Unified coupled-channel description for the five near-threshold structures $\psi (3770)$, $G(3900)$, $R(3760)$, $R(3780)$ and $R(3810)$ from $e^{+}{e}^{-}$ annihilation

Abstract

The recent observation of multiple near-threshold structures in $e^{+}{e}^{-}$ annihilation-including $\psi (3770)$, $G(3900)$, $R(3760)$, $R(3780)$, and $R(3810)$-reveals limitations in existing models of charmonium and exotic hadrons. In this paper, we propose a unified coupled-channel description that simultaneously incorporates all five near-threshold structures using parameters constrained by hadron spectroscopy. Our model accurately reproduces the line shapes in both $D\bar{D}$ and nonopen-charm hadron (nOCH) channels, resolves the asymmetric profile of $\psi (3770)$, and produces the $G(3900)$ bump. We identify the $R(3780)$ as the dominant manifestation of $\psi (3770)$, attribute $R(3760)$ to $D\bar{D}\to \text{nOCH}$ rescattering and suggest that $R(3810)$ arises from coupling between the $\psi (1D)$ state and the $h_c\pi \pi$ channel. The significant non-$D\bar{D}$ decay of $\psi (3770)$ is explained by its near-threshold position. This analysis provides a coherent, unquenched framework centered on a charmonium $\psi (1D)$ core for near-threshold phenomena and offers a predictive approach extendable to bottomonium systems and future data from Belle II.

Comments: 7 pages, 3 figures and 2 tables