We demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element M(P z3, z 2 3 ) as a function of the Ioffe time ν = P z3 and the distance z3. The next step is to divide M(P z3, z 2 3 ) by the rest-frame density M(0, z 2 3 ). Our lattice calculation shows a linear exponential z3-dependence in the rest-frame function, expected from the Z(z 2 3 ) factor generated by the gauge link. Still, we observe that the ratio M(P z3, z 2 3 )/M(0, z 2 3 ) has a Gaussian-type behavior with respect to z3 for 6 values of P used in the calculation. This means that Z(z 2 3 ) factor was canceled in the ratio. When plotted as a function of ν and z3, the data are very close to z3-independent functions. This phenomenon corresponds to factorization of the x-and k ⊥ -dependence for the TMD F(x, k 2 ⊥ ). For small z3 ≤ 4a, the residual z3-dependence is explained by perturbative evolution, with αs/π = 0.1.

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 present a calculation of the pion valence quark distribution extracted using the formalism of reduced Ioffe time pseudo-distributions or more commonly known as pseudo-PDFs. Our calculation is carried out on two different 2+1 flavor QCD ensembles using the isotropic-clover fermion action, with lattice dimensions 24 3 × 64 and 32 3 × 96 at the lattice spacing of a = 0.127 fm, and with the quark mass equivalent to a pion mass of mπ 415 MeV. We incorporate several combinations of smeared-point and smeared-smeared pion source-sink interpolation fields in obtaining the lattice QCD matrix elements using the summation method. After one-loop perturbative matching and combining the pseudo-distributions from these two ensembles, we extract the pion valence quark distribution using a phenomenological functional form motivated by the global fits of parton distribution functions. We also calculate the lowest four moments of the pion quark distribution through the "OPE without OPE". We present a qualitative comparison between our lattice QCD extraction of the pion valence quark distribution with that obtained from global fits and previous lattice QCD calculations.arXiv:1909.08517v1 [hep-lat]

In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution functions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings a = 0.127 fm and a = 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume extrapolation systematic errors of the PDF are estimated. In addition to the x dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.

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 examine the relation of moments of parton distribution functions to matrix elements of non-local operators computed in lattice quantum chromodynamics. We argue that after the continuum limit is taken, these non-local matrix elements give access to moments that are finite and can be matched to those defined in the M S scheme. We demonstrate this fact with a numerical computation of moments through non-local matrix elements in the quenched approximation and we find that these moments are in agreement with the moments obtained from direct computations of local twist-2 matrix elements in the quenched approximation.

The computation of the parton distribution functions (PDF) or distribution amplitudes (DA) of hadrons from first principles lattice QCD constitutes a central open problem. In this study, we present and evaluate the efficiency of a selection of methods for inverse problems to reconstruct the full x-dependence of PDFs. Our starting point are the so called Ioffe time PDFs, which are accessible from Euclidean time calculations in conjunction with a matching procedure. Using realistic mock data tests, we find that the ill-posed incomplete Fourier transform underlying the reconstruction requires careful regularization, for which both the Bayesian approach as well as neural networks are efficient and flexible choices.

We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudo-distributions. Beyond the reconstruction of the Bjorken-x dependence we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudo-distribution. We compare our findings with the pertinent phenomenological determinations.