Is the $3S$-$2D$ mixing strong for the charmonia $\psi(4040)$ and $\psi(4160)$?

TL;DR

This paper investigates the strength of the 3S-2D mixing in charmonia states ψ(4040) and ψ(4160), finding that the proposed coupled-channel mechanism alone cannot account for the experimentally suggested large mixing angles.

Contribution

The study introduces a coupled-channel mechanism distinct from tensor-force effects and demonstrates its insufficiency in explaining the observed large mixing angles.

Findings

Mixing angles of 7° and 10° are obtained, smaller than experimental estimates.

The coupled-channel mechanism alone cannot produce the large mixing angles suggested by data.

Future experiments are needed to resolve the discrepancy in mixing angle measurements.

Abstract

In this work, we revisit the $3S$-$2D$ mixing scheme for the charmonia $\psi(4040)$ and $\psi(4160)$. We introduce a coupled-channel mechanism-distinct from the tensor-force contribution in potential models, which alone is insufficient to induce significant mixing-to describe the mixing between these states. Our analysis yields mixing angles of $\theta_1=7^\circ$ and $\theta_2=10^\circ$, inconsistent with the larger angle inferred from experimental data, such as the dilectronic widths of the $\psi(4040)$ and $\psi(4160)$. We discuss possible origins of this discrepancy and emphasize the need for future experiments to resolve it. Precise measurements of the resonance parameters and dilectronic decay widths, via both inclusive and exclusive processes, will be crucial in clarifying this issue.