Two-dimensional charge distributions of the $\Delta$ baryon: Interpolation between the nonrelativistic and ultrarelativistic limit

TL;DR

This paper explores how the charge distributions of the $elta$ baryon evolve with increasing longitudinal momentum, revealing polarization-dependent symmetry and multipole moment induction in a phase-space framework.

Contribution

It introduces a phase-space perspective to analyze the momentum-dependent charge distributions of the $elta$ baryon, highlighting polarization effects and multipole moment emergence.

Findings

Longitudinal polarization maintains spherical symmetry across momenta.

Transverse polarization leads to quadrupole contributions at rest.

Increasing $P_z$ induces electric dipole and octupole moments, affecting charge distribution deformation.

Abstract

We investigate how the charge distributions of both the unpolarized and transversely polarized $\Delta$ baryon change as the longitudinal momentum~($P_{z}$) of the $\Delta$ baryon increases from $P_{z}=0$ to $P_{z}=\infty$ in a Wigner phase-space perspective. When the $\Delta$ baryon is longitudinally polarized, its two-dimensional charge distribution is kept to be spherically symmetric with $P_{z}$ varied, whereas when the $\Delta$ baryon is transversely polarized along the $x$-axis, the quadrupole contribution emerges at the rest frame ($P_{z}=0$). When $P_{z}$ grows, the electric dipole and octupole moments are induced. The induced dipole moment dominates over other higher multipole contributions and governs the deformation of the charge distribution of the $\Delta$ baryon.