Transverse charge distributions of the nucleon and their Abel images

TL;DR

This paper explores how the transverse charge distributions of the nucleon change with increasing longitudinal momentum and how Abel transformations relate 3D distributions to 2D transverse ones, revealing induced electric dipole moments.

Contribution

It introduces a detailed analysis of the evolution of transverse charge distributions with momentum and applies Abel transformations to connect 3D and 2D distributions in nucleons.

Findings

Electric dipole moment increases with nucleon momentum

Maximum dipole moment occurs around 3.2 GeV

Abel transformations effectively relate 3D and 2D distributions

Abstract

We investigate the two-dimensional transverse charge distributions of the transversely polarized nucleon. As the longitudinal momentum ($P_z$) of the nucleon increases, the electric dipole moment is induced, which causes the displacement of the transverse charge and magnetization distributions of the nucleon. The induced dipole moment of the proton reaches its maximum value at around $P_z \approx 3.2$ GeV due to the kinematical reason. We also investigate how the Abel transformations map the three-dimensional charge and magnetization distributions in the Breit frame on to the transverse charge and magnetization ones in the infinite momentum frame.