Probing the structure of the $D_{s 0}^*(2317)$ and $X(3872)$ states through correlation functions

Over the past 20 years, many new hadron states have been discovered, but understanding their nature remains a key experimental and theoretical challenge. Recent studies have established that hadron-hadron interactions primarily govern the generation of new hadronic states, with their spectroscopy serving as a powerful tool for probing these interactions and determining the corresponding compositeness. In this work, we study four scenarios to determine the $DK$ interaction by reproducing the mass of the $D_{s0}^*(2317)$, i.e., assuming the $D_{s0}^*(2317)$ as a $DK$ molecule, a mixture of a $DK$ molecule and a bare state, a $DK-D_s\eta$ molecule, and a mixture of a $DK-D_s\eta$ molecule and a bare state. Using the $D^{0}K^{+}$ interactions derived from these scenarios, we predict the $D^{0}K^{+}$ correlation functions. Our results demonstrate that the lineshape of the $D^{0}K^{+}$ correlation function is sensitive to the admixture effects from the coupled-channel $D^+K^0$ and the bare state. Furthermore, we find that the $D^{0}K^{+}$ correlation function can probe the position of the bare state, if such a QCD bare state exists. Using the shallow-bound state candidate $X(3872)$ as input, we study the $D^0\bar{D}^{*0}$ correlation functions. These functions are highly sensitive to short-range dynamics and bare-state admixtures, resulting in clearly distinguishable correlation-function line shapes across different values of compositeness.