Line shape and ${D}^{\left(*\right)}{\overline{D}}^{\left(*\right)}$ probabilities of $\psi \left(3770\right)$ from the ${e}^{+}{e}^{-}\to D\overline{D}$ reaction

We have performed a calculation of the $D\overline{D}$, $D{\overline{D}}^{*}$, ${D}^{*}\overline{D}$, ${D}^{*}{\overline{D}}^{*}$ components in the wave function of the $\psi \left(3770\right)$. For this we make use of the ${}^{3}{P}_{0}$ model to find the coupling of $\psi \left(3770\right)$ to these components, that with an elaborate angular momentum algebra can be obtained with only one parameter. Then we use data for the ${e}^{+}{e}^{-}\to D\overline{D}$ reaction, from where we determine a form factor needed in the theoretical framework, as well as other parameters needed to evaluate the meson-meson self-energy of the $\psi \left(3770\right)$. Once this is done we determine the $Z$ probability to still have a vector core and the probability to have the different meson components. We find $Z$ about 80%–85%, and the individual meson-meson components are rather small, providing new empirical information to support the largely $q\overline{q}$ component of vector mesons, and the $\psi \left(3770\right)$ in particular. A discussion is done of the meaning of the terms obtained for the case of the open channels where the concept of probability cannot be strictly used.