Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^(700)

• Published in: The European physical journal. ST, Special topics Vol. 230; no. 6; pp. 1539 - 1574
• Main Authors: Peláez, José R., Rodas, Arkaitz, Ruiz de Elvira, Jacobo
• Format: Journal Article
• Language: English
• Published: United States Springer 16.06.2021
• Subjects: PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
• ISSN: 1951-6355; 1951-6401; 1951-6401
• DOI: 10.1140/epjs/s11734-021-00142-9

For several decades, the $\sigma /f_0(500) $ and $\kappa /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 $\sigma /f_0(500) $ and $\kappa /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.