We use the BLM scale-fixing prescription to derive a renormalization-scheme invariant relation between the coefficient function for the Bjorken sum rule for polarized deep inelastic scattering and the R-ratio for the e+e- annihilation cross section. This relation provides a generalization of the Crewther relation to non-conformally invariant gauge theories. The derived relations allow one to calculate unambiguously without renormalization scale or scheme ambiguity the effective charges 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 relations, but measurements at higher precision and energies will be needed to decisively test these fundamental relations in QCD.
|Number of pages
|Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
|Published - Apr 4 1996
ASJC Scopus subject areas
- Nuclear and High Energy Physics