Gluonic contributions to the pion parton distribution functions

Abstract

We investigate the role of a dynamical gluon in the pion within the Basis Light-Front Quantization (BLFQ) framework and compare it with the solution of the Minkowski space Bethe-Salpeter equation (BSE), focusing on contributions beyond the valence sector. We develop a framework to compute the quark-antiquark-gluon component of the pion, starting from its valence light-front wave function. Additionally, the quark and gluon parton distribution functions (PDFs) are derived by considering this higher Fock component in the pion state. The proposed operator, which acts on the valence state to produce the quark-antiquark-gluon component of the pion, is tested against results from BLFQ for its contribution to the quark and gluon PDFs, as well as with results from the BSE. In the BLFQ framework, we identify the effect of dynamical chiral symmetry breaking on the pion structure through the enhancement of the spin-flip matrix element. This enhancement is captured in the $|q\bar{q}g\rangle$ component of the light-front wave function and the associated gluon PDF. We explicitly demonstrate an enhancement of the low-$x$ contribution in the quark PDF, which is associated with the large spin-flip matrix element, which also drives the $\pi-\rho$ mass splitting. The proposed framework also enables an exploration of the effect of the dressed gluon mass for a given valence state at the pion scale. We show that when the gluon mass vanishes, departing from the constituent gluon picture, it has a significant impact on the gluon PDF.