Eur. Phys. J. C (2021) 81: 179
https://doi.org/10.1140/epjc/s10052-021-08980-6

Regular Article - Theoretical Physics

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

¹ School of Space and Environment, Beihang University, 100191, Beijing, China
² School of Physics, Beihang University, 100191, Beijing, China
³ Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, 100191, Beijing, China
⁴ Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, School of Medicine and Engineering, Beihang University, 100191, Beijing, China
⁵ School of Physics and Microelectronics, Zhengzhou University, 450001, Zhengzhou, Henan, China

^b lisheng.geng@buaa.edu.cn

Received: 20 December 2020
Accepted: 13 February 2021
Published online: 22 February 2021

Abstract

The $D^{(\ast )}{\mathrm{\Xi }}_{\mathit{cc}}^{(\ast )}$ system and ${\overline{\mathrm{\Xi }}}_{\mathit{cc}}^{(\ast )}{\mathrm{\Xi }}_{\mathit{cc}}^{(\ast )}$ system can be related to the $D^{(\ast )}{\overline{D}}^{(\ast )}$ 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 $1^{++}D{\overline{D}}^{\ast }$ 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 $J^{\mathit{PC}}=2^{++}{\overline{D}}^{\ast }{D}^{\ast }$ 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, $J^P=1/2^{-}{D}^{\ast }{\mathrm{\Xi }}_{\mathit{cc}}$ and $J^P=5/2^{-}{D}^{\ast }{\mathrm{\Xi }}_{\mathit{cc}}^{\ast }$. In the baryon-baryon system, there exist seven di-baryon molecules, $J^{\mathit{PC}}=0^{-+}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}{\mathrm{\Xi }}_{\mathit{cc}}$, $J^{\mathit{PC}}=1^{--}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}{\mathrm{\Xi }}_{\mathit{cc}}$, $J^{\mathit{PC}}=1^{-+}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}{\mathrm{\Xi }}_{\mathit{cc}}^{\ast }$, $J^{\mathit{PC}}=1^{--}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}{\mathrm{\Xi }}_{\mathit{cc}}^{\ast }$, $J^{\mathit{PC}}=2^{-+}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}{\mathrm{\Xi }}_{\mathit{cc}}^{\ast }$, $J^{\mathit{PC}}=2^{-+}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}^{\ast }{\mathrm{\Xi }}_{\mathit{cc}}^{\ast }$, and $J^{\mathit{PC}}=3^{--}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}^{\ast }{\mathrm{\Xi }}_{\mathit{cc}}^{\ast }$. Among them, the $J^{\mathit{PC}}=0^{-+}{\overline{\mathrm{\Xi }}}_{\mathit{cc}}{\mathrm{\Xi }}_{\mathit{cc}}$ molecule 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 $B^{(\ast )}{\overline{B}}^{(\ast )}$, ${\overline{B}}^{(\ast )}{\mathrm{\Xi }}_{\mathit{bb}}^{(\ast )}$, and ${\overline{\mathrm{\Xi }}}_{\mathit{bb}}^{(\ast )}{\mathrm{\Xi }}_{\mathit{bb}}^{(\ast )}$ systems.