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

Abstract

A systematic calculation of the coupled-channel effects in hadronic transitions in the cc\ifmmode\bar\else\textasciimacron\fi{} and bb\ifmmode\bar\else\textasciimacron\fi{} 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 \ensuremath{\Gamma}(\ensuremath{\psi}'\ensuremath{\rightarrow}J/\ensuremath{\psi} \ensuremath{\pi}\ensuremath{\pi}) and d\ensuremath{\Gamma}(\ensuremath{\psi}'\ensuremath{\rightarrow}J/\ensuremath{\psi} \ensuremath{\pi}\ensuremath{\pi})/${\mathit{dM}}_{\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{\pi}}}$ as inputs to determine the two unknown parameters in the theory, we predict the transition rates and ${\mathit{M}}_{\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{\pi}}}$ distributions in the bb\ifmmode\bar\else\textasciimacron\fi{} system. The obtained rates for \ensuremath{\Upsilon}'\ensuremath{\rightarrow}\ensuremath{\Upsilon}\ensuremath{\pi}\ensuremath{\pi}, \ensuremath{\Upsilon}''\ensuremath{\rightarrow}\ensuremath{\Upsilon}\ensuremath{\pi}\ensuremath{\pi}, \ensuremath{\Upsilon}''\ensuremath{\rightarrow}\ensuremath{\Upsilon}'\ensuremath{\pi}\ensuremath{\pi} and the distribution d\ensuremath{\Gamma}(\ensuremath{\Upsilon}'\ensuremath{\rightarrow}\ensuremath{\Upsilon}\ensuremath{\pi}\ensuremath{\pi})/${\mathit{dM}}_{\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{\pi}}}$ are in good agreement with the experiments. For d\ensuremath{\Gamma}(\ensuremath{\Upsilon}''\ensuremath{\rightarrow}\ensuremath{\Upsilon}\ensuremath{\pi}\ensuremath{\pi})/${\mathit{dM}}_{\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{\pi}}}$, the present theory does give a bigger low-${\mathit{M}}_{\mathrm{\ensuremath{\pi}}\mathrm{\ensuremath{\pi}}}$ distribution than the pure QCD multipole expansion does, but it is still too small to fit the CLEO data.