The hadronic decay ${\eta }_c(2S)\to 3({\pi }^{+}{\pi }^{-})$ is observed with a statistical significance of 9.3 standard deviations using $(448.1\pm 2.9)\times {10}^6\psi (3686)$ events collected by the BESIII detector at the BEPCII collider. The measured mass and width of ${\eta }_c(2S)$ are $(3643.4\pm 2.3(\mathrm{stat})\pm 4.4(\mathrm{syst}))\mathrm{MeV}/c^2$ and $(19.8\pm 3.9(\mathrm{stat})\pm 3.1(\mathrm{syst}))\mathrm{MeV}$, respectively, which are consistent with the world average values within two standard deviations. The product branching fraction $\mathcal{B}[\psi (3686)\to \gamma {\eta }_c(2S)]\times \mathcal{B}[{\eta }_c(2S)\to 3({\pi }^{+}{\pi }^{-})]$ is measured to be $(9.2\pm 1.0(\mathrm{stat})\pm 1.2(\mathrm{syst}))\times {10}^{-6}$. Using $\mathcal{B}[\psi (3686)\to \gamma {\eta }_c(2S)]=(7.0_{-2.5}^{+3.4})\times {10}^{-4}$, we obtain $\mathcal{B}[{\eta }_c(2S)\to 3({\pi }^{+}{\pi }^{-})]=(1.31\pm 0.15(\mathrm{stat})\pm 0.17(\mathrm{syst})(\genfrac{}{}{0ex}{}{+0.64}{-0.47})(\mathrm{extr}))\times {10}^{-2}$, where the third uncertainty is from $\mathcal{B}[\psi (3686)\to \gamma {\eta }_c(2S)]$. We also measure the ${\chi }_{cJ}\to 3({\pi }^{+}{\pi }^{-})$ ($J=0$, 1, 2) decays via ${\psi }^{\prime }\to \gamma {\chi }_{cJ}$ transitions. The branching fractions are $\mathcal{B}[{\chi }_{c0}\to 3({\pi }^{+}{\pi }^{-})]=(2.080\pm 0.006(\mathrm{stat})\pm 0.068(\mathrm{syst}))\times {10}^{-2}$, $\mathcal{B}[{\chi }_{c1}\to 3({\pi }^{+}{\pi }^{-})]=(1.092\pm 0.004(\mathrm{stat})\pm 0.035(\mathrm{syst}))\times {10}^{-2}$, and $\mathcal{B}[{\chi }_{c2}\to 3({\pi }^{+}{\pi }^{-})]=(1.565\pm 0.005(\mathrm{stat})\pm 0.048(\mathrm{syst}))\times {10}^{-2}$.

• Received 19 June 2022
• Accepted 28 July 2022

DOI:https://doi.org/10.1103/PhysRevD.106.032014

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Published by the American Physical Society