Coupled-channel analysis for vector charmonia and their nature

High-precision e^+e^-\to c\barc data (20 final states) from the BESIII and Belle at \sqrts=3.75–4.7 GeV are analyzed with a semi three-body unitary coupled-channel model. After fitting the data, we extract J^\mathrmPC=1^-- charmonium poles from the obtained amplitudes. We find well-known \psi states listed in the PDG (particle data group), and also several states near thresholds of open-charm channels. The compositeness analysis suggests that \psi(4040) could mainly consist of a D^*\barD^*—molecule component, rather than a conventionally accepted quark-model \psi(3S) state. Additionally, \psi(4230) and \psi(4360) might be substantial mixtures of D_1(2420)\barD, D_1(2420)\barD^*, D_s^*\barD_s^*, and c\barc components.