Both unitary chiral theories and lattice QCD simulations show that the DK interaction is attractive and can form a bound state, namely, \(D^*_{s0}(2317)\). Assuming the validity of the heavy antiquark–diquark symmetry, the \(\Xi _{cc}{\bar{K}}\) interaction is the same as the DK interaction, which implies the existence of a \(\Xi _{cc}{\bar{K}}\) bound state with a binding energy of \(49-64\) MeV. In this work, we study whether a \(\Xi _{cc}\Xi _{cc}{\bar{K}}\) three-body system binds. The \(\Xi _{cc}\Xi _{cc}\) interaction is described by exchanging \(\pi \), \(\sigma \), \(\rho \), and \(\omega \) mesons, with the corresponding couplings related to those of the NN interaction via the quark model. We indeed find a \(\Xi _{cc}\Xi _{cc}{\bar{K}}\) bound state, with quantum numbers \(J^P=0^-\), \(I=\frac{1}{2}\), \(S=1\) and \(C=4\), and a binding energy of 80–118 MeV. With the same formalism, we find that the \(\Xi _{cc}\bar{\Xi }_{cc}{\bar{K}}\) system also binds, yielding a \(I(J^P)=\frac{1}{2}(0^+)\) state and a \(\frac{1}{2}(1^+)\) state with binding energies of 56–68 MeV and 56–67 MeV respectively. As a byproduct, we show the existence of a \(NN{\bar{K}}\) state with a binding energy of 35–43 MeV, consistent with the results of other theoretical works and experimental data, which serves as a consistency check on the predicted \(\Xi _{cc}\Xi _{cc}{\bar{K}}\) bound state.

单一手性理论和晶格QCD仿真均表明DK相互作用具有吸引力，并且可以形成束缚状态，即\（D ^ * _ {s0}（2317）\）。假设重反夸克-双夸克对称性的有效性，\（\ Xi _ {cc} {\ bar {K}} \）相互作用与DK相互作用相同，这意味着存在\（\ Xi _ { cc} {\ bar {K}} \）绑定状态，绑定能量为\（49-64 \） MeV。在这项工作中，我们研究\（\ Xi _ {cc} \ Xi _ {cc} {\ bar {K}} \）三体系统是否绑定。的\（\僖_ {CC} \僖_ {CC} \）相互作用是通过交换描述\（\ PI \） ，\（\西格玛\） ，\（\ rho \）和\（\ omega \）介子，其对应的耦合与通过夸克模型进行的NN交互相关。我们确实找到了\（\ Xi _ {cc} \ Xi _ {cc} {\ bar {K}} \）束缚态，其量子数为\（J ^ P = 0 ^-\），\（I = \ frac {1} {2} \），\（S = 1 \）和\（C = 4 \）以及80–118 MeV的结合能。使用相同的形式主义，我们发现\（\ Xi _ {cc} \ bar {\ Xi} _ {cc} {\ bar {K}} \）系统也绑定，产生\（I（J ^ P） = \ frac {1} {2}（0 ^ +）\）状态和\（\ frac {1} {2}（1 ^ +）\）结合能分别为56–68 MeV和56–67 MeV的原子态。作为副产品，我们显示存在一个（（NN {\ bar {K}} \）状态，其结合能为35–43 MeV，与其他理论工作和实验数据的结果一致，这是一致的检查预测的\（\ Xi _ {cc} \ Xi _ {cc} {\ bar {K}} \）绑定状态。