Evidence for $η_c$(2S)$\to\pipieta$ decay

The decay $η_c(2S)\to\pipieta$ is searched for through the radiative transition $ψ(3686) \toγη_c(2S)$ using 448 million $ψ$(3686) events accumulated at the BESIII detector. The first evidence of $η_c(2S)\toπ^+π^-η$ is found with a statistical significance of 3.5$σ$. The product of the branching fractions of $ψ(3686)\toγη_c(2S)$ and $η_c(2S)\to\pipieta$ is measured to be $Br(ψ(3686)\toγη_c(2S))\times Br(η_c(2S)\to\pipieta)=(2.97\pm0.81\pm0.26)\times10^{-6}$, where the first uncertainty is statistical and the second one is systematic. The branching fraction of the decay $η_c(2S)\to\pipieta$ is determined to be $Br(η_c(2S)\to\pipieta)=(42.4\pm11.6\pm3.8\pm30.3)\times10^{-4}$, where the third uncertainty is transferred from the uncertainty of the branching fraction of $ψ(3686)\toγη_c(2S)$.