Scheme-invariant perturbation theory in massive QCD

The results of renormalization-group-improved perturbation theory in renormalized quantum field theory depend on the renormalization scheme. Recently it has been shown that such improved perturbation theory can be formulated in terms of scheme-invariant quantities. In this paper we first give arguments in favor of this scheme-invariant perturbation theory which we apply to analyzing the decay of the UPSILON meson and the hyperfine splitting of the J/psi meson in the framework of QCD. For Λ/sub( approximatelyM/S) we obtain the most probable values Λ/sub( approximatelyM/S) = 230 +- 30 MeV for f = 3 and Λ/sub( approximatelyM/S) = 200 +- 30 MeV for f = 4. Second, we construct a generalization of the scheme-invariant perturbation theory for the case with quark masses taken into account. For functions which depend on a single invariant kinematic argument we obtain expressions which explicitly take into account threshold effects. In a similar way we generalize formulas that relate the scales of different processes