How big is a proton? Unlike an electron or neutrino, which are fundamental particles that behave like points, a proton is a messy collection of quarks, gluons, and virtual particles that occupies what should be a measurable amount of space. And just how much space can be rather significant; as the authors of a new paper on the proton's size put it, "The proton structure is important because an electron in an S [ground] state has a nonzero probability to be inside the proton." (Emphasis ours.)

Within experimental error, various measurements of the proton's size have all put it about 0.88 femtometers (an fm is 10-15 meters). But a team of researchers, working at a particle accelerator in Switzerland, has found a different way of measuring the proton's size: put a muon—a heavy, unstable, relative of the electron—in orbit around a proton. The resulting atom, called muonic hydrogen, can be measured during the brief time it exists before the muon decays. Those measurements have produced a new, very high-precision value for the proton's radius. Just one small problem: it differs from the other measurements by nearly seven standard deviations.

The paper describing these measurements, published in today's Science, does a nice job of illustrating how measuring the emissions of simple hydrogen atoms has a profound effect on physics. The fact that hydrogen only emits or absorbs specific frequencies as its electrons hop between orbitals was critical to the development of quantum mechanics. Better precision measurements revealed that many of these absorption or emissions lines were actually two closely spaced frequencies; that provided experimental validation of the Dirac equation. Small deviations from this equation eventually helped trigger the development of quantum electrodynamics.

Because the physics of a hydrogen atom is so well defined, it's possible to use these precise measures of how it absorbs and emits light to generate measures of the atom's components. These include things like the size, magnetic radius, and charge radius of the proton at the center of it all. These have produced values generally in the area of 0.88fm, which is great, because that agrees with measures of the proton's radius obtained by scattering electrons off it. Everything looked good.

And then the Swiss got involved. (It's actually a large, international team that happened to use a particle accelerator in Switzerland's Paul Scherrer Institute to produce its muons.) Muons come from the same family of particles as electrons. They carry an identical charge but are 207 times heavier than their more familiar cousins. They also typically decay in about 2 x 10-6 seconds. Still, if everything is timed perfectly, it's possible to put one into orbit around a proton, creating an atom of muonic hydrogen (also called µp).

In this case, the research team had some lasers poised to go off, waiting on a trigger provided by a muon detector. As soon as the muonic hydrogen was likely to be present, the lasers fired, allowing spectroscopic measurements of this atom. Because of the muon's (relatively) large mass, these measurements provided very precise values for some of the basic properties of the protons they were orbiting. The researchers also measured two different energy level transitions, allowing them to get a second set of independent values.

Both of them placed the proton's radius at 0.84fm. That may not seem like a huge difference, but the high precision meant that there was very little statistical error. So little, in fact, that the value they calculate is about seven standard deviations (or seven sigma) out from the value obtained by the other methods.

This isn't the first time this team found something funny while measuring muonic hydrogen. But their previous report only used a single energy transition and was over ten times less precise. The new paper really nails down the fact that something funny is going on here. And nobody is quite sure what. The authors spend a good chunk of the paper going through all the factors that can throw their measurements off, but none of them seem to amount to anything very significant, much less big enough to account for a seven-sigma difference.

The other, and potentially most exciting, possibility is that muons interact with protons in a fundamentally different way than electrons. That shouldn't be the case, and if it actually turns out to be, then it's a sign there must be some new physics out there. Even then, things are tough, as the authors say: "The window for such 'new physics' is small," given how many existing results we have that would all have to be compatible with it. The one option they seem to like is the existence of relatively light force carriers that somehow remained undiscovered until now.

Science, 2013. DOI: 10.1126/science.1230016 (About DOIs).