Is $X(7200)$ the heavy anti-quark diquark symmetry partner of $X(3872)$?

Abstract

The $D^{(\ast )}{\Xi }_{cc}^{(\ast )}$ system and ${\bar{\Xi }}_{cc}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ system can be related to the $D^{(\ast )}{\bar{D}}^{(\ast )}$ system via heavy anti-quark di-quark symmetry (HADS). In this work, we employ a contact-range effective field theory to systematically investigate the likely existence of molecules in these systems in terms of the hypothesis that X(3872) is a $1^{++}$~$D{\bar{D}}^{\ast }$ bound state in the isospin symmetry limit, with some of the unknown low energy constants estimated using the light-meson saturation approximation. In the meson-meson system, a $J^{PC}=2^{++}$~${\bar{D}}^{\ast }{D}^{\ast }$ molecule commonly referred to as $X(4013)$ is reproduced, which is the heavy quark spin partner of $X(3872)$. In the meson-baryon system, we predict two triply charmed pentaquark molecules, $J^P=1/2^{-}$~$D^{\ast }{\Xi }_{cc}$ and $J^P=5/2^{-}$~$D^{\ast }{\Xi }_{cc}^{\ast }$. In the baryon-baryon system, there exist seven di-baryon molecules, $J^{PC}=0^{-+}$~${\bar{\Xi }}_{cc}{\Xi }_{cc}$, $J^{PC}=1^{--}$~${\bar{\Xi }}_{cc}{\Xi }_{cc}$, $J^{PC}=1^{-+}$~${\bar{\Xi }}_{cc}{\Xi }_{cc}^{\ast }$, $J^{PC}=1^{--}$~${\bar{\Xi }}_{cc}{\Xi }_{cc}^{\ast }$, $J^{PC}=2^{-+}$~${\bar{\Xi }}_{cc}{\Xi }_{cc}^{\ast }$, $J^{PC}=2^{-+}$~${\bar{\Xi }}_{cc}^{\ast }{\Xi }_{cc}^{\ast }$ and $J^{PC}=3^{--}$~${\bar{\Xi }}_{cc}^{\ast }{\Xi }_{cc}^{\ast }$. Among them, the $J^{PC}=0^{-+}$~${\bar{\Xi }}_{cc}{\Xi }_{cc}$ and/or $J^{PC}=1^{--}$~${\bar{\Xi }}_{cc}{\Xi }_{cc}$ molecules may contribute to the $X(7200)$ state recently observed by the LHCb Collaboration, which implies that $X(7200)$ can be related to $X(3872)$ via HADS. As a byproduct, with the heavy quark flavor symmetry we also study likely existence of molecular states in the $B^{(\ast )}{\bar{B}}^{(\ast )}$, ${\bar{B}}^{(\ast )}{\Xi }_{bb}^{(\ast )}$, and ${\bar{\Xi }}_{bb}^{(\ast )}{\Xi }_{bb}^{(\ast )}$ systems.

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