$DDK$ system in finite volume

TL;DR

This paper develops a finite-volume quantization condition for the $DDK$ three-body system using non-relativistic effective theory and particle-dimer models, providing lattice spectrum predictions to explore its bound state nature and relation to $D^*(2317)$.

Contribution

It introduces a novel 3-body quantization scheme in finite volume for the $DDK$ system, linking phenomenological models with lattice QCD predictions.

Findings

Lattice spectrum of the $DDK$ system calculated with existing model inputs.

Spectrum indicates potential bound states and properties relevant to the $D^*(2317)$.

Predicted spectrum can be tested in future lattice simulations.

Abstract

The $DDK$ 3-body system is supposed to be bound due to the strongly attractive interaction between the $D$ meson and the $K$ meson in the isospin zero channel. The minimum quark content of this 3-body bound state is $cc\bar{q}\bar{s}$ with $q=u,d$. It will be an explicitly exotic tetraquark state once discovered. In order to confirm the phenomenological study of the $DDK$ system, we can refer to lattice QCD as a powerful theoretical tool parallel to the experiment measurement. In this paper, a 3-body quantization condition scheme is derived via the non-relativistic effective theory and the particle-dimer picture in finite volume. Lattice spectrum of this 3-body system is calculated within the existing model inputs. The spectrum shows various interesting properties of the $DDK$ system, and it may reveal the nature of the $D^*(2317)$. This predicated spectrum is expected to be tested in future lattice simulations.