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Search for ${\eta }_{c}\left(2S\right)\to 2\left({\pi }^{+}{\pi }^{-}\right)$ and improved measurement of ${\chi }_{cJ}\to 2\left({\pi }^{+}{\pi }^{-}\right)$

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    <subfield code="a">&lt;p&gt;We search for the hadronic decay ${\eta }_{c}\left(2S\right)\to 2\left({\pi }^{+}{\pi }^{-}\right)$ in the $\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)$ radiative decay using $\left(27.12±0.14\right)×{10}^{8}$ $\psi \left(3686\right)$ events collected by the BESIII detector at the BEPCII collider. No significant signal is found, and the upper limit of $B\left[\psi \left(3686\right)\to \gamma {\eta }_{c}\left(2S\right)\right]B\left[{\eta }_{c}\left(2S\right)\to 2\left({\pi }^{+}{\pi }^{-}\right)\right]$ is determined to be $1.43×{10}^{-6}$ at the 90% confidence level. Using $\psi \left(3686\right)\to \gamma {\chi }_{cJ}$ transitions, we also measure the branching fractions of $B\left[{\chi }_{cJ\left(J=0,1,2\right)}\to 2\left({\pi }^{+}{\pi }^{-}\right)\right]$, which are $B\left[{\chi }_{c0}\to 2\left({\pi }^{+}{\pi }^{-}\right)\right]=\phantom{\rule{0ex}{0ex}}\left(2.127±0.002\left(\mathrm{stat}\right)±0.101\left(\mathrm{syst}\right)\right)%$, $B\left[{\chi }_{c1}\to 2\left({\pi }^{+}{\pi }^{-}\right)\right]=\left(0.685±0.001\left(\mathrm{stat}\right)±0.031\left(\mathrm{syst}\right)\right)%$, and $B\left[{\chi }_{c2}\to 2\left({\pi }^{+}{\pi }^{-}\right)\right]=\left(1.153±0.001\left(\mathrm{stat}\right)±0.063\left(\mathrm{syst}\right)\right)%$.&lt;/p&gt;</subfield>
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