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

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 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.

Evolution of parton distribution functions in the short-distance factorization scheme

“…The leading order DGLAP evolution was first used in [5], where numerical evidence suggested that the quenched lattice QCD results for M(ν, z 2 ) indeed follow this evolution in z 2 . More generally, a wealth of numerical analyses have shown that for z < 0.2 ∼ 0.3 fm, various truncations of the perturbative matching give rather similar results, mostly compatible with the phenomenological knowledge of unpolarized PDFs [40,52,[58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75].…”

Overview of hadron structure from lattice QCD

“…A recent calculation of the iso-vector helicity quark PDF was reported in Ref. [39] by the HadStruc Collaboration. A single lattice spacing a = 0.094 fm and slightly heavier than physical quark mass was used.…”