Analysis of the $\psi \left(4040\right)$ and $\psi \left(4160\right)$ decay into ${D}^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)}$ , ${D}_{s}^{\left(\ast \right)}{\overline{D}}_{s}^{\left(\ast \right)}$

We have performed an analysis of the ${e}^{+}{e}^{-}\to {D}^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)}$ data in the region of the $\psi \left(4040\right)$ and $\psi \left(4160\right)$ resonances which have a substantial overlap and require special care. By using the ${}^{3}{P}_{0}$ model to relate the different ${D}^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)}$ 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 $c\overline{c}$ states and the weight of the meson–meson components in the wave function is very small.