On the structure of the scalar mesons $f_0(975)$ and $a_0(980)$

Abstract

We investigate the structure of the scalar mesons $f_0(975)$ and $a_0(980)$ within realistic meson-exchange models of the $ππ$ and $πη$ interactions. Starting from a modified version of the Jülich model for $ππ$ scattering we perform an analysis of the pole structure of the resulting scattering amplitude and find, in contrast to existing models, a somewhat large mass for the $f_0(975)$ ($m_{f_0}=1015$ MeV, $Γ_{f_0}=30$ MeV). It is shown that our model provides a description of $J/ψ\rightarrowϕππ/ϕKK$ data comparable in quality with those of alternative models. Furthermore, the formalism developed for the $ππ$ system is consistently extended to the $πη$ interaction leading to a description of the $a_0(980)$ as a dynamically generated threshold effect (which is therefore neither a conventional $q\overline{q}$ state nor a $K\overline{K}$ bound state). Exploring the corresponding pole position the $a_0(980)$ is found to be rather broad ($m_{a_0}=991$ MeV, $Γ_{a_0}=202$ MeV). The experimentally observed smaller width results from the influence of the nearby $K\overline{K}$ threshold on this pole.