On the nature of $X(2370)$

We address the nature of the $X(2370)$ resonances observed in the $J/\psi$ radiative decays, $J/\psi\rightarrow\gamma K^{+} K^{-}\eta'$, $J/\psi\rightarrow\gamma K_S K_S\eta'$ and $J/\psi\rightarrow\gamma \pi^{+}\pi^{-}\eta'$. By studying the invariant mass spectra we confirm that decays of the $X(2370)$ into three pseudo-scalars are well described by an effective chiral Lagrangian. We extract the branching ratio of $J/\psi\to X(2370)\gamma$ and show that it is an order of magnitude larger compared to the glueball production rate predicted by lattice QCD. This indicates that $X(2370)$ is not likely to be a glueball candidate.