Quark spin-orbit correlations in the proton

TL;DR

This paper uses lattice QCD to calculate quark spin-orbit correlations in the proton, revealing strong coupling between quark spin and orbital angular momentum through GTMDs at physical pion mass.

Contribution

It provides the first lattice QCD calculation of quark spin-orbit correlations using GTMDs at physical pion mass, directly connecting quark position and momentum distributions.

Findings

Evidence for strong quark spin-orbit coupling in the proton

First direct lattice calculation of quark spin-orbit correlations at physical pion mass

Extraction of both Jaffe-Manohar and Ji spin-orbit correlations

Abstract

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.