Precise determination of the proton magnetic radius from electron scattering data

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 ≈ 0.5 GeV 2 for constraining the radii and overcomes the difficulties of empirical fits and Q 2 → 0 extrapolation. We obtain a magnetic radius r p M = 0.850 ± 0.001 ( 1 σ fit uncertainty) + 0.009 − 0.004 (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 p E = 0.842 ± 0.002 ( 1 σ fit uncertainty) + 0.005 − 0.002 (full-range theory uncertainty) fm.