Hadronic Molecular States Composed of Heavy Flavor Baryons

Abstract

We investigate the possible molecules composed of two heavy flavor baryons such as "$A_Q{B}_Q$"(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 $[{\Sigma }_Q{\Xi }_Q^{{}^{\prime }}{]}_{S=1}^{I=1/2}$(Q=b, c), $[{\Sigma }_Q{\Lambda }_Q{]}_{S=1}^{I=1}$(Q=b, c), $[{\Sigma }_b{\Xi }_b^{{}^{\prime }}{]}_{S=1}^{I=3/2}$ and $[{\Xi }_b{\Xi }_b^{{}^{\prime }}{]}_{S=1}^{I=0}$ where the S-D mixing plays an important role. In contrast, the $\pi$ exchange does not form the spin-singlet $A_Q{B}_Q$ 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 $A_Q{B}_Q$ 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 $10^{-13}\sim 10^{-12}$s.

Published in PRD

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