In 1977, two physicists named Roberto Peccei and Helen Quinn came along and proposed something radical: let’s add an additional U(1) symmetry to the standard model. This wouldn’t just be any symmetry, they said – it’ll be a global symmetry that we will force to be spontaneously broken, resulting in a new gauge boson that will take the place of the troublesome “theta” in QCD. There is a lot of jargon in these last few sentences, so let’s break it down.
Spontaneous symmetry breaking is when you have a physical system that is all physically symmetrical, and do something to “break” the symmetry, like force your physical system to change in some way. For example, the Higgs field “breaks” the electroweak symmetry when it acquires a vacuum expectation value and changes all of the masses in the electroweak sector of the standard model.
Usually, when you spontaneously break a global symmetry, you get something called a “Nambu-Goldstone boson”. These Nambu-Goldstone bosons don’t have any spin, charge, or mass. The Higgs, which I mentioned in Part 1, is almost a Nambu-Goldstone boson, with one exception: it has mass. When the symmetry is broken in a certain way, if the symmetry isn’t “exact”, the Nambu-Goldstone boson acquires mass, and becomes a pseudo-Nambu-Goldstone boson.
This is exactly what happens with the Peccei-Quinn mechanism. Basically, you add an additional U(1) symmetry to the standard model (like I mentioned earlier). This additional symmetry comes with its own field, i.e., with a gauge boson called the axion. When you force this symmetry to be spontaneously broken, the potential of the axion falls into its minimum. Like in the case of the Higgs, the symmetry isn’t exact, which is due to that crazy QCD vacuum that Gerard ‘t Hooft figured out. This means that the axion is a pseudo-Nambu-Goldstone boson – it has no spin, and no charge, but isn’t massless.
Adding the axion field changes everything in QCD, because you can make it fit into the QCD Lagrangian so that it replaces that “theta” that screwed everything up. Since the axion replaces “theta” and its sitting at the bottom of its potential (where it is zero), it gives us a perfect explanation as to why CP violation doesn’t occur in strong (QCD) interactions.
There is one problem, however: we still haven’t solved the Strong CP Problem, because, while we’ve been searching for the axions like we searched for the Higgs, we haven’t found it yet. The axion is extremely hard to find, because it doesn’t interact with many of the particles in the standard model, with the exception of photons, which it can decay to. While this makes it difficult to detect, it makes it the perfect candidate for dark matter.
Read: Peccei and Quinn’s 1977 paper: http://prl.aps.org/abstract/PRL/v38/i25/p1440_1