Imaging the charge distributions of flavor-symmetric and -asymmetric mesons

TL;DR

This paper reconstructs charge distributions of various mesons using electromagnetic form factors and a Maximum Entropy Method, revealing size differences related to quark mass and spin effects.

Contribution

It introduces a novel application of the Maximum Entropy Method to meson charge distributions derived from Dyson-Schwinger and Bethe-Salpeter form factors.

Findings

Lightest quarkonia have charge distributions about five times larger than the heaviest.

Vector mesons are 5-15% larger than pseudoscalar mesons due to spin effects.

The study provides estimates for meson sizes and quark motion ranges.

Abstract

We investigate the internal structure of a comprehensive set of pseudoscalar and vector mesons, including both flavor-symmetric and flavor-asymmetric systems, by reconstructing their charge distributions from electromagnetic form factors. To achieve this, we employ a Maximum Entropy Method optimized for charge distributions, utilizing previously published form factor data obtained within the Dyson-Schwingers and Bethe-Salpeter equations framework. Furthermore, we calculate the average distance between the valence quark and antiquark that constitute the meson, interpreting it as an estimate for both the meson's spatial size and the typical range of quark motion. Our results reveal that this distance for the lightest quarkonia is approximately five times larger than that for the heaviest. Moreover, due to spin effects, vector mesons exhibit sizes that are 5-15\% larger than their pseudoscalar counterparts.