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

TL;DR

This paper numerically solves the leading order QCD evolution equations for quark and gluon orbital angular momentum distributions at small-$x$, revealing significant cancellations that impact the nucleon spin sum rule.

Contribution

It provides the first numerical solution of the evolution equations for orbital angular momentum distributions and explains the observed cancellations analytically.

Findings

Gluon and quark orbital angular momentum distributions are of similar magnitude but opposite sign at small-$x$.

Significant cancellations occur between gluon helicity and orbital angular momentum distributions.

Analytical explanation for the cancellation phenomena is provided.

Abstract

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.