Quark structure of the $X(3872)$ and $\chi_b(3P)$ resonances

Abstract

We discuss the nature of the $\chi_b(3P)$ and $X(3872)$ mesons: Are the $\chi_b(3P)$'s standard $b \bar b$ mesons or $b \bar b$ states with a significative continuum component? Is the $X(3872)$ a $c \bar c$ state with continuum coupling effects or a meson-meson molecule? To do that, we compare quark model and unquenched quark model results for the mass barycenter and splittings of the $\chi_b(3P)$ multiplet. Future and more precise experimental results will discriminate between the two interpretations. In the case of the $X(3872)$, we interpret it a $c \bar c$ core plus higher Fock components due to the coupling to the meson-meson continuum, thus we think that it is compatible with the meson $\chi_{c1}(2P)$, with $J^{PC} = 1^{++}$. The $J^{PC} = 1^{++}$ quantum numbers are in agreement with the experimental results found by the LHCb collaboration. In our view, the $X(3872)$'s mass is lower than the quark model's predictions because of self energy shifts. We also provide an estimation of the open charm/bottom strong decay modes of the $X(3872)$ and $\chi_b(3P)$ mesons, such as $X(3872) \rightarrow D \bar D^*$ and $\chi_{b2}(3P) \rightarrow B \bar B$, and radiative transitions.