Proton rms-radii and electron scattering

Introduction. Accurate knowledge of the proton rootmean-square (rms) radii is important for both an understanding of proton structure and the interpretation of the extremely precise data on transition energies in the Hydrogen atom. Traditionally, the rms-radii have been derived from data on elastic electron-proton scattering at low momentum transfer q. The best determinations are based on parameterizations of the Sachs form factors Ge(q) and Gm(q) with the parameters directly fitted to the observables, i.e. cross sections and polarization transfer data. The slope of the parameterized form factors at q=0 yields the charge- and magnetic rms-radii, respectively. This topic of the proton radii has recently become a subject of intense discussion with the publication of the charge rms-radius determined from the Lamb shift in muonic Hydrogen [1]. This radius, 0.8409±0.0004fm, disagrees by many standard deviations with the value 0.8775±0.005fm from the world data on electron scattering [2], and it also disagrees with the recent value extracted from the transition energies in electronic Hydrogen [3], 0.8758±0.0077 fm. This disagreement has led to a large number of studies dealing with problems with the determination of the radii, or new physics [4]-[12]. The discrepancy has also led to renewed scrutiny of the procedure used to extract rms-radii from electron scattering data. Problematic in particular is the fact that the (e,e)-data sensitive to proton finite size are the ones in the region of momentum transfer q = 0.6÷1.2fm 1 [13]; the determination of the rms-radius involves an (implicit or explicit) extrapolation to q = 0.