Commensurate scale relations in quantum chromodynamics

The BLM method is used to directly relate perturbatively calculable QCD observables to the commensurate scale relations connecting the effective charges and provides the generalization of the Crewther relation to non-conformally invariant gauge theory.

Abstract

We use the BLM method to show that perturbatively-calculable observables in\nQCD can be related to each other without renormalization scale or scheme\nambiguity. We define and study the commensurate scale relations. We show that\nthe commensurate scales satisfy the renormalization group transitivity rule\nwhich ensures that predictions in PQCD are independent of the choice of an\nintermediate renormalization scheme. We generalize the BLM procedure to higher\norder. The application of this procedure to relate known physical observables\nin QCD gives surprisingly simple results. In particular, the annihilation ratio\n$R_{e^+e^-}$ and the Bjorken sum rule for polarized electroproduction are\nrelated through simple coefficients, which reinforces the idea of a hidden\nsymmetry between these two observables.\n