Proton rms charge radius

The proton is not a point; its charge is smeared over roughly 0.84 fm, measured either by elastic electron-proton scattering (extrapolating the form factor to zero momentum transfer) or from the Lamb shift in hydrogen, where the electron's overlap with the nucleus shifts the S levels.

Both methods agreed on about 0.877 fm until 2010, when a Paul Scherrer Institute experiment on muonic hydrogen — where the muon's 207-times-smaller orbit makes the effect 8 million times more sensitive — returned 0.842 fm, a 5σ discrepancy dubbed the proton radius puzzle. A decade of new hydrogen spectroscopy and the 2019 PRad scattering experiment gradually converged on the smaller value, and CODATA 2022 recommends 0.840 75(64) fm. The lesson was not new physics but underestimated systematics in the older extractions — a useful reminder that "5σ tension" more often means a bad error bar than a new particle.