GLUONIC AND LEPTONIC DECAYS OF HEAVY QUARKONIA AND THE DETERMINATION OF αs(mc) AND αs(mb) Kuang-Ta CHAO

QCD running coupling constant αs(mc) and αs(mb) are determined from heavy quarkonia cc and bb decays. The decay rates of V → 3g and V → e+e− for V = J/ψ and Υ are estimated by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the BetheSalpeter formalism, and the decay rates are estimated by using the meson wavefunctions which are obtained with a QCD-inspired inter-quark potential. For the V → 3g decay we find the relativistic correction to be very large and to severely suppress the decay rate. Using the experimental values of ratio Rg ≡ Γ(V −→3g) Γ(V−→e+e−) ≈ 10, 32 for V = J/ψ, Υ respectively, and the calculated widths , we find αs(mc) = 0.29±0.02 and αs(mb) = 0.20±0.02. These values for the QCD running coupling constant are substantially enhanced, as compared with the ones obtained without relativistic corrections, and are consistent with the QCD scale parameter Λ (4) MS ≈ 200MeV . We also find that these results are mainly due to kinematic corrections and not sensitive to the dynamical models.