Disagreement between electron-scattering values of the proton charge radius

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.

Low-momentum-transfer $\mathrm{e}-\mathrm{p}$ and $\mu-\mathrm{p}$ scattering (PRad-II, MUSE, AMBER) analyzed with a common radiative-correction and fitting treatment, together with an independent reanalysis of the Mainz A1 data.