Threshold effects in $\chi_{\rm c}(2P)$ and $\chi_{\rm b}(3P)$ multiplets and $J/\Psi \rho, J/\Psi \omega$ hidden-flavor strong decays of the $X(3872)$

We calculate the masses of $\chi_{\rm c}(2P)$ and $\chi_{\rm b}(3P)$ states with threshold corrections. Only the closest thresholds are taken into account, under the hypothesis that the others are supposed to give some kind of global contribution, which can be subtracted. We also hypothesize that the presence of a threshold does not affect the properties of a single resonance, but influences those of all the multiplet members, similarly to a spin-orbit or hyperfine splitting. We also compute the hidden-flavor $J/\Psi \rho$ and $J/\Psi \omega$ strong decays of the $X(3872)$. The decays are calculated as the dissociation of the $X(3872)$'s $D^0 \bar D^{0*}$ component into a $c \bar c$ state ($J/\Psi$) plus a light meson ($\rho$ or $\omega$). Our results are compared to the existing experimental data.