General unquenching properties of two-meson scattering and production amplitudes

TL;DR

This paper explores the unquenching properties of two-meson scattering and production amplitudes, emphasizing the importance of singularity behavior and resonance pole movement under parameter variation.

Contribution

It introduces a unified analytic framework for understanding resonance pole dynamics and highlights limitations of perturbative approaches in multi-resonance scattering.

Findings

Resonance poles move in predictable ways with parameter changes

Resonances can transition into bound states below threshold

Perturbative methods often violate natural unitarity conditions

Abstract

Besides the unitarity and symmetry requirements for a multi-resonance scattering amplitude, several other natural conditions can easily exclude unrealistic proposals. In particular, the behaviour of singularities under the variation of model parameters yields important information. We discuss how resonance poles should move in the complex-energy plane when coupling constants and masses are varied, how resonances above threshold can turn into bound states below threshold and how the light-quark spectrum can be turned into the spectrum of heavy quarks, with one and the same analytic expression for the scattering amplitude. Moreover, it is shown that perturbative approximations usually do not satisfy those natural conditions.