Coupled-channel study of $4S$-$3D$ mixing dynamics in $\psi(4220)$ and $\psi(4380)$

TL;DR

This paper develops a coupled-channel model to study the mixing dynamics of $ ext{4S}$-$ ext{3D}$ states in $ ext{ψ(4220)}$ and $ ext{ψ(4380)}$, explaining their properties and decay behaviors in the charmonium spectrum.

Contribution

It introduces a novel coupled-channel approach to explain the large $ ext{4S}$-$ ext{3D}$ mixing in $ ext{ψ(4220)}$ and $ ext{ψ(4380)}$, highlighting the influence of specific decay channels.

Findings

The $DD_1$ channel significantly affects $ ext{ψ(4220)}$.

The $D^*D_1$ channel primarily influences $ ext{ψ(4380)}$.

The model aligns with experimental data on decay widths.

Abstract

Among charmoniumlike $XYZ$ states, the $\psi(4220)$ and $\psi(4380)$ states have emerged as key candidates for exploring the charmonium spectrum. In this work, we propose a $4S$-$3D$ charmonium mixing scheme for the $\psi(4220)$ and $\psi(4380)$, induced by coupled-channel effects. By constructing a coupled-channel model, we identify the dynamical mechanism responsible for the large mixing angle observed in previous studies, which cannot be explained by conventional potential models alone. Our analysis reveals that the $DD_1$ channel significantly influences the lower state ($\psi(4220)$), while the $D^*D_1$ channel primarily affects the higher state ($\psi(4380)$). Furthermore, we investigate the two-body Okubo-Zweig-Iizuka (OZI)-allowed strong decay behaviors of these states, providing insights into their total widths. This study not only supports the $4S$-$3D$ mixing scheme but also offers a deeper understanding of the role of coupled channels in shaping the charmonium spectrum above 4 GeV. Our results align with experimental observations and provide a framework for interpreting future data on charmonium states.