Pion and nucleon relativistic electromagnetic four-current distributions

TL;DR

This paper develops a relativistic phase-space formalism to analyze electromagnetic current distributions in spin-0 and spin-1/2 particles, comparing with light-front results and emphasizing Sachs form factors.

Contribution

It extends previous charge distribution studies to current distributions, clarifies the role of Wigner rotations, and applies the formalism to pion and nucleon form factors from experimental data.

Findings

Electromagnetic current distributions depend on frame choice.

Sachs form factors provide a natural description of electromagnetic properties.

Results align with experimental form factor data.

Abstract

The quantum phase-space approach allows one to define relativistic spatial distributions inside a target with arbitrary spin and arbitrary average momentum. We apply this quasiprobabilistic formalism to the whole electromagnetic four-current operator in the case of spin-$0$ and spin-$\frac{1}{2}$ targets, study in detail the frame dependence of the corresponding spatial distributions, and compare our results with those from the light-front formalism. While former works focused on the charge distributions, we extend here the investigations to the current distributions. We clarify the role played by the Wigner rotation and argue that electromagnetic properties are most naturally understood in terms of Sachs form factors, contrary to what the light-front formalism previously suggested. Finally, we illustrate our results using the pion and nucleon electromagnetic form factors extracted from experimental data.