The leptonic widths of high $\psi$-resonances in unitary coupled-channel model

The leptonic widths of high $\psi$-resonances are calculated in a coupled-channel model with unitary inelasticity, where analytical expressions for mixing angles between $(n+1){}^3{S}_1$ and $n{}^3{D}_1$ states and probabilities $Z_i$ of the $c\bar{c}$ component are derived. Since these factors depend on energy (mass), different values of mixing angles $\theta (\psi (4040))={27.7}^{\circ }$ and $\theta (\psi (4160))={29.5}^{\circ }$, $Z_1(\psi (4040))=0.76$, and $Z_2(\psi (4160))=0.62$ are obtained. It gives the leptonic widths ${\mathrm{\Gamma }}_{ee}(\psi (4040))=Z_{1}1.17=0.89$~keV, ${\mathrm{\Gamma }}_{ee}(\psi (4160))=Z_{2}0.76=0.47$~keV in good agreement with experiment. For $\psi (4415)$ the leptonic width ${\mathrm{\Gamma }}_{ee}(\psi (4415))=0.55$~keV is calculated, while for the missing resonance $\psi (4510)$ we predict $M(\psi (4500))=(4515\pm 5)$~MeV and ${\mathrm{\Gamma }}_{ee}(\psi (4510))\cong 0.50$~keV.