Quark Orbital Angular Momentum from Lattice QCD

TL;DR

This paper uses lattice QCD to calculate the quark orbital angular momentum and gluon angular momentum contributions to the proton spin, providing quantitative insights into the spin structure of the nucleon.

Contribution

It introduces a stochastic estimation method for disconnected insertions that reduces errors, enabling precise calculation of quark and gluon angular momentum contributions on the lattice.

Findings

Quark orbital angular momentum accounts for about 34% of proton spin.

Total quark contribution to proton spin is approximately 30%.

Gluon angular momentum contributes around 40% to the proton spin.

Abstract

We calculate the quark orbital angular momentum of the nucleon from the quark energy-momentum tensor form factors on the lattice. The disconnected insertion is estimated stochastically which employs the $Z_2$ noise with an unbiased subtraction. This reduced the error by a factor of 4 with negligible overhead. The total quark contribution to the proton spin is found to be $0.30 \pm 0.07$. From this and the quark spin content we deduce the quark orbital angular momentum to be $0.17 \pm 0.06$ which is $\sim 34$% of the proton spin. We further predict that the gluon angular momentum to be $0.20 \pm 0.07$, i. e. $\sim$ 40% of the proton spin is due to the glue.