Radiative decays of $X(3872)$ within $D{\bar{D}}^{\ast }$ molecular framework

Within the framework of nonrelativistic effective field theory, we calculate the radiative decay width of the process $X(3872)\to \bar{D}D\gamma$ while taking into account the $D\bar{D}$ final-state interactions. In this work, the $X(3872)$, with the spin-parity quantum numbers $J^{PC}=1^{++}$, is treated as a $D^{\ast }\bar{D}+\mathrm{c}\mathrm{.}\mathrm{c}\mathrm{.}$ bound state comprising equal proportions of neutral and charged components. Our numerical calculations predict the tree-level partial decay width of approximately $11.0$ keV for the decay process $X(3872)\to {\bar{D}}^0{D}^0\gamma$, while the partial width for $X(3872)\to D^{-}{D}^{+}\gamma$ is less than $1.0$ keV. It is found that the $D\bar{D}$ rescattering effect enhances the tree-level width of $X(3872)\to {\bar{D}}^0{D}^0\gamma$ by $6\mathrm{\%}$. In contrast, the rescattering effect makes a suppression to the charged channel $X(3872)\to D^{-}{D}^{+}\gamma$ by roughly $38\mathrm{\%}$. We expect that the present predictions based on the molecular picture of the $X(3872)$ can be tested by future experiments.