Molecular components in the $J/ψ$ and the $ρ$-$π$ puzzle
Motivated by the large branching fractions of $J/ψ\to f_0 (1710) ω/f_0(1710) ϕ$ and the light exotic candidates, we find that there may exist molecular states composed of $f_0(1710) ω$ and $f_0 (1710) ϕ$, which correspond to $X(2440)$ and $X(2680)$ observed in a few decades before. The branching fraction of $X(2440)$ and $X(2680)$ to various $PV$ channels and $KKω(ϕ)$ channels are estimated in the molecular scenario. In addition, the large branching fractions of $J/ψ\to f_0 (1710) ω/f_0(1710) ϕ$ indicate the sizable molecular components in the $J/ψ$ state. Thus, we consider the $J/ψ$ as the supperposition of $c\bar{c}(1S)$, $f_0(1710) ω$ and $f_0 (1710) ϕ$ molecular states, and these molecular components have significant impact on the light hadron decays of $J/ψ$, which may shield light on the long standing $ρ-π$ puzzle.