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 \(\pi\pi\) and \(\pi\eta\) interactions. Starting from a modified version of the J\"ulich model for \(\pi\pi\) 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, \(\Gamma_{f_0}=30\) MeV). It is shown that our model provides a description of \(J/\psi\rightarrow\phi\pi\pi/\phi KK\) data comparable in quality with those of alternative models. Furthermore, the formalism developed for the \(\pi\pi\) system is consistently extended to the \(\pi\eta\) 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, \(\Gamma_{a_0}=202\) MeV). The experimentally observed smaller width results from the influence of the nearby \(K\overline{K}\) threshold on this pole.