Theoretical Analysis of Polarized Structure Functions
G. Altarelli, R. D. Ball, S. Forte, G. Ridolfi
TL;DR
The paper addresses the problem of determining the spin content of the nucleon from polarized structure functions within perturbative QCD. Its approach combines a review with an updated NLO analysis using the latest data to extract polarized parton distributions, their first moments, and the strong coupling $\alpha_s(Q^2)$, while examining theoretical issues and comparing with other analyses. Key findings include that the Bjorken sum rule for $g_1$ holds within about one standard deviation, while the Ellis–Jaffe sum rule is violated by about three standard deviations, with particular emphasis on the gluon polarization $\Delta g(x,Q^2)$ and the small-$x$ behavior driven by QCD evolution. The work also notes the unreliability of Regge extrapolations at large $Q^2$ and highlights the availability of complete two-loop evolution kernels for polarized PDFs at NLO and Wilson coefficients up to NNNLO, strengthening the theoretical framework for future analyses. This provides tighter constraints on $\Delta q(x,Q^2)$, $\Delta g(x,Q^2)$, and $\alpha_s(Q^2)$, guiding future experiments.
Abstract
We review the analysis of polarized structure function data using perturbative QCD at next-to-leading order. We use the most recent experimental data to obtain updated results for polarized parton distributions, first moments and the strong coupling. We also discuss several theoretical issues involved in this analysis and in the interpretation of its results. Finally, we compare our results with other similar analyses in the recent literature.