Decays of $J/ψ$ and $ψ^\prime$ into vector and pseudoscalar meson and the pseudoscalar glueball-$q\bar{q}$ mixing

Abstract

We introduce a parametrization scheme for $J/ψ(ψ^\prime)\to VP$ 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-$q\bar{q}$ mixing within the pseudoscalar mesons. We also include the contributions from the electromagnetic (EM) decays of $J/ψ$ and $ψ^\prime$ via $J/ψ(ψ^\prime)\to γ^*\to VP$. Via study of the isospin violated channels, such as $J/ψ(ψ^\prime)\to ρη$, $ρη^\prime$, $ωπ^0$ and $ϕπ^0$, reasonable constraints on the EM decay contributions are obtained. With the up-to-date experimental data for $J/ψ(ψ^\prime)\to VP$, $J/ψ(ψ^\prime)\to γP$ and $P\to γγ$, 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 $ψ^\prime\to 3g$ form factors, which sheds some light on the long-standing "$ρπ$ puzzle". By determining the glueball components inside the pseudoscalar $η$ and $η^\prime$ in three different glueball-$q\bar{q}$ mixing schemes, we deduce that the lowest pseudoscalar glueball, if exists, has rather small $q\bar{q}$ component, and it makes the $η(1405)$ a preferable candidate for $0^{-+}$ glueball.