Disagreement between electron-scattering values of the proton charge radius
In plain words
Muonic hydrogen (a proton orbited by a muon, a heavy cousin of the electron) and the most precise hydrogen measurements give a proton radius of about $0.84\,\mathrm{fm}$ ($1\,\mathrm{fm} = 1e-13\,\mathrm{cm}$). Electron-scattering experiments disagree with each other, one giving $0.83\,\mathrm{fm}$ and an older one $0.88\,\mathrm{fm}$, and the cause is not identified.
Precise statement
The rms charge radius $r_{p} = 0.84087(39)\, \mathrm{fm}$ from the muonic hydrogen Lamb shift (2013) agrees with hydrogen $2\mathrm{S}-6\mathrm{P}$ spectroscopy (0.8406(15) fm, Maisenbacher et al., 2026) and with PRad low-momentum-transfer e-p scattering (0.831(14) fm, 2019), whereas Mainz A1 e-p scattering gives 0.879(8) fm (2010). Identify the cause of the scattering discrepancy: radiative corrections, cross-section normalization, or the functional form used to extrapolate $G_{E}(Q^{2})$ to $Q^{2} = 0$. The remaining spectroscopic outliers (LKB $1\mathrm{S}-3\mathrm{S}$, 0.877(13) fm, 2018; Colorado State $2\mathrm{S}-8\mathrm{D}$, about 0.86 fm, 2022) are a question of hydrogen line shapes and QED corrections and are treated as an atomic-physics problem. Answer: the identified systematic effect, shown by reanalysis or new data that bring the scattering values into agreement.
What would settle it
Low-momentum-transfer e-p and mu-p scattering (PRad-II, MUSE, AMBER) analyzed with a common radiative-correction and fitting treatment, together with an independent reanalysis of the Mainz A1 data.
Status in the literature
Unverified note
The MPQ hydrogen 2S-6P measurement (Maisenbacher et al., Nature 2026, arXiv 2602.14980) confirmed the small radius; the origin of the larger Mainz A1 scattering value remained unexplained as of 2026.