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

## TL;DR

This paper proposes a new charmonium classification scheme for the $Y(4220)$ state based on updated data, predicts related states, and offers insights into the higher charmonium spectrum above 4 GeV.

## Contribution

It introduces a $4S$-$3D$ mixing scheme for $Y(4220)$, supports its charmonium assignment, and predicts partner states like $ ext{psi}(4380)$ and $ ext{psi}(4500)$, advancing the understanding of higher charmonia.

## Key findings

- $Y(4220)$ can be categorized as a $4S$-$3D$ mixed charmonium state.
- Predicted $ ext{psi}(4380)$ and $ ext{psi}(4500)$ as charmonium partners.
- Resonance parameters and decay widths consistent with experimental data.

## 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.