Modern meson spectroscopy: the fundamental role of unitarity

TL;DR

This paper reviews the critical role of $S$-matrix unitarity in meson spectroscopy, highlighting its impact on understanding meson resonances, limitations of traditional models, and recent advances including lattice QCD and unitarised frameworks.

Contribution

It provides a comprehensive overview of unitarity's role in meson spectroscopy, emphasizing recent developments and proposing future directions.

Findings

Unitarity significantly influences meson resonance analysis.

Many mesons cannot be explained by simple quark-antiquark models.

Recent lattice QCD approaches offer new insights into meson structure.

Abstract

The importance of $S$-matrix unitarity in realistic meson spectroscopy is reviewed, both its historical development and more recent applications. First the effects of imposing $S$-matrix unitarity on meson resonances is demonstrated in both the elastic and the inelastic case. Then, the static quark model is revisited and its theoretical as well as phenomenological shortcomings are highlighted. A detailed account is presented of the mesons in the tables of the Particle Data Group that cannot be explained at all or only poorly in models describing mesons as pure quark-antiquark bound states. Next the earliest unitarised and coupled-channel models are revisited, followed by several examples of puzzling meson resonances and their understanding in a modern unitarised framework. Also, recent and fully unquenched lattice descriptions of such mesons are summarised. Finally, attention is paid to production processes, which require an unconventional yet related unitary approach. Proposals for further improvement are discussed.