Comparison of molecular and compact states for the 𝑻 cc (3875) and 𝑿 (3872)

The dilemma between molecular states and compact quark states is the subject of a continuous debate in hadron physics. We explore this important question from a novel and different perspective. In this talk, firstly we present our recent work on $T_{\rm cc}(3875)$ state [Phys Lett B 846 (2023) 138200], in which the general formalism is developed in the single-channel calculation, we derive the molecular probability, the scattering length and effective range. We find that the binding energy by itself cannot give a proof of the nature of the state, which clarify the previous conclusion on this important issue. Secondly, we make an extension to the coupled-channel calculation for $X(3872)$ state [Phys Rev D 108 (2023) 114017]. The calculated results are discussed in different scenarios. Compared with the available experimental information, we find that the unavoidable molecular nature of these two states are dominated.