Model independent extraction of the proton magnetic radius from electron scattering

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 $ππ\to N\bar{N}$ 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 $ππ$ 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 $ππ$ data.

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