The Spin Structure of the Nucleon

TL;DR

This review surveys the spin structure of the nucleon in the framework of QCD, detailing how spins and orbital angular momenta of quarks and gluons combine to yield the proton’s half-unit spin. It integrates perturbative and nonperturbative insights through DIS, resonance, elastic processes, and sum rules, while highlighting modern formalisms like light-front dynamics, GPDs, and TMDs. The text discusses how experimental data from DIS, SIDIS, Drell–Yan, and collider measurements constrain $ ext{ΔΣ}$, $ ext{ΔG}$, and $ ext{L}_q, ext{L}_g$, and it emphasizes the role of lattice QCD and light-front holographic QCD in linking hadron spectroscopy to partonic degrees of freedom. The findings show a nucleon spin composed of significant quark OAM and moderate gluon contributions, with hadron-parton duality and higher-twist effects providing a coherent picture across energy scales, informing the nonperturbative dynamics of color confinement. The work also outlines future prospects, including extended kinematic coverage at an EIC and GPD/GTMD measurements, to precisely map spin decompositions and the origin of confinement in QCD.

Abstract

We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nucleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions since it involves fundamental aspects of hadron structure, and it can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpolarized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experiments provide various ways to investigate non-perturbative QCD. Fundamental sum rules -- such as the Bjorken sum rule for polarized photoabsorption on polarized nucleons -- are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of...

Figures (19)

• Figure 1: Inclusive electron scattering off a nucleon, in the first Born approximation. The blob represents the nonperturbative response of the target to the photon.
• Figure 2: Definitions of the polar angle $\theta^{*}$ and azimuthal angle $\phi^{*}$ of the target spin $\vec{S}$. The scattering plane is defined by $x\otimes z$.
• Figure 3: Response of the nucleon to the electromagnetic probe as a function of $Q^2$ and $\nu$. The $\nu$-positions of the peaks (N, $\Delta$,...) change as $Q^2$ varies. (After Gross:1985dn.)
• Figure 4: Various $\overrightarrow{p} \overrightarrow{p}$ reactions probing the proton spin structure. Panel A: Drell-Yan process and its underlying LO diagram. Panel B: Direct diphoton production at LO. Panel C: $W^{+ / -}$ production at LO. Panel D: LO process dominating photon, pion and/or Jet production in $\overrightarrow{p} \overrightarrow{p}$ scattering. Panel E: heavy-flavor meson production at LO.
• Figure 5: Annihilation of $e^+ ~ e^-$ with only one detected hadron from the final state.