Both unitary chiral theories and lattice QCD simulations show that the DK interaction is attractive and can form a bound state, namely, Ds0∗(2317). Assuming the validity of the heavy antiquark–diquark symmetry, the Ξ ccK¯ interaction is the same as the DK interaction, which implies the existence of a Ξ ccK¯ bound state with a binding energy of 49 - 64 MeV. In this work, we study whether a Ξ ccΞ ccK¯ three-body system binds. The Ξ ccΞ cc interaction is described by exchanging π, σ, ρ, and ω mesons, with the corresponding couplings related to those of the NN interaction via the quark model. We indeed find a Ξ ccΞ ccK¯ bound state, with quantum numbers JP= 0 -, I=12, S= 1 and C= 4 , and a binding energy of 80–118 MeV. With the same formalism, we find that the Ξ ccΞ ¯ ccK¯ system also binds, yielding a I(JP)=12(0+) state and a 12(1+) state with binding energies of 56–68 MeV and 56–67 MeV respectively. As a byproduct, we show the existence of a NNK¯ 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 Ξ ccΞ ccK¯ bound state.
ASJC Scopus subject areas
- Engineering (miscellaneous)
- Physics and Astronomy (miscellaneous)