Threshold corrections of $χ_{\rm c}(2P)$ and $χ_{\rm b}(3P)$ states and $J/ψρ$ and $J/ψω$ transitions of the $X(3872)$ in a coupled-channel model

Abstract

We calculate the masses of $χ_{\rm c}(2P)$ and $χ_{\rm b}(3P)$ states with threshold corrections in a coupled-channel model. Here, the meson quarkonium core is augmented by higher Fock components due to pair-creation effects. According to our results, we interpret the resonances characterized by very small threshold corrections, like $χ_{\rm b}(3P)$'s, as almost pure quarkonia, and those states characterized by non-negligible threshold corrections, like the $X(3872)$, as quarkonium cores plus meson-meson components. We also study the $J/ψρ$ and $J/ψω$ hidden-flavor strong decays of the $X(3872)$. The decays are calculated as the dissociation of one of these components ($D^0 \bar D^{0*}$) into a $c \bar c$ state ($J/ψ$) plus a light meson ($ρ$ or $ω$) in a potential model. In particular, our result for the ratio between the $X(3872) \rightarrow J/ψω$ and $J/ψρ$ widths (0.6) is compatible with the present experimental data ($0.8\pm0.3$) within the experimental error.