Electromagnetic multipole structure of a spin-one particle: Abel tomography case

TL;DR

This paper explores the multipole structure of spin-one particles, analyzing how 3D charge distributions project onto 2D distributions in different frames, highlighting the effects of geometry and relativistic boosts.

Contribution

It introduces a method to relate 2D and 3D charge distributions of spin-one particles using Abel transformation and differential equations, accounting for relativistic effects.

Findings

Derived connections between 2D and 3D charge distributions.

Established differential equations for frame transformations.

Highlighted the spin-dependent nature of 2D distributions.

Abstract

We investigate the three-dimensional~(3D) and two-dimensional~(2D) charge distributions of a spin-one particle in terms of the multipole expansion. On account of the geometrical difference between 2D and 3D spaces, projecting the 3D electric distribution to the 2D one in the Breit frame brings about the influence of the quadrupole distribution upon the monopole one. Thus, the 2D charge distribution becomes spin-dependent. This effect should be sorted out from the relativistic effects arising from the Lorentz boost. We first provide the connections between the 2D and 3D distributions in the Breit frame in terms of the angle-dependent Abel transformation. We then provide the differential equations that enable us to map 2D distributions in the Breit frame to those in the infinite momentum frame.