A stubbornly different size
For decades, the proton's size was a settled issue in physics. Two independent methods, electron-proton scattering and hydrogen spectroscopy, converged on a charge radius of about 0.877 femtometers. Electron scattering experiments involved firing beams of electrons at hydrogen and analyzing how they recoil to map the proton's charge distribution. Spectroscopy, on the other hand, measured the precise energy levels of the electron in a hydrogen atom. These energy levels are subtly affected by the proton's volume; the electron in some orbitals spends a tiny amount of time "inside" the proton, which shifts its energy. By comparing these shifts, known as the Lamb shift to theoretical predictions, physicists could calculate the radius. The results were consistent.
This consensus was shattered in 2010. A team at the Paul Scherrer Institute (PSI) in Switzerland announced a new measurement that was dramatically different. The experiment, known as CREMA (Charge Radius Experiment with Muonic Atoms), used a clever variation on the spectroscopy method. They created "muonic hydrogen," a special type of atom where the electron is replaced by its heavier cousin, the muon. A muon is 207 times more massive than an electron, causing it to orbit much closer to the proton. This proximity makes the muon's energy levels vastly more sensitive to the proton's size; the probability of the muon being inside the proton is about 8 million times higher than for an electron.
The result was an order of magnitude more precise than previous attempts and yielded a proton radius of roughly 0.84 femtometers. This value is about 4% smaller than the established figure, a shocking discrepancy of seven standard deviations in a field where three is usually enough to announce a new discovery. The "Proton Radius Puzzle" was born.
Resolving the discrepancy
The 2010 result from PSI left physicists with a few possibilities. One was that the experiment contained a subtle, overlooked error. Another was that quantum electrodynamics (QED)—the highly successful theory describing how light and matter interact—was incomplete. A third, more exotic possibility was the existence of a new force of nature that interacts differently with electrons and muons, violating a principle called lepton universality.
Follow-up experiments were launched worldwide to solve the puzzle. A second measurement on muonic deuterium (a proton and neutron nucleus orbited by a muon) at PSI in 2016 confirmed the smaller radius. New spectroscopy experiments on regular hydrogen in Germany and Canada also found a smaller radius, closer to the muonic value. Newer electron-scattering experiments, like the PRad experiment at Jefferson Lab in the United States, also produced results more consistent with the smaller proton.
As of the early 2020s, the consensus has shifted. It is now widely believed that the smaller value is correct and that the older, larger measurements suffered from unaccounted-for systematic errors. The Particle Data Group, which compiles and averages experimental results, now lists the official proton charge radius as approximately 0.841 fm. While the puzzle appears to be mostly resolved in favor of the smaller proton, experiments like MUSE at PSI continue to scrutinize the interactions of both electrons and muons with protons, ensuring no new physics is hiding in the discrepancy.