Abstract
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 no 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.
Highlights
It is well known that the three-dimensional (3D) description of hadrons can be accessed by studying generalized parton distributions (GPDs) [1–5], which are physically related to the parton distribution functions (PDFs) [6–8], e.g., with the help of double distribution representation [1,9]
A good approach to find the unknown parameters of the parametrized distributions in any χ2 analysis of the experimental data is performing a parametrization scan as it is usually used in the global analysis of PDFs [33]
We utilize this procedure to find the optimum values of the parameters and overcome the positivity problem described at the end of the previous section
Summary
It is well known that the three-dimensional (3D) description of hadrons can be accessed by studying generalized parton distributions (GPDs) [1–5], which are physically related to the parton distribution functions (PDFs) [6–8], e.g., with the help of double distribution representation [1,9]. One advantage of GPDs over PDFs is that they provide quantitative information on both the longitudinal and transverse distributions of partons inside the nucleon. In this way, the structure of the nucleon can be investigated in more details using GPDs which include more degrees of freedom. We include the data of the charge and magnetic radius of the nucleons in the analysis to investigate their impacts on the extracted GPDs. The content of the present paper is as follows.
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