Search for $\eta_{c}(2S)\rightarrow\omega\omega$ and $\omega\phi$ and measurements of $\chi_{cJ} \rightarrow\omega\omega$ and $\omega\phi$ in $Psi(2S)$ radiative processes

Using $(2712\pm 14)$ $\times$ 10$^{6}$ $ψ(2S)$ events collected with the BESIII detector at the BEPCII collider, we search for the decays $η_{c}(2S)\toωω$ and $η_{c}(2S)\toωϕ$ via the process $ψ(2S)\toγη_{c}(2S)$. Evidence of $η_{c}(2S)\toωω$ is found with a statistical significance of $3.2σ$. The branching fraction is measured to be $\mathcal{B}(η_{c}(2S)\toωω)=(5.65\pm3.77(\rm stat.)\pm5.32(\rm syst.))\times10^{-4}$. No statistically significant signal is observed for the decay $η_{c}(2S)\toωϕ$. The upper limit of the branching fraction at the 90\% confidence level is determined to be $\mathcal{B}(ψ(2S)\toγη_{c}(2S),η_{c}(2S)\toωϕ)<2.24\times 10^{-7}$. We also update the branching fractions of $χ_{cJ}\to ωω$ and $χ_{cJ}\toωϕ$ decays via the $ψ(2S)\toγχ_{cJ}$ transition. The branching fractions are determined to be $\mathcal{B}(χ_{c0}\toωω)=(10.63\pm0.11\pm0.46)\times 10^{-4}$, $\mathcal{B}(χ_{c1}\toωω)=(6.39\pm0.07\pm0.29)\times 10^{-4}$, $\mathcal{B}(χ_{c2}\toωω)=(8.50\pm0.08\pm0.38)\times 10^{-4}$, $\mathcal{B}(χ_{c0}\toωϕ)=(1.18\pm0.03\pm0.05)\times 10^{-4}$, $\mathcal{B}(χ_{c1}\toωϕ)=(2.03\pm0.15\pm0.12)\times 10^{-5}$, and $\mathcal{B}(χ_{c2}\toωϕ)=(9.37\pm1.07\pm0.59)\times 10^{-6}$, where the first uncertainties are statistical and the second are systematic.