Effects of evolution at high-x in the pion valence parton distribution

In its simplest picture, the pion is represented by a pair of up and anti-down valence quarks. Hard scattering processes which probe the pion’s structure have revealed an increasing number of quarks, antiquarks, and gluons with increasing momentum transfer Q². Parton distribution functions (PDFs) describe the momentum distributions of the pion’s constituent partons in terms of x, the fraction of the pion’s momentum carried by each parton. We expect the behavior of the valence PDFs to be represented by (1-x)^β as x→1. Brodsky-Farrar quark counting rules predict limiting values of β(x, Q²), but theoretical models disagree on their predictions of β(x, Q²). We have carried out leading order perturbative evolution of the valence PDFs of two models, based on light front holographic QCD and Dyson-Schwinger methods respectively, from their starting scales. We calculated moments of the distributions, and compared our results to experiment, lattice calculations, and global PDF fits. We determined asymptotic values of β(x, Q²) for the models in the high-x and high-Q² limit. The models disagree at all Q², so the tension between models remains and more experimental data is needed. Forthcoming experimental data from Jefferson Lab and from the Electron-Ion Collider will provide a crucial test of the models and of the QCD counting rules.