Observation of $η_c(2S) \to 3(π^+π^-)$ and measurements of $χ_{cJ} \to 3(π^+π^-)$ in $ψ(3686)$ radiative transitions

The hadronic decay $η_c(2S) \to 3(π^+π^-)$ is observed with a statistical significance of 9.3 standard deviations using $(448.1\pm2.9)\times10^6$ $ψ(3686)$ events collected by the BESIII detector at the BEPCII collider. The measured mass and width of $η_c(2S)$ are $(3643.4 \pm 2.3 (\rm stat.) \pm 4.4 (\rm syst.))$ MeV/$c^2$ and $(19.8 \pm 3.9 (\rm stat.) \pm 3.1 (\rm syst.))$ MeV, respectively, which are consistent with the world average values within two standard deviations. The product branching fraction $\mathcal{B}[ψ(3686)\to γη_c(2S)]\times\mathcal{B}[η_c(2S)\to3(π^+π^-)]$ is measured to be $(9.2 \pm 1.0 (\rm stat.) \pm 0.9 (\rm syst.))\times10^{-6}$. Using $\mathcal{B}[ψ(3686)\to γη_c(2S)]=(7.0^{+3.4}_{-2.5})\times10^{-4}$, we obtain $\mathcal{B}[η_c(2S) \to 3(π^+π^-)] = (1.31 \pm 0.15 (\rm stat.) \pm 0.13 (\rm syst.)(^{+0.64}_{-0.47}) (\rm extr))\times10^{-2}$, where the third uncertainty is from $\mathcal{B}[ψ(3686) \to γη_c(2S)]$. We also measure the $χ_{cJ} \to 3(π^+π^-)$ ($J=0, 1, 2$) decays via $ψ(3686) \to γχ_{cJ}$ transitions. The branching fractions are $\mathcal{B}[χ_{c0} \to 3(π^+π^-)] = (2.080\pm0.006 (\rm stat.)\pm0.068 (\rm syst.))\times10^{-2}$, $\mathcal{B}[χ_{c1} \to 3(π^+π^-)] = (1.092\pm0.004 (\rm stat.)\pm0.035 (\rm syst.))\times10^{-2}$, and $\mathcal{B}[χ_{c2} \to 3(π^+π^-)] = (1.565\pm0.005 (\rm stat.)\pm0.048 (\rm syst.))\times10^{-2}$.
12 pages, 5 figures