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 1.43×10-6 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))%.