Proton root-mean-square radii and electron scattering

Abstract: The standard procedure of extracting the proton root-mean-square radii from models for the Sachs form factors $G_e (q)$ and $G_m (q)$ fitted to elastic electron-proton scattering data %has a serious flaw. is more uncertain than traditionally assumed. The extrapolation of $G(q)$, from the region $q_{min} < q < q_{max}$ covered by data to momentum transfer $q=0$ where the $rms$-radius is obtained, often depends on uncontrolled properties of the parameterization used. Only when ensuring that the corresponding densities have a physical behavior at large radii $r$ can reliable $rms$-radii be determined.