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

Abstract

The dielectron 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 D 1 state, would have very small dielectron width, Γ 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 θ = 34.8°, Γ ee (ψ(4415)) = 0.57 keV coincides with the experimental number, while a second physical resonance, probably Y (4360), has also a rather large Γ ee (Y (∼4400)) = 0.61 keV. For the higher Y (4660) resonance, considered as a pure 5 3 S 1 state, we predict the dielectron width Γ 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 has the characteristic value θ = 34°. The mass and dielectron width of the 6 3 S 1 charmonium state are calculated.