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

• Main Authors: Tian-Wei Wu, Ming-Zhu Liu, Li-Sheng Geng, Emiko Hiyama, Manuel Pavon Valderrama, Wen-Ling Wang
• Format: Article
• Language: English
• Published: SpringerOpen 2020-09-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-020-08483-w
• ISSN: 1434-6044; 1434-6052

Abstract 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.