Pion Interactions in Chiral Field Theories

TL;DR

This paper investigates various pion interactions within chiral models, demonstrating that a quark-level linear sigma-model approach aligns well with experimental data on pion properties and scattering processes.

Contribution

It shows that a quark-level linear sigma-model, consistent with vector meson dominance, effectively describes multiple pion interaction phenomena.

Findings

The linear sigma-model matches experimental data on pion charge radius.

It accurately predicts the $ au_{e3}$ form factor ratio.

The approach is compatible with low-energy scattering amplitudes.

Abstract

We study in various chiral models the pion charge radius, $\pi_{e3}$ form factor ratio, $\pi^\circ \to \gamma \gamma$ amplitude, charge pion polarizabilities, $\gamma\gamma \to \pi^\circ \pi^\circ$ amplitude at low energies and the $\pi\pi$ s-wave I = 0 scattering length. We find that a quark-level linear sigma-model approach (also being consistent with tree-level vector meson dominance) is quite compatible with all of the above data.