Observation of $η_{c}$(1S, 2S) and $χ_{cJ}$ decays to 2$(π^{+}π^{-})η$ via $ψ$(3686) radiative transitions

Based on $2.7 \times 10^9~ψ(3686)$ decays collected with the BESIII detector, the radiative decay $ψ(3686)\to\gamma2(π^{+}π^{-})η$ is investigated to measure properties of S- and P-wave charmonium states. The branching fraction of the decay $η_{c}(1S) \to 2(π^{+}π^{-})η$, which is found to have a strong dependence on the interference pattern between $η_c(1S)$ and non-$η_c(1S)$ processes, is measured in both destructive and constructive interference scenarios for the first time. The mass and width of the $η_{c}(1S)$ are measured to be $M=(2984.14 \pm 0.13 \pm 0.38)$ MeV/$c^{2}$ and $Γ=(28.82 \pm 0.11 \pm 0.82)$ MeV, respectively. Clear signals for the decays of the $χ_{cJ}(J=0,1,2)$ and the $η_{c}(2S)$ to $2(π^{+}π^{-})η$ are also observed for the first time, and the corresponding branching fractions are measured. The ratio of the branching fractions between the $η_{c}(2S)$ and $η_{c}(1S)$ decays is significantly lower than the theoretical prediction, which might suggest different dynamics in their decays.