Eef van Beveren, George Rupp
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.
Comments: Invited review paper, 51 pages, 16 figures, 4 tables; to be published in "Progress in Particle and Nuclear Physics" 2021