Global coupled-channel analysis of $e^+e^-\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV

Recent high-precision $e^+e^-\to c\bar{c}$ data from the BESIII and Belle are highly useful to understand vector charmonium ($\psi$) pole structures and puzzling lineshapes due to the exotic hadron candidates $Y$. We thus perform a global coupled-channel analysis of most of the available data (10 two-body, 9 three-body, and 1 four-body final states) in $\sqrt{s}=3.75-4.7$ GeV. Not only cross sections but also invariant-mass distributions of subsystems are fitted. The $e^+e^-\to \mu^+\mu^-$ cross sections are also predicted. Our model includes dozens of (quasi) two-body states that nonperturbatively couple with each other through bare $\psi$ excitations, particle-exchange, and short-range mechanisms; approximate three-body unitarity is considered. The amplitudes obtained from the fit are analytically continued to $\psi$ and $Z_c$ poles. We find $\psi$ states similar to those in the Particle Data Group listing and $Y(4320)$. Moreover, several $\psi$ states, including new ones, are found close to open charm thresholds. Trajectories and compositeness of the near-threshold poles suggest dominant hadron-molecule contents in their internal structures. Two $Z_c$ poles are found as virtual states $\sim$40 MeV below the $D^*\bar{D}^{(*)}$ thresholds, being consistent with lattice QCD results. This work presents the first global analysis to determine $\psi$ and $Z_c$ poles, thereby paving the way to extracting detailed properties of the prominent exotic hadron candidates from data.