Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$

Abstract

For several decades, the $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$ 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 $\kappa /K_0^{\ast }(700)$. Generically, 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.

Comments: Invited tutorial-review for European Physical Journal Special Topics. Final version to appear published. Expanded discussions and reference list. 50 pages