QCD Analysis of Polarized Deep Inelastic Data and Parton Distributions

TL;DR

This work delivers a comprehensive QCD analysis of world polarized DIS data at LO and NLO, extracting polarized parton densities and the QCD scale $\Λ_{\rm QCD}$ while providing fully correlated $1\sigma$ error bands. It implements both a standard $\overline{\rm MS}$ evolution and a scheme-invariant approach based on observables, enabling cross-checks and insight into scale dependence and future data potential. The study furnishes two parameterizations to account for poorly constrained low-$x$ gluon and sea quark behavior, propagating uncertainties to predictions for other polarized observables and lattice-comparable moments. The results indicate that current inclusive data robustly determine valence densities but leave gluon and sea flavors relatively weakly constrained, with $\α_s(M_Z^2)$ around 0.113–0.114 and $\Λ_{\rm QCD}^{(4)}$ near 235–240 MeV, within the stated errors and scheme considerations.

Abstract

A QCD analysis of the world data on polarized deep inelastic scattering is presented in leading and next-to-leading order. New parameterizations are derived for the quark and gluon distributions for the kinematic range $x ε[10^{-9},1], Q^2 ε[1,10^6] \GeV^2$. The extrapolation far outside the domain of the current measurements is given both to allow for applications at higher values of $Q^2$ and to be able to calculate integral properties of the present distributions. The values of $Λ_{\rm QCD}$ and $α_s(M_z)$ are determined. Emphasis is put on the derivation of the fully correlated $1σ$ error bands for these distributions, which are also given in terms of parameterizations and are directly applicable to determine experimental errors of other polarized observables. The impact of the variation of both the renormalization and factorization scales on the value of $α_s$ is studied. Finally we perform a factorization--scheme invariant QCD analysis based on the observables $g_1(x,Q^2)$ and $d g_1(x,Q^2)/d \log(Q^2)$ in next-to-leading order, which is compared to the standard analysis. A series of low moments of parton densities, accounting for error correlation, are given to allow for comparison with results from lattice simulations.

Figures (13)

• Figure 1: LO polarized parton distributions at the input scale $Q_0^2 = 4.0~\,\hbox{GeV}^2$, ISET = 1, (solid line) compared to results obtained by GRSV (dashed--dotted line) GRSV and AAC (dashed line) AAC. The shaded areas represent the fully correlated $1\sigma$ error bands calculated by Gaussian error propagation. The dark dotted lines indicate the positivity bounds choosing the distributions GRV for reference.
• Figure 2: LO polarized parton distributions at the input scale $Q_0^2 = 4.0~\,\hbox{GeV}^2$, ISET=2, (solid line) compared to results obtained by GRSV (dashed--dotted line) GRSV and AAC (dashed line) AAC. The shaded areas represent the fully correlated $1\sigma$ error bands calculated by Gaussian error propagation. The dark dotted lines correspond to the positivity bounds according to the parameterization GRV.
• Figure 3: NLO polarized parton distributions at the input scale $Q_0^2 = 4.0~\,\hbox{GeV}^2$, ISET=3, (solid line) compared to results obtained by GRSV (dashed--dotted line) GRSV and AAC (dashed line) AAC. The shaded areas represent the fully correlated $1\sigma$ error bands calculated by Gaussian error propagation. The dark dotted lines correspond to the positivity bounds choosing GRV for reference.
• Figure 4: NLO polarized parton distributions at the input scale $Q_0^2 = 4.0~\,\hbox{GeV}^2$, ISET=4, (solid line) compared to results obtained by GRSV (dashed--dotted line) GRSV and AAC (dashed line) AAC. The shaded areas represent the fully correlated $1\sigma$ error bands calculated by Gaussian error propagation. The dark dotted lines indicate the positivity bound if reference is taken to the distributions GRV.
• Figure 5: NLO polarized momentum distribution for the gluon at the input scale $Q_0^2 = 5.0~\,\hbox{GeV}^2$ for ISET=3 (BB1, dashed line) and ISET =4 (BB2, dash-dotted line) with 1$\sigma$ error bands shown (shaded areas). The solid line corresponds to the unpolarized distribution GRV. To the latter we added the experimental error of the unpolarized gluon distribution as determined in the H1 experiment H1 (hatched area), see also [48].