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The S − D mixing and di-electron widths of higher charmonium 1 − − states

By A. M. Badalian, B. L. G. Bakker and I. V. Danilkin

Abstract

The di-electron widths of ψ(4040), ψ(4160), and ψ(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 θ ∼ = 34 ◦ 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 D1 state, would have very small di-electron width, Γee(Y (4360)) = 0.060 keV. On the contrary, for large mixing between the 4 3 S1 and 3 3 D1 states with the mixing angle θ = 34.8 ◦ , Γee(ψ(4415)) = 0.57 keV coincides with the experimental number, while a second physical resonance, probably Y (4360), has also a rather large Γee(Y ( ∼ 4400)) = 0.61 keV. For the higher Y (4660) resonance, considered as a pure 5 3 S1 state, we predict the di-electron width Γee(Y (4660)) = 0.70 keV, but it becomes significantly smaller, namely 0.31 keV, if the mixing angle between the 5 3 S1 and 4 3 D1 states θ = 34 ◦. The mass and di-electron width of the 6 3 S1 charmonium state are calculated.

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