A Study of $T_{cc}(3875)^+$ Nature : Compact v.s. Molecule

A central question in exotic-hadron physics is their internal structure whether these states are loosely bound hadronic molecules or compact multiquark configurations. To shed light on this issue, we develop a model that incorporates mixing between hadronic-molecular and compact multiquark components. We then apply this framework to the specific case of the $T_{cc}(3875)^+$ and analyze the peak structure in the $D^0D^0\pi^+$ invariant-mass spectrum reported by LHCb. We find that a scenario based on a predominantly compact tetraquark provides the best fitted solution which can explain the $T_{cc}(3875)^+$. We also find that the model admits two more solutions of comparable quality, both of which imply that the $T_{cc}(3875)^+$ is a molecular state: (1) the $T_{cc}(3875)^+$ is a $D^{*+}D^0$ molecule and there is a $D^{*0}D^+$ molecular state in addition; (2) the $T_{cc}(3875)^+$ is a $D^{*0}D^+$ molecule and an aditional $D^{*+}D^0$ molecular state is found below $D^0D^0\pi^+$ threshold. These molecular states are not simple $I = 0$ states, but mixtures of $I = 0$ and $I = 1$ states. We show that all three scenarios are also consistent with the experimentally observed near-threshold $D^0D^0$ and $D^0D^+$ invariant-mass distributions.