Low Energy Constants from High Energy Theorems

TL;DR

This paper derives new constraints on low-energy constants in chiral perturbation theory based on high-energy theorems and symmetry considerations, linking resonance saturation schemes to QCD symmetries and revealing implications for meson dominance and scalar meson masses.

Contribution

It establishes a novel connection between resonance saturation, chiral symmetry, and high-energy theorems, providing new bounds and insights into low-energy constants and meson dominance.

Findings

Vector meson dominance results from the lowest-dimensional chiral representation.

Chiral symmetry imposes an upper bound on the lightest scalar meson mass.

Resonance saturation schemes must correspond to full QCD chiral symmetry representations.

Abstract

New constraints on resonance saturation in chiral perturbation theory are investigated. These constraints arise because each consistent saturation scheme must map to a representation of the full QCD chiral symmetry group. The low-energy constants of chiral perturbation theory are then related by a set of mixing angles. It is shown that vector meson dominance is a consequence of the fact that nature has chosen the lowest-dimensional nontrivial chiral representation. It is further shown that chiral symmetry places an upper bound on the mass of the lightest scalar in the hadron spectrum.