Pseuduscalar Heavy Quarkonium Decays with Both Relativistic and Qcd Radiative Corrections

We estimate the decay rates of ηc → 2γ, η c → 2γ, and J/ψ → ee, ψ → ee, by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism. The Bethe-Salpeter equation with a QCD-inspired interquark potential are used to calculate the wave functions and decay widths for these cc̄ states. We find that the relativistic correction to the ratio R ≡ Γ(ηc → 2γ)/Γ(J/ψ → ee) is negative and tends to compensate the positive contribution from the QCD radiative correction. Our estimate gives Γ(ηc → 2γ) = (6 − 7) keV and Γ(η c → 2γ) = 2 keV , which are smaller than their nonrelativistic values. The hadronic widths Γ(ηc → 2g) = (17− 23) MeV and Γ(η c → 2g) = (5− 7) MeV are then indicated accordingly to the first order QCD radiative correction, if αs(mc) = 0.26 − 0.29. The decay widths for bb̄ states are also estimated. We show that when making the assmption that the quarks are on their mass shells our expressions for the decay widths will become identical with that in the NRQCD theory to the next to leading order of v and αs. Charmonium physics is in the boundary domain between perturbative and nonperturbative QCD. Charmonium decays may pvovide useful information on understanding the nature of interquark forces and decay mechanisms. Both QCD radiative corrections and relativistic corrections are important for charmonium decays, because for charmonium the strong coupling constant αs(mc) ≈ 0.3 [defined in theMS scheme (the modified minimal subtraction scheme)] and the velocity squared of the quark in the meson rest frame v ≈ 0.3, both are not small. Decay rates of heavy quarkonia in the nonrelativistic limit with QCD radiative corrections have been studied (see, e.g., refs.[1,2,3]). However, the decay rates of many processes are subject to substantial