Hadronic Molecular States Composed of Heavy Flavor Baryons

We investigate the possible molecules composed of two heavy flavor baryons such as "$A_QB_Q$"(Q=b, c) within the one-pion-exchange model (OPE). Our results indicate that the long-range $\pi$ exchange force is strong enough to form molecules such as $[\Sigma_Q\Xi_Q^{'}]^{I=1/2}_{S=1}$(Q=b, c), $[\Sigma_Q\Lambda_Q]^{I=1}_{S=1}$(Q=b, c), $[\Sigma_b\Xi_b^{'}]^{I=3/2}_{S=1}$ and $[\Xi_b\Xi^{'}_b]^{I=0}_{S=1}$ where the S-D mixing plays an important role. In contrast, the $\pi$ exchange does not form the spin-singlet $A_QB_Q$ bound states. If we consider the heavier scalar and vector meson exchanges as well as the pion exchange, some loosely bound spin-singlet S-wave states appear while results of the spin-triplet $A_QB_Q$ system does not change significantly, which implies the pion exchange plays an dominant role in forming the spin-triplet molecules. Moreover, we perform an extensive coupled channel analysis of the $\Lambda_Q\Lambda_Q$ system within the OPE and one-boson-exchange (OBE) framework and find that there exist loosely bound states of $\Lambda_Q\Lambda_Q$(Q=b,c) with quantum numbers $I(J^P)=0(0^+)$, $0(0^-)$ and $0(1^-)$. The binding solutions of $\Lambda_Q\Lambda_Q$ system mainly come from the coupled-channel effect in the flavor space. Besides the OPE force, the medium- and short-range attractive force also plays a significant role in the formation of the loosely bound $\Lambda_c\Lambda_c$ and $\Lambda_b\Lambda_b$ states. Once produced, they will be very stable because such a system decays via weak interaction with a very long lifetime around $10^{-13}\sim10^{-12}$s.