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

Hi Susan Fowler nice to meet you its Anirban here, a undergrad student of physics. It was interesting reading your article. I found a connection of this idea set-up by Peccei-Quinn with what I have been trying with xxz problems of spin chains lately. Thought I could share a bit about it with you. You could enlighten me more in this regard by giving your comments. Well here it is you would know probably that antiferromagnetic interactions in ising spin in 1D chains give rise to degenerate ground states. This ground states have the property that they spontaneously break the only symmetry associated with the ising hamiltonian. And that is the translation symmetry. The connection with your point arose in the writing that U(1) symmetry which is added to the problem is a global symmetry and is spontaneously broken. So here is the interesting thing the heisenberg antiferromagnet has a single ground state. And the connection of the ising antiferromagnet to the heisenberg antiferromagnet is the additional quantum fluctuations (along with the ising term)present in the heisenberg antiferromagnet. This quantum fluctuations when reduced below a particular value leads to ground state that break the translational symmetry and the ground state is doubly degenerate. If you look at the ground state configuration you would realize that the translational symmetry is broken in a global sense that is if you put all the even sites together and odd sites together. Then even to odd site going translational symmetry is broken. There is definitely more to say, if you are also interested then we could discuss about it via email. I am adding it below. Will be delighted to hear back from you.

Thank you for the general overview as well as background on Axions – it’s a well written post that gives a clear general overview to the interested novice on this topic – what would make the post more complete would be Feynman diagrams as well as graphics to better convey key concepts