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 with the quenched approximation. The disconnected insertion is estimated stochastically which employs the $Z_2$ noise with an unbiased subtraction. This reduced the error by a factor of 3–4 with negligible overhead. The total quark contribution to the proton spin is found to be $0.30\pm \mathrm{0.07.}$ 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 is $0.20\pm 0.07;$ i.e., $\sim 40\%$ of the proton spin is due to the glue.