Wobbling muons hint strongly at the existence of bizarre new physics

Muons aren't spinning the way the best physics model predicts. Why not? It may be due to completely unknown subatomic particles popping into and out of existence in the quantum foam.

This isn't some sort of sci-fi technobabble. This is from quite real experimental results, and may very well be the Universe telling us we don't yet understand everything about it.

These extremely interesting and possibly game-changing results come from Fermilab, a high-energy particle accelerator laboratory in Illinois. They do a lot of different types of experiments there, and one is called Muon g-2 (literally, "g minus 2"), which examines a subatomic particle called a muon.

Muons are similar to electrons — they have a negative charge, for example, and the same spin (a fundamental property of particles, which will become important in a moment), though they're 200 times more massive.

Using everything we know about subatomic particles (called the Standard Model), physicists can predict a lot about the behavior of a muon. For example, a spinning charged particle has a magnetic property associated with it called a moment, which is a measure of the strength of its magnetic field and its orientation. If you put a muon into a magnetic field, it will undergo a wobble called precession; this is physically similar to a toy top wobbling as it spins on a tabletop.

The models predict this precession extremely precisely. Extremely. Physicists assign a value to this called the g-factor, and it's very close to but doesn't precisely equal 2.

Here's where things get fun: On our macroscopic scale, we like to think that space is smooth and continuous. But on a quantum scale, an incredibly tiny scale (like 10^-35 meters!) quantum mechanics implies that space is not continuous and smooth, and instead may come in discrete units, like tick marks on a graph. This means, on that scale, space may not be empty, but instead boils and froths with energy.

Sometimes this energy will spontaneously create a pair of subatomic particles (because mass and energy are two sides of the same coin, E being equal to mc² and all that). These particles can pop into existence, but these same laws of quantum reality demand that the particles immediately interact and become energy again, going back into the vacuum energy. This is called (and I love this) the quantum foam.

Illustration of quantum foam, where energies forth on a scale of one-billion-trillion-trillionth of a centimeter, and particles pop into and out of existence. Credit: NASA/CXC/M.Weiss

A muon spinning in a magnetic field is affected by the quantum foam. If there were no foam, the value of the g-factor would be very close to 2. But the particles popping into and out of existence affect the muon's wobble. This is called the anomalous magnetic moment, the deviation from the usual value.

The Standard Model makes a prediction of the value of this anomalous moment by looking at everything known about forces and particles. It should be very accurate. Still, it's always nice to make sure, and that's what the Muon g-2 experiment does. It injects muons into a very stable magnetic field and measures the wobble, which can then be compared to the prediction. If they agree, then yay, we understand how the quantum mechanical Universe behaves.

If not... well. That would be interesting isn't it?

The ring magnet at the heart of the Muon g-2 experiment at Fermilab provides a stable magnetic field in which muons spin. Credit: Fermilab / Reidar Hahn

The Standard Model predicts the muon's anomalous magnetic moment value to be 0.00116591810 (±0.00000000043; like I said, very precise).

The new experiment gets a value of 0.00116592061 (±0.00000000041).

Those are different. The difference is small, sure, just 0.0002%. But still, they should be equal. And they're not.

This tiny difference means a lot. It means that there are forces and/or particles acting on the quantum scale that we don't know about!

Well, maybe. Here's the monkey in the wrench: The results aren't quite up to statistical snuff. It's very slightly possible that they are due to random chance. It's like flipping a coin: If it comes up heads three times in a row you might think the coin is rigged, but there's a one out of eight chance that will happen randomly. The more times you flip it and it comes up heads, the less likely it's random.

At Fermilab, protons accelerated by powerful magnets circle at extremely high speed around a ring about a kilometer across, and then are fed to Muon g-2 target station, where they collide with a target and produce muons that are injected into a stable magnetic field for study. Credit: Fermilab

Scientists use a term called sigma to measure this chance. The gold standard in particle physics experiments is when an experiment is in the five sigma range, meaning it has a random possibility to occur of about one in three million, or, if you prefer, it's a 99.99997% chance of being real (one sigma is about 68%, two is 95%, three is 97%, and so on, creeping ever closer to 100%). The Muon g-factor experiment results are only 4.2 sigma, meaning they still have about a 1 in 38,000 chance of being due to random noise.

Still, that's a 99.997% chance of it being not due to random chance, and that's pretty dang good^*. It's just not quite enough for physicists to declare victory. The good news is that they're not done yet. The experiment has been run three times so far, is doing a fourth, and a fifth run is planned. The scientists have been examining the data from those first runs, but that amounts to only about 6% of the total amount of data they expect from the experiment. To use the analogy above, it's like they've flipped the coin a few times and gotten weird results, but will continue to flip it many more times to be sure.

If the rest of the data line up with what they've seen so far, they'll pass the five-sigma certainty. And if that happens, it means for sure that the Universe is weirder and more mysterious than even the quantum mechanics we know is telling us… and that's already been telling us the Universe is damned weird.

If you want all this in comic form, then Jorge Cham has you covered:

So this is potentially very exciting. The Standard Model is pretty successful (for example it predicted the existence of the Higgs boson, which was found for the first time a few years ago) but we know there are cracks in it, things it doesn't predict as well. In this case muons floating and spinning and wobbling in a magnetic field are beckoning us further down that path, waving us toward more physics we don't as yet understand, or even know anything about.

And that is the dream of every particle physicist. When experiments verify theory that's nice, because it's like showing that the road behind us is paved smoothly.

But what lies on the road ahead?

[Correction (16:00 UTC on April 8, 2021): I originally calculated the percentages incorrectly on those chances, adding an extra two 9s in the decimal point (in other words I had written them as straight odds, not percentages, like a 0.01 chance is 1%). Arg! The numbers are now fixed. Also, I changed the phrasing a bit; the statistics only cover random chance. There could also be systematic errors, that is, something not accounted for in the equipment, or the math, or whatever. Those aren't random, and are difficult to account for. I just want to make sure I'm covering the bases here.]