Partners of the $X(3872)$ and HQSS breaking

Abstract: Since the discovery of the $X(3872)$ the study of heavy meson molecules has been the subject of many investigations. On the experimental side different experiments have looked for its spin partners and the bottom analogs. On the theoretical side different approaches have been used to understand this state. Some of them are EFT that impose HQSS and so they make predictions for the partners of the $X(3872)$, suggesting the existence of a $J^{PC}=2^{++}$ partner in the charm sector or $J^{PC}=1^{++}$ or $2^{++}$ analogs in the bottom. In our work, in order to understand the $X(3872)$, we use a Chiral quark model in which, due to the proximity to the $DD^*$ threshold, we include $c\bar c$ states coupled to $DD^*$ molecular components. In this coupled channel model the relative position of the bare $c\bar c$ states with two meson thresholds are very important. We have looked for the $X(3872)$ partners and we don't find a bound state in the $D^D^$ $J^{PC}=2^{++}$. In the bottom sector we find the opposite situation where the $B^B^$ with $J^{PC}=2^{++}$ is bounded while the $J^{PC}=1^{++}$ is not bounded. These results shows how the coupling with $c\bar c$ states can induced different results than those expected by HQSS. The reason is that this symmetry is worse in the open heavy meson sector than in the hidden heavy meson sector.