Electromagnetic proton form factors for neutrino physics and atomic spectroscopy

We provide a parametric representation of nucleon form factors, uncertainties, and correlations at momentum transfers below a few GeV^2 incorporating all our knowledge about electromagnetic nucleon structure from electron scattering data and precise charge radii measurements as well as recent advances in radiative corrections and fit procedure. The proton magnetic form factor measurements of A1 Collaboration are strikingly different to older data resulting in a 3-5% difference for the central value of quasielastic cross sections and sizable shifts of energy levels in ordinary and muonic hydrogen. A successful realization of precise neutrino measurements and first measurements of the ground-state hyperfine splitting in muonic hydrogen call for further experimental investigations of the proton magnetic form factor at low momentum transfer \lesssim 1-3 GeV^2