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

We present the first direct lattice-QCDcalculation of the Bjorken-$x$ dependence of the valence quark distribution in the pion. Using large-momentum effective theory (LaMET), we calculate the boosted pionstate with long Wilson link operators. With lattice data calculated at 310 MeV pionmass, we illustrate the numerical impact of one-loop matching and meson mass corrections. Our results are comparable quantitatively with the results extracted from experimental data as well as from the Dyson-Schwinger equation. Future calculations at physical pionmass and larger momentum will be able to discern discrepancies in various existing analyses.