Pion Rescattering in Two-Pion Decay of Heavy Quarkonia

The role of pion rescattering in $\pi\pi$ decay of radially excited heavy quarkonia modeled in terms of a $Q\pi\pi$ coupling, is investigated within the framework of the covariant Blankenbecler-Sugar equation. The effects of pion rescattering (or pion exchange) are shown to be large, unless the coupling of the two-pion system to the heavy quarks is mediated by a fairly light scalar $\sigma$ meson, which couples to the gradients of the pion fields. The Hamiltonian model for the quarkonium states is formed of linear scalar confining, screened one-gluon exchange and instanton induced interaction terms. The widths and energy distributions of the basic decays $\psi'\to J/\psi \pi\pi$ and $\Upsilon'\to \Upsilon \pi\pi$ are shown to be satisfactorily described by this model. The implications of this model for the decays of the $\Upsilon(3S)$ state are discussed.