Observation of Charmonium $h_c$ Radiative Decays to Multiple Light Hadrons and the Tensor State $f_2(1270)$

Using $\psi (3686)\to {\pi }^0{h}_c$ decays from a data sample of $(27.12\pm 0.14)\times {10}^8$ $\psi (3686)$ events collected by the BESIII detector at the BEPCII collider, $h_c$ radiative decays to $\gamma {\pi }^{+}{\pi }^{-},\gamma {\pi }^{+}{\pi }^{-}\eta ,\gamma 2({\pi }^{+}{\pi }^{-})$, and $\gamma p\bar{p}$ are observed for the first time, each with a significance greater than $5\sigma$. The corresponding branching fractions are measured. Furthermore, intermediate states below 2.8 GeV/$c^2$ are investigated, leading to the first observation of the decay process of $h_c\to \gamma f_2(1270)\to \gamma {\pi }^{+}{\pi }^{-}$ with a significance of $5.5\sigma$. This observation represents the first instance of $h_c$ radiative decay to a tensor state.