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The theory and phenomenology of polarized deep inelastic scattering

M. Anselmino, A. Efremov, E. Leader

TL;DR

This review synthesizes the theory and phenomenology of polarized deep inelastic scattering, detailing how spin-dependent structure functions $g_1(x)$ and $g_2(x)$ arise from both naive parton models and full QCD-based formalisms. It highlights the central role of the axial anomaly and the gluon spin density $oldsymbol{\\Delta g}$ in reconciling experimental results (notably the EMC spin measurements) with the nucleon's total spin, and it connects perturbative QCD corrections via the Operator Product Expansion to observable moments like $oldsymbol{\\Gamma_1}$ and the Bjorken sum rule. The article contrasts the Naive Parton Model, the QCD-improved Parton Model, and the QCD Field Theoretic Model, clarifying how factorization, higher-twist effects, and nonperturbative topological phenomena shape the interpretation of spin observables. It also surveys key experimental strategies (asymmetries $A_ ext{parallel}$ and $A_ ext{perp}$, semi-inclusive jet channels) and the status of sum-rule tests, emphasizing the ongoing interplay between theory and data in understanding the spin structure of the nucleon. The work underscores that the proton’s spin composition evolves with QCD scale, with gluon and orbital angular momentum contributions growing at higher $Q^2$, while preserving fundamental sum rules as required by QCD symmetries.

Abstract

Comprehensive review paper on the theory and phenomenology of polarized deep inelastic scattering, to appear in Physics Reports

The theory and phenomenology of polarized deep inelastic scattering

TL;DR

This review synthesizes the theory and phenomenology of polarized deep inelastic scattering, detailing how spin-dependent structure functions and arise from both naive parton models and full QCD-based formalisms. It highlights the central role of the axial anomaly and the gluon spin density in reconciling experimental results (notably the EMC spin measurements) with the nucleon's total spin, and it connects perturbative QCD corrections via the Operator Product Expansion to observable moments like and the Bjorken sum rule. The article contrasts the Naive Parton Model, the QCD-improved Parton Model, and the QCD Field Theoretic Model, clarifying how factorization, higher-twist effects, and nonperturbative topological phenomena shape the interpretation of spin observables. It also surveys key experimental strategies (asymmetries and , semi-inclusive jet channels) and the status of sum-rule tests, emphasizing the ongoing interplay between theory and data in understanding the spin structure of the nucleon. The work underscores that the proton’s spin composition evolves with QCD scale, with gluon and orbital angular momentum contributions growing at higher , while preserving fundamental sum rules as required by QCD symmetries.

Abstract

Comprehensive review paper on the theory and phenomenology of polarized deep inelastic scattering, to appear in Physics Reports

Paper Structure

This paper contains 74 sections, 574 equations.

Table of Contents

  1. Introduction
  2. Notation
  3. Polarized lepton-nucleon Deep Inelastic Scattering - General aspect
  4. General formalism in one photon exchange approximation
  5. Structure functions and Bjorken scaling
  6. Cross-section differences
  7. Experimental measurement of $g_1$ and $g_2$ on nucleon targets
  8. Measurement of $g_{1,2}$ on nuclear targets
  9. Neutral and charged current weak interactions initiated by charged leptons
  10. Weak interaction structure functions and their measurement
  11. The Naive Parton Model in polarized DIS
  12. Projection of $F_1, F_2, g_1$ and $g_2$ from the hadronic tensor $W_{\mu\nu}$
  13. The hadronic tensor and the nucleon structure functions in the Naive Parton Model
  14. Intrinsic $p_\perp$ and $g_2 (x)$
  15. Conflicting Parton Model results for $g_2 (x)$
  16. ...and 59 more sections