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

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.