Lattice QCD Determination of the Bjorken-x Dependence of Parton Distribution Functions at Next-to-Next-to-Leading Order

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings a=0.04 and 0.06 fm and valence pion mass mπ=300 MeV, at boost momentum as large as 2.42 GeV. As a crucial step to control the systematics, we renormalize the pion valence quasidistribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the MS¯ scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-x space yield a reliable determination of the valence quark distribution for 0.03x0.80 with 5%-20% uncertainties.