The charge and magnetic radii of the nucleons from the generalized parton distributions

The proton-radius puzzle refers to the discrepancy observed in measurements of the proton's charge radius when using different methods. This inconsistency has prompted extensive research and debate within the physics community, as it challenges the understanding of quantum electrodynamics and the fundamental properties of protons. In the present study, we determine the charge and magnetic radii of the proton and neutron through a global analysis of the generalized parton distributions (GPDs) at zero skewness. We emphasize the importance of a simultaneous analysis of all available experimental data related to nucleon radii, rather than relying on individual experiments, specific observables, or limited kinematic regions. This comprehensive approach ensures robust and consistent results, avoiding values that are either too small or too large. Our analysis yields the following results: $ r_{pE} = 0.8558 \pm 0.0135~\textrm{fm} $, $ r_{pM} = 0.8268 \pm 0.0533~\textrm{fm} $, $ \left<r_{nE}^2\right> = -0.1181 \pm 0.0270~\textrm{fm}^2 $, and $ r_{nM} = 0.8367 \pm 0.0845~\textrm{fm} $.