Empirical transverse charge densities in the nucleon and the nucleon-to-$\Delta$ transition

TL;DR

This paper maps the transverse charge densities of the nucleon and the nucleon-to-Delta transition using empirical electromagnetic form factors, revealing dipole, monopole, and quadrupole patterns related to charge distribution deformations.

Contribution

It provides the first empirical mapping of transverse charge densities for the nucleon and N to Delta transition, highlighting their complex charge distribution patterns.

Findings

Charge densities exhibit dipole and monopole patterns.

Transition densities show monopole, dipole, and quadrupole structures.

Deformation of hadron charge distribution is observed.

Abstract

Using only the current empirical information on the nucleon electromagnetic form factors we map out the transverse charge density in proton and neutron as viewed from a light front moving towards a transversely polarized nucleon. These charge densities are characterized by a dipole pattern, in addition to the monopole field corresponding with the unpolarized density. Furthermore, we use the latest empirical information on the $N \to \Delta$ transition form factors to map out the transition charge density which induces the $N \to \Delta$ excitation. This transition charge density in a transversely polarized $N$ and $\Delta$ contains both monopole, dipole and quadrupole patterns, the latter corresponding with a deformation of the hadron's charge distribution.