Pion generalized parton distributions at zero skewness

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.