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Study of ${h}_{c}\to 3\left({\pi }^{+}{\pi }^{-}\right){\pi }^{0}$, ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right)\omega $, ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right){\pi }^{0}\eta $, ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right)\eta $, and ${h}_{c}\to p\overline{p}$

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    <subfield code="a">&lt;p&gt;Based on $\left(2712.4±14.1\right)×{10}^{6}$ $\psi \left(3686\right)$ events collected with the BESIII detector, we study the decays ${h}_{c}\to 3\left({\pi }^{+}{\pi }^{-}\right){\pi }^{0}$, ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right)\omega $, ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right){\pi }^{0}\eta $, ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right)\eta $, and ${h}_{c}\to p\overline{p}$ via $\psi \left(3686\right)\to \phantom{\rule{0ex}{0ex}}{\pi }^{0}{h}_{c}$. The decay channel ${h}_{c}\to 3\left({\pi }^{+}{\pi }^{-}\right){\pi }^{0}$ is observed for the first time, and its branching fraction is determined to be $\left(9.28±1.14±0.77\right)×{10}^{-3}$, where the first uncertainty is statistical and the second is systematic. In addition, first evidence is found for the modes ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right){\pi }^{0}\eta $ and ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right)\omega $ with significances of $4.8\sigma $ and $4.7\sigma $, and their branching fractions are determined to be $\left(7.55±1.51±0.77\right)×{10}^{-3}$ and $\left(4.00±0.86±0.35\right)×{10}^{-3}$, respectively. No significant signals of ${h}_{c}\to 2\left({\pi }^{+}{\pi }^{-}\right)\eta $ and ${h}_{c}\to p\overline{p}$ are observed, and the upper limits of the branching fractions of these decays are determined to be $&amp;lt;6.19×{10}^{-4}$ and $&amp;lt;4.40×{10}^{-5}$ at the 90% confidence level, respectively.&lt;/p&gt;</subfield>
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