Nucleon Generalized Parton Distributions from Full Lattice QCD

Calculated quark spin and orbital angular momentum contributions to the spin of the nucleon for up- and down-quarks versus the pion mass squared. The stars at the physical pion mass denote the experimental values of the quark spin contributions, ΔΣu and ΔΣd

Understanding how the structure of hadrons emerges from QCD is one of the central challenges of contemporary nuclear physics. Recent advances in lattice field theory, developments in computer technology and investment in computer resources for fundamental QCD research have now made lattice QCD a powerful quantitative tool that provides an unprecedented opportunity to understand the phenomena arising from QCD from first principles, and to make precision calculations of the predictions of QCD.

A revealing example is exhibited in an investigation of the source of the spin of the nucleon. The contribution of the quark spin to nucleon spin is known relatively well from polarized deep-inelastic scattering experiments. More recently, it has been shown how to determine the contribution of the total angular momentum of the quarks to nucleon spin, and hence the orbital angular momentum carried by the quarks, from generalized parton distributions (GPDs) using Ji's sum rule [1]. The figure shows the calculation [2] of the contribution from up and down quarks to the angular momentum of the nucleon (neglecting the disconnected diagrams in the lattice simulations).  While the contributions of the orbital angular momentum of the u and d quarks separately are not small, only a negligible fraction of the nucleon's spin is found to arise from the total quark angular momentum.

References:
[1] X. Ji, Phys. Rev. Lett. 78 (1997) 610
[2] P. Haegler et al., Phys. Rev. D 77 (2008) 094502