Search for $ {\eta }_{c}(2S)\to \omega \omega $ and $ \omega \varphi $ and measurements of $ {\chi }_{cJ}\to \omega \omega $ and $ \omega \varphi $ in $ \psi (2S)$ radiative processes

Using $ (2712\pm 14)\times {10}^{6}$ $ \psi (2S)$ events collected with the BESIII detector at the BEPCII collider, we search for the decays $ {\eta }_{c}(2S)\to \omega \omega $ and $ {\eta }_{c}(2S)\to \omega \varphi $ via the process $ \psi (2S)\to \gamma {\eta }_{c}(2S)$. No statistically significant signals are observed. The upper limits of their product branching fractions at the 90% confidence level are determined to be $ \mathcal{B}(\psi (2S)\to \gamma {\eta }_{c}(2S),{\eta }_{c}(2S)\to \omega \omega )<1.04\times {10}^{-6}$ and $ \mathcal{B}(\psi (2S)\to \phantom{\rule{0ex}{0ex}}\gamma {\eta }_{c}(2S),{\eta }_{c}(2S)\to \omega \varphi )<1.85\times {10}^{-7}$, respectively. We also update the branching fractions of $ {\chi }_{cJ}\to \omega \omega $ and $ {\chi }_{cJ}\to \omega \varphi $ via the $ \psi (2S)\to \gamma {\chi }_{cJ}$ transition. Their branching fractions are determined to be $ \mathcal{B}({\chi }_{c0}\to \omega \omega )=(10.66\pm 0.11\pm 0.57)\times {10}^{-4}$, $ \mathcal{B}({\chi }_{c1}\to \omega \omega )=(6.43\pm 0.07\pm 0.31)\times {10}^{-4}$, $ \mathcal{B}({\chi }_{c2}\to \omega \omega )=\phantom{\rule{0ex}{0ex}}(8.75\pm 0.08\pm 0.42)\times {10}^{-4}$, $ \mathcal{B}({\chi }_{c0}\to \omega \varphi )=(1.18\pm 0.03\pm 0.07)\times {10}^{-4}$, $ \mathcal{B}({\chi }_{c1}\to \omega \varphi )=(2.04\pm \phantom{\rule{0ex}{0ex}}0.15\pm 0.11)\times {10}^{-5}$, and $ \mathcal{B}({\chi }_{c2}\to \omega \varphi )=(9.58\pm 1.07\pm 0.76)\times {10}^{-6}$, where the first uncertainties are statistical and the second are systematic.