Observation of the $X(2370)$ in $J\mathrm{/}\psi \to \gamma K_S^0{K}_S^0{\pi }^0$ and $J\mathrm{/}\psi \to \gamma {\pi }^0{\pi }^0\eta$

Based on $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected with the BESIII detector, the $J\mathrm{/}\psi \to \gamma K_S^0{K}_S^0{\pi }^0$ and $J\mathrm{/}\psi \to \gamma {\pi }^0{\pi }^0\eta$ processes are studied. The $X(2370)$ is observed in both the $K_S^0{K}_S^0{\pi }^0$ and ${\pi }^0{\pi }^0\eta$ invariant mass spectra, with statistical significances greater than $14\sigma$ and $20\sigma$, respectively. Combining measurements from these processes with measurements from the previously reported $J\mathrm{/}\psi \to \gamma K_S^0{K}_S^0{\eta }^{\mathrm{\prime }}$ process, the mass and width of the $X(2370)$ are determined to be $2359_{-14}^{+13}\text{ MeV}\mathrm{/}{c}^2$ and $170_{-29}^{+44}\text{ MeV}$, respectively. In addition, the decay $X(2370)\to a_0(980{)}^0{\pi }^0$ with $a_0(980{)}^0\to {\pi }^0\eta$ is observed with a statistical significance exceeding $9\sigma$. The similarities in decay modes between the $X(2370)$ and ${\eta }_c$ are consistent with the features of a pseudoscalar glueball.