Observation and Spin-Parity Determination of the $X(1835)$ in $J/psirightarrowgamma K^0_S K^0_Seta$

We report an observation of the process $J/psirightarrowgamma X(1835)rightarrowgamma K^0_S K^0_Seta$ 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 $1844pm9(text{stat})^{+16}_{-25}(text{syst})$~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 $J/psirightarrowgammapi^+pi^-eta^{prime}$.