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

TL;DR

This paper compares dispersive methods and unitarized Chiral Perturbation Theory to analyze the lightest scalar mesons, clarifying their existence, properties, and underlying nature through model-independent and effective theory approaches.

Contribution

It provides a comprehensive comparison of dispersive techniques and unitarized Chiral Perturbation Theory for scalar mesons, highlighting their respective advantages and insights into meson nature.

Findings

Dispersive methods confirm the existence of $\sigma/f_0(500)$ and $\kappa/K_0^*(700)$.

Dispersive approaches precisely determine resonance parameters.

Unitarized Chiral Perturbation Theory elucidates the nature and QCD dependence of these resonances.

Abstract

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 $\kappa/K_0^*(700)$. 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.