Model independent extraction of the proton charge radius from electron scattering

Constraints from analyticity are combined with experimental electron-proton scattering data to determine the proton charge radius. In contrast to previous determinations, we provide a systematic procedure for analyzing arbitrary data without model-dependent assumptions on the form factor shape. We also investigate the impact of including electron-neutron scattering data, and $\pi\pi\to N\bar{N}$ data. Using representative datasets we find $r_E^p=0.870 \pm 0.023 \pm 0.012 \,{\rm fm}$ using just proton scattering data; $r_E^p=0.880^{+0.017}_{-0.020} \pm 0.007 \,{\rm fm}$ adding neutron data; and $r_E^p=0.871 \pm 0.009 \pm 0.002 \pm 0.002 \,{\rm fm}$ adding $\pi\pi$ data. The analysis can be readily extended to other nucleon form factors and derived observables.