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Drawbacks of applying perturbative schemes to meson spectroscopy

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.