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Off-Forward Parton Distributions

Xiangdong Ji

TL;DR

Off-Forward Parton Distributions (OFPDs) extend forward parton densities by including momentum transfer and skewness, enabling access to the nucleon's spin structure and to hard diffractive processes. The paper defines H(x,ξ,t) and E(x,ξ,t) through twist-two operator form factors, discusses their light-cone interpretation, and surveys alternative notations. It reviews what is known at hadron-mass scales, the leading-order evolution kernels, and the qualitative effects of evolution on OFPDs, as well as experimental probes via DVCS and vector-meson production with factorization. It highlights modeling challenges, theoretical constraints, and future directions including higher-order QCD corrections and lattice input.

Abstract

Recently, there have been some interesting developments involving off-forward parton distributions of the nucleon, deeply virtual Compton scattering, and hard diffractive vector-meson production. These developments are triggered by the realization that the off-forward distributions contain information about the internal spin structure of the nucleon and that diffractive electroproduction of vector mesons depends on these unconventional distributions. This paper gives a brief overview of the recent developments.

Off-Forward Parton Distributions

TL;DR

Off-Forward Parton Distributions (OFPDs) extend forward parton densities by including momentum transfer and skewness, enabling access to the nucleon's spin structure and to hard diffractive processes. The paper defines H(x,ξ,t) and E(x,ξ,t) through twist-two operator form factors, discusses their light-cone interpretation, and surveys alternative notations. It reviews what is known at hadron-mass scales, the leading-order evolution kernels, and the qualitative effects of evolution on OFPDs, as well as experimental probes via DVCS and vector-meson production with factorization. It highlights modeling challenges, theoretical constraints, and future directions including higher-order QCD corrections and lattice input.

Abstract

Recently, there have been some interesting developments involving off-forward parton distributions of the nucleon, deeply virtual Compton scattering, and hard diffractive vector-meson production. These developments are triggered by the realization that the off-forward distributions contain information about the internal spin structure of the nucleon and that diffractive electroproduction of vector mesons depends on these unconventional distributions. This paper gives a brief overview of the recent developments.

Paper Structure

This paper contains 14 sections, 65 equations, 3 figures.

Table of Contents

  1. introduction
  2. Definitions and Interpretations
  3. Elastic Form Factors of Twist-Two Operators
  4. OFPD's in Light-Cone Coordinates and Gauge
  5. Other Notations and Definitions
  6. OFPD's and The Spin Structure of the Nucleon
  7. What do we know about OFPD's?
  8. OFPD's at Hadron-Mass Scale
  9. Evolution Equations
  10. Effects of Evolution
  11. Probing OFPD's in High-energy Experiment
  12. Deeply Virtual Compton Scattering
  13. Vector Meson Production
  14. summary and outlook

Figures (3)

  • Figure 1: Diagrams showing $\xi$ symmetry of the off-forward parton distributions: a) $x>\xi$; b) $\xi>x>-\xi$; c) $x<-\xi$.
  • Figure 2: a). Compton scattering; b) Leading Feynman diagrams for DVCS.
  • Figure 3: a). A representative Feynman diagram for neutral meson production through off-forward gluon distributions in the nucleon; b) A representative Feynman diagram for meson production through off-forward quark distributions in the nucleon.