Observation of X(2370) and search for X(2120) in $J/\psi \to \gamma K\overline{K}{\eta }^{\prime }$

Using a sample of $1.31×{10}^{9}\phantom{\rule{3.33333pt}{0ex}}J/\psi $ events collected with the BESIII detector, we perform a study of $J/\psi \to \gamma K\overline{K}{\eta }^{\prime }$ . X(2370) is observed in the $K\overline{K}{\eta }^{\prime }$ invariant-mass distribution with a statistical significance of $8.3\sigma $ . Its resonance parameters are measured to be $M=2341.6±6.5\phantom{\rule{0.166667em}{0ex}}\text{(stat.)}±5.7\phantom{\rule{0.166667em}{0ex}}\text{(syst.)}\phantom{\rule{3.33333pt}{0ex}}\text{MeV}/{c}^{2}$ and $\Gamma =117±10\phantom{\rule{0.166667em}{0ex}}\text{(stat.)}±8\phantom{\rule{0.166667em}{0ex}}\text{(syst.)}\phantom{\rule{3.33333pt}{0ex}}\text{MeV}$ . The product branching fractions for $J/\psi \to \gamma X\left(2370\right),X\left(2370\right)\to {K}^{+}{K}^{-}{\eta }^{\prime }$ and $J/\psi \to \gamma X\left(2370\right),X\left(2370\right)\to {K}_{S}^{0}{K}_{S}^{0}{\eta }^{\prime }$ are determined to be $\left(1.79±0.23\phantom{\rule{0.166667em}{0ex}}\text{(stat.)}±0.65\phantom{\rule{0.166667em}{0ex}}\text{(syst.)}\right)×{10}^{-5}$ and $\left(1.18±0.32\phantom{\rule{0.166667em}{0ex}}\text{(stat.)}±0.39\phantom{\rule{0.166667em}{0ex}}\text{(syst.)}\right)×{10}^{-5}$ , respectively. No evident signal for X(2120) is observed in the $K\overline{K}{\eta }^{\prime }$ invariant-mass distribution. The upper limits for the product branching fractions of $B\left(J/\psi \to \gamma X\left(2120\right)\to \gamma {K}^{+}{K}^{-}{\eta }^{\prime }\right)$ and $B\left(J/\psi \to \gamma X\left(2120\right)\to \gamma {K}_{S}^{0}{K}_{S}^{0}{\eta }^{\prime }\right)$ are determined to be $1.49×{10}^{-5}$ and $6.38×{10}^{-6}$ at the 90% confidence level, respectively.