Eur. Phys. J. C (2022) 82: 908
https://doi.org/10.1140/epjc/s10052-022-10881-1

Regular Article - Theoretical Physics

Hadronic molecules composed of a doubly charmed tetraquark state and a charmed meson

¹ School of Physics, Beihang University, 100191, Beijing, China
² School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, 310024, Hangzhou, China
³ University of Chinese Academy of Sciences, 100049, Beijing, China
⁴ School of Space and Environment, Beihang University, 100191, Beijing, China
⁵ Peng Huanwu Collaborative Center for Research and Education, Beihang University, 100191, Beijing, China
⁶ Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, 100191, Beijing, China
⁷ School of Physics and Microelectronics, Zhengzhou University, 450001, Zhengzhou, Henan, China

^c zhengmz11@buaa.edu.cn

Received: 17 August 2022
Accepted: 6 October 2022
Published online: 13 October 2022

Abstract

The three pentaquark states, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by the LHCb Collaboration in 2019, can be arranged into a complete heavy quark spin symmetry multiplet of hadronic molecules of ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{(\ast )}$. In the heavy quark mass limit, the ${\mathrm{\Sigma }}_c^{(\ast )}$ baryons can be related to the doubly charmed tetraquark states of isospin 1, i.e., $T_{\overline{c}\overline{c}}^{(\ast )}$( $T_{\overline{c}\overline{c}}^0$, $T_{\overline{c}\overline{c}}^1$, $T_{\overline{c}\overline{c}}^2$), via heavy antiquark diquark symmetry, which dictates that the ${\overline{D}}^{(\ast )}{\mathrm{\Sigma }}_c^{(\ast )}$ interactions are the same as the ${\overline{D}}^{(\ast )}{T}_{\overline{c}\overline{c}}^{(\ast )}$ interactions up to heavy antiquark diquark symmetry breakings. In this work, we employ the contact-range effective field theory to systematically study the ${\overline{D}}^{(\ast )}{T}_{\overline{c}\overline{c}}^{(\ast )}$ systems, and we show the existence of a complete heavy quark spin symmetry multiplet of hadronic molecules composed of a doubly charmed tetraquark state and a charmed meson. These are a new kind of hadronic molecules and, if discovered, can lead to a better understanding of the many exotic hadrons discovered so far. In addition, we summarise the triply charmed hexaquark states formed by different combinations of hadrons. In particular, we show that ${\overline{\mathrm{\Omega }}}_{\mathit{ccc}}p$ system can bind by the Coulomb force, which is analogous to a hydrogenlike atom.