Analysis of the $\psi(4040)$ and $\psi(4160)$ decay into $D^{(\ast)} \bar D^{(\ast)}$, $D_s^{(\ast)}\bar D_s^{(\ast)}$

TL;DR

This paper analyzes the decay processes of the $ ext{psi}(4040)$ and $ ext{psi}(4160)$ resonances into various D meson pairs, using a theoretical model to predict production rates and assess their quark composition.

Contribution

It applies the $^3 P_0$ model to relate different decay channels and provides insights into the nature of the resonances as primarily $car c$ states with minimal meson-meson components.

Findings

Resonances are largely $car c$ states.

Predicted decay channels agree with experimental data.

Meson-meson components in wave functions are small.

Abstract

We have performed an analysis of the $e^+ e^- \to D^{(*)} \bar D^{(*)}$ data in the region of the $\psi(4040)$ and $\psi(4160)$ resonances which have a substantial overlap and require special care. By using the $^3 P_0$ model to relate the different $D^{(*)} \bar D^{(*)}$ production modes, we make predictions for production of these channels and compare with experiment and other theoretical approaches. As a side effect we find that these resonances qualify largely as $c \bar c$ states and the weight of the meson-meson components in the wave function is very small.