Gluon Distributions in the Pion

Abstract

We formulate a light-front model for the pion that explicitly incorporates the gluonic degree of freedom. In this framework, high-energy scattering off the pion is described by an active gluon, while the remaining constituents are treated as a spectator system with an effective mass. The mass spectrum and light-front wave functions (LFWFs) of the pion are determined by solving two Schr\"odinger-like equations derived from quantum chromodynamics: the light-front holographic equation in the chiral limit and the 't~Hooft equation. Using the resulting LFWFs, we compute the gluon distributions within pion, including the parton distribution functions in comparison with the available global fits, generalized parton distributions, and transverse momentum-dependent distributions. The present analysis is restricted to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) domain of the pion's gluon GPD, without explicit construction of the Efremov-Radyushkin-Brodsky-Lepage (ERBL) region. Consequently, the polynomiality condition for full Mellin moments is not satisfied by construction. Furthermore, we demonstrate that the obtained LFWFs provide a good description of the gravitational form factors of pion when compared with the recent lattice QCD results.