We combine constraints from analyticity with experimental electron-proton scattering data to determine the proton magnetic radius without model-dependent assumptions on the shape of the form factor. We also study the impact of including electron-neutron scattering data, and $\pi\pi\to N\bar{ N}$ data. Using representative datasets we find for a cut of $Q^2\leq0.5$ GeV$^2$, $r_M^p=0.91^{ +0.03}_{ -0.06}\pm0.02$ fm using just proton scattering data; $r_M^p=0.87^{ +0.04}_{ -0.05}\pm0.01$ fm adding neutron data; and $r_M^p=0.87^{ +0.02}_{ -0.02}$ fm adding $\pi\pi$ data. We also extract the neutron magnetic radius from these data sets obtaining $r_M^n=0.89^{ +0.03}_{ -0.03}$ fm from the combined proton, neutron, and $\pi\pi$ data.
Categories: hep-ph nucl-th