THE GENERALIZED CREWTHER RELATION IN QCD AND ITS EXPERIMENTAL CONSEQUENCES

We use the BLM scale-fixing prescription to derive a renormalization-s cheme invariant relation between the coefficient function for the Bjor ken sum rule for polarized deep inelastic scattering and the R-ratio f or the e(+)e(-) annihilation cross section. This relation provides a g eneralization of the Crewther relation to non-conformally invariant ga uge theories. The derived relations allow one to calculate unambiguous ly without renormalization scale or scheme ambiguity the effective cha rges of the polarized Bjorken and the Gross-Llewellen Smith sum rules from the experimental value for the effective charge associated with R -ratio, Present data are consistent with the generalized Crewther rela tions, but measurements at higher precision and energies will be neede d to decisively test these fundamental relations in QCD.