Abstract
We extract the proton magnetic radius from the 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 $Q^2\sim$ 0.5 GeV$^2$ for constraining the radii and overcomes the difficulties of empirical fits and $Q^2 \rightarrow 0$ extrapolation. We obtain a magnetic radius $r_M^p$ = 0.850 $\pm$0.001 (fit 68%) $\pm$0.010 (theory full range) fm, significantly different from earlier results obtained from the same data, and close to the extracted electric radius $r_E^p$ = 0.842 $\pm$0.002 (fit) $\pm$0.010 (theory) fm.
Highlights
The electromagnetic form factors (EM FFs) are the most basic expressions of the nucleon’s finite spatial extent and composite internal structure
The statistically significant deviations observed in some E and Q2 regions are likely due to systematic effects in the data. (b) Most of the impact on the fit comes from data in the midrange E bins (0.45, 0.585, 0.72 GeV), where the data are most precise
Our theory-based method allows us to determine the proton’s magnetic radius with a precision comparable to the electric one. This is because the dispersion-theoretical framework correlates the values of the radii with the behavior of the FFs at finite Q2 ≈ 0.1–0.5 GeV2, where the magnetic FF contributes to the cross section with a strength comparable to the electric one
Summary
The electromagnetic form factors (EM FFs) are the most basic expressions of the nucleon’s finite spatial extent and composite internal structure. They describe the elastic response to external electric and magnetic fields as a function of the four-momentum transfer Q2 and can be associated with the spatial distributions of charge and current in the nucleon. The traditional representation of FFs in terms of three-dimensional spatial densities at fixed instant time x0 is appropriate only for nonrelativistic systems such as nuclei [1] For relativistic systems such as hadrons, the spatial structure is expressed through two-dimensional transverse densities at fixed light-front time x+ = x0 + x3. The EM FFs reveal aspects of the spatial distribution of quarks and their orbital motion and spin and have become objects of great interest in nucleon structure studies [5,6]
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