Description of the \psi(3770) resonance interfering with the background

The parameters of the interfering $\psi(3770)$ resonance should be determined from the data on the reactions $e^+e^-$\,$\to$\,$D\bar D$ with the use of the models satisfying the elastic unitarity requirement. The selection of such models can be realized by comparing their predictions with the relevant data on the shape of the $\psi(3770)$ peak in the non-$D\bar D$ decay channels. Here, we illustrate this unitarity approach by the example of the most simple variant of the model of the mixed $\psi(3770)$ and $\psi(2S)$ resonances. When new high-statistics data become available, it will be interesting to test this clarity variant.