On the definition of local spatial densities in hadrons

TL;DR

This paper clarifies how local operator matrix elements define unambiguous spatial densities in hadrons, revising the interpretation of these densities and related moments like the charge radius.

Contribution

It provides a clear framework for defining spatial densities in hadrons via local operator matrix elements, addressing ambiguities in previous interpretations.

Findings

Matrix elements of local operators define unambiguous spatial densities.

Charge density interpretation varies between rest and moving frames.

Reassessment of the physical meaning of moments like the charge radius.

Abstract

We show that the matrix element of a local operator between hadronic states gives rise to an unambiguous definition of the associated spatial density. As an explicit example, we consider the charge density of a spinless particle in the rest and moving frames and clarify its relationship to the electric form factor. Our results suggest that the interpretation of the spatial densities of local operators and their moments such as the mean square charge radius needs to be revised.