Rapidity-Dependent Spin Decomposition of the Nucleon

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 ($\eta \ne 0$) 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 $H,E,\tilde{H}$ 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.

Comments: v1: 7 pages, 5 figures; v2: restructured manuscript, published version