Quark spin and orbital angular momentum from proton GPDs

TL;DR

This paper computes the proton's spin structure using generalized parton distributions within the NJL model, revealing detailed quark and gluon angular momentum contributions and emphasizing the importance of diquark correlations.

Contribution

It provides a novel calculation of the proton's spin decomposition from GPDs in the NJL model, including the effects of diquark correlations and comparison with lattice QCD.

Findings

Up and down quarks carry specific intrinsic spins and orbital angular momenta.

Diquark correlations significantly affect flavor decomposition.

Gluons contribute a measurable amount to the proton's total angular momentum.

Abstract

We calculate the leading-twist helicity-dependent generalized parton distributions (GPDs) of the proton at finite skewness in the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics (QCD). From these (and previously calculated helicity-independent GPDs) we obtain the spin decomposition of the proton, including predictions for quark intrinsic spin and orbital angular momentum. The inclusion of multiple species of diquarks is found to have a significant effect on the flavor decomposition, and resolving the internal structure of these dynamical diquark correlations proves essential for the mechanical stability of the proton. At a scale of $Q^2=4\,$GeV$^2$ we find that the up and down quarks carry an intrinsic spin and orbital angular momentum of $S_u=0.534$, $S_d=-0.214$, $L_u=-0.189$, and $L_d=0.210$, whereas the gluons have a total angular momentum of $J_g=0.151$. The down quark is therefore found to carry almost no total angular momentum due to cancellations between spin and orbital contributions. Comparisons are made between these spin decomposition results and lattice QCD calculations.