First direct lattice-QCD calculation of the x -dependence of the pion parton distribution function

Abstract

We present the first direct lattice-QCD calculation of the Bjorken-x dependence of the valence quark distribution of the pion. Using large-momentum effective theory (LaMET), we calculate the boosted pion state with long Wilson link operators. After implementing the one-loop matching and meson mass corrections, our result at mπ≈310 MeV is in agreement with those extracted from experimental data as well as from the Dyson-Schwinger equation in the small-x region, but there is a sizeable discrepancy in the large-x region. This discrepancy provides a nice opportunity to systematically study and disentangle the artifacts in the LaMET approach, which will eventually help to discern various existing analyses in the literature.