Using a sample of (1310.6±7.0)×106 J/ψ events recorded with the Beijing Spectrometer III detector at the Beijing Electron Positron Collider II, we report the observation of the decay of the (11S0) charmonium state ηc into a pair of ω mesons in the process J/ψ→γωω. The branching fraction is measured for the first time to be B(ηc→ωω)=(2.88±0.10±0.46±0.68)×10-3, where the first uncertainty is statistical, the second systematic, and the third is from the uncertainty of B(J/ψ→γηc). The mass and width of the ηc are determined as M=(2985.9±0.7±2.1) MeV/c2 and Γ=(33.8±1.6±4.1) MeV.
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