# Monopole and quadrupole contributions to the angular momentum density

## TL;DR

This paper investigates the monopole and quadrupole contributions to the angular momentum density in nucleons, revealing their unique relationship and emphasizing their roles in visualizing angular momentum distributions.

## Contribution

It demonstrates that monopole and quadrupole contributions are uniquely related, with the quadrupole being induced by the monopole, clarifying their roles in angular momentum density visualization.

## Key findings

- Quadrupole contribution is induced by the monopole contribution.
- Monopole and quadrupole contributions are uniquely related.
- Both contributions are important for visualizing angular momentum density.

## Abstract

The energy-momentum tensor form factors contain a wealth of information about the nucleon. It is insightful to visualize this information in terms of 3D or 2D densities related by Fourier transformations to the form factors. The densities associated with the angular momentum distribution were recently shown to receive monopole and quadrupole contributions. We show that these two contributions are uniquely related to each other. The quadrupole contribution can be viewed as induced by the monopole contribution, and contains no independent information. Both contributions however play important roles for the visualization of the angular momentum density.