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The Spin Structure of the Nucleon

Christine A. Aidala, Steven D. Bass, Delia Hasch, Gerhard K. Mallot

TL;DR

The paper surveys the global effort to unravel the nucleon's spin composition, tracing the journey from the EMC discovery of a small quark spin contribution to the modern picture where valence quark spin, gluon polarization, and orbital angular momentum (via GPDs and TMDs) together build the proton's spin. It integrates experimental results from polarized DIS and polarized pp collisions with QCD-based interpretations, highlighting the axial anomaly, spin sum rules, and the emerging three-dimensional structure of the nucleon. Key findings include a flavor-singlet axial charge $g_A^{(0)}|_{ m pDIS} \approx 0.35$, evidence for nonzero but not dominant gluon polarization, and substantial orbital angular momentum implications explored through GPDs and TMDs. The work emphasizes a coherent, multi-pronged approach—longitudinal spin, transversity, and 3D nucleon structure—that maps the spin puzzle and guides next-generation experiments like the EIC and upgraded facilities.

Abstract

This article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed at understanding the transverse structure of the nucleon. We discuss present experimental investigations of the nucleon's internal spin structure, the theoretical interpretation of the different measurements and the open questions and challenges for future investigation.

The Spin Structure of the Nucleon

TL;DR

The paper surveys the global effort to unravel the nucleon's spin composition, tracing the journey from the EMC discovery of a small quark spin contribution to the modern picture where valence quark spin, gluon polarization, and orbital angular momentum (via GPDs and TMDs) together build the proton's spin. It integrates experimental results from polarized DIS and polarized pp collisions with QCD-based interpretations, highlighting the axial anomaly, spin sum rules, and the emerging three-dimensional structure of the nucleon. Key findings include a flavor-singlet axial charge , evidence for nonzero but not dominant gluon polarization, and substantial orbital angular momentum implications explored through GPDs and TMDs. The work emphasizes a coherent, multi-pronged approach—longitudinal spin, transversity, and 3D nucleon structure—that maps the spin puzzle and guides next-generation experiments like the EIC and upgraded facilities.

Abstract

This article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed at understanding the transverse structure of the nucleon. We discuss present experimental investigations of the nucleon's internal spin structure, the theoretical interpretation of the different measurements and the open questions and challenges for future investigation.

Paper Structure

This paper contains 37 sections, 37 equations, 23 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Spin Structure Functions and Parton Distributions
  3. Experiments
  4. SLAC experiments
  5. CERN experiments
  6. The EMC and SMC experiments
  7. The COMPASS experiment
  8. The HERMES experiment at DESY
  9. JLab experiments
  10. Hadronic scattering experiments
  11. The Relativistic Heavy Ion Collider
  12. RHIC as a polarized $p+p$ collider
  13. RHIC experiments
  14. The PHENIX detector
  15. The STAR detector
  16. ...and 22 more sections

Figures (23)

  • Figure 1: The Compass spectrometer, for a description see text.
  • Figure 2: Semi-inclusive DIS studied at COMPASS, HERMES and JLab.
  • Figure 3: The PHENIX detector at RHIC as configured for data taking in 2012.
  • Figure 4: World data on $x g_1$ as a function of $x$ for the proton (top), the deuteron (middle) and the neutron (bottom) at the $Q^2$ of the measurement. Only data points for $Q^2> 1~\mathrm{GeV}^2$ and $W>2.5~\mathrm{GeV}$ are shown. Error bars are statistical errors only.
  • Figure 5: World data for $g_1(x,Q^2)$ for the proton with $Q^2> 1~\mathrm{GeV}^2$ and $W>2.5~\mathrm{GeV}$. For clarity a constant $c_i = 0.28(11.6-i)$ has been added to the $g_1$ values within a particular $x$ bin starting with $i=0$ for $x=0.006$. Error bars are statistical errors only. (Also shown is the QCD fit of Leader:2005ci.)
  • ...and 18 more figures