# Commensurate scale relations in quantum chromodynamics

- Authors
- Journal
- Nuclear Physics B - Proceedings Supplements 0920-5632
- Publisher
- Elsevier
- Publication Date
- Volume
- 39
- Identifiers
- DOI: 10.1016/0920-5632(95)00093-o

## Abstract

We use the BLM method to directly relate perturbatively calculable QCD observables. The commensurate scale relations connecting the effective charges for observables A and B have the form α A ( Q A ) = α B ( Q B ) (1 + Γ A/B α B π + …), where the coefficient r A/B is independent of the number of flavors f contributing to coupling constant renormalization. The generalization of the BLM procedure to higher order assigns a different renormalization scale for each order in the perturbative series. The coefficients in the commensurate scale relation can be identified with those obtained in conformally-invariant gauge theory. The application of this procedure to perturbatively-calculable physical observables in QCD gives rather simple results. For example, the relation between the annihilation ratio R e +e −1 and the polarized Bjorken sum rule is given by α¾ g1( Q) = α¾ R ( Q * ) − α¾ R 2( Q **) + α¾ R 3( Q ***), where α¾ = (3 C F /4 π) α. This relation provides the generalization of the Crewther relation to non-conformally invariant gauge theory.

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