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For several decades, the $\sigma/f_0(500)$ and $\kappa/K_0^*(700)$ resonanceshave been subject to long-standing debate. Both their existence and propertieswere controversial until very recently. In this tutorial review we comparemodel-independent dispersive and analytic techniques versus unitarized ChiralPerturbation Theory, when applied to the lightest scalar mesons$\sigma/f_0(500)$ and $\kappa/K_0^*(700)$. Generically, the former have settledthe long-standing controversy about the existence of these states, providing aprecise determination of their parameters, whereas unitarization of chiraleffective theories allows us to understand their nature, spectroscopicclassification and dependence on QCD parameters. Here we review in apedagogical way their uses, advantages and caveats.

the european physical journal. special topics

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