Observation of ${\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}\eta $

By analyzing $\left(27.12±0.14\right)×{10}^{8}\text{}\text{}\psi \left(3686\right)$ events accumulated with the BESIII detector, the decay ${\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}\eta $ is observed for the first time with a significance of $6.2\sigma $ after considering systematic uncertainties. The product of the branching fractions of $\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)$ and ${\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}\eta $ is measured to be $B\left(\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)\right)×B\left({\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}\eta \right)=\left(2.39±0.32±0.34\right)×{10}^{-6}$, where the first uncertainty is statistical, and the second one is systematic. The branching fraction of ${\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}\eta $ is determined to be $B\left({\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}\eta \right)=\left(3.42±0.46±0.48±2.44\right)×{10}^{-3}$, where the third uncertainty is due to the branching fraction of $\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)$. Using a recent BESIII measurement of $B\left({\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}{\pi }^{0}\right)$, we also determine the ratio between the branching fractions of ${\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}\eta $ and ${\eta }_{c}\left(2S\right)\to {K}^{+}{K}^{-}{\pi }^{0}$ to be $1.49±0.22±0.25$, which is consistent with the previous result of BABAR at a comparable precision level.