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Test of the $h_1(1830)$ made of $K^{*}\bar{K}^*$ with the $η_c\rightarrow ϕK^{*}\bar{K}^{*}$ decay

We present a new reaction, complementary to the $J/ψ\rightarrow ηK^{*0}\bar{K}^{*0}$ from which an $h_1$ resonance with mass around $1830$ MeV was reported from a BESIII experiment. The new reaction is $η_c\rightarrow ϕK^*\bar{K}^*$, or $η_c(2S)\rightarrow ϕK^*\bar{K}^*$. Using the information from the analysis of $J/ψ\rightarrow ηK^{*0}\bar{K}^{*0}$, we find that the $K^*\bar{K}^*$ invariant mass distribution for those two $η_c$ decays exhibits a clear peak around $1830$ MeV perfectly distinguishable from what one obtains with pure phase space. We suggest the implementation of these reactions to assert the existence of this elusive resonance which, by its nature as a vector-vector molecule with $0^-(1^{+-})$ quantum numbers, only couples to the $K^*\bar{K}^*$ channel.