Search for η_c (2S)→π^+π^-η_c and η_c (2S)→π^+π^-K^0_S K^±π^∓ decays

Based on (27.12± 0.14)× 10^8 ψ(2S) events collected with the BESIII detector, we search for the decay η_c (2S) →π^+π^-η_c with η_c→ K_S^0 K^±π^∓ and η_c→ K^+K^-π^0. No significant signal is observed, and the upper limit on the product branching fraction ℬ(ψ(2S)→γη_c(2S))×ℬ(η_c (2S) →π^+π^-η_c) is determined to be 2.21×10^-5 at the 90% confidence level. In addition, the analysis of the process ψ(2S)→γη_c(2S), η_c(2S)→π^+π^-K^0_SK^±π^∓ gives a clear η_c(2S) signal with a statistical significance of 10σ for the first time, branching fraction ℬ(ψ(2S)→γη_c(2S))×ℬ(η_c(2S)→π^+π^-K^0_SKπ) is measured to be (9.31 ± 0.72 ± 2.77)× 10^-6, and and the branching fraction ℬ(η_c(2S)→π^+π^-K^0_SK^±π^∓) is determined to be (1.33 ± 0.11 ± 0.4 ± 0.95)× 10^-2, where the first uncertainty is statistical, the second is systematic, and the third uncertainty is due to the quoted ℬ(ψ(2S)→γη_c(2S)).