The $\mathbf{S}-\mathbf{D}$ mixing and di-electron widths of higher charmonium $1^{--}$ states

Abstract

The di-electron widths of $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$, and their ratios are shown to be in good agreement with experiment, if in all cases the $S-D$ mixing with a large mixing angle $\theta \approx 34^{\circ }$ is taken. Arguments are presented why continuum states give small contributions to the wave functions at the origin. We find that the Y(4360) resonance, considered as a pure $3{}^3{D}_1$ state, would have very small di-electron width, ${\Gamma }_{ee}(Y(4360))=0.060$ keV. On the contrary, for large mixing between the $4{}^3{S}_1$ and $3{}^3{D}_1$ states with the mixing angle $\theta =34.8^{\circ }$, ${\Gamma }_{ee}(\psi (4415))=0.57$ keV coincides with the experimental number, while a second physical resonance, probably Y(4360), has also a rather large ${\Gamma }_{ee}(Y(\sim 4400))=0.61$ keV. For the higher resonance Y(4660), considered as a pure $5{}^3{S}_1$ state, we predict the di-electron width ${\Gamma }_{ee}(Y(4660))=0.70$ keV, but it becomes significantly smaller, namely 0.31 keV, if the mixing angle between the $5{}^3{S}_1$ and $4{}^3{D}_1$ states $\theta =34^{\circ }$. The mass and di-electron width of the $6{}^3{S}_1$ charmonium state are calculated.

19 pages, no figures

References in corpus (4)

• Decay constants of the heavy-light mesons from the field correlator method
• Interpretations for the X(4160) observed in the double charm production at B factories
• Di-electron and two-photon widths in charmonium
• Masses of the η_c(nS) and η_b(nS) mesons

Cited by in corpus (2)

• Long-distance behavior of the quark-antiquark static potential. Application to light-quark mesons and heavy quarkonia
• Exotic ccbar spectroscopy