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 ³P₀ 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)/dM_ππ as inputs to determine the two unknown parameters in the theory, we predict the transition rates and M_ππ distributions in the bb¯ system. The obtained rates for Υ’→Υππ, Υ’’→Υππ, Υ’’→Υ’ππ and the distribution dΓ(Υ’→Υππ)/dM_ππ are in good agreement with the experiments. For dΓ(Υ’’→Υππ)/dM_ππ, the present theory does give a bigger low-M_ππ distribution than the pure QCD multipole expansion does, but it is still too small to fit the CLEO data.