Improving reliability of perturbative QCD predictions at moderate   energies
  The problem of precise evaluation of the perturbative QCD predictions at moderate energies is considered. Substantial renormalization scheme dependence of the perturbative predictions obtained with the conventional renormalization group improved perturbative approximants is discussed, using as an example the QCD effective charge appearing in the static interquark potential and the QCD corrections to the Gross-Llewellyn-Smith sum rule in the deep inelastic neutrino-nucleon scattering. A new method for evaluating the QCD predictions at moderate energies is proposed, based on a modified couplant, which is constructed to be free from Landau singularity and less renormalization scheme dependent than the conventional couplant. The modified couplant contains an adjustable parameter, which may be used to improve the modified perturbative predictions in low orders by utilizing some information outside of perturbation theory. This parameter is fixed by matching the modified predictions to the phenomenological expression for the effective charge in the interquark potential. The renormalization scheme dependence of the perturbative predictions in the modified expansion is then discussed in detail, including the predictions selected by the Principle of Minimal Sensitivity applied to the modified expansion. It is shown that the predictions obtained in the modified expansion are much more stable with respect to change of the renormalization scheme parameters than the predictions obtained in the conventional approach. It is also found that the modified predictions display somewhat weaker energy dependence then the predictions obtained with the conventional expansion, which may help accommodate in a consistent way some low values of the strong coupling parameter measured at low energies with the values measured at high energies. 
Piotr A. Raczka