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Dynamical gluon effects in the three-dimensional structure of the pion

Jiangshan Lan1,2,3,4,*, Kaiyu Fu1,†, Satvir Kaur1,3,4,‡, Zhimin Zhu1,3,4,§, Chandan Mondal1,3,4,∥, Xingbo Zhao1,2,3,4,¶, and James P. Vary5,** (BLFQ Collaboration)

  • *Contact author: jiangshanlan@impcas.ac.cn
  • †Contact author: kaiyufu94@gmail.com
  • ‡Contact author: satvir@impcas.ac.cn
  • §Contact author: zhuzhimin@impcas.ac.cn
  • ∥Contact author: mondal@impcas.ac.cn
  • Contact author: xbzhao@impcas.ac.cn
  • **Contact author: jvary@iastate.edu
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Phys. Rev. D 113, 056016 – Published 18 March, 2026

DOI: https://doi.org/10.1103/r3g8-7f2l

Abstract

We investigate the internal structure of the pion, including the contributions from one dynamical gluon, using the basis light-front quantization approach. By solving a light-front QCD Hamiltonian with a three-dimensional confining potential, we obtain the light-front wave functions for both the quark-antiquark and quark-antiquark-gluon Fock sectors. These wave functions are then employed to compute the unpolarized generalized parton distributions and the transverse momentum–dependent parton distributions of valence quarks and gluons. We also extract the transverse spatial distributions, providing the squared radii of quark and gluon densities in the impact parameter space. This work contributes toward a three-dimensional understanding of the pion’s internal structure in both momentum and coordinate space.

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Phys. Rev. D 113, 056016– Published 18 March, 2026
  • Received 15 October 2025
  • Accepted 4 February 2026
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