The standard model of particle physics describes the elementary building blocks of nature with scary accuracy (most of the time). At some level, it’s clearly “correct,” but at others, it’s totally off. There’s a reason why we didn’t just abandoned the standard when it makes a false prediction, it’s because some of the most well tested and confirmed predictions in all of physics have come from the standard model. On one hand it makes predictions that agree with experimental results to one part in a billion, and on the other hand, it refuses to cooperate with Einstein’s general theory of relativity. So what’s going on here? The answer, is new physics.
Uniting the standard model of particle physics and Einstein’s general theory of relativity, is perhaps the greatest quest mankind has embarked on. We don’t have many leads, so we’re thoroughly investigating the ones we do have. One of these leads is the anomalous magnetic dipole moment of the muon, being looked into by Fermilab via their g-2 (pronounced: “g minus 2”) experiment.
Think of the muon as the heavier cousin of the electron, they have identical properties except their mass. The anomalous magnetic dipole moment of a particle is how hard that particle rotates (or how much of a torque it experiences) when it is placed in an external magnetic field. This rotation is determined by a number called the g factor.
The standard model predicts a value for the electron’s g factor which matches experimental results to one part in a billion, by far the most accurate prediction in all of physics. For whatever reasons, the standard model DOES NOT correctly predict the g factor of the muon. The g factor of the electron is around 2, so g-2 refers to finding the value of how much the g factor differs from 2, which is what the”anomalous” in anomalous magnetic dipole moment refers to. The g factor actually has a pretty nice physical meaning (something very hard to come by in quantum mechanics). The electron g factor represents how much more torque a quantum object the size and mass of an electron would feel when compared with a classical object of the same size and mass. So this would mean, an electron experiences around twice as much torque when it it placed in a magnetic field than it would have, had it been a classical object.
Now that all the exposition is over, we can move on to the exciting part, Fermilab’s g-2 experiment.
What has already happened with the electron, Fermilab is now trying to do with the muon. Whenever we try to find the g factor of the muon, we see that it is ever so slightly off compared to experiments results. How can we get the wrong value for thr muon, but get the right value for the electron? Well, many people hope that the the disagreement is due to the muon’s interaction with some unknown virtual particle. The muon is 200 times heavier than the electron. And therefore, it is 200 times more likely to interact with a virtual particle because of its mass. After accounting for interactions between the muon and all relevant virtual particles, we STILL get a g factor which disagrees with experiment. So the rising hope is that an as of it unknown particle is at work here.
Prior to the Fermilab muon g-2 experiment, many labs over the years have refined the muon g factor measurements. Until now, it had been measured precisely enough to claim a 3.7 sigma difference compared to theory. A 3.7 sigma difference basically means that there is roughly a one in ten thousand chance that random fluctuations could lead to that degree of difference. Physicists, however prefer a 5 sigma (1 in 3.5 million chance of difference due to random fluctuations) difference in order to declare a discovery. The Fermilab experiment, which has currently achieved a 4.2 sigma confidence level, hopes to reach 5 sigma and declare a discovery.
And that’s it! That’s the bare minimum you need to know to follow whatever is happening and will happen with Fermilab’s muon g-2 experiment. Before I leave, I want to leave you with something to look into yourself. Why is the electron g factor so close to 2, and not exactly 2? The answer is really, really fascinating.