Document Type

Conference Paper

Publication Date




Publication Title

Proceedings of the 38th International Symposium on Lattice Field Theory- Proceedings of Science




413 (1-8)

Conference Name

The 38th International Symposium on Lattice Field Theory, LATTICE2021, 26-30 July, 2021, Zoom/Gather@Massachusetts Institute of Technology


Generalized transverse momentum-dependent parton distributions (GTMDs) provide a comprehensive framework for imaging the internal structure of the proton. In particular, by encoding the simultaneous distribution of quark transverse positions and momenta, they allow one to directly access longitudinal quark orbital angular momentum, and, moreover, to correlate it with the quark helicity. The relevant GTMD is evaluated through a lattice calculation of a proton matrix element of a quark bilocal operator (the separation in which is Fourier conjugate to the quark momentum) featuring a momentum transfer (which is Fourier conjugate to the quark position), as well as the Dirac structure appropriate for capturing the quark helicity. The weighting by quark transverse position requires a derivative with respect to momentum transfer, which is obtained in unbiased fashion using a direct derivative method. The lattice calculation is performed directly at the physical pion mass, using domain wall fermions to mitigate operator mixing effects. Both the Jaffe-Manohar as well as the Ji quark spin-orbit correlations are extracted, yielding evidence for a strong quark spin-orbit coupling in the proton.

Original Publication Citation

Engelhardt, M., Green, J., Hasan, N., Izubuchi, T., Kallidonis, C., Krieg, S., Liuti, S., Meinel, S., Negele, J., Pochinsky, A., Rajan, A., Silvi, G., & Syritsyn, S. (2022). Quark spin-orbit correlations in the proton. The 38th International Symposium on Lattice Field Theory, LATTICE2021, Zoom/Gather@Massachusetts Institute of Technology.