Relativistic Cornell-type mechanism of exotic scalar resonances

Abstract

The physical masses of the lowest scalar mesons strongly disagree with the calculated $q\overline{q}$ pole values. It is the purpose of this paper to explain theoretically the unusual spectrum of scalar mesons for both the ground and excited states, using the known spectra of the corresponding $q\overline{q}$ states and their connection to the meson resonances. The well-known Cornell coupled-channel mechanism is exploited for this connection together with the quark-chiral Lagrangian without fitting parameters. In addition to the scalars previously obtained using this method, ${f}_{0}(500)$, ${f}_{0}(980)$, ${a}_{0}(980)$, we predict all ground and first excited scalar states, ${f}_{0}(500)$, ${f}_{0}(980)$, ${a}_{0}(980)$, ${a}_{0}(1450)$, ${K}_{0}^{*}(700)$, ${K}_{0}^{*}(1430)$, ${f}_{0}(1370)$, ${f}_{0}(1710)$, which are in reasonably good agreement with experimental data.