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

Yoshitaka Hatta,Dong-Jing Yang

doi:10.1016/j.physletb.2018.03.081

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.

Highlights

Over the past decades, tremendous effort has been poured into determining the partonic helicity contributions to the nucleon spin
We find that there is a significant cancellation between the helicity and orbital angular momentum distributions at small-x both in the quark and gluon sectors
We restrict ourselves to the Q2-evolution equation, and do not discuss the evolution equation in x. The latter requires an intricate resummation of double logarithms αs ln2 1/x which has recently enjoyed renewed interest for the helicity distributions [15,16,17,18,19], but not yet for the orbital angular momentum distributions

Summary

INTRODUCTION

Tremendous effort has been poured into determining the partonic helicity contributions to the nucleon spin. A recent NLO global QCD analysis has found a nonzero contribution from the helicity of gluons ∆G [1]. We find that there is a significant cancellation between the helicity and orbital angular momentum distributions at small-x both in the quark and gluon sectors. We restrict ourselves to the Q2-evolution equation, and do not discuss the evolution equation in x The latter requires an intricate resummation of double logarithms αs ln2 1/x which has recently enjoyed renewed interest for the helicity distributions [15,16,17,18,19], but not yet for the orbital angular momentum distributions. Where and how exactly this transition occurs is presently not understood

EVOLUTION EQUATION

NUMERICAL RESULTS

ANALYTICAL INSIGHTS

CONCLUSIONS