Pion valence quark distribution from current-current correlation in lattice QCD

Abstract

We extract the pion valence quark distribution $q_{\mathrm{v}}^{\pi }(x)$ 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 $q_{\mathrm{v}}^{\pi }(x)$ and that obtained from experimental data across the entire $x$-range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{\mathrm{v}}^{\pi }(x)$ 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.

arXiv commentPublished version, Physical Review D

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