Electromagnetic form factors of the nucleon from Nf=2+1 lattice QCD

There is a long-standing discrepancy between different measurements of the electric and magnetic radii of the proton. Lattice QCD calculations are a well-suited tool for theoretical investigations of the structure of the nucleon from first principles. However, all previous lattice studies of the proton’s electromagnetic radii have either neglected quark-disconnected contributions or were not extrapolated to the continuum and infinite-volume limit. Here, we present results for the electromagnetic form factors of the proton and neutron computed on the (2+1)-flavor coordinated lattice simulations (CLS) ensembles including both quark-connected and -disconnected contributions. From simultaneous fits to the Q2-, pion-mass, lattice-spacing, and finite-volume dependence of the form factors, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain as our final values ⟨rE2⟩p=(0.672±0.014(stat)±0.018(syst)) fm2, ⟨rM2⟩p=(0.658±0.012(stat)±0.008(syst)) fm2, and μMp=(2.739±0.063(stat)±0.018(syst). The magnetic moment is in good agreement with the experimental value, as is the one of the neutron. On the one hand, our result for the electric (charge) radius of the proton clearly points towards a small value, as favored by muonic hydrogen spectroscopy and the recent ep-scattering experiment by PRad. Our estimate for the magnetic radius, on the other hand, is well compatible with that inferred from the A1 ep-scattering experiment. Published by the American Physical Society 2024