Abstract

The rms-radius R of the proton charge distribution is a fundamental quantity needed for precision physics. This radius, traditionally determined from elastic electron-proton scattering via the slope of the Sachs form factor 𝐺𝑒(𝑞2)extrapolated to momentum transfer 𝑞2=0, shows a large scatter. We discuss the approaches used to analyze the e-p data, partly redo these analyses in order to identify the sources of the discrepancies and explore alternative parameterizations. The problem lies in the model dependence of the parameterized 𝐺(𝑞) needed for the extrapolation. This shape of 𝐺(𝑞 < 𝑞𝑚𝑖𝑛) is closely related to the shape of the charge density 𝜌(𝑟) at large radii r, a quantity that is ignored in most analyses. When using our physics knowledge about this large-r density together with the information contained in the high-q data, the model dependence of the extrapolation is reduced, and different parameterizations of the pre-2010 data yield a consistent value for 𝑅=0.887±0.012 fm. This value disagrees with the more precise value 0.8409±0.0004fm determined from the Lamb shift in muonic hydrogen.