Search for ηc(2S)→ 2(π⁺π⁻) and improved measurement of χcJ→ 2(π⁺π⁻)

We search for the hadronic decay ηc(2S)→ 2(π⁺π⁻) in the ψ(3686)→γηc(2S) radiative decay using (27.12± 0.14)× 10⁸ ψ(3686) events collected by the BESIII detector at the BEPCII collider. No significant signal is found, and the upper limit of B[ψ(3686)→γηc(2S)]B[ηc(2S)→ 2(π⁺π⁻)] is determined to be 0.78× 10⁻⁶ at the 90% confidence level. Using ψ(3686)→γχcJ transitions, we also measure the branching fractions of B[χcJ(J=0,1,2)→ 2(π⁺π⁻)], which are B[χc0→ 2(π⁺π⁻)]=(2.127± 0.002~(stat.)± 0.101~(syst.))%, B[χc1→ 2(π⁺π⁻)]=(0.685± 0.001~(stat.)± 0.031~syst.))%, and B[χc2→ 2(π⁺π⁻)]=(1.153± 0.001~(stat.)± 0.063~(syst.))%.