Muon g-2: The muon

I've previously discussed quite a few topics in particle physics, including a brief introduction to leptons and a discussion of parity-violating weak decays. Now I'd like to go into a little more depth regarding my current favorite elementary particle: the muon.

As mentioned previously, the muon is a sort of strange second cousin of the electron. The two interact with other particles and forces very similarly, so the two major differences are the muon's mass (207 times that of the electron) and its lifetime (a mere 2.2 microseconds - yes, that's millionths of a second). Like the electron and quarks, the muon is a 'spin-one-half' particle, which for our purposes means it has a spin of either 1/2 (unitless) or $\hbar/2$ (unitful) either along or against any axis you choose to measure. But of course, the muon doesn't actually take up any space (it's a point particle), so it's not really spinning...that's an interesting quantum phenomenon that will have to await another post for a deeper explanation.

One interesting property of many subatomic particles is called the magnetic moment, generally denoted as $\mu$. Macroscopically, a loop of current has a magnetic moment, which determines the amount of torque it will feel from a magnetic field. Similarly, a muon's magnetic moment determines its behavior in a magnetic field. Just as a top spinning on a table spins a bit (precesses) as it starts to slow down, a muon in a magnetic field experiences a precession of its spin direction. The magnetic moment of a particle is determined by a particle-specific constant called $g$, which is short for the gyromagnetic ratio (thus the 'g-2' in the experiment's name), and this determines how fast the particle's spin precesses in a magnetic field. We can talk specifically about the muon's gyromagnetic ratio as $g_\mu$. Another consequence of throwing muons at a magnetic field is that they end up on a curved path, as charged particles in magnetic fields are wont to do. In the Muon g-2 experiment, we inject muons into a very uniform magnetic field. It's tuned just right so that the muons go around in a circle inside our storage ring, and we can (indirectly) measure the spin angle of the muon when it decays. By studying a lot of muons, we can see how the muon's spin compares to its momentum over time, and after 20-30 turns, it's overtaken the momentum by a full turn. Well, that's pretty neat, but I can very clearly hear you asking "so what?"

Let me take a brief step back in time. Once upon a time, many years ago, a brilliant physicist named Paul Dirac came up with a very elegant equation describing the behavior of a free charged particle, which we now (very creatively) call the Dirac Equation. In this model, the value of the gyromagnetic ratio was exactly two. Well, it turns out that nothing in particle physics is so simple, and so the value of $g$ is actually a tiny bit higher. This is a result of these crazy things called virtual particles. They're sort of like nature's own particle accelerator, and basically pairs of particles are constantly popping into and out of existence - quarks, bosons, muons, electrons - all the time, everywhere. It turns out that while these little fellows may be short-lived, they have an effect on the value of the gyromagnetic ratio $g$. As a result, the value that we're measuring isn't $g$ so much as $g-2$, which is important enough that it gets its own name: the anomalous magnetic moment of the muon ($a_\mu$).

The interesting thing about muons is that because of their higher mass, they're more sensitive to these virtual particles than the less massive electron, and they live long enough to be a pretty good candidate for study. Furthermore, the last time an experiment (E821 at Brookhaven National Lab) measured their precession rate and gyromagnetic ratio, what they found disagreed pretty substantially from what theory predicted at the time. In mathematical parlance, there was a $3\sigma$ (so three standard deviations) disagreement, which isn't enough to claim a discovery (in particle physics, we require $5\sigma$), but it's certainly enough to label the issue as interesting. If we make the same measurement again (but better, of course, thanks to improved detector technology and vastly improved beam quality at Fermilab) and that difference persists, it will be a good indication that something that we don't understand is going on at the most fundamental level. That could mean the existence of new particles, and the really exciting thing about the measurement is that it could find traces of new particles that even the Large Hadron Collider in Switzerland couldn't produce! And all from a very precise measurement of a single property of a single particle. Wow - physics is awesome.

If you want to learn more about the Muon g-2 experiment, some of my other blog posts can be found here, or you can check out the experiment's webpage here.