Study of exotic hadron states in the $D{D}^{\ast }$ system via the complex momentum representation and Green's function method

Abstract

In this paper, we propose a novel approach to investigate exotic hadronic states. For the $D{D}^{\ast }$ system, we employ the projection operator method to derive the momentum-space interaction potential. Subsequently, the complex momentum representation (CMR) method is adopted to realize a unified description of bound states, resonant states, and the continuum. By combining the Green's function and the CMR, the scattering phase shifts and cross sections are determined. This integrated approach provides a comprehensive framework for analyzing the scattering dynamics of the $D{D}^{\ast }$ system. In the hadronic molecular state framework, the $X(3872)$, $T_{cc}^{+}$, 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. The decomposition of the scattering phase shifts and cross sections facilitates understanding the roles of resonant and continuum spectrum.

Comments: 13 pages, 6 figures, accepted by Phys. Rev. D