Distinguishing Quarks and Gluons in Pion and Kaon Parton Distribution Functions.

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 nonperturbative 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 nonperturbative 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 etal. pion-induced Drell-Yan data, but nevertheless exhibits the q_{π}(x)≃(1-x)^{2} behavior as x→1 predicted by perturbative QCD.