Strong decays of the explicitly exotic doubly charmed $DDK$ bound state

TL;DR

This paper investigates the strong decay properties of a hypothesized exotic $DDK$ bound state, predicting a narrow decay width into $DD_s\pi$, which could be observed in current experiments like BelleII, supporting its molecular nature.

Contribution

It provides the first calculation of the two-body strong decay widths of the $DDK$ bound state using triangle diagrams, suggesting a promising experimental search channel.

Findings

Decay width into $DD_s\pi$ is about 2-3 MeV.

The $DDK$ bound state is predicted to have a narrow decay width.

Experimental detection via current facilities is feasible.

Abstract

Nowadays, it is generally accepted that the $DK$ interaction in isospin zero is strongly attractive and the $D_{s0}^*(2317)$ can be described as a $DK$ molecular state. Recent studies show that the three-body $DDK$ system binds as well with a binding energy about 60$\sim$70 MeV. The $DDK$ bound state has isospin $1/2$ and spin-parity $0^-$. If discovered either experimentally or in lattice QCD, it will not only provide further support on the molecular nature of the $D_{s0}^*(2317)$, but also provide a way to understand other exotic hadrons expected to be of molecular nature. In the present work, we study its two-body strong decay widths via triangle diagrams. We find that the partial decay width into $DD_s\pi$ is at the order of $2\sim3$ MeV, which seems to be within the reach of the current experiments such as BelleII. As a result, we strongly recommend this decay channel of the $DDK$ bound state to be searched for experimentally.