We present the first exploratory lattice QCD calculation of the pion valence quark distribution extracted from spatially separated current-current correlations in coordinate space. We show that an antisymmetric combination of vector and axial-vector currents provides direct information on the pion valence quark distribution. Using the collinear factorization approach, we calculate the perturbative tree-level kernel for this current combination and extract the pion valence distribution. The main goal of this article is to demonstrate the efficacy of this general lattice QCD approach in the reliable extraction of parton distributions. With controllable power corrections and a good understanding of the lattice systematics, this method has the potential to serve as a complementary to the many efforts to extract parton distributions in global analyses from experimentally measured cross sections. We perform our calculation on an ensemble of 2+1 flavor QCD using the isotropicclover fermion action, with lattice dimensions 32 3 × 96 at a lattice spacing a = 0.127 fm and the quark mass equivalent to a pion mass mπ 416 MeV.

We extract the pion valence quark distribution q π v ðxÞ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted q π v ðxÞ and that obtained from experimental data across the entire x range. Further, we demonstrate that the oneloop matching coefficient relating the LQCD matrix computed in position space to the q π v ðxÞ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD-calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.

We investigate the application of the distillation smearing approach, and the use of the variational method with an extended basis of operators facilitated by this approach, on the calculation of the nucleon isovector charges g u−d S , g u−d A , and g u−d T . We find that the better sampling of the lattice enabled through the use of distillation yields a substantial reduction in the statistical uncertainty in comparison with the use of alternative smearing methods, and furthermore, appears to offer better control over the contribution of excited-states compared to use of a single, local interpolating operator. The additional benefit arising through the use of the variational method in the distillation approach is less dramatic, but nevertheless significant given that it requires no additional Dirac inversions.A routinely come up short. Recent work by [1] employs a methodology inspired by the Feynman-Hellman theorem to control excited-state effects by summing over all current insertion times, engendering extrapolation in a single Euclidean temporal variable rather than two -agreement was found to within arXiv:1810.09991v1 [hep-lat]