Search for ${\eta }_{c}\left(2S\right)\to {\pi }^{+}{\pi }^{-}{\eta }_{c}$ and ${\eta }_{c}\left(2S\right)\to {\pi }^{+}{\pi }^{-}{K}_{S}^{0}{K}^{±}{\pi }^{\mp }$ decays

Based on $\left(27.12±0.14\right)×{10}^{8}\text{}\text{}\psi \left(2S\right)$ events collected by the BESIII detector, we search for the decay ${\eta }_{c}\left(2S\right)\to {\pi }^{+}{\pi }^{-}{\eta }_{c}$ via $\psi \left(2S\right)\to \gamma {\eta }_{c}\left(2S\right)$. No significant signal is observed, and the upper limit on the product branching fraction $B\left(\psi \left(2S\right)\to \gamma {\eta }_{c}\left(2S\right)\right)×B\left({\eta }_{c}\left(2S\right)\to {\pi }^{+}{\pi }^{-}{\eta }_{c}$) is determined to be $2.21×{10}^{-5}$ at the 90% confidence level. In addition, the ${\eta }_{c}\left(2S\right)\to {\pi }^{+}{\pi }^{-}{K}_{S}^{0}{K}^{±}{\pi }^{\mp }$ decay is studied via $\psi \left(2S\right)\to \gamma {\eta }_{c}\left(2S\right)$ and is observed with a statistical significance of $10\sigma $ for the first time. The branching fraction of ${\eta }_{c}\left(2S\right)\to {\pi }^{+}{\pi }^{-}{K}_{S}^{0}{K}^{±}{\pi }^{\mp }$ is determined to be ($1.33±0.11±0.40±0.95$)$×{10}^{-2}$, where the first uncertainty is statistical, the second is systematic, and the third uncertainty is due to the quoted $B\left(\psi \left(2S\right)\to \gamma {\eta }_{c}\left(2S\right)\right)$.