Eur. Phys. J. C (2023) 83: 1071
https://doi.org/10.1140/epjc/s10052-023-12199-y

Regular Article - Theoretical Physics

$Z_{\mathit{cs}}$, $Z_c$ and $Z_b$ states under the complex scaling method

¹ College of Science, China University of Petroleum, 266580, Qingdao, Shandong, China
² School of Physics and Center of High Energy Physics, Peking University, 100871, Beijing, China

^a jbcheng@pku.edu.cn

Received: 30 July 2023
Accepted: 29 October 2023
Published online: 23 November 2023

Abstract

We investigate the $Z_b$, $Z_c$ and $Z_{\mathit{cs}}$ states within the chiral effective field theory framework and the S-wave single channel molecule picture. With the complex scaling method, we accurately solve the Schrödinger equation in momentum space. Our analysis reveals that the $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$ states are the resonances composed of the S-wave $(B{\overline{B}}^{\ast }+B^{\ast }\overline{B})/\sqrt{2}$, $B^{\ast }{\overline{B}}^{\ast }$, $(D{\overline{D}}^{\ast }+D^{\ast }\overline{D})/\sqrt{2}$ and $D^{\ast }{\overline{D}}^{\ast }$, respectively. Furthermore, although the $Z_{\mathit{cs}}(3985)$ and $Z_{\mathit{cs}}(4000)$ states exhibit a significant difference in width, these two resonances may originate from the same channel, the S-wave $(D_s{\overline{D}}^{\ast }+D_s^{\ast }\overline{D})/\sqrt{2}$. Additionally, we find two resonances in the S-wave $D_s^{\ast }{\overline{D}}^{\ast }$ channel, corresponding to the $Z_{\mathit{cs}}(4123)$ and $Z_{\mathit{cs}}(4220)$ states that await experimental confirmation.