Pion Valence Quark Distribution at Large $x$ from Lattice QCD

Raza Sabbir Sufian, Colin Egerer, Joseph Karpie, Robert G. Edwards, Bálint Joó, Yan-Qing Ma, Kostas Orginos, Jian-Wei Qiu, David G. Richards

Published 2020-01-14Version 1

Using a short-distance collinear factorization, the pion valence quark distribution $q^\pi_{\rm v}(x)$ is extracted from spacelike correlations of antisymmetrized vector and axial-vector (V-A) currents, where the employed perturbative hard coefficient is derived to one-loop. Finite lattice spacing, volume, and quark mass dependencies are investigated in a simultaneous fit of matrix elements computed on four gauge ensembles, providing a physical limit Ioffe time distribution. Using two different phenomenologically motivated parametrizations of $q^\pi_{\rm v}(x)$, the $q^\pi_{\rm v}(x)$ distribution is found to be in very good agreement with that extracted from experimental data. At large $x$, a softer valence quark distribution is slightly favored by the figure of merit of this calculation. These two distributions are consistent within uncertainty and reproduce the extraction of $q^\pi_{\rm v}(x)$ from the experimental data in the entire $x$-region, showing the robustness of our calculation.