Reaction $e^+e^-\to\bar DD$ and $\psi'$ mesons

TL;DR

This study analyzes the $e^+e^- oar DD$ reaction near threshold using a non-relativistic quark model, revealing insights into meson mixing angles and the nature of the $X(3940)$ resonance.

Contribution

It provides a detailed theoretical analysis of the reaction including intermediate meson states and constrains the $ ext{ψ}(2S)$-$ ext{ψ}(3770)$ mixing angles based on experimental data.

Findings

Experimental data favor a specific $ ext{ψ}(2S)$-$ ext{ψ}(3770)$ mixing angle.

The $X(3940)$ resonance is unlikely to be a conventional $car c$ state.

The reaction dynamics are well described by the $^3P_0$ non-relativistic quark model.

Abstract

We study the reaction $e^+e^-\to\bar DD$ near threshold in the $^3P_0$ non-relativistic quark model, including as intermediate states the $J/\psi$, $\psi(2S)$, $\psi(3770)$ and $\psi(4040)$ mesons. The work reveals that experimental data strongly favor one of the two $\psi(2S)-\psi(3770)$ mixing angles derived by fitting to the $e^-e^+$ partial decay widths of the $\psi(2S)$ and $\psi(3770)$ mesons. The meson $X(3940)$ as well as the resonance around 3.9 GeV observed by Belle and BaBar Collaborations in the reaction $e^+e^-\rightarrow \bar DD$ is unlikely to be a $c\bar c$ $I^G(J^{PC})=0^-(1^{--})$ state.