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arXiv · 2211.04434

Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions

Robert G. Edwards·Colin Egerer·Joseph Karpie·Nikhil Karthik·Christopher J. Monahan·Wayne Morris·Kostas Orginos·Anatoly Radyushkin·David Richards·Eloy Romero·Raza Sabbir Sufian·Savvas Zafeiropoulos
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Abstract

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 $z^2$ 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 $z^2$ 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 $\mu^2$. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned $z^2$ 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.

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Robert G. Edwards, Colin Egerer, Joseph Karpie, Nikhil Karthik, Christopher J. Monahan, Wayne Morris, Kostas Orginos, Anatoly Radyushkin, David Richards, Eloy Romero, Raza Sabbir Sufian, Savvas Zafeiropoulos. 2022-11-08. Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions. https://doi.org/10.1007/jhep03(2023)086

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