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

Using $ (27.12\pm 0.14)\times {10}^{8}$ $ \psi \left(2S\right)$ events collected by the BESIII detector operating at BEPCII, we search for the decay $ {\eta }_{c}\left(2S\right)\to p\overline{p}$ via the process $ \psi \left(2S\right)\to \gamma {\eta }_{c}\left(2S\right)$ 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 $ B\left(\psi \right(2S)\to \gamma {\eta }_{c}(2S\left)\right)\times B\left({\eta }_{c}\right(2S)\to p\overline{p})<2.4\times {10}^{-7}$. The branching fractions of $ {\chi }_{cJ}\to p\overline{p}\text{}\text{}(J=0,1,2)$ are also measured to be $ B({\chi }_{c0}\to p\overline{p})=(2.51\pm 0.02\pm 0.08)\times {10}^{-4}$, $ B({\chi }_{c1}\to p\overline{p})=(8.16\pm 0.09\pm 0.25)\times {10}^{-4}$, and $ B({\chi }_{c2}\to p\overline{p})=(8.33\pm 0.09\pm 0.22)\times {10}^{-4}$, where the first uncertainty is statistical and the second systematic.