Annihilation rates of heavy 1−− S-wave quarkonia in Salpeter method

Annihilation rates of vector 1−− charmonium and bottomonium S13 states V→e+e− and V→3γ, V→γgg and V→3g are estimated in the relativistic Salpeter method. In our calculations, special attention is paid to the relativistic correction, which is important and cannot be ignored for excited 2S, 3S and higher excited states. We obtain Γ(J/ψ→3γ)=6.8×10−4 keV, Γ(ψ(2S)→3γ)=2.5×10−4 keV, Γ(ψ(3S)→3γ)=1.7×10−4 keV, Γ(ϒ(1S)→3γ)=1.5×10−5 keV, Γ(ϒ(2S)→3γ)=5.7×10−6 keV, Γ(ϒ(3S)→3γ)=3.5×10−6 keV and Γ(ϒ(4S)→3γ)=2.6×10−6 keV.