Singular Charge Density at the Center of the Pion?

TL;DR

This paper investigates the charge density distribution of the pion, revealing a potential logarithmic divergence at its center based on various theoretical models and form factor data, with future experiments needed for confirmation.

Contribution

It connects the pion's spatial charge density to its electromagnetic form factor and compares multiple models, highlighting a possible singularity at the pion's center.

Findings

Charge density at the pion's center may diverge logarithmically.

Relativistic models do not show this singularity.

Future high-momentum transfer measurements are needed to confirm the divergence.

Abstract

We relate the three-dimensional infinite momentum frame spatial charge density of the pion to its electromagnetic form factor. Diverse treatments of the measured form factor data including: phenomenological fits, non-relativistic quark models, the application of perturbative QCD, QCD sum rules, holographic QCD, and the Nambu Jona-Lasinio (NJL) model all lead to the result that the charge density at the center of the pion has a logarithmic divergence. Relativistic constituent quark models do not display this singularity. Future measurements planned for larger values of momentum transfer may determine whether or not a singularity actually occurs.