Study of ${e}^{+}{e}^{-}\to \omega X\left(3872\right)$ and $\gamma X\left(3872\right)$ from 4.66 to 4.95 GeV

Using data samples with an integrated luminosity of $4.5\text{}\text{}{\mathrm{fb}}^{-1}$ collected by the BESIII detector at center-of-mass energies ranging from 4.66 GeV to 4.95 GeV, we study the processes of ${e}^{+}{e}^{-}\to \omega X\left(3872\right)$ and ${e}^{+}{e}^{-}\to \gamma X\left(3872\right)$. With the ${e}^{+}{e}^{-}\to \omega X\left(3872\right)$ process, the branching fraction ratio $R\equiv \frac{B\left(X\left(3872\right)\to \gamma J/\psi \right)}{B\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)}$ is measured to be $0.38±0.2{0}_{\mathrm{stat}}±0.0{1}_{\mathrm{syst}}$ ($R<0.83$ at 90% confidence level). In addition, we measure the ratio of the average cross section of ${e}^{+}{e}^{-}\to \omega X\left(3872\right)$ to ${e}^{+}{e}^{-}\to \omega {\chi }_{c1}\left(\omega {\chi }_{c2}\right)$ to be ${\sigma }_{\omega X\left(3872\right)}/{\sigma }_{\omega {\chi }_{c1}}\left({\sigma }_{\omega X\left(3872\right)}/{\sigma }_{\omega {\chi }_{c2}}\right)=5.2±{1.0}_{\mathrm{stat}}±{1.9}_{\mathrm{syst}}\left(5.5±{1.1}_{\mathrm{stat}}±{2.4}_{\mathrm{syst}}\right)$. Finally, we search for the process of ${e}^{+}{e}^{-}\to \gamma X\left(3872\right)$, and no obvious signal is observed. The upper limit on the ratio of the average cross section of ${e}^{+}{e}^{-}\to \gamma X\left(3872\right)$ to ${e}^{+}{e}^{-}\to \omega X\left(3872\right)$ is set as ${\sigma }_{\gamma X\left(3872\right)}/{\sigma }_{\omega X\left(3872\right)}<0.23$ at 90% confidence level.