<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mi>D</mml:mi><mml:mi>K</mml:mi></mml:math> system in finite volume
Jin-Yi Pang, Jia-Jun Wu, Li‐Sheng Geng
Abstract
The $DDK$ three-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 three-body bound state is $cc\overline{q}\overline{s}$ 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 three-body quantization condition scheme is derived via the nonrelativistic effective theory and the particle-dimer picture in a finite volume. The lattice spectrum of this three-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.