Mechanical structure of a spin-1 particle

TL;DR

This paper explores the internal energy-momentum tensor distributions of a spin-1 particle across different frames, revealing geometric monopole and dipole structures and visualizing polarization effects.

Contribution

It introduces a comprehensive analysis of EMT distributions in 2D and 3D frames for spin-1 particles, highlighting induced monopole and dipole structures and polarization-dependent mass distributions.

Findings

Mass distribution includes monopole contributions in 2D Breit frame.

Induced dipole structures appear in infinite momentum frame.

Polarization affects the visualized mass distribution patterns.

Abstract

We investigate the mechanical structure of a spin-1 particle. Introducing three different frameworks, i.e., the three-dimensional (3D) Breit frame, the two-dimensional (2D) Breit frame, and the 2D infinite momentum frame (equivalently the two-dimensional Drell-Yan frame), we scrutinize the 2D and 3D energy-momentum tensor (EMT) distributions in these frames. We first derive the EMT distributions in the 2D Breit frame by performing the Abel transformation. The mass distribution in the 2D Breit frame contains an additional monopole contribution induced geometrically. The pressure distribution in the 2D Breit frame also gets an induced monopole structure. When the Lorentz boost is carried out, the mass distribution in the 2D infinite-momentum frame acquires the induced dipole term. Similarly, we also have the induced dipole contributions to the pressure and shear-force densities. We visualize the 2D mass distributions when the spin-1 particle is polarized along the $x$- and $z$-axes. We observe that the 2D mass distribution in the infinite momentum frame exhibit clearly the induced dipole structure when the spin-1 particle is polarized along the $x$-axis. We also discuss the strong force fields inside a polarized spin-1 particle.