DK, DDK, and DDDK molecules-understanding the nature of the Ds0∗ (2317)

The DK interaction is strong enough to form a bound state, the Ds0∗(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 JP=0-, I=12, S=1 and C=2. The minimum quark content of this state is ccqs 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.