Our story begins in 1975, before axions were proposed. There was this big problem in Quantum Chromodynamics (QCD), which Weinberg named “The U(1) Problem”…before I describe it, let’s back up a little bit and decipher what all of this means, and we’ll get to it in the next post.

To put it really simply, the Standard Model of particle physics is composed of several sub-theories that describe the interactions between different types of particles: quarks (which carry a “color” charge), leptons (like electrons), gauge bosons (like photons), and the Higgs boson. The way that these particles interact has to do with specific gauge symmetries in the standard model. QCD describes the interactions between quarks, and has a special particle called a gluon which is the “gauge boson” of the gauge group that describes QCD, which is called SU(3). For leptons, we have the Electroweak theory, which describes electromagnetic and weak interactions; the electroweak theory deals with the leptons we all know and love (electrons, muons, taus, and their antiparticles), along with gauge bosons that come from this symmetry group called SU(2) x U(1), which are called W’s, Z’s, and photons. The quarks in the standard model are part of the SU(2) x U(1) interactions too, but the leptons don’t interact with quarks through the strong force** because they are only part of the SU(2) x U(1) group, and not of SU(3). All together, the gauge group of the standard model is all of these gauge groups combined: SU(3) x SU(2) x U(1).

The Higgs boson plays a special role in all of this. See, there was an unexplained problem in the Standard Model: except for the W and Z bosons, all the gauge bosons were massless. The fact that the photon and gluon were massless made sense, but the W and Z not only had mass, they were very heavy, and there was no reason why.

A bunch of guys in the 1960’s came up with this crazy idea: suppose that there was some extra field in the standard model, that did something to break a symmetry that would otherwise prevent the W and Z bosons from having mass. They worked it out, and discovered that if they assumed this field was real, it would indeed solve this problem! The particle associated with this new field was called the Higgs boson, named after one of the many guys who worked on it (Peter Higgs).

The fact that a symmetry can be spontaneous broken, and give us a particle, like in the case of the Higgs mechanism, is really important to my later discussion about axions, because axions are kind of like the Higgs. At a really, really high energies, before the Higgs breaks the electroweak symmetry, there are no W bosons, Z bosons, or photons, there are just three special particles called W’s (of which there are three) and B (of which there is one), and the Higgs field is just hanging out, and not doing anything to these W’s and B’s.

At some point, the Higgs acquires what is called a “vacuum expectation value”, which is the lowest value of energy that the field can have (it’s the minimum!), and the electroweak symmetry is broken. Everything in the electroweak sector goes crazy, and the three W’s and the one B get all mixed up. The B and one of the W’s get mixed together, and out come two different particles: the photon and the neutral Z boson (which gets a mass!). The two leftover W’s get mass from this weird mixing, which is described in terms of what is called the “weak mixing angle” (which is how we quantify the particles getting mixed up), and two different, massive, charged bosons come out: the W+ and the W-. This leaves us with all of the electroweak gauge bosons in the standard model, along with the Higgs boson!

Now that I’ve mentioned the basics of the Standard Model, and little bit about symmetry breaking, we can get back to axions…

** many thanks to redditor /u/tychotheduelist for pointing this out to me!

shoutout to redditor ididnoteatyourcat for helping me explain the Higgs!