Based on the updated data of charmoniumlike state Y(4220) reported in the hidden-charm channels of the e + e − annihilation, we propose a 4S -3D mixing scheme to categorize Y(4220) into the J/ψ family. We find that the present experimental data can support this charmonium assignment to Y(4220). Thus, Y(4220) plays a role of a scaling point in constructing higher charmonia above 4 GeV. To further test this scenario, we provide more abundant information on the decay properties of Y(4220), and predict its charmonium partner ψ(4380), whose evidence is found by analyzing the e + e − → ψ(3686)π + π − data from BESIII. If Y(4220) is indeed a charmonium, we must face how to settle the established charmonium ψ(4415) in the J/ψ family. In this work, we may introduce a 5S -4D mixing scheme, and obtain the information of the resonance parameters and partial open-charm decay widths of ψ(4415), which do not contradict the present experimental data. Additionally, we predict a charmonium partner ψ(4500) of ψ(4415), which can be accessible at future experiments, especially, BESIII and BelleII. The studies presented in this work provide new insights to establish the higher charmonium spectrum.PACS numbers:
I. INTRODUCTIONIn 1974, J/ψ particle was discovered by the E598 [1] Collaboration in the p + Be → e + + e − + x reaction and the SLAC-SP-017 Collaboration [2] in the e + e − annihilation at the same time. The observation of J/ψ confirmed the existence of a charm quark predicted by the Glashow-Iliopoulos-Maiani mechanism [3]. Since then, a series of charmoniumlike states, ψ(3686) [4], ψ(3770) [5], ψ(4040) [6], ψ(4160) [7], and ψ(4415) [8], were reported, which construct a main body of the observed charmonium spectrum as shown in Particle Data Group (PDG) [9]. In Fig. 1, we collect the corresponding information of the observed charmonia with the year for their first discoveries. It is obvious that the year 1978 is an important time point since most of charmonia listed in the latest PDG were announced.Under this experimental background, the Cornell model was proposed by Eichten et al. [18,19], where the Cornell potential V(r) = −k/r + r/a 2 composed of Coulomb-type and linear potentials, which depicts the interaction between charm and anticharm quarks, was postulated and applied to study the observed charmonia [20]. As a successful phenomenological model, the Cornell model can describe the observed charmonia at that time. Inspired by the Cornell model, different potential models were developed by various groups [21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Among these, a famous one is the Godfrey-Isgur (GI) model [34], which has semi-relativistic expression of the kinetic and potential energy terms. The GI model was employed to quan- * Electronic address: