# $DK$, $DDK$, and $DDDK$ molecules--understanding the nature of the $D_{s0}^*(2317)$

## TL;DR

This paper investigates the potential existence of exotic tetraquark states formed by multiple charmed mesons and a kaon, using the Gaussian Expansion Method to analyze the binding of $DDK$ and $DDDK$ systems.

## Contribution

The study demonstrates that the $DDK$ and $DDDK$ systems are likely bound states, providing evidence for possible exotic tetraquark molecules with specific quantum numbers.

## Key findings

- $DDK$ and $DDDK$ systems are predicted to be bound.
- Existence of these states is robust against interaction variations.
- These states could be counterparts of atomic nuclei or molecules.

## Abstract

The $DK$ interaction is strong enough to form a bound state, the $D_{s0}^*(2317)$. This in turn begs the question of whether there are bound states composed of several charmed mesons and a kaon. Previous calculations indicate that the three-body $DDK$ system is probably bound, where the quantum numbers are $J^P = 0^{-}$, $I=\tfrac{1}{2}$, $S = 1$ and $C = 2$. The minimum quark content of this state is $cc\bar{q}\bar{s}$ with $q=u,d$, which means that, if discovered, it will be an explicitly exotic tetraquark. In the present work. we apply the Gaussian Expansion Method to study the $DDDK$ system and show that it binds as well. The existence of these three and four body states is rather robust with respect to the $DD$ interaction and subleading (chiral) corrections to the $DK$ interaction. If these states exist, it is quite likely that their heavy quark symmetry counterparts exist as well. These three-body $DDK$ and four-body $DDDK$ molecular states could be viewed as counterparts of atomic nuclei, which are clusters of nucleons bound by the residual strong force, or chemical molecules, which are clusters of atoms bound by the residual electromagnetic interaction.