Extraction of Pion Unpolarized Quark Generalized Parton Distribution from Charge Form Factors

TL;DR

This paper presents a data-driven extraction of the pion's unpolarized quark GPDs at zero skewness, combining experimental form factor and PDF data within a unified theoretical framework.

Contribution

It introduces a flexible parameterization and a GPD framework that links electromagnetic form factors and parton distributions for the pion, providing new insights into its internal structure.

Findings

Extracted pion GPDs consistent with experimental data

Provided impact-parameter-space interpretations of the pion structure

Supplied essential input for future collider and lattice studies

Abstract

Based on a global fit to experimental measurements of the pion electromagnetic form factor and parton distribution functions (PDFs), we report a data-driven determination of the unpolarized quark generalized parton distributions (GPDs) for the case of pion in the zero-skewness limit ($\xi = 0$). The form factor is parameterized using a flexible functional form constrained by data and embedded into a GPD framework constructed from collinear PDFs and a profile function encoding transverse dynamics. This approach provides a unified description of the pion's electromagnetic structure and its spatial parton distributions. We present the extracted pion GPDs and their impact-parameter-space interpretations, offering new insights into the internal structure of the lightest QCD bound state and providing essential input for future electron-ion collider studies via the Sullivan process, as well as for the exclusive $\pi^+$ electroproduction at the 12~GeV Jefferson Lab program, pion-induced exclusive measurements at COMPASS, proposed pion-beam experiments at AMBER, and phenomenological and lattice investigations of the structure of the meson.