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

A recent quark-model description of X(3872) as an unquenched $2\,{}^{3\!}P_1$ $c\bar{c}$ state is generalised by now including all relevant meson-meson configurations, in order to calculate the widths of the experimentally observed electromagnetic decays $X(3872) \to γJ/ψ$ and $X(3872) \to γψ(2S)$. 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 $D^0\bar{D}^{\star0}$ component remains the dominant one. As for the electromagnetic decays, unquenching strongly reduces the $γψ(2S)$ decay rate yet even more sharply enhances the $γJ/ψ$ 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 $Γ( X(3872) \to γψ(2S) )=28.9$ keV and $Γ( X(3872) \to γJ/ψ)=24.7$ keV, with branching ratio $\mathcal{R}_{γψ}=1.17$.