Merits and constraints of low-${\bm K^2}$ experimental data for the proton radius determination

Abstract

The question of the determination of the proton charge radius $R_p$ from electron scattering data led to an unprecedented experimental effort for measurements of the electric form factor of the proton at low and very low momentum transfer in electron and muon elastic scattering. On the basis of basic properties of densities and fitting bias considerations, a procedure is developed in order to evaluate the impact of forthcoming data on $R_p$. Particularly, it is shown that a 0.1\% precision on these future cross section data is necessary to establish indisputably the $R_p$-value as determined from lepton scattering. The ProRad (Proton Radius) experiment at the PRAE (Platform for Research and Applications with Electrons) facility in Orsay is further discussed, especially the experimental method to meet this stringent constraint.