Observation of the $X(2370)$ and search for the $X(2120)$ in $J/psitogamma Kbar{K} eta$

Using a sample of $1.31times10^{9} ~J/psi$ events collected with the BESIII detector, we perform a study of $J/psitogamma Kbar{K}eta$. The $X(2370)$ is observed in the $Kbar{K}eta$ invariant-mass distribution with a statistical significance of 8.3$sigma$. Its resonance parameters are measured to be $M = 2341.6 pm 6.5text{(stat.)} pm 5.7text{(syst.)}$~MeV/$c^{2}$ and $Gamma = 117 pm 10 text{(stat.)} pm 8 text{(syst.)}$~MeV. The product branching fractions for $J/psito gamma X(2370), X(2370) to K^{+} K^{-}eta$ and $J/psito gamma X(2370), X(2370) to K_{S}^{0} K_{S}^{0}eta$ are determined to be $(1.79 pm 0.23 text{(stat.)} pm 0.65 text{(syst.)}) times 10^{-5}$ and $(1.18 pm 0.32 text{(stat.)} pm 0.39 text{(syst.)}) times 10^{-5}$, respectively. No evident signal for the $X(2120)$ is observed in the $Kbar{K}eta$ invariant-mass distribution. The upper limits for the product branching fractions of $mathcal{B}(J/psi to gamma X(2120)togamma K^{+} K^{-} eta)$ and $mathcal{B}(J/psitogamma X(2120)togamma K_{S}^{0} K_{S}^{0} eta)$ are determined to be $1.49times10^{-5}$ and $6.38times10^{-6}$ at the 90% confidence level, respectively.