Chiral symmetry constraints on resonant amplitudes

TL;DR

This paper explores how chiral symmetry constrains the quark-mass dependence of meson resonance poles, providing model-independent conditions to ensure accurate representation of quark-mass effects in scattering amplitudes.

Contribution

It derives model-independent conditions on meson scattering amplitude parametrizations to correctly incorporate quark-mass dependence of resonance poles.

Findings

Derived conditions guarantee correct quark-mass dependence

Tested model amplitudes against these conditions

Ensured reliable extraction of resonance properties

Abstract

We discuss the impact of chiral symmetry constraints on the quark-mass dependence of meson resonance pole positions, which are encoded in non-perturbative parametrizations of meson scattering amplitudes. Model-independent conditions on such parametrizations are derived, which are shown to guarantee the correct functional form of the leading quark-mass corrections to the resonance pole positions. Some model amplitudes for $\pi\pi$ scattering, widely used for the determination of $\rho$ and $\sigma$ resonance properties from results of lattice simulations, are tested explicitly with respect to these conditions.