Determination of spin-parity quantum numbers of X(2370) as $0^{-+}$ from $J/ψ\rightarrowγK^{0}_{S}K^{0}_{S}η^{\prime}$

Based on $(10087\pm44)\times10^{6}$ $J/ψ$ events collected with the BESIII detector, a partial wave analysis of the decay $J/ψ\rightarrowγK^{0}_{S}K^{0}_{S}η^{\prime}$ is performed. The mass and width of the $X(2370)$ are measured to be $2395 \pm 11 ({\rm stat})^{+26}_{-94}({\rm syst})\ \mathrm{MeV}/c^{2}$ and $188^{+18}_{-17}({\rm stat})^{+124}_{-33}({\rm syst})~\mathrm{MeV}$, respectively. The corresponding product branching fraction is $\mathcal{B}[J/ψ\rightarrowγX(2370)] \times \mathcal{B}[X(2370) \rightarrow f_{0}(980)η^{\prime}] \times \mathcal{B}[f_{0}(980) \rightarrow K^{0}_{S}K^{0}_{S}] = \left( 1.31 \pm 0.22 ({\rm stat})^{+2.85}_{-0.84}({\rm syst}) \right) \times 10^{-5}$. The statistical significance of the $X(2370)$ is greater than $11.7σ$ 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.