Generalized Parton Distributions and Distribution of Partons in the Transverse Plane

TL;DR

The paper analyzes Generalized Parton Distributions at zero skewness ($ξ=0$), showing that the $t$-dependence encodes the transverse spatial distribution of partons through a Fourier transform to impact-parameter space. It derives an overlap representation for $H(x,0,t)$ using light-front wave functions and establishes a gauge-invariant, positive density $f(x,{f b}_ot)$ describing parton distributions in the transverse plane. The work also clarifies the role of $E(x,0,t)$ in spin-dependent distortions and derives the connection to Ji's angular momentum sum rule, illustrating how GPDs unify momentum and spatial information to access total quark angular momentum. Practical implications include positivity constraints, modeling guidance for GPDs, and insights into the x-dependence of transverse structure.

Abstract

I discuss the physical interpretation of GPDs in the limit $ξ=0$, where the $t$ dependence contains information about the distribution of partons in the transverse plane. GPDs thus allow a simultaneous determination of the longitudinal momentum and transverse position of partons in the infinite momentum frame, which also provides a physical interpretation for Ji's angular momentum sum rule.