Do near-threshold molecular states mix with neighbouring $\bar QQ$ states?

Abstract

The last two decades are marked by a renaissance in hadronic spectroscopy caused by the arrival of vast experimental information on exotic states in the spectrum of charmonium and bottomonium. Most of such states have properties at odds with the predictions of the quark model and reside very close to strong hadronic thresholds. Prominent examples are provided by the glorious $X(3872)$ charmonium-like state and the doubly charmed tetraquark $T_{cc}^+$ with the masses within less than 1 MeV from the $D\bar{D}^*$ and $DD^*$ open-charm thresholds, respectively. The universality of this feature hints towards the existence of a general pattern for such exotic states. In this work we discuss a possible generic mechanism for the formation of near-threshold molecular states as a result of the strong coupling of compact quark states with a hadronic continuum channel. The compact states that survive the strong coupling limit decouple from the continuum channel and therefore also from the formed hadronic molecule - if realised this scenario would provide a justification to treat hadronic molecules isolated, ignoring the possible influence from surrounding, compact quark-model states. We confront the phenomenology of the $D_{s1}(2460)$ and $D_{s1}(2536)$ with this picture and find consistency, although other explanations remain possible for those states.