On the small-$x$ behavior of the orbital angular momentum distributions in QCD

Yoshitaka Hatta, Dong-Jing Yang

Published 2018-02-08Version 1

We present the numerical solution of the leading order QCD evolution equation for the orbital angular momentum distributions of quarks and gluons and discuss its implications for the nucleon spin sum rule. We observe that at small-$x$, the gluon helicity and orbital angular momentum distributions are roughly of the same magnitude but with opposite signs, indicating a significant cancellation between them. A similar cancellation occurs also in the quark sector. We explain analytically the reason for this cancellation.