Importance of Tail of Proton Density: Or: How to Get the rms -Radius from (e, e) Data

Triggered by the discrepancy between electron-proton scattering and muonic hydrogen results we scrutinize the determination of the charge rms-radius from (e, e) data. We find that the standard procedure of fitting parameterizations for the Sachs form factors G(q) to the data is more uncertain than traditionally assumed. This is related to the (implicit) extrapolation from the q-range sensitive to finite size to momentum transfer q=0 where the rms-radius is extracted. A reliable determination of the rms-radius requires a constraint on the large-r tail of the density, which can be imposed starting from our physics understanding of proton structure