The Generalized Crewther relation in QCD and its experimental consequences

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.

Note:

16 pages, LATEX file Report-no: DESY-95-245, SLAC-PUB-95-7085, RU-95-93, AZPH-TH-95/27

gauge field theory
invariance: conformal
quantum chromodynamics: perturbation theory
lepton nucleon: deep inelastic scattering
deep inelastic scattering: lepton nucleon
polarization
sum rule
electron positron: annihilation
annihilation: electron positron
cross section: hadronic

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