Rapidity-dependent spin decomposition of the nucleon

We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At η = 0 it reduces to the standard impact-parameter density, while at η ≠ 0 it is an amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point t = − c η = − 4 η 2 m N 2 / ( 1 − η 2 ) and decreases monotonically with the rapidity gap Δ y = ln [ ( 1 + η ) / ( 1 − η ) ] = 2 artanh ( η ) . This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full ( x , η , t ) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet x -space channels at μ = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and t -slope systematics).