Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
Résumé
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. Novel to this calculation is the establishment of a prescription for rigorously removing this contamination from the leading-twist signal. An analysis of the short-distance behavior of the leading pseudo-distribution using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF. 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 $\mu^2$. In particular, the leading-twist helicity PDFs as well as several sources of systematic error, such as higher-twist effects and discretization errors, are jointly determined by characterizing the computed pseudo-distributions in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the leading 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.