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 Z₂ 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±0.07. From this and the quark spin content we deduce the quark orbital angular momentum to be 0.17±0.06 which is ~34% of the proton spin. We further predict that the gluon angular momentum is 0.20±0.07; i.e., ~40% of the proton spin is due to the glue.