The Overlap Representation of Skewed Quark and Gluon Distributions

TL;DR

This work develops an exact overlap representation for skewed parton distributions (SPDs) of quarks and gluons within light-cone quantization, unifying unpolarised, polarised, and helicity-changing cases. By performing a detailed Fock-state decomposition and employing light-cone wave function overlaps, the authors derive region-by-region expressions for SPDs and connect them to PDFs and hadronic form factors via reduction formulas and sum rules. They emphasize symmetry properties, positivity bounds, and the central ERBL region, which requires overlaps between states of differing parton numbers, revealing the role of orbital angular momentum in helicity-flip SPDs. The framework provides a principled basis for modeling SPDs (e.g., with Gaussian LCWFs) and for interpreting hard exclusive processes like DVCS and meson electroproduction, while outlining challenges related to polynomiality and higher Fock-state contributions.

Abstract

Within the framework of light-cone quantisation we derive the complete and exact overlap representation of skewed parton distributions for unpolarised and polarised quarks and gluons. Symmetry properties and phenomenological applications are discussed.

Figures (2)

• Figure 1: Illustration of two common choices to fix the longitudinal direction in the definition of the non-diagonal hadronic matrix element which defines skewed parton distributions. The flow of momenta is indicated on the lines.
• Figure 2: Overlap representations for SPDs in different kinematic regions for the case $\xi>0$. The flow of momenta is indicated on the lines. Top (bottom) right: the region $\xi<\bar{x}<1$ ($-1<\bar{x}<-\xi$), where the SPDs are given by $N\to N$ overlaps. Middle right: the central region $-\xi<\bar{x}<\xi$, where $N+1\to N-1$ overlaps are relevant.