Towards more reliable perturbative QCD predictions at moderate energies

Abstract

The problem of improving the reliability of perturbative QCD predictions at moderate energies is considered. These predictions suffer from substantial renormalization scheme dependence, which is illustrated 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. To reduce this scheme dependence, it is proposed to use a modified perturbation expansion, based on a modified couplant, which is perturbatively consistent with the conventional running coupling parameter, but is free from Landau singularity and has smaller renormalization scheme dependence. The modified couplant is obtained by integrating the renormalization group equation with an appropriately constructed nonpolynomial generator. The renormalization scheme dependence of the perturbative predictions in the modified expansion is discussed in detail, including the predictions selected by the Principle of Minimal Sensitivity. It is shown that the modified predictions 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 than the predictions obtained with the conventional expansion, which may be interesting from the point of view of comparing the low energy and high energy determinations of the strong coupling parameter.