The $X(3872) \to J/\psi \gamma$ decay in the $D \bar D^*$ molecular picture

TL;DR

This paper investigates the radiative decay of the X(3872) as a molecular state of D and D* mesons, calculating decay widths and ratios that align with experimental data, and emphasizing the importance of its full component structure.

Contribution

It provides a detailed calculation of the X(3872) decay into J/psi gamma within a molecular D D* picture using a specific theoretical approach, highlighting the significance of its full component structure.

Findings

Decay width into J/psi gamma matches experimental values.

Decay ratios into J/psi omega and J/psi rho are consistent with experiments.

Considering only the neutral D D* component yields unrealistic results.

Abstract

From a picture of the X(3872) where the resonance is a bound state of $\bar{D}D^*-c.c.$, 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. Simultaneusly, 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 the grossly unacceptable results that come from taking only the $\bar{D}^0D^{*0}+c.c.$ component.