Pion rescattering in two-pion decay of heavy quarkonia Original Research Article

The role of pion rescattering in ππ decay of radially excited heavy quarkonia modeled in terms of a Qππ 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 σ 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 ψ′→J/ψππ and ϒ′→ϒππ are shown to be satisfactorily described by this model. The implications of this model for the decays of the ϒ(3S) state are discussed.