Coupled-channel effects in hadronic transitions in heavy-quarkonium systems

A systematic calculation of the coupled-channel effects in hadronic transitions in the cc¯ and bb¯ systems is given. The unitarized quark model based on the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ quark-pair-creation mechanism is adopted as the coupled-channel model. The emitted pions can now be produced both from the conventional Okubo-Zweig-Iizuka- (OZI) forbidden process described by QCD multipole-gluon emissions and from the light-quark loop through an OZI-allowed process described by the quark-pair-creation model. There is interference between the two kinds of transition amplitudes. Taking the experimental values of Γ(ψ’→J/ψ ππ) and dΓ(ψ’→J/ψ ππ)/${\mathit{dM}}_{\mathrm{\pi }\mathrm{\pi }}$ as inputs to determine the two unknown parameters in the theory, we predict the transition rates and ${\mathit{M}}_{\mathrm{\pi }\mathrm{\pi }}$ distributions in the bb¯ system. The obtained rates for Υ’→Υππ, Υ’ ’→Υππ, Υ’ ’→Υ’ππ and the distribution dΓ(Υ’→Υππ)/${\mathit{dM}}_{\mathrm{\pi }\mathrm{\pi }}$ are in good agreement with the experiments. For dΓ(Υ’ ’→Υππ)/${\mathit{dM}}_{\mathrm{\pi }\mathrm{\pi }}$, the present theory does give a bigger low-${\mathit{M}}_{\mathrm{\pi }\mathrm{\pi }}$ distribution than the pure QCD multipole expansion does, but it is still too small to fit the CLEO data.