Abstract from arXiv:1205.6606
On the size of the sigma meson and its nature
In this work the nature of the $\sigma$ or $f_0(600)$ resonance is discussed by evaluating its quadratic scalar radius, $r^2$. This allows one to have a quantitative estimate for the size of this resonance. We obtain that the $\sigma$ resonance is a compact object with $ r^2=(0.19\pm0.02)-i(0.06\pm 0.02)$ $fm^2$. Within our approach, employing unitary chiral perturbation theory, the $\sigma$ is a dynamically generated resonance that stems from the pion-pion interactions. Given its small size we conclude that the two pions inside the resonance are merged. A four-quark picture is then more appropriate. However, when the pion mass increases, for pion masses somewhat above 400 MeV, the picture of a two-pion molecule is the appropriate one. The $\sigma$ is then a spread $\pi\pi$ bound state.