$X(3872)$ electromagnetic decay in a coupled-channel model

A multichannel Schr"odinger equation with both quark-antiquark and meson-meson components, using a harmonic-oscillator potential for $q\bar{q}$ confinement and a delta-shell string-breaking potential for decay, is applied to the axial-vecor $X(3872)$ and lowest vector charmonia. The model parameters are fitted to the experimental values of the masses of the $X(3872)$, $J\mathrm{/}\psi$ and $\psi (2S)$. The wave functions of these states are computed and then used to calculate the electromagnetic decay widths of the $X(3872)$ into $J\mathrm{/}\psi \gamma$ and $\psi (2S)\gamma$.