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

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

2008-05-15

arxiv.org/abs/0805.2291v2

Phys.Atom.Nucl.72:638-646,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

19 pages, no figures

Scientific paper

10.1134/S1063778809040085

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 $3 {}^3D_1$ state, would have very small di-electron width, $\Gamma_{ee}(Y(4360))=0.060$ keV. On the contrary, for large mixing between the $4 {}^3S_1$ and $3 {}^3D_1$ 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 $5 {}^3S_1$ 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 $5 {}^3S_1$ and $4 {}^3D_1$ states $\theta=34^\circ$. The mass and di-electron width of the $6 {}^3S_1$ charmonium state are calculated.

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