Results released yesterday from Fermilab confirm measurements from about 20 years ago that are in tension with the Standard Model’s prediction about the instrinsic magnetic properties of muons.

Have we discovered anything yet? No, not yet. Updates to these Standard Model-based calculations appear to bring them into closer alignment with these new experiments. But these new calculations are not completely vetted yet and if there is a problem, then it would seem we’re very close to a discovery. So, much like the recent LHCb results, we’re in a situation where tentative or cautious excitement is warranted, but it’s important not to get ahead of ourselves!

Here’s a really nice video from the Fermilab team that details aspects of this measurement:

https://www.youtube.com/watch?v=ZjnK5exNhZ0

And an excellent article that takes into account some key caveats:

https://www.quantamagazine.org/muon-g-2-experiment-at-fermilab-finds-hint-of-new-particles-20210407/

If you want more background about intrinsic spin, magnetic moments, and why mismatches could indicate new particles read on!

The muon is a heavier cousin of electrons. Both of them feature an intrinsic spin of half-hbar, where hbar is the reduced Planck constant. (Planck’s constant has dimensions of angular momentum.) The charge and spin properties of these particles mean that they act like microscopic bar-magnets, and hence, have a magnetic moment. (If you set an electrically charged object spinning, you create a rotating current that generates a magnetic field. There’s a quantum version of this happening with these particles.)

In a pristine world where particles never interact, the ratio between the intrinsic spin of electrons or muons and their magnetic moments would be 2. But that world is silly because magnetism is an interaction, so what does it matter if particles don’t interact?

In the real world, there’s a sense in which particles are really only approximate entities. The underlying description of particles comes from quantum field theory (QFT). In QFT, particles arise as states of a quantum field that carry definite amounts of momentum and are very well separated from each other. The assumption that these particle-like things are well-separated is essential because it means that they barely interact and so we can think of them as approximately equivalent to their counterparts in the silly, non-interacting world.

But this is only a first-approximation, because even if these approximate particle states aren’t interacting significantly with anything, the very possibility that they could interact with other particle-like things has to be accounted for in the definition of these states. Again, to a first approximation, we don’t take these possible interactions into account, but we then iteratively redefine the physical particle states by adding contributions that deform them away from the pristine, free particle approximation. Oftentimes such additions are described using the language of “virtual particles”. The idea is that even a muon left by itself in a vacuum is somehow affected by the existence of other particles because they may “fluctuate” out of the vacuum, interact, and then go away again, altering the muon’s physical behavior.

This is a very appealing picture but it’s important to understand that it’s not literal. There are no literal particles fluctuating into and out of existence. There is merely the fact that our free particle version of the muon and the actual, physical version are not identical because a theory with interactions is different from a theory without them. The virtual particles give us a convenient way to organize calculations that layer on corrections to the free particle theory, bringing its results closer to the physically, more realistic theory.

Anyway, it turns out that the muon’s magnetic moment is sensitive to the possibility of interacting with other particles in a way that causes the physical magnetic moment to diverge ever-so-slightly from the theoretical prediction with no interactions included. This divergence is called g – 2, also known as the “anomalous magnetic moment.”

These anomalies have been calculated and tested for both electrons and muons and the calculations and experiments agree to amazing levels of accuracy. However, measurements from around the year 2000 at Brookhaven National Labs and the more recent results from Fermilab indicate that the muon is more anomalous than what we’d expect from including interactions with just Standard Model particles. The most straightforward reading of this, assuming the anomaly is confirmed in future experiments, is that there is more for the muon to interact with than just the Standard Model particles, and thus, this would be very strong evidence for existence of particles beyond what we currently know.

But…(there’s always a “but”)…it could be that the experiments are fine and it’s the calculations that are messing up. The Standard Model is pretty tough to calculate with precisely because the contributions from all the possible interactions begin to get very intricate. So, magnetic moment calculations involve approximations and there are errors associated with these approximations. A recent calculation based on new techniques brings the theoretical prediction much closer to the new experimental results. If it turns out that these new techniques are valid, then it would mean that we *don’t* need new particles to explain the result.

So as I said early in the post, these new experimental results are exciting. They could indeed mean that there are new particles out there, just on the verge of discovery. But they could also mean that we’ve just got to find a better way to do our approximations using just the plain, vanilla Standard Model. So we can’t get too excited just yet.

Here’s a nice discussion of the situation from a more technical perspective:

http://resonaances.blogspot.com/2021/04/why-is-it-when-something-happens-it-is.html