Document Type


Publication Date




Publication Title

Journal of High Energy Physics






86 (1-51)


The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z2 contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z2 contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale μ2. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned z2 contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.


This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original authors and source are credited.

Original Publication Citation

Edwards, R., Egerer, C., Karpie, J., Karthik, N., Monahan, C., Morris, W., Orginos, K., Radyushkin, A., Richards, D., & Romero, E. (2023). Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions. Journal of High Energy Physics, 2023(3), 1-51, Article 86.


0000-0002-9326-1300 (Radyushkin)