### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 133-140 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 372 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 4 1996 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*372*(1-2), 133-140. https://doi.org/10.1016/0370-2693(96)00057-3