The Spin Structure of the Proton

TL;DR

The article surveys the proton spin problem within QCD, detailing how quark spins, gluon spin, and topology may combine to generate the proton’s 1/2 spin. It outlines spin sum rules derived from dispersion relations and the operator product expansion, and then maps these to parton-model and light-cone formalisms that connect to experimental observables. The review covers extensive experimental programs (DIS, SIDIS, SIDIS, SIDIS with semi-inclusive hadrons, RHIC, DVCS) and the theoretical interplay between the axial anomaly, gluon topology, transversity, and generalized parton distributions. It closes with open questions about the size of Δg, potential fixed-pole corrections, orbital angular momentum, and the role of small-x dynamics in spin structure, highlighting upcoming experiments as crucial tests of QCD spin dynamics.

Abstract

This article reviews our present understanding of the QCD spin structure of the proton. We first outline the proton spin puzzle and its possible resolution in QCD. We then review the present and next generation of experiments to resolve the proton's spin-flavour structure, explaining the theoretical issues involved, the present status of experimental investigation, and the open questions and challenges for future investigation.

Figures (21)

• Figure 1: The world data on $xg_1$ with data points shown at the $Q^2$ they were measured at. Figure courtesy of U. Stoesslein.
• Figure 2: The world data on $g_1$ with data points shown at the $Q^2$ they were measured at. Figure courtesy of U. Stoesslein.
• Figure 3: $Q^2$ dependence of $g_1^p$ for $Q^2 > 1$GeV$^2$ together with a simple fit according to Anthony:2000 and a NLO perturbative QCD fit from Stoesslein:2002.
• Figure 4: Difference between the measured proton (SLAC E-143) and neutron (SLAC E-154) integrals calculated from a minimum $x$ value, $x_{\rm min}$ up to $x$ of 1. The value is compared to the theoretical prediction from the Bjorken sum rule which makes a prediction over the full $x$ range. For the prediction, the Bjorken sum rule is evaluated up to third order in $\alpha_s$Larin:1997 and at $Q^2$ = 5 (GeV/c)$^2$. Error bars on the data are dominated by systematic uncertainties and are highly correlated point-to-point. Figure from Abe:1997.
• Figure 5: The $Q^2$ averaged measured of $x g_2$ (SLAC data) compared with the twist-two Wandzura-Wilczek contribution $g_2^{WW}$ term (solid line) and several quark model calculations. Figure from Anthony:2003.