Pion Rescattering in Two-Pion Decay of Heavy Quarkonia

Abstract

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 ${\psi }^{\prime }\to J/\psi \pi \pi$ and ${{\rm Y}}^{\prime }\to {\rm Y}\pi \pi$ are shown to be satisfactorily described by this model. The implications of this model for the decays of the ${\rm Y}(3S)$ state are discussed.

Comments: 27 pages, 13 figures, uses Feynmf. Submitted to Nuclear Physics A v2: Minor corrections to formatting v3: Corrected Feynman diagram labels. v4: 25 pages, 10 figures, Accepted version