Proton Charge Radius from Electron Scattering

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 G e ( q 2 ) extrapolated to momentum transfer q 2 = 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 < q m i n ) 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 ± 0.0004 fm determined from the Lamb shift in muonic hydrogen. View Full-Tex