Dynamics and SU(3) violation in J/ψ decays

Abstract

The strong-interaction part of the amplitude for J/ψ decays into specific final hadronic states is computed by evaluating corrections arising from unitarity to the Okubo-Zweig-Iizuka rule. Dispersion relations for the relevant amplitudes are evaluated keeping only the contributions of charmed-hadron states to the absorptive part and assuming Regge asymptotic behavior for charmed hadrons→ ordinary hadrons. To obtain an estimate of the absolute magnitude of an amplitude such as ψ→ρ π we use SU(4) symmetry for the connected vertices and find a suppression factor of the order of 10^-4 for g_{ψ ρ π} as compared to g_{ω ρπ}. Assuming a mass splitting of 100 MeV for m_F-m_D and m_F-m_D leads to dynamical breaking of SU(3) symmetry even if the couplings characterizing connected vertices obey SU(3) symmetry. If the latter circumstance is true, we estimate the ratio of the amplitudes ψ → ρ ⁺π ^- and ψ→K⁺K^- to be between 1.5 and 2. Such dynamical violation of SU(3) arising from mass splitting between charmed hadrons in the same SU(3) multiplet tends to cancel in ψ →KK^- . Related matters such as SU(3) symmetry in the decays of χ states and comparison of ψ '→ψ η , ψ '→ρ π , and ψ →ρ π are also discussed.