Charge distributions of pseudo-scalar and vector mesons from Dyson-Schwinger equations

TL;DR

This paper uses Dyson-Schwinger equations and numerical methods to derive and validate charge distributions of mesons from their electromagnetic form factors, revealing insights into their internal structure at very small distances.

Contribution

It introduces a novel combination of Dyson-Schwinger/Bethe-Salpeter equations with numerical reconstruction to analyze meson charge distributions at sub-femtometer scales.

Findings

Charge radii are consistent with form factor slopes at zero momentum transfer.

Reconstruction captures charge distributions reliably down to 0.1 fm.

Potential application to mass density extraction from gravitational form factors.

Abstract

We combine the Dyson-Schwinger/Bethe-Salpeter equations framework with modern numerical reconstruction methods to derive the three-dimensional and transverse two-dimensional charge distribution of an array of ground-state pseudoscalar and vector mesons from their elastic electromagnetic form factor in the low-momentum region. The charge radii obtained by averaging over the reconstructed charge distributions have been checked to be consistent with those calculated from the slope of the elastic electromagnetic form factor at zero transferred momentum. The capability of the reconstruction procedure for capturing a reliable low-distance charge distribution is discussed and argued to work down to distances of around 0.1 fm, such that it might be potentially applied to extract, {\it e.g.}, mass densities from gravitational form factors.