle physics — clearly isn’t invariant under just C or P. Only left-handed particles and right-handed antiparticles participate in the Weak Interaction.

For a while, physicists thought CP — charge conjugation accompanied by a simultaneous parity transformation — would be a symmetry of the Weak Interaction. But that is violated as well.

Ref: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.13.138

Anyway, quantum chromodynamics (QCD) is the theory of quarks and gluons that describes the Strong Interaction.

Based on the rules for how we construct theories of particle physics, there's good reason to expect CP transformations wouldn't be symmetries of the Strong Interaction.

Except, when we do experiments looking for evidence of CP violating processes in QCD, we don’t find anything. This leads to what physicists call "the Strong CP problem."

There’s a number θ appearing in the rules for the Strong Interaction that quantifies the amount of CP violation. It could take any value between 0 and 2π; as far as we know there is no physical principle that fixes it to a particular value.

Experimental bounds put θ *very* close to zero, which is surprising. Zero is the only value of θ where CP violation does not occur.

There’s more real estate not close to zero than there is close to zero, so why did θ end up taking this one special value?

Another name for this sort of problem is “fine tuning.” Unless a number in your theory has a good reason to be very small, you don’t expect it to be very small. If it happens to take a special value, you expect it must be the result of some physical mechanism.

(Some physicists question how much stock we put in "fine tuning” and “naturalness” as criteria for whether or not some aspect of a theory is problematic or requires explanation. That is justified, but it's a topic for another thread.)

In 1977, Quinn and Peccei proposed a mechanism to explain the lack of CP violation in QCD.

The parameter θ isn’t static, they reasoned. Rather, it’s a field itself. The dynamics of this field within QCD naturally cause it to settle down to a value of zero.

Ref: https://link.aps.org/doi/10.1103/PhysRevLett.38.1440

In quantum field theory particles arise as excitations of fields.

Wilczek and Weinberg both worked out the details of the new particle produced by the Peccei-Quinn mechanism.

Wilczek named it “axion” after a brand of detergent, because it cleaned up some outstanding problems.

The original version of the axion, studied by Weinberg and Wilczek, was experimentally ruled out. But it’s a lovely idea that fits naturally into our expectations for particle physics, and there are many variants that are of phenomenological interest.

In particular, some models with axions lead to light (small mass) particles that are unlikely to interact with most Standard Model particles. The numbers of axions produced in the early Universe make them attractive candidates for Dark Matter.