Pion valence-quark parton distribution function

Within the Dyson–Schwinger equation formulation of QCD, a rainbow ladder truncation is used to calculate the pion valence-quark distribution function (PDF). The gap equation is renormalized at a typical hadronic scale, of order 0.5 GeV, which is also set as the default initial scale for the pion PDF. We implement a corrected leading-order expression for the PDF which ensures that the valence-quarks carry all of the pion's light-front momentum at the initial scale. The scaling behavior of the pion PDF at a typical partonic scale of order 5.2 GeV is found to be (1−x)ν(1−x)ν, with ν≃1.6ν≃1.6, as x approaches one.