Parton Decomposition of Nucleon Spin and Momentum: Gluons from Dressed Quarks

The lowest two Mellin moments of hadronic Generalized Parton Distributions are explored within a model that allows investigation of the inter-related quark and gluon contributions. For light quarks their dynamical connection is strong due to quark dressing. Our principal focus is the angular momentum $J$ of the nucleon. This work employs and extends dynamical insights obtained from our recent model results for quark and gluon momentum fractions $\langle x \rangle_{\rm q/g}$ in both pion and nucleon. The employed model is based on the Rainbow-Ladder truncation of the Dyson-Schwinger equations of QCD. The special case of a 1-loop treatment of a single hadronic quark is used to motivate several insights and obtain initial estimates such as the Wilson line correction to the established Landau gauge model ($ -7\%$ for both $J_{\rm q}$ and $\langle x \rangle_{\rm q}$), and the "binding gluon" contribution to $\langle x \rangle_{\rm g}$ ($\leq 10\%$). We obtain the proton $J$ within 1\% after inclusion of the pion cloud mechanism to produce the sea. The gluon second Mellin moments of the proton reflect similar dynamics; ($\langle x \rangle_{\rm g}$, $J_{\rm g}$) are (26\% , 24\%) at model scale, and (40\%, 38\%) at $2$ GeV. We also find that $J_{\rm tot}$ is shared almost equally between the total orbital and total intrinsic spin contributions.