Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1995-12-20
Phys.Lett.B372:133-140,1996
Physics
High Energy Physics
High Energy Physics - Phenomenology
16 pages, LATEX file
Scientific paper
10.1016/0370-2693(96)00057-3
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.
Brodsky Stanley J.
Gabadadze G. T.
Kataev Andrei L.
Lu Hou-Jun
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