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Spin, Twist and Hadron Structure in Deep Inelastic Processes

Robert L. Jaffe

TL;DR

The notes develop a unified, twist-based framework for spin-dependent phenomena in hard QCD processes, emphasizing how kinematics, light-cone dynamics, and the operator product expansion organize results across DIS, $e^+e^-$ annihilation, and Drell–Yan. By introducing generalized distribution and fragmentation functions, the work connects forward-scattering amplitudes to measurable structure functions (F1,F2,g1,g2) and their higher-twist corrections, while highlighting the distinct roles of helicity and transversity (h1) in nucleon spin. The analysis provides both the formal machinery (OPE, twist counting, light-cone quantization) and practical implications (WW decomposition of g2, Soffer-like bounds, Drell–Yan spin asymmetries, and fragmentation-based probes of h1). Overall, it offers a comprehensive, methodical toolkit for disentangling quark–gluon correlations and spin dynamics in high-energy hadronic processes, with clear paths to experimental access through polarized DIS, Drell–Yan, and fragmentation studies.

Abstract

These notes provide an introduction to polarization effects in deep inelastic processes in QCD. We emphasize recent work on transverse asymmetries, subdominant effects, and the role of polarization in fragmentation and in purely hadronic processes. After a review of kinematics and some basic tools of short distance analysis, we study the twist, helicity, chirality and transversity dependence of a variety of high energy processes sensitive to the quark and gluon substructure of hadrons.

Spin, Twist and Hadron Structure in Deep Inelastic Processes

TL;DR

The notes develop a unified, twist-based framework for spin-dependent phenomena in hard QCD processes, emphasizing how kinematics, light-cone dynamics, and the operator product expansion organize results across DIS, annihilation, and Drell–Yan. By introducing generalized distribution and fragmentation functions, the work connects forward-scattering amplitudes to measurable structure functions (F1,F2,g1,g2) and their higher-twist corrections, while highlighting the distinct roles of helicity and transversity (h1) in nucleon spin. The analysis provides both the formal machinery (OPE, twist counting, light-cone quantization) and practical implications (WW decomposition of g2, Soffer-like bounds, Drell–Yan spin asymmetries, and fragmentation-based probes of h1). Overall, it offers a comprehensive, methodical toolkit for disentangling quark–gluon correlations and spin dynamics in high-energy hadronic processes, with clear paths to experimental access through polarized DIS, Drell–Yan, and fragmentation studies.

Abstract

These notes provide an introduction to polarization effects in deep inelastic processes in QCD. We emphasize recent work on transverse asymmetries, subdominant effects, and the role of polarization in fragmentation and in purely hadronic processes. After a review of kinematics and some basic tools of short distance analysis, we study the twist, helicity, chirality and transversity dependence of a variety of high energy processes sensitive to the quark and gluon substructure of hadrons.

Paper Structure

This paper contains 57 sections, 177 equations, 30 figures, 5 tables.

Table of Contents

  1. Kinematics and other Generalities
  2. Deep Inelastic Scattering
  3. Basic Variables
  4. Cross Section and Structure Functions
  5. Structure Functions
  6. Scaling and Kinematic Domains
  7. Flavor Generalizations
  8. Cross Section for Electron-Hadron Scattering
  9. Other Basic Deep Inelastic Processes
  10. Inclusive $e^+$ $e^-$ Annihilation
  11. Inclusive $e^+e^-$ Annihilation with One Observed Hadron
  12. Lepton Pair Production
  13. Deep Inelastic Processes from a Coordinate Space Viewpoint
  14. $e^+ e^- \rightarrow$ hadrons -- The Short-distance Expansion
  15. $l p\rightarrow l X$ -- The Light-Cone Expansion
  16. ...and 42 more sections

Figures (30)

  • Figure 1: Kinematics of lepton-hadron scattering in the target rest frame
  • Figure 2: The squared amplitude ${\cal A}$ for electron-hadron scattering can be separated into a leptonic tensor $l^{\mu \nu}$ and a hadronic tensor $W^{\mu \nu}$.
  • Figure 3: The optical theorem relates the hadronic structure tensor, $W^{\mu\nu}$ to the imaginary part of forward ($P=P'$, $q=q'$), virtual ($Q^2<0$) Compton scattering
  • Figure 4: Kinematic domains in electron-nucleon scattering.
  • Figure 5: Kinematic variables in polarized lepton scattering from a polarized target.
  • ...and 25 more figures