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

We have performed an analysis of the $e^+ e^- \to D^{(*)} \bar D^{(*)}$ data in the region of the $ψ(4040)$ and $ψ(4160)$ 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.