Search for ${\eta }_c(2S)\to p\bar{p}$ and branching fraction measurements of ${\chi }_{cJ}\to p\bar{p}$ via $\psi (2S)$ radiative decays

Using $(27.12\pm 0.14)\times {10}^8$ $\psi (2S)$ events collected by the BESIII detector operating at BEPCII, we search for the decay ${\eta }_c(2S)\to p\bar{p}$ via the process $\psi (2S)\to \gamma {\eta }_c(2S)$, and only find a signal with a significance of $1.7\sigma$. The upper limit of the product branching fraction at the 90% confidence level is determined to be $\mathcal{B}(\psi (2S)\to \gamma {\eta }_c(2S))\times \mathcal{B}({\eta }_c(2S)\to p\bar{p})<2.4\times {10}^{-7}$. The branching fractions of ${\chi }_{cJ}\to p\bar{p}(J=0,1,2)$ are also measured to be $\mathcal{B}({\chi }_{c0}\to p\bar{p})=(2.51\pm 0.02\pm 0.08)\times {10}^{-4}$, $\mathcal{B}({\chi }_{c1}\to p\bar{p})=(8.16\pm 0.09\pm 0.25)\times {10}^{-4}$, and $\mathcal{B}({\chi }_{c2}\to p\bar{p})=(8.33\pm 0.09\pm 0.22)\times {10}^{-4}$, where the first uncertainty is statistical and the second systematic.