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

Abstract

The $D^{(\ast)}Ξ_{cc}^{(\ast)}$ system and $\barΞ_{cc}^{(\ast)}Ξ_{cc}^{(\ast)}$ 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, $J^{P}=1/2^{-}$~$D^{\ast}Ξ_{cc}$ and $J^{P}=5/2^{-}$~$D^{\ast}Ξ_{cc}^{\ast}$. In the baryon-baryon system, there exist seven di-baryon molecules, $J^{PC}=0^{-+}$~$\barΞ_{cc}Ξ_{cc}$, $J^{PC}=1^{--}$~$\barΞ_{cc}Ξ_{cc}$, $J^{PC}=1^{-+}$~$\barΞ_{cc}Ξ_{cc}^{\ast}$, $J^{PC}=1^{--}$~$\barΞ_{cc}Ξ_{cc}^{\ast}$, $J^{PC}=2^{-+}$~$\barΞ_{cc}Ξ_{cc}^{\ast}$, $J^{PC}=2^{-+}$~$\barΞ_{cc}^{\ast}Ξ_{cc}^{\ast}$ and $J^{PC}=3^{--}$~$\barΞ_{cc}^{\ast}Ξ_{cc}^{\ast}$. Among them, the $J^{PC}=0^{-+}$~$\barΞ_{cc}Ξ_{cc}$ and/or $J^{PC}=1^{--}$~$\barΞ_{cc}Ξ_{cc}$ 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 $B^{(\ast)}\bar{B}^{(\ast)}$, $\bar{B}^{(\ast)}Ξ_{bb}^{(\ast)}$, and $\barΞ_{bb}^{(\ast)}Ξ_{bb}^{(\ast)}$ systems.