Search for the $\eta_c(2S)/h_c\to p\bar{p}$ decays and measurements of the $\chi_{cJ}\to p\bar{p}$ branching fractions

Using a sample of $1.06\times10^{8}~\psi(3686)$ events collected with the BESIII detector at BEPCII, the decays $\eta_{c}(2S)\to p\bar{p}$ and $h_{c}\to p\bar{p}$ are searched for, where $\eta_c(2S)$ and $h_c$ are reconstructed in the decay chains $\psi(3686)\to\gamma\eta_{c}(2S)$, $\eta_{c}(2S)\to p\bar{p}$ and $\psi(3686)\to\pi^{0}h_{c}$, $h_{c}\to p\bar{p}$, respectively. No significant signals are observed. The upper limits of the product branching fractions are determined to be $\mathcal{B}(\psi(3686)\to\gamma\eta_c(2S))\times\mathcal{B}(\eta_{c}(2S)\to p\bar{p})<1.4\times10^{-6}$ and $\mathcal{B}(\psi(3686)\to\pi^0h_c)\times\mathcal{B}(h_{c}\to p\bar{p})<1.3\times10^{-7}$ at the 90% C.L.. The branching fractions for $\chi_{cJ}\to p\bar{p}$ $(J=0,~1,~2)$ are also measured to be $(24.5\pm0.8\pm1.3,~8.6\pm0.5\pm0.5,~8.4\pm0.5\pm0.5)\times10^{-5}$, which are the world's most precise measurements.