Orbital Angular Momentum Distribution of Gluons at Small-$x$ : Analytic interpolation between Ji and Jaffe-Manohar

TL;DR

This paper introduces a generalized gauge link that smoothly interpolates between Ji and Jaffe-Manohar orbital angular momentum operators, providing a unified framework for analyzing gluon angular momentum at small-x.

Contribution

It develops an analytic interpolation method between two prominent orbital angular momentum definitions using a generalized Wilson line gauge link.

Findings

Reproduces both Ji and Jaffe-Manohar operators in specific limits

Provides a continuous analytical interpolation between the two operators

Enhances understanding of gluon angular momentum distribution at small-x

Abstract

In this work, we first introduced a generalized Wilson line gauge link that reproduces both staple and near straight links along the light cone in different parameter limits. We then studied the gauge-invariant bi-local orbital angular momentum operator with such a general gauge link, in the framework of Chen et. al. decomposition of gauge fields. At the appropriate combination of limits, the operator reproduces both Jaffe-Manohar and Ji's operator structure and offers a continuous analytical interpolation between the two.