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 $m_\pi \approx 310$ MeV is in agreement with those extracted from experimental data as well as from Dyson-Schwinger equation in small $x$ region, but 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.