The generalized Crewther relation in QCD and its experimental consequences

S. J. Brodsky; G. T. Gabadadze; A. L. Kataev; H. J. Lu

doi:10.1016/0370-2693(96)00057-3

The generalized Crewther relation in QCD and its experimental consequences

S. J. Brodsky, G. T. Gabadadze, A. L. Kataev, H. J. Lu

Research output: Contribution to journal › Article › peer-review

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)
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	https://doi.org/10.1016/0370-2693(96)00057-3
State	Published - Apr 4 1996

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/0370-2693(96)00057-3

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title = "The generalized Crewther relation in QCD and its experimental consequences",

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.",

author = "Brodsky, {S. J.} and Gabadadze, {G. T.} and Kataev, {A. L.} and Lu, {H. J.}",

note = "Funding Information: authors are grateful to the organizers and the participants of thesec onferencesf or the interesti n this work and useful discussions. The work of S.J.B. and H.J.L. is supported in part by the Department of Energy, contracts DE-ACO3-76SFOO51 5 and DE-FG02-93ER-40792. The work of A.L.K. is done within the project N 96-02-18897-as ubmittedt o the Russian Fund for Fundamental research.T he work of G.T.G. is supportedb y the International Student Foundation grant N6JOOO and ICFPM graduates tudentf ellowship, grant 932492. Funding Information: *Work partially supported by the Department of Energy, contracts DE-AC03-76SFOO5 15 and DE-FG02-93ER-40792. {\textquoteright} On leave of absence from Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia.",

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AU - Brodsky, S. J.

AU - Gabadadze, G. T.

AU - Kataev, A. L.

AU - Lu, H. J.

N1 - Funding Information: authors are grateful to the organizers and the participants of thesec onferencesf or the interesti n this work and useful discussions. The work of S.J.B. and H.J.L. is supported in part by the Department of Energy, contracts DE-ACO3-76SFOO51 5 and DE-FG02-93ER-40792. The work of A.L.K. is done within the project N 96-02-18897-as ubmittedt o the Russian Fund for Fundamental research.T he work of G.T.G. is supportedb y the International Student Foundation grant N6JOOO and ICFPM graduates tudentf ellowship, grant 932492. Funding Information: *Work partially supported by the Department of Energy, contracts DE-AC03-76SFOO5 15 and DE-FG02-93ER-40792. ’ On leave of absence from Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia.

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N2 - 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.

AB - 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.

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The generalized Crewther relation in QCD and its experimental consequences

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