Pion generalized parton distributions at zero skewness

TL;DR

This study investigates the pion's generalized parton distributions at zero skewness using a covariant NJL model, successfully matching experimental, lattice, and QCD analysis data for form factors and parton distributions.

Contribution

It provides a comprehensive calculation of pion GPDs and form factors within the covariant NJL model, aligning well with experimental and lattice results, and offers new insights into pion structure.

Findings

Pion PDFs agree with experimental data and JAM analysis at multiple scales.

Generalized form factors are consistent with recent lattice data.

Computed pion charge radii for scalar, vector, and tensor form factors.

Abstract

In this paper, we systematically study the generalized parton distributions (GPDs) of the pion Goldstone Boson at zero skewness ($\xi =0$) in the framework of the covariant Nambu--Jona-Lasinio model with the help of the proper time regularization scheme to cure the divergence simultaneously to simulate the confinement. To this end, we evaluate the generalized form factors and parton distribution functions derived, respectively, from the first Mellin moments and the forward limit pion GPDs, in comparison to existing experimental data, recent lattice QCD simulations, and JAM global QCD analyses. We find that the pion parton distribution functions derived from the pion GPDs have excellent agreement with the experimental data and JAM analysis at renormalization scale $\mu^2 =$ 4 and 27 GeV$^2$. In addition, our results for the pion generalized form factors involving the scalar, vector, and tensor dressed form factors are consistent with recent lattice data and existing data. We then compute the charge radii for those dressed generalized form factors, and we obtain $r_{S}^{\pi} =$ 0.56 fm, $ r_V^{\pi} =$ 0.63 fm, and $r_{T}^{\pi} =$ 0.83 fm for the pion scalar, vector, and tensor form factors, respectively.