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 $\pi \pi \to N\bar{N}$ data. Using representative datasets we find for a cut of $Q^2\le 0.5$ GeV${}^2$, $r_M^p=0.91_{-0.06}^{+0.03}\pm 0.02$ fm using just proton scattering data; $r_M^p=0.87_{-0.05}^{+0.04}\pm 0.01$ 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.