Search for $ {\eta }_{c}(2S)\to p\overline{p}{K}^{+}{K}^{-}$ and measurement of $ {\chi }_{cJ}\to p\overline{p}{K}^{+}{K}^{-}$ in $ \psi (3686)$ radiative decays

A search for $ {\eta }_{c}(2S)\to p\overline{p}{K}^{+}{K}^{-}$, together with measurement of branching fractions of $ {\chi }_{cJ(J=0,1,2)}\to p\overline{p}{K}^{+}{K}^{-}$ in the $ \psi (3686)\to \gamma {\eta }_{c}(2S)$ and the $ \psi (3686)\to \gamma {\chi }_{cJ}$ radiative decays, is performed with $ (2712.4\pm 14.3)\times {10}^{6}\text{}\text{}\psi (3686)$ events collected with the BESIII detector at the BEPCII collider. An evidence for $ {\eta }_{c}(2S)\to p\overline{p}{K}^{+}{K}^{-}$ is found, with a significance of $ 3.3\sigma $. The product branching fraction of $ \mathcal{B}[\psi (3686)\to \gamma {\eta }_{c}(2S)]·\mathcal{B}[{\eta }_{c}(2S)\to p\overline{p}{K}^{+}{K}^{-}]$ is determined to be $ (1.98\pm 0.4{1}_{\mathrm{stat}}\pm 0.9{9}_{\mathrm{syst}})\times {10}^{-7}$. The product branching fractions of $ \mathcal{B}[\psi (3686)\to \gamma {\chi }_{cJ}]·\mathcal{B}[{\chi }_{cJ}\to p\overline{p}{K}^{+}{K}^{-}]$ are measured to be $ (2.49\pm 0.0{3}_{\mathrm{stat}}\pm 0.1{5}_{\mathrm{syst}})\times {10}^{-5}$, $ (1.83\pm 0.0{2}_{\mathrm{stat}}\pm 0.1{1}_{\mathrm{syst}})\times {10}^{-5}$, and $ (2.43\pm 0.0{2}_{\mathrm{stat}}\pm 0.1{5}_{\mathrm{syst}})\times {10}^{-5}$, for $ J=0$, 1, and 2, respectively.