Drawbacks of applying perturbative schemes to meson spectroscopy

TL;DR

This paper demonstrates that perturbative methods in meson spectroscopy can significantly mispredict resonance properties, highlighting the unreliability of such approximations in quark models.

Contribution

It introduces a soluble model for meson interactions and shows that perturbative expansions up to fourth order fail to accurately reproduce resonance poles.

Findings

Perturbative expansions do not match exact resonance poles.

Resonance predictions from perturbation theory are unreliable.

Higher-order corrections do not improve accuracy.

Abstract

We study meson-meson scattering in a soluble model which describes asymptotically free mesons and confined quark-antiquark pairs via coupled channels. Concretely, the two scattered mesons are assumed to interact through s-channel meson-exchange diagrams. Furthermore, we develop a perturbative expansion of the model, and show that the thus found resonance pole positions, including contributions up to fourth order in perturbation theory, completely fail to reproduce the exact results. This shows that the resonance predictions based on perturbative approximations in quark models may be highly unreliable.