Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$σ /f_0(500) $$ and $$κ /K_0^(700) - Peláez, José R.; Rodas, Arkaitz; Ruiz de Elvira, Jacobo (The European physical journal. ST, Special topics, 2021)
For several decades, the $σ /f_0(500) $ and $κ /K_0^*(700) $ resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review, we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons $σ /f_0(500) $ and $κ /K_0^*(700) $. Here, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats.