Problems with meson spectroscopy involving perturbative loop corrections

TL;DR

This paper critically examines the use of perturbative loop corrections in meson spectroscopy within a quark model, revealing significant limitations and inaccuracies in resonance predictions when coupling to scattering channels is strong.

Contribution

It demonstrates that perturbative expansions in meson loop corrections fail to accurately reproduce resonance poles compared to the full model, highlighting the need for non-perturbative approaches.

Findings

Perturbative corrections up to fourth order do not match full model resonance poles.

Resonance predictions are unreliable when coupling to scattering channels is large.

Perturbative methods are insufficient for accurate meson spectroscopy in certain regimes.

Abstract

In this talk we review the limitations of including meson loops as perturbative corrections in a solvable quark model. We first discuss meson-meson scattering within a formalism which treats confined quark pairs and mesons on an equal footing. The interaction between the mesons proceeds through $s$-channel meson-exchange diagrams. Next, we develop a perturbative expansion of the model, and show that the resonance poles found in such a treatment, even by accounting for contributions up to fourth order, do not coincide with those obtained with the full model. We conclude that the resonance predictions based on perturbative approximations in quark models are not reliable, especially in those cases where the coupling to the scattering channels is large.