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

We study the reaction $e^+e^-\to\bar DD$ near threshold in the $^3P_0$ non-relativistic quark model, including as intermediate states the $J/ψ$, $ψ(2S)$, $ψ(3770)$ and $ψ(4040)$ mesons. The work reveals that experimental data strongly favor one of the two $ψ(2S)-ψ(3770)$ mixing angles derived by fitting to the $e^-e^+$ partial decay widths of the $ψ(2S)$ and $ψ(3770)$ 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.

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