Determination of spin-parity quantum numbers of X(2370) as $0^{-+}$ from $J\mathrm{/}\psi \to \gamma K_S^0{K}_S^0{\eta }^{\mathrm{\prime }}$

Based on $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected with the BESIII detector, a partial wave analysis of the decay $J\mathrm{/}\psi \to \gamma K_S^0{K}_S^0{\eta }^{\mathrm{\prime }}$ is performed. The mass and width of the $X(2370)$ are measured to be $2395\pm 11(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-94}^{+26}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ and $188_{-17}^{+18}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-33}^{+124}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mathrm{M}\mathrm{e}\mathrm{V}$, respectively. The corresponding product branching fraction is $\mathcal{B}[J\mathrm{/}\psi \to \gamma X(2370)]\times \mathcal{B}[X(2370)\to f_0(980){\eta }^{\mathrm{\prime }}]\times \mathcal{B}[f_0(980)\to K_S^0{K}_S^0]=(1.31\pm 0.22(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-0.84}^{+2.85}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))\times {10}^{-5}$. The statistical significance of the $X(2370)$ is greater than $11.7\sigma$ and the spin-parity is determined to be $0^{-+}$ for the first time. The measured mass and spin-parity of the $X(2370)$ are consistent with the predictions of the lightest pseudoscalar glueball.