Relativistic Quarkonium Model : Mass Level and Lepton Pair Decay

概要

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The validity of application of the instantaneous ladder BS equation to the quarkonium system is examined. The charmonium and the bottonium systems are investigated by using this equation with a standard (linear confining + one gluon exchange) pseude-potential. It is found that the relativistic effect is 15% in the charmonium and 5% in the bottonium. The QCD prediction for the flavor dependence of α_s is shown to be consistent with the quarkonium phenomenology of this model which is characterized by α_s(cc^^-)=0.39 and α_s(bb^^-)=0.31. The scale parameter Λ_<MS>^^- is estimated to be 170~260 MeV. The model yields a good description for mass levels including the fine and the hyperfine splittings. It is found that the masses of ^1S_0 and ^3P_0 states are sensitive to the innermost part(γ<0.02 fm) of the potential. The renormalization and the relativistic effects on the lepton-pair decay of the vector meson are found to be large. The model gives that Γ(φ→e^+e^-)=5.9 keV and Γ(γ→e^+e^-) = 1.3 keV. The ratio Γ(excited state)/Γ(ground state) does not agree with its non-relativistic value even for the bottonium. This is due to the gluonic correction.
理論物理学刊行会の論文
1983-08-25