Precise determination of the proton magnetic radius from electron scattering data
J. M. Alarcón, D. W. Higinbotham, C. Weiss
Abstract
We extract the proton magnetic radius from high-precision electron-proton elastic scattering cross section data. Our theoretical framework combines dispersion analysis and chiral effective field theory and implements the dynamics governing the shape of the low-${Q}^{2}$ form factors. It allows us to use data up to ${Q}^{2}\ensuremath{\approx}0.5\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$ for constraining the radii and overcomes the difficulties of empirical fits and ${Q}^{2}\ensuremath{\rightarrow}0$ extrapolation. We obtain a magnetic radius ${r}_{M}^{p}=0.850\ifmmode\pm\else\textpm\fi{}0.001$ ($1\ensuremath{\sigma}$ fit uncertainty) ${}_{\ensuremath{-}0.004}^{+0.009}$ (full-range theory uncertainty) fm, significantly different from earlier results obtained from the same data using empirical fits, and close to our extracted electric radius ${r}_{E}^{p}=0.842\ifmmode\pm\else\textpm\fi{}0.002$ ($1\ensuremath{\sigma}$ fit uncertainty) ${}_{\ensuremath{-}0.002}^{+0.005}$ (full-range theory uncertainty) fm.