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

Abstract

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 $\psi (2S)\to \gamma {\eta }_c(2S)$. Evidence of ${\eta }_c(2S)\to \omega \omega$ is found with a statistical significance of $3.2\sigma$. The branching fraction is measured to be $\mathcal{B}({\eta }_c(2S)\to \omega \omega )=(5.65\pm 3.77(stat.)\pm 5.32(syst.))\times 10^{-4}$. No statistically significant signal is observed for the decay ${\eta }_c(2S)\to \omega \varphi$. The upper limit of the branching fraction at the 90\% confidence level is determined to be $\mathcal{B}(\psi (2S)\to \gamma {\eta }_c(2S),{\eta }_c(2S)\to \omega \varphi )<2.24\times 10^{-7}$. We also update the branching fractions of ${\chi }_{cJ}\to \omega \omega$ and ${\chi }_{cJ}\to \omega \varphi$ decays via the $\psi (2S)\to \gamma {\chi }_{cJ}$ transition. The branching fractions are determined to be $\mathcal{B}({\chi }_{c0}\to \omega \omega )=(10.63\pm 0.11\pm 0.46)\times 10^{-4}$, $\mathcal{B}({\chi }_{c1}\to \omega \omega )=(6.39\pm 0.07\pm 0.29)\times 10^{-4}$, $\mathcal{B}({\chi }_{c2}\to \omega \omega )=(8.50\pm 0.08\pm 0.38)\times 10^{-4}$, $\mathcal{B}({\chi }_{c0}\to \omega \varphi )=(1.18\pm 0.03\pm 0.05)\times 10^{-4}$, $\mathcal{B}({\chi }_{c1}\to \omega \varphi )=(2.03\pm 0.15\pm 0.12)\times 10^{-5}$, and $\mathcal{B}({\chi }_{c2}\to \omega \varphi )=(9.37\pm 1.07\pm 0.59)\times 10^{-6}$, where the first uncertainties are statistical and the second are systematic.