The shape of the $\Delta$ baryon in a covariant spectator quark model

TL;DR

This paper employs a covariant spectator quark model to analyze the electromagnetic form factors of the $$ baryon, revealing its oblate charge distribution and discussing implications for its shape and deformation.

Contribution

It introduces a covariant spectator quark model that accurately describes lattice QCD and experimental data for the $$ baryon, providing new insights into its shape and electromagnetic properties.

Findings

The $^+$ charge distribution is oblate.

Quadrupole moment indicates deformation.

Transverse moments do not conclusively determine shape.

Abstract

Using a covariant spectator quark model that describes the recent lattice QCD data for the $\Delta$ electromagnetic form factors and all available experimental data on $\gamma N \to \Delta$ transitions, we analyze the charge and magnetic dipole distributions of the $\Delta$ baryon and discuss its shape. We conclude that the quadrupole moment of the $\Delta$ is a good indicator of the deformation and that the $\Delta^+$ charge distribution has an oblate shape. We also calculate transverse moments and find that they do not lead to unambiguous conclusions about the underlying shape.