Test of h₁(1830) made of $K^* \bar K^*$ with the $\eta _c \to \varphi K^* \bar K^*$ decay

Abstract

We present a new reaction, complementary to $J/\psi \to \eta K^{*0} \bar K^{*0}$ from which an h ₁ resonance with mass around 1830 MeV was reported from a BESIII experiment. The new reaction is $\eta _c \to \varphi K^* \bar K^*$, or $\eta _c (2S) \to \varphi K^* \bar K^*$. Using the information from the analysis of $J/\psi \to \eta K^{*0} \bar K^{*0}$, we find that the $K^* \bar K^*$ invariant mass distribution for those two Η 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.