Production of $f_0(1710)$, $f_0(1500)$, and $f_0(1370)$ in $J/ψ$ hadronic decays

Abstract

A coherent study of the production of $f_0^i$ ($i=1$, 2, 3 corresponding to $f_0(1710)$, $f_0(1500)$, and $f_0(1370)$) in $J/ψ\to V f_0 \to V PP$ is reported based on a previously proposed glueball and $Q\bar{Q}$ nonet mixing scheme, and a factorization for the decay of $J/ψ\to V f_0^i$, where $V$ denotes the isoscalar vector mesons $ϕ$ and $ω$, and $P$ denotes pseudoscalar mesons. The results show that the $J/ψ$ decays are very sensitive to the structure of those scalar mesons, and suggest a glueball in the $1.5-1.7$ GeV region, in line with Lattice QCD. The presence of significant glueball mixings in the scalar wavefunctions produces peculiar patterns in the branching ratios for $J/ψ\to V f_0^i\to VPP$, which are in good agreement with the recently published experimental data from the BES collaboration.