Decays of J/ψ and ψ into vector and pseudoscalar meson and the pseudoscalar glueball-qq̄ mixing

We introduce a parametrization scheme for J/ψ(ψ′) → V P where the effects of SU(3) flavor symmetry breaking and doubly OZI-rule violation (DOZI) can be parametrized by certain parameters with explicit physical interpretations. This scheme can be used to clarify the glueball-qq̄ mixing within the pseudoscalar mesons. We also include the contributions from the electromagnetic (EM) decays of J/ψ and ψ′ via J/ψ(ψ′) → γ∗ → V P . Via study of the isospin violated channels, such as J/ψ(ψ′) → ρη, ρη′, ωπ and φπ, reasonable constraints on the EM decay contributions are obtained. With the up-to-date experimental data for J/ψ(ψ′) → V P , J/ψ(ψ′) → γP and P → γγ, etc, we arrive at a consistent description of the mentioned processes with a minimal set of parameters. As a consequence, we find that there exists an overall suppression of the ψ′ → 3g form factors, which sheds some light on the long-standing “ρπ puzzle”. By determining the glueball components inside the pseudoscalar η and η′ in three different glueball-qq̄ mixing schemes, we deduce that the lowest pseudoscalar glueball, if exists, has rather small qq̄ component, and it makes the η(1405) a preferable candidate for 0 glueball.