Radial spectra and hadronic decay widths of light and heavy mesons

A potential model for mesons is presented, which combines quark confinement and strong decay in a realistic approach. The multichannel Schrödinger formalism is employed to describe a system of one or more permanently closed quark-antiquark channels in interaction with several two-meson channels. For the potential in the $q\overline{q}$ channels a harmonic oscillator with constant frequency is taken. As for the meson channels only Okubo-Zweig-Iizuka-rule-allowed decays into two mesons of the pseudoscalar or vector type are considered. Final-state interactions between these mesons are not yet taken into account. The communication between confined and free channels is supposed to take place via the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ mechanism, for which a locally approximated transition potential is derived. In order to obtain an analytic solution for the $S$ matrix, the transition potential is treated by using a multi-$\delta$-shell method. Kinematically relativistic corrections and color splitting allow a fairly successful treatment of pseudoscalar as well as vector mesons for all quark flavors. The results are confronted with the data and discussed.