Synchronization effects on rest frame energy and momentum densities in the proton

TL;DR

This paper explores how different synchronization conventions affect the calculated energy and momentum densities in a proton at rest, revealing angular modulations and spin-dependent effects using tilted light front coordinates.

Contribution

It introduces a novel coordinate system for analyzing relativistic densities, providing clearer physical interpretations and uncovering effects not seen in standard approaches.

Findings

Angular modulations in densities due to synchronization effects

Energy dipole moment in transversely polarized targets

Differences in results depending on energy-momentum tensor choice

Abstract

We obtain two-dimensional relativistic densities and currents of energy and momentum in a proton at rest. These densities are obtained at surfaces of fixed light front time, which physically corresponds to using an alternative synchronization convention. Mathematically, this is done using tilted light front coordinates, which consist of light front time and ordinary spatial coordinates. In this coordinate system, all sixteen components of the energy-momentum tensor obtain clear physical interpretations, and the nine Galilean components reproduce results from standard light front coordinates. We find angular modulations in several densities that are absent in the corresponding instant form results, which are explained as optical effects arising from using fixed light front time when motion is present within the target. Additionally, transversely-polarized spin-half targets exhibit an energy dipole moment -- which evaluates to $-1/4$ for all targets if the Belinfante EMT is used, but which is target dependent and vanishes for pointlike fermions if the asymmetric EMT is instead used.