Rapidity-Dependent Spin Decomposition of the Nucleon

TL;DR

This paper explores the rapidity dependence of nucleon spin decomposition through Fourier transforms of GPDs, deriving new identities and providing comprehensive GPD models validated by lattice data and relevant experiments.

Contribution

It introduces a novel rapidity-dependent framework for nucleon spin decomposition and develops GPD models constrained by empirical data and Regge trajectories.

Findings

Rapidity dependence affects impact-parameter densities and parton-nucleon correlations.

Derived universal rapidity-modified Ji identities linking angular momenta.

GPD models agree with lattice data and predict outcomes for upcoming experiments.

Abstract

We show that the two-dimensional Fourier transform of the generalized parton distributions (GPDs) has two distinct interpretations: at zero skewness ($\eta=0$) it yields the familiar impact-parameter density, while at finite skewness ($\eta \neq 0$) it encodes a genuine parton-nucleon correlation whose norm decreases predictably with the rapidity gap $\Delta y = 2\mathrm{artanh} \eta$. This rapidity dependence produces universal rapidity-modified Ji identities linking helicity, orbital, and total angular momenta analytically. Using linear open- and closed string Regge trajectories constrained by empirical PDFs, spectroscopy and form factor data, we obtain the leading twist GPDs $H,E,\widetilde{H}$ across the full $(x,\eta,t)$ range. Numerical Mellin Barnes inversion agrees with existing lattice data and yields rapidity resolved predictions for Jefferson Lab 12 GeV, the Electron Ion Collider, and forthcoming lattice studies.