Abstract
Based on the updated data of charmoniumlike state $Y(4220)$ reported in the hidden-charm %and open-charm channels of the $e^+e^-$ annihilation, we propose a $4S$-$3D$ mixing scheme to categorize $Y(4220)$ into the $J/\psi$ 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 $\psi(4380)$, whose evidence is found by analyzing the $e^+e^-\to \psi(3686)\pi^+\pi^-$ data from BESIII. If $Y(4220)$ is indeed a charmonium, we must face how to settle the established charmonium $\psi(4415)$ in the $J/\psi$ 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 $\psi(4415)$, which do not contradict the present experimental data. Additionally, we predict a charmonium partner $\psi(4500)$ of $\psi(4415)$, 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.
Highlights
In 1974, the J=ψ particle was discovered by the E598 [1] Collaboration in the p þ Be → eþ þ e− þ x reaction and the SLAC-SP-017 Collaboration [2] in the eþe− annihilation at the same time
Based on the updated data of charmoniumlike state Yð4220Þ reported in the hidden-charm channels of the eþe− annihilation, we propose a 4S-3D mixing scheme to categorize Yð4220Þ into the J=ψ family
The Cornell model was proposed by Eichten et al [18,19], where the Cornell potential VðrÞ 1⁄4 −k=r þ r=a2 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]
Summary
In 1974, the J=ψ particle was discovered by the E598 [1] Collaboration in the p þ Be → eþ þ e− þ x reaction and the SLAC-SP-017 Collaboration [2] in the eþe− annihilation at the same time. In the past 40 years, the charmonium spectrum above 4.16 GeV was not established, which reflects how poorly we understand the nonperturbative behavior of quantum chromodynamics This situation stimulates our interest in hunting the evidence of missing higher charmonia by combining with the updated experimental information of charmoniumlike Y states in the eþe− annihilations. (3) It is crucial how to settle ψð4415Þ in the J=ψ family since ψð4415Þ is an established charmonium by different experiments To quantitatively illustrate these three key points, we adopt an unquenched potential model to study the charmonium mass spectrum, which is introduced . To give a definite conclusion, we need more precise measurements of ψð4415Þ like the resonance parameters, and the partial widths of open-charm and hidden-charm decays Under this mixing scheme, we naturally predict a charmonium partner of ψð4415Þ, which is still missing.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
