The Proton Radius from Electron Scattering Data

Abstract

[Background] The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. [Purpose] In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. [Method] We make use of stepwise regression techniques using the $F$-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. [Results] Starting with the precision, low four-momentum transfer ($Q^2$) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the $F$-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on $G_E$ from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-$Q^2$ data on $G_E$ to select functions which extrapolate to high $Q^2$, we find that a Padé ($N=M=1$) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, $G_E(Q^2)=(1+Q^2/0.66{\mathrm{GeV}}^2{)}^{-2}$. [Conclusions] From this statistical analysis, we conclude that the electron scattering result and the muonic hydrogen result are consistent. It is the atomic hydrogen results that are the outliers.

10 pages, 7 figures, 7 tables

References in corpus (7)

• High-precision determination of the electric and magnetic form factors of the proton
• Global analysis of proton elastic form factor data with two-photon exchange corrections
• The Proton Radius Puzzle
• Extraction of the proton radius from electron-proton scattering data
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Evaluation of the strength of electron-proton scattering data for determining the proton charge radius
• Polynomial fits and the proton radius puzzle

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