Quark Orbital Angular Momentum from Lattice QCD

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.

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