Radiative Decays of the $X(3872)$ in the Charmonium-Molecule Hybrid Picture

The X(3872) radiative decay is discussed by employing a two-meson multichannel model with the charmonium components, which explains many of the other observed features of X(3872). We have found that the ratio of the branching fractions of the X(3872) radiative decays, $R_\gamma =\text{Br}(X(3872)\rightarrow\psi(2S)\gamma)$ / Br$(X(3872)\rightarrow J/\psi\gamma)$, is 1.1 $\sim$ 3.4 if one assumes that the decay occurs only from the charmonium components. The invariant mass spectra of $cc^{bar}$($2P$)$\rightarrow J/\psi \gamma$ and $cc^{bar}$($2P$)$\rightarrow \psi(2S) \gamma$ are also investigated. It is found that an enhancement appears at around $E\sim 3960$ MeV in the $\psi(2S) \gamma$ spectrum but not in the $J/\psi\gamma$ spectrum. This corresponds to the missing $cc^{bar}$($2P$) pole which was predicted by the quark models but has not been observed due to the coupling to the $DD^{bar}$ states. We argue that the fluctuation seen in the experimental $\psi(2S) \gamma$ spectrum reported by LHCb may correspond to this $cc^{bar}$($2P$) pole.