Transverse charge density and the radius of the proton

A puzzling discrepancy exists between the values of proton charge radius obtained using different experimental techniques: elastic electron-proton scattering and spectroscopy electronic muonic hydrogen. The is defined through slope electric form factor, $G_E(Q^2)$, at zero four-momentum transfer, which inaccessible in experiments. We propose a novel method for extracting from data over broad $Q^2$ range rather than attempting to directly determine $G_E$ $Q^2 = 0$. This relates its transverse density, two-dimensional Fourier transform Dirac $F_1(Q^2)$. apply our reanalyze extensive by A1 Collaboration [J. C. Bernauer et al., Phys. Rev. Lett. 105, 242001 (2010)] extract value, $r_E 0.889(5)_{\text{stat}}(5)_{\text{syst}}(4)_{\text{model}}~\text{fm}$, that consistent with original result. also provide new parametrizations Pauli factors magnetization densities proton. Our reanalysis shows cannot be explained issues fitting extrapolating