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

Abstract

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 ${\Gamma }_{ee}(\psi (4040))=Z_{1}1.17=0.89$~keV, ${\Gamma }_{ee}(\psi (4160))=Z_{2}0.76=0.47$~keV in good agreement with experiment. For $\psi (4415)$ the leptonic width ${\Gamma }_{ee}(\psi (4415))=0.55$~keV is calculated, while for the missing resonance $\psi (4510)$ we predict $M(\psi (4500))=(4515\pm 5)$~MeV and ${\Gamma }_{ee}(\psi (4510))\cong 0.50$~keV.

Comments: 10 pages, 6 references corrected, some new material added