Effect of a repulsive three-body interaction on the $DD^{(*)}K$ molecule

TL;DR

This study investigates how a repulsive three-body interaction influences the structure and binding energy of the $DD^{(*)}K$ molecular system using the Gaussian expansion method, revealing size increase and potential breakup into two-body states.

Contribution

It provides a detailed analysis of the effects of a repulsive three-body interaction on the $DD^{(*)}K$ system, highlighting the transition from three-body to two-body bound states.

Findings

Increasing repulsive three-body interaction enlarges the bound state's size.

Strong three-body repulsion can break the three-body bound state into a two-body state.

The $DDK$ system tends to form an isosceles triangle-shaped configuration.

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 $DD^{*}K$ 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 $DD^{(*)}K$ bound state gradually increases. Further enhancement of the three-body interaction causes the $DD^{(*)}K$ three-body bound state to break into a $D^{(*)}K$ 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.