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A possible explanation of the threshold enhancement in the process $e^+e^-\rightarrow Λ\barΛ$

Inspired by the recent measurement of the process $e^+e^-\rightarrow Λ\barΛ$, we calculate the mass spectrum of the $ϕ$ meson with the GI model. For the excited vector strangeonium states $ϕ(3S,~4S,~5S,~6S)$ and $ϕ(2D,~3D,~4D,~5D)$, we further investigate the electronic decay width with the Van Royen-Weisskopf formula, and the partial widths of the $Λ\barΛ$, $Ξ^{-(*)}\barΞ^+$, and $Σ^{+(*)}\barΣ^{-(*)}$ decay modes with the extended quark pair creation model. We find that the electronic decay width of the $D$-wave vector strangeonium is about $3\sim8$ times larger than that of the $S$-wave vector strangeonium. Around 2232 MeV the partial decay width of the $Λ\barΛ$ mode can reach up to several MeV for $ϕ(3^3S_1)$, while the partial $Λ\barΛ$ decay width of $ϕ(2^3D_1)$ is $\mathcal{O}(10^{-3})$ keV. If the threshold enhancement reported by the BESIII Collaboration arises from the strangeonium meson, this state is very likely to be the $ϕ(3^3S_1)$ state. We also note that the $Λ\barΛ$ and $Σ^{+}\barΣ^{-}$ partial decay widths of the states $ϕ(3^3D_1)$ and $ϕ(4^3S_1)$ are about several MeV, respectively, which are enough to be observed in future experiments.