Distinguishing Quarks and Gluons in Pion and Kaon PDFs

Abstract

The leading-twist parton distribution functions of the pion and kaon are calculated for the first time using a rainbow-ladder truncation of QCD's Dyson-Schwinger equations (DSEs) that self-consistently sums all planar diagrams. The non-perturbative gluon dressing of the quarks is thereby correctly accounted for, which in practice means solving the inhomogeneous Bethe-Salpeter equation (BSE) for the quark operator that defines the spin-independent quark distribution functions. An immediate consequence of using this dressed vertex is that gluons carry 35% of the pion's and 30% of the kaon's light-cone momentum, with the remaining momentum carried by the quarks. The scale associated with these DSE results is $μ_0 = 0.78\,$GeV. The gluon effects generated by the inhomogeneous BSE are inherently non-perturbative and cannot be mimicked by the perturbative QCD evolution equations. A key consequence of this gluon dressing is that the valence quarks have reduced support at low-to-intermediate $x$, where the gluons dominate, and increased support at large $x$. As a result, our DSE calculation of the pion's valence quark distribution is in excellent agreement with the Conway et al. pion-induced Drell-Yan data, but nevertheless exhibits the $q_π(x) \simeq (1-x)^2$ behavior as $x\to 1$ predicted by perturbative QCD.