Abstract
The rms-radius R of the proton charge distribution is a fundamental quantity needed for precision physics. This radius, traditionally determined from elastic electron-proton scattering via the slope of the Sachs form factor G e ( q 2 ) extrapolated to momentum transfer q 2 = 0 , shows a large scatter. We discuss the approaches used to analyze the e-p data, partly redo these analyses in order to identify the sources of the discrepancies and explore alternative parameterizations. The problem lies in the model dependence of the parameterized G ( q ) needed for the extrapolation. This shape of G ( q < q m i n ) is closely related to the shape of the charge density ρ ( r ) at large radii r, a quantity that is ignored in most analyses. When using our physics knowledge about this large-r density together with the information contained in the high-q data, the model dependence of the extrapolation is reduced, and different parameterizations of the pre-2010 data yield a consistent value for R = 0.887 ± 0.012 fm. This value disagrees with the more precise value 0.8409 ± 0.0004 fm determined from the Lamb shift in muonic hydrogen.
Highlights
The interest in the root-mean-square radius R of the proton charge distribution is twofold: First, R is an integral quantity that characterizes the size of an elementary particle, the proton.Second, an accurate value for R is required in order to precisely calculate transition energies in the hydrogen atom, needed in connection with the definition of fundamental constants, the Rydberg constant in particular [1], and precision tests of QED
When using our physics knowledge about this large-r density together with the information contained in the high-q data, the model dependence of the extrapolation is reduced, and different parameterizations of the pre-2010 data yield a consistent value for R = 0.887 ± 0.012 fm
From electron scattering disagrees with the more precise value from muonic hydrogen, 0.8409 ± 0.0004 fm [3,4,5]; the comparison to the radius from electronic hydrogen [6,7] is not yet conclusive. This so-called “proton radius puzzle” has generated an extensive discussion ranging from a reevaluation of the uncertainties of R from the determination via electron scattering to understanding the difference in terms of new physics
Summary
The interest in the root-mean-square (rms) radius R of the proton charge distribution is twofold: First, R is an integral quantity that characterizes the size of an elementary particle, the proton. The value of R from electron scattering (a recent compilation listed 0.879 ± 0.009 fm [2]) disagrees with the more precise value from muonic hydrogen, 0.8409 ± 0.0004 fm [3,4,5]; the comparison to the radius from electronic hydrogen [6,7] is not yet conclusive. This so-called “proton radius puzzle” has generated an extensive discussion ranging from a reevaluation of the uncertainties of R from the determination via electron scattering to understanding the difference in terms of new physics. We will summarize the situation on the determination of R via electron-proton scattering and provide a critical analysis of the extractions of R described in the literature; in some cases, we repeat analogous determinations to better understand the origins of discrepant results
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