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Pion generalized parton distributions at zero skewness

Fernando Chandra, Parada T. P. Hutauruk, Terry Mart

Abstract

In this paper, we systematically study the generalized parton distributions (GPDs) of the pion Goldstone Boson at zero skewness ($ξ=0$) 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 $μ^2 =$ 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 $r_{S}^π =$ 0.56 fm, $ r_V^π =$ 0.63 fm, and $r_{T}^π =$ 0.83 fm for the pion scalar, vector, and tensor form factors, respectively.

Pion generalized parton distributions at zero skewness

Abstract

In this paper, we systematically study the generalized parton distributions (GPDs) of the pion Goldstone Boson at zero skewness () 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 4 and 27 GeV. 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 0.56 fm, 0.63 fm, and 0.83 fm for the pion scalar, vector, and tensor form factors, respectively.

Paper Structure

This paper contains 9 sections, 23 equations, 7 figures.

Table of Contents

  1. Introduction
  2. NJL model framework
  3. Generalized parton distributions
  4. Numerical Result and Discussion
  5. Vector, tensor, and scalar pion GPDs
  6. Pion PDFs
  7. Pion generalized form factors
  8. Charge radii
  9. Summary and conclusion

Figures (7)

  • Figure 1: The vector pion GPDs $\mathcal{H}^u (x,\xi,t)$ as functions of $\xi$ and $x$ for different $t =0.0$ GeV$^2$ (upper left panel), $-t=0.2$ GeV$^2$ (upper right panel), $-t=0.5$ GeV$^2$ (bottom left panel) and $-t=1.0)$ GeV$^2$ (bottom right panel).
  • Figure 2: Same as in Fig. \ref{['gpd1']} but for the tensor pion GPDs $E^u (x,\xi,t)$.
  • Figure 3: Same as in Fig. \ref{['gpd1']}, but for the scalar pion GPDs $\mathcal{H}_S^u (x,\xi,t)$.
  • Figure 4: Pion PDFs at $\mu^2 =$ 27 (left panel) and 4 (right panel) GeV$^2$. The pion PDFs are evolved from the initial model scale $\mu_0^2 = 0.18$ GeV$^2$. Note that the pion PDFs are computed from the pion GPDs. Experimental and JAM data are taken from Refs. E615:1989bda, and Barry:2021osv, respectively.
  • Figure 5: The vector pion form factors $F^V_\pi (Q^2) = A_{1,0} (t)$ (upper left panel), scalar pion form factors $F^S_\pi (Q^2)$ (bottom center panel), and tensor pion form factors $F^T_\pi (Q^2) = B_{1,0} (t)$ (upper right panel) in comparison with the recent lattice QCD Alexandrou:2021ztx and experimental data Amendolia:1984nzNA7:1986vavJeffersonLabFpi-2:2006yshJeffersonLabFpi:2007virJeffersonLab:2008jveJeffersonLab:2008gyl. Note that each panel is plotted with a different vertical scale.
  • ...and 2 more figures