Nucleon GPDs in nonlocal chiral effective theory

Representation of the convolution formula and the three-dimensional distribution of u quarks as a function of x and t for fixed skewness ξ = 0.1.

The Science

Generalized parton distributions (GPDs) are powerful tools for investigating nucleon structure, providing three-dimensional images of the nucleon’s internal quark and gluon substructure. The spin-averaged GPDs Hq and Eq for the u and d quarks in the nucleon, as well as their moments, were studied in the framework of nonlocal chiral effective field theory (EFT). Chiral EFT is a powerful tool for studying flavor asymmetries in quark distributions, particularly those associated with the pion cloud of the nucleon. Nonlocal EFT imposes local gauge invariance and generates a covariant correlation function, which renders loop integrals convergent, and extends the range of applicability of the theory to larger momentum transfers than in local EFT. The obtained three-dimensional GPDs can then be used to compute physical observables up to momentum transfers squared of t = 1 GeV^2 and compared with experiment.

The Impact

This study derived generalized convolution formulas for nonzero skewness GPDs, which involve both the DGLAP and ERBL regions, and verified that the moments of the GPDs satisfy the correct polynomial properties. The gauge invariant introduction of a covariant correlation function within the nonlocal chiral EFT, representing the finite extent of hadrons, extends the applicability of the theory up to momentum transfers ~ 1 GeV. An obvious extension of this work is the inclusion of contributions from the coupling to intermediate state baryons. The strategy employed would also facilitate calculation of chiral loop contributions to spin-dependent GPDs, and even generalized transverse momentum distributions, which can provide further insights into the three-dimensional structure of the proton.

Summary

Within the framework of nonlocal chiral EFT, we computed the one-loop contributions to the spin-averaged GPDs of the nucleon at nonzero skewness from coupling to pseudoscalar mesons with intermediate octet and decuplet baryons. Generalizing the forward convolution formulas to nonzero skewness in both the DGLAP and ERBL regions, we derived the three-dimensional distributions Hq and Eq, which are functions of parton momentum fraction x, skewness ξ and four-momentum transfer squared t. Our results are consistent with phenomenological extractions of sea quark asymmetries for forward scattering from experimental data.

Contact

Wally Melnitchouk
Jefferson Lab
wmelnitc@jlab.org

Publications

• Zhengyang Gao, Fangcheng He, Chueng-Ryong Ji, W. Melnitchouk, Y. Salamu and P. Wang, Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness, Phys. Rev. D110, 054049 (2024).

• P. Wang, Fangcheng He, Chueng-Ryong Ji and W. Melnitchouk, Nucleon form factors and parton distributions in nonlocal chiral effective theory, Prog. Part. Nucl. Phys. 129, 104017 (2023).