Effect of a repulsive three-body interaction on the $D{D}^{(\ast )}K$ molecule

Abstract

The hadronic molecular picture of the observed exotic states has inspired numerous investigations into few-body systems. Recently, the lattice effective field theory studied the effect of a three-body interaction on the binding energy of the $D{D}^{\ast }K$ system, revealing an intriguing phenomenon in the binding energy. This work uses the Gaussian expansion method to explore the underlying physics. Our results show that as the repulsive three-body interaction strengthens, the spatial size of the $D{D}^{(\ast )}K$ bound state gradually increases. Further enhancement of the three-body interaction causes the $D{D}^{(\ast )}K$ three-body bound state to break into a $D^{(\ast )}K$ two-body bound state, accompanied by a distant $D$ meson. The identical nature of the two $D$ mesons leads to the fact that the $DDK$ system consistently resembles an isosceles triangle-shaped spatial configuration.

Comments: 8 pages, 6 figures