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Searching for exotic multiquark states and elucidating their nature remains acentral topic in understanding quantum chromodynamics--the underlying theory ofthe strong interaction. Two of the most studied such states are thecharm-strange states $D_{s0}^*(2317)$ and $D_{s1}(2460)$. In this letter, weshow for the first time that their prompt production yields in inclusive$e^+e^-\to c\bar{c}$ collisions near $\sqrt{s}=10.6$ GeV measured by the BABARCollaboration, $Y(D_{s0}^*(2317))$ and $Y(D_{s1}(2460))$, in particular theratio $R=Y(D_{s0}^*(2317))/Y(D_{s1}(2460))$, can be well explained in themolecular picture, which provide a highly nontrivial verification of theirnature being $DK/D^*K$ molecules. On the contrary, treating them as pure$c\bar{s}$ $P-$wave states, the statistical model predicts a ratio $R$ smallerthan unity, in contrast with the experimental central value, though inagreement with it considering its relatively large uncertainty. In addition, wepredict the production yield of the $D\bar{D}K$ three-body bound state,$K_{c\bar{c}}(4180)$, in $e^+e^-\to c\bar{c}$ collisions and find that it iswithin the reach of the ongoing Belle II experiment. The present studydemonstrates the feasibility of a novel method to unravel the nature of exotichadrons and the potential of electron-positron collisions in this regard.

physical review. d/physical review. d.

Theoretical investigation of the molecular nature of $D_{s0}^*(2317)$  and $D_{s1}(2460)$ and the possibility of observing the $D\bar{D}K$ bound  state $K_{c\bar{c}}(4180)$ in inclusive $e^+e^-\to c\bar{c}$ collisions