Publication Date:
2020-09-01
Description:
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 $$Xi _{cc}{ ar{K}}$$ Ξ cc K ¯ interaction is the same as the DK interaction, which implies the existence of a $$Xi _{cc}{ ar{K}}$$ Ξ cc K ¯ bound state with a binding energy of $$49-64$$ 49 - 64 MeV. In this work, we study whether a $$Xi _{cc}Xi _{cc}{ ar{K}}$$ 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 , $$
ho $$ ρ , and $$omega $$ ω mesons, with the corresponding couplings related to those of the NN interaction via the quark model. We indeed find a $$Xi _{cc}Xi _{cc}{ ar{K}}$$ 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 $$Xi _{cc} ar{Xi }_{cc}{ ar{K}}$$ 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 $$NN{ ar{K}}$$ 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 $$Xi _{cc}Xi _{cc}{ ar{K}}$$ Ξ cc Ξ cc K ¯ bound state.
Print ISSN:
1434-6044
Electronic ISSN:
1434-6052
Topics:
Physics
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