Proper identification of the gluon spin

TL;DR

This paper investigates the properties of a gauge-invariant definition of gluon spin, revealing it differs from the conventional polarization and suggesting the gluon contribution to nucleon spin may be smaller than previously thought.

Contribution

It introduces and analyzes a gauge-invariant gluon spin $S_g$, showing its relation to the usual polarization and its implications for nucleon spin composition.

Findings

$S_g$ is proportional to $rac{5}{9}\Delta g$

A significant part of $S_g$ cancels with static-field contributions in $L_g$

The gluon contribution to nucleon spin may be much smaller than traditionally estimated.

Abstract

Properties of the recently proposed gauge-invariant gluon spin $S_g$ are studied and compared to the usually defined "gluon polarization" $\Delta g$. By explicit 1-loop calculations in a quark state, it is found that $S_g= \frac 59\Delta g$. Furthermore, $\frac 45$ of $S_g$ can actually be identified as a "static-field" contribution and shown to cancel exactly an analogous static term in the gluon orbital angular momentum $L_g$, leaving $S_g+L_g$ unaltered. These observations suggest that if properly identified, the gluon contribution to the nucleon spin may be drastically smaller than in the conventional wisdom.