Eur. Phys. J. C (2025) 85: 920
https://doi.org/10.1140/epjc/s10052-025-14649-1

Regular Article - Theoretical Physics

The bound and resonant states of $D_{}^{(\ast )}D_{}^{(\ast )}$ and $D_{}^{(\ast )}{\overline{D}}^{(\ast )}$ with the complex scaling method

School of Physics and Optoelectronic engineering, Anhui University, 230601, Hefei, China

^a songmao@ahu.edu.cn

Received: 17 June 2025
Accepted: 14 August 2025
Published online: 29 August 2025

Abstract

In this paper, a systematic investigation is conducted to explore the potential molecular states formed by heavy meson pairs $D_{}^{(\ast )}D_{}^{(\ast )}$ and $D_{}^{(\ast )}{\overline{D}}^{(\ast )}$ with the complex scaling method, in the framework of the one-boson-exchange (OBE) model. The exchange interactions are mediated by the pseudoscalar, scalar and vector mesons($\pi$, $\sigma$, $\rho$, $\omega$). The interaction potential within the OBE model is derived using the Bonn approximation, followed by the application of the complex scaling method to determine the bound and resonant states. The results demonstrate that the $D_{}^{(\ast )}D_{}^{(\ast )}$ and $D_{}^{(\ast )}{\overline{D}}^{(\ast )}$ systems can form not only multiple bound states, but also several P-wave resonant states. In the hadronic molecular state framework, the X(3872), $T_{\mathit{cc}}^{+}$, and $Z_c(3900)$ states can be consistently explained as bound states, while the G(3900) can be interpreted as a P-wave resonant state. Furthermore, we also predict other new bound and resonant states, which have the potential to be observed experimentally.