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 ($η=0$) it yields the familiar impact-parameter density, while at finite skewness ($η\neq 0$) it encodes a genuine parton-nucleon correlation whose norm decreases predictably with the rapidity gap $Δy = 2\mathrm{artanh} η$. 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 $(x,η,t)$ 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.