Observation and Spin-Parity Determination of the $X(1835)$ in $J/\psi\rightarrow\gamma K^0_S K^0_S\eta$

We report an observation of the process $J/\psi\rightarrow\gamma X(1835)\rightarrow\gamma K^0_S K^0_S\eta$ at low $K^0_S K^0_S$ mass with a statistical significance larger than 12.9$\sigma$ using a data sample of $1.31 \times 10^{9}$ $J/\psi$ events collected with the BESIII detector. In this region of phase space the $K^0_S K^0_S$ system is dominantly produced through the $f_0(980)$. By performing a partial wave analysis, we determine the spin-parity of the $X(1835)$ to be $J^{PC}=0^{-+}$. The mass and width of the observed $X(1835)$ are $1844\pm9(\text{stat})^{+16}_{-25}(\text{syst})$~\MeV~and $192^{+20}_{-17}(\text{stat})^{+62}_{-43}(\text{syst})$~MeV, respectively, which are consistent with the results obtained by BESIII in the channel $J/\psi\rightarrow\gamma\pi^+\pi^-\eta^{\prime}$.