Search for $η_c(2S)\to p\bar{p}$ and branching fraction measurements of $χ_{cJ} \to p\bar{p}$ via $ψ(2S)$ radiative decays
Using $(27.12\pm0.14) \times 10^{8}$ $ψ(2S)$ events collected by the BESIII detector operating at BEPCII, we search for the decay $η_c(2S)\to p\bar{p}$ via the process $ψ(2S)\to γη_c(2S)$, and only find a signal with a significance of $1.7\,σ$. The upper limit of the product branching fraction at the 90% confidence level is determined to be $\mathcal{B}(ψ(2S)\to γη_c(2S))\times \mathcal{B}(η_c(2S)\to p\bar{p})<2.4\times 10^{-7}$. The branching fractions of $χ_{cJ}\to p\bar{p}~(J=0,1,2)$ are also measured to be $\mathcal{B}(χ_{c0}\to p\bar{p})=(2.51\pm0.02\pm0.08)\times 10^{-4}$, $\mathcal{B}(χ_{c1}\to p\bar{p})=(8.16\pm0.09\pm0.25)\times 10^{-4}$, and $\mathcal{B}(χ_{c2}\to p\bar{p})=(8.33\pm0.09\pm0.22)\times 10^{-4}$, where the first uncertainty is statistical and the second systematic.