Unquenched quark-model calculation of X(3872) electromagnetic decays

A recent quark-model description of X(3872) as an unquenched $2{}^{3\text{\hspace{0.17em}⁣}}{P}_1$ $c\bar{c}$ state is generalised by now including all relevant meson-meson configurations, in order to calculate the widths of the experimentally observed electromagnetic decays $X(3872)\to \gamma J\mathrm{/}\psi$ and $X(3872) \to \gamma\psi(2S)$. Interestingly, the inclusion of additional two-meson channels, most importantly $D^{\pm }{D}^{\star \mp }$, leads to a sizeable increase of the $c\bar{c}$ probability in the total wave function, although the $D^0{\bar{D}}^{\star 0}$ component remains the dominant one. As for the electromagnetic decays, unquenching strongly reduces the $\gamma \psi (2S)$ decay rate yet even more sharply enhances the $\gamma J\mathrm{/}\psi$ rate, resulting in a decay ratio compatible with one experimental observation but in slight disagreement with two others. Nevertheless, the results show a dramatic improvement as compared to a quenched calculation with the same confinement force and parameters. Concretely, we obtain $\Gamma ( X(3872) \to \gamma \psi(2S) )=28.9$keVand$\Gamma ( X(3872) \to \gamma J/\psi)=24.7$ keV, with branching ratio ${\mathcal{R}}_{\gamma \psi }=1.17$.