Quark orbital angular momentum from lattice QCD

Abstract

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 $0.30\ifmmode\pm\else\textpm\fi{}0.07.$ From this and the quark spin content we deduce the quark orbital angular momentum to be $0.17\ifmmode\pm\else\textpm\fi{}0.06$ which is $\ensuremath{\sim}34%$ of the proton spin. We further predict that the gluon angular momentum is $0.20\ifmmode\pm\else\textpm\fi{}0.07;$ i.e., $\ensuremath{\sim}40%$ of the proton spin is due to the glue.