Eur. Phys. J. Spec. Top. (2021) 230: 1539-1574
https://doi.org/10.1140/epjs/s11734-021-00142-9

Review

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

¹ Departamento de Física Teórica, Universidad Complutense and IPARCOS, 28040, Madrid, Spain
² Department of Physics, College of William and Mary, 23187, Williamsburg, VA, USA
³ Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, 23606, Newport News, VA, USA
⁴ Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

^a jrpelaez@fis.ucm.es

Received: 10 January 2021
Accepted: 10 May 2021
Published online: 16 June 2021

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.