# Constructing $J/\psi$ family with updated data of charmoniumlike $Y$ states

Wang, Jun-Zhang (School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China) (Research Center for Hadron and CSR Physics, Lanzhou University & Institute of Modern Physics of CAS, Lanzhou 730000, China) ; Chen, Dian-Yong (School of Physics, Southeast University, Nanjing 211189, China) ; Liu, Xiang (School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China) (Research Center for Hadron and CSR Physics, Lanzhou University & Institute of Modern Physics of CAS, Lanzhou 730000, China) ; Matsuki, Takayuki (Tokyo Kasei University, 1-18-1 Kaga, Itabashi, Tokyo 173-8602, Japan) (Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan)

05 June 2019

Abstract: Based on the updated data of charmoniumlike state $Y\left(4220\right)$ reported in the hidden-charm channels of the ${e}^{+}{e}^{-}$ annihilation, we propose a $4S$-$3D$ mixing scheme to categorize $Y\left(4220\right)$ into the $J/\psi$ family. We find that the present experimental data can support this charmonium assignment to $Y\left(4220\right)$. Thus, $Y\left(4220\right)$ 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 $Y\left(4220\right)$, and predict its charmonium partner $\psi \left(4380\right)$, whose evidence is found by analyzing the ${e}^{+}{e}^{-}\to \psi \left(3686\right){\pi }^{+}{\pi }^{-}$ data from BESIII. If $Y\left(4220\right)$ is indeed a charmonium, we must face how to settle the established charmonium $\psi \left(4415\right)$ 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 $\psi \left(4415\right)$, which do not contradict the present experimental data. Additionally, we predict a charmonium partner $\psi \left(4500\right)$ of $\psi \left(4415\right)$, 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.

Published in: Physical Review D 99 (2019)