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.

10 pages, 6 references corrected, some new material added

References in corpus (10)

• Heavy quarkonium: progress, puzzles, and opportunities
• Constituent quark model study of the meson spectra
• Higher Charmonia and X,Y,Z states with Screened Potential
• Potential model calculations and predictions for heavy quarkonium
• Observation of $\psi (4415)\to D\bar{D}{}_2^{\ast }(2460)$ decay using initial-state radiation
• Decay constants of the heavy-light mesons from the field correlator method
• The $\mathbf{S}-\mathbf{D}$ mixing and di-electron widths of higher charmonium $1^{--}$ states
• Charmonium states in QCD-inspired quark potential model using Gaussian expansion method
• Di-electron and two-photon widths in charmonium
• Heavy quarkonium wave functions at the origin and excited heavy quarkonium production via top quark decays at the LHC

Cited by in corpus (6)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Radial and orbital Regge trajectories in heavy quarkonia
• Charmonium states in a coupled-channel model
• Revisiting the Heavy Vector Quarkonium Leptonic Widths
• The two-channel exotic charmonium-like resonances in the mass region $(3900-4700)$ MeV
• $B_u$ $\to$ $\psi M$ decays and $S$-$D$ wave mixing effects