We introduce gauge-invariant quark and gluon angular momentum distributions after making a generalization of the angular momentum density operators. From the quark angular momentum distribution, we define the gauge-invariant and leading-twist quark orbital angular momentum distribution $L_q\mathrm{}\left(x\right).$ The latter can be extracted from data on the polarized and unpolarized quark distributions and the off-forward distribution $E\left(x\right)\mathrm{}$ in the forward limit. We comment upon the evolution equations obeyed by this as well as other orbital distributions considered in the literature.

• Received 12 August 1998

DOI:https://doi.org/10.1103/PhysRevD.59.014013