Ambiguities in the definition of local spatial densities in light hadrons

TL;DR

This paper discusses the conceptual and definitional ambiguities in local spatial densities within light hadrons, highlighting the challenges in unambiguously defining or measuring intrinsic charge distributions in systems like the proton.

Contribution

It clarifies the limitations of relating form factors to spatial densities in light hadrons and emphasizes the conceptual ambiguities involved.

Findings

The matrix element-form factor relationship fails for systems with size comparable to their Compton wavelength.

There is no unambiguous way to define or measure the intrinsic charge density in the proton.

The intrinsic size and charge distribution in light hadrons remain conceptually ambiguous.

Abstract

The relationship between the matrix element of a local operator and the Fourier transform of the associated form factor fails for systems such as the nucleon where its intrinsic size is of order its Compton wavelength. Although one can conceive of an intrinsic charge density distribution in the proton, there does not seem to be an unambiguous way to define, compute, or measure it precisely.