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

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• Exploring open-charm decay mode ${\Lambda }_c{\bar{\Lambda }}_c$ of charmonium-like state $Y(4630)$
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• Theory of hadron decay into baryon-antibaryon final state
• Charmonium states in a coupled-channel model
• Role of $Y(4630)$ in the $p\bar{p}\to {\Lambda }_c{\bar{\Lambda }}_c$ reaction near threshold
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• Radial Regge trajectories for higher $\psi (nS)$ and $\psi (nD)$ states
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• Study of structures and dynamical decay mechanisms for multiquark systems
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• Possible molecular states from interactions of charmed baryons
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• The charmed mesons in the region above 3.0 GeV
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