From a picture of the $X(3872)$ where the resonance is a bound state of $\overline{D}{D}^{*}-\mathrm{c}.\mathrm{c}.$, we evaluate the decay width into the $J/\psi \gamma$ channel, which is sensitive to the internal structure of this state. For this purpose we evaluate the loops through which the $X(3872)$ decays into its components, and the $J/\psi$ and the photon are radiated from these components. We use the local hidden gauge approach extrapolated to $SU(4)$ with a particular $SU(4)$ breaking. The radiative decay involves anomalous couplings, and we obtain acceptable values which are compared to experiments and results of other calculations. Simultaneously, we evaluate the decay rate for the $X(3872)$ into $J/\psi \omega$ and $J/\psi \rho$, and the results obtained for the ratio of these decay widths are compatible with the experiment. We also show that considering only the ${\overline{D}}^0{D}^{*0}-\mathrm{c}.\mathrm{c}.$ component in the radiative decay reduces the partial decay width in more than three orders of magnitude, in large discrepancy with experiment.

• Received 31 July 2012

DOI:https://doi.org/10.1103/PhysRevD.86.113007