Quadruply charmed dibaryons as heavy quark symmetry partners of the DDK bound state

Both unitary chiral theories and lattice QCD simulations show that the DK interaction is attractive and can form a bound state, namely, $$D^*_{s0}(2317)$$ D s 0 ∗ ( 2317 ) . Assuming the validity of the heavy antiquark–diquark symmetry, the $$\Xi _{cc}{\bar{K}}$$ Ξ cc K ¯ interaction is the same as the DK interaction, which implies the existence of a $$\Xi _{cc}{\bar{K}}$$ Ξ cc K ¯ bound state with a binding energy of $$49-64$$ 49 - 64 MeV. In this work, we study whether a $$\Xi _{cc}\Xi _{cc}{\bar{K}}$$ Ξ cc Ξ cc K ¯ three-body system binds. The $$\Xi _{cc}\Xi _{cc}$$ Ξ cc Ξ cc interaction is described by exchanging $$\pi $$ π , $$\sigma $$ σ , $$\rho $$ ρ , and $$\omega $$ ω mesons, with the corresponding couplings related to those of the NN interaction via the quark model. We indeed find a $$\Xi _{cc}\Xi _{cc}{\bar{K}}$$ Ξ cc Ξ cc K ¯ bound state, with quantum numbers $$J^P=0^-$$ J P = 0 - , $$I=\frac{1}{2}$$ I = 1 2 , $$S=1$$ S = 1 and $$C=4$$ C = 4 , and a binding energy of 80–118 MeV. With the same formalism, we find that the $$\Xi _{cc}\bar{\Xi }_{cc}{\bar{K}}$$ Ξ cc Ξ ¯ cc K ¯ system also binds, yielding a $$I(J^P)=\frac{1}{2}(0^+)$$ I ( J P ) = 1 2 ( 0 + ) state and a $$\frac{1}{2}(1^+)$$ 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 $$NN{\bar{K}}$$ N N 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 $$\Xi _{cc}\Xi _{cc}{\bar{K}}$$ Ξ cc Ξ cc K ¯ bound state.