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The precise determination of the proton radius from recent elastic scattering electron–proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that its uncertainty is two orders of magnitude larger that the error on the cross section, that is the measured observable. Different fits of the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associated to the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions and the range of the data sample. This error is shown to be also orders of magnitude larger than commonly assumed.

Sensitivity of the elastic electron–proton cross section to the proton radius