Determination of the generalized parton distributions through the analysis of the world electron scattering data considering two-photon exchange corrections

We determine the valence generalized parton distributions (GPDs) ${H}_{v}^{q}$ and ${E}_{v}^{q}$ with their uncertainties at zero skewness by performing a ${\chi }^{2}$ analysis of the world electron scattering data considering two-photon exchange corrections. The data include a wide and updated range of the electric and magnetic form factors (FFs) of the proton and neutron. As a result, we find that there are not enough constraints on GPDs ${E}_{v}^{q}$ from FFs data solely though ${H}_{v}^{q}$ are well constrained. By including the new data of the charge and magnetic radius of the nucleon in the analysis, we show that they put new constraints on the final GPDs, especially on ${E}_{v}^{q}$. Moreover, we calculate the gravitational FF ${M}_{2}$ and the total angular momentum ${J}^{q}$ using the extracted GPDs and compare them with the FFs obtained from the light-cone QCD sum rules (LCSR) and lattice QCD. We show that our results are interestingly in a good consistency with the pure theoretical predictions.