QCD Analysis of Polarized Deep Inelastic Scattering Data

TL;DR

This work delivers a comprehensive NLO QCD analysis of world polarized DIS data, extracting polarized parton densities and the strong coupling constant while accounting for heavy-flavor contributions and scale uncertainties. The authors parameterize the input polarized PDFs, perform a correlated error treatment, and compute Mellin-space evolution and moments, comparing results with lattice QCD and other global fits. They find a notably smaller polarized gluon density than earlier analyses and αs(MZ^2) values consistent with other DIS determinations, with higher-twist effects compatible with zero within current precision. A public FORTRAN code and error grids are provided to propagate PDF uncertainties to polarized observables, enabling precise phenomenology for current and future experiments.

Abstract

A QCD analysis of the world data on polarized deep inelastic scattering is presented in next--to--leading order, including the heavy flavor Wilson coefficient in leading order in the fixed flavor number scheme. New parameterizations are derived for the quark and gluon distributions and the value of $α_s(M_z^2)$ is determined. The impact of the variation of both the renormalization and factorization scales on the distributions and the value of $α_s$ is studied. We obtain $α_s^{\rm NLO}(M_Z^2) = 0.1132~~\begin{array}{l} + 0.0056 \\ -0.0095 \end{array}$. The first moments of the polarized twist--2 parton distribution functions are calculated with correlated errors to allow for comparisons with results from lattice QCD simulations. Potential higher twist contributions to the structure function $g_1(x,Q^2)$ are determined and found to be compatible with zero both for proton and deuteron targets.

Figures (7)

• Figure 1: NLO polarized parton distributions at the input scale $Q_0^2 = 4.0~$ GeV$^2$ (solid line) compared to results obtained by GRSV (dashed--dotted line) GRSV, DSSV (long dashed--dotted line) DSSV, AAC (dashed line) AAC, and LSS (long dashed line) LSS. The shaded areas represent the fully correlated $1\sigma$ error bands calculated by Gaussian error propagation.
• Figure 2: The polarized parton density $x\Delta G(x)$ at $Q_0^2 = 4.0~$GeV$^2$ as a function of $x$ (solid line). The shaded area is the fully correlated $1\sigma$ statistical error band and the hatched areas are the systematic uncertainties. Results from GRSV (dashed--dotted line) GRSV, DSSV (long dashed--dotted line) DSSV, AAC (dashed line) AAC, and LSS (long dashed line) LSS are shown for comparison.
• Figure 3: The polarized parton density $x\Delta \Sigma(x)$ at $Q_0^2 = 4.0~$GeV$^2$ as a function of $x$ (solid line). The shaded area is the fully correlated $1\sigma$ statistical error band and the hatched areas are the systematic uncertainties. Results from GRSV (dashed--dotted line) GRSV, DSSV (long dashed--dotted line) DSSV, AAC (dashed line) AAC, and LSS (long dashed line) LSS are shown for comparison.
• Figure 4: The spin--dependent structure functions $xg_1^p(x)$, $xg_1^d(x)$ and $xg_1^n(x)$ as a function of $x$. The experimental data are evolved to a common value of $Q^2 = 5~{\rm GeV^2}$. The error bars shown are the statistical and systematic ones added in quadrature. The experimental distributions are well described (solid curve) within the statistical (shaded areas) and systematic (hatched areas) error bands. The curves obtained by GRSV (dashed-dotted) GRSV and AAC (dashed) AAC are shown for comparison.
• Figure 5: The spin--dependent structure function $xg_1^p(x,Q^2)$ as a function of $x$ and $Q^2$. The experimental data are compared to the fit result (solid curve) with the statistical error bands (shaded areas). The curves obtained by GRSV (dashed-dotted) GRSV, AAC (short dashed) AAC and LSS (long dashed) LSS are shown for comparison.