Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
Robert Edwards (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Ave., Newport News, VA, 23606, USA); Colin Egerer (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Ave., Newport News, VA, 23606, USA); Joseph Karpie (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Ave., Newport News, VA, 23606, USA); Nikhil Karthik (Department of Physics, William and Mary, 300 Ukrop Way, Williamsburg, VA, 23187, USA); Christopher Monahan (Thomas Jefferson National Accelerator Facility, 12000 Jefferson Ave., Newport News, VA, 23606, USA, Department of Physics, William and Mary, 300 Ukrop Way, Williamsburg, VA, 23187, USA); et al - Show all 12 authors
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 μ 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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