Infrared freezing of Euclidean QCD observables

Brooks, Paul M; Maxwell, C J

doi:10.1103/PHYSREVD.74.065012

Title: Infrared freezing of Euclidean QCD observables

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Abstract

We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q{sup 2}>{lambda}{sup 2}, where Q{sup 2}={lambda}{sup 2} is the Landau pole of the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q{sup 2}<{lambda}{sup 2} the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q{sup 2}-dependence of the perturbative corrections to the Adler-D function, the GLS sum rule and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q{sup 2}={lambda}{sup 2}, and then exhibits freezing behavior, vanishing at Q{sup 2}=0. Finiteness at Q{sup 2}={lambda}{sup 2} implies specific relations between the residues of IR and UV renormalon singularities in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained), are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of nonperturbative and perturbative ambiguities we are led to a result for the Q{sup 2}-dependence of these observables atmore »« less

Authors:

Brooks, Paul M; Maxwell, C J ^[1]

Institute for Particle Physics Phenomenology, University of Durham, South Road, DH1 3LE (United Kingdom)

Publication Date:: Fri Sep 15 00:00:00 EDT 2006

OSTI Identifier:: 20871245

Resource Type:: Journal Article

Journal Name:: Physical Review. D, Particles Fields

Additional Journal Information:: Journal Volume: 74; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.74.065012; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRECTIONS; COUPLING; EUCLIDEAN SPACE; EXPANSION; QUANTUM CHROMODYNAMICS; SINGULARITY; SUM RULES; ULTRAVIOLET RADIATION

Citation Formats


                    Brooks, Paul M, and Maxwell, C J. Infrared freezing of Euclidean QCD observables.  United States: N. p., 2006. 
        Web.  doi:10.1103/PHYSREVD.74.065012.

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                    Brooks, Paul M, & Maxwell, C J. Infrared freezing of Euclidean QCD observables.  United States.  https://doi.org/10.1103/PHYSREVD.74.065012

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                    Brooks, Paul M, and Maxwell, C J. 2006.  
        "Infrared freezing of Euclidean QCD observables".  United States.  https://doi.org/10.1103/PHYSREVD.74.065012.

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@article{osti_20871245,

  title        = {Infrared freezing of Euclidean QCD observables},

  author       = {Brooks, Paul M and Maxwell, C J},

  abstractNote = {We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q{sup 2}>{lambda}{sup 2}, where Q{sup 2}={lambda}{sup 2} is the Landau pole of the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q{sup 2}<{lambda}{sup 2} the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q{sup 2}-dependence of the perturbative corrections to the Adler-D function, the GLS sum rule and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q{sup 2}={lambda}{sup 2}, and then exhibits freezing behavior, vanishing at Q{sup 2}=0. Finiteness at Q{sup 2}={lambda}{sup 2} implies specific relations between the residues of IR and UV renormalon singularities in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained), are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of nonperturbative and perturbative ambiguities we are led to a result for the Q{sup 2}-dependence of these observables at all Q{sup 2}, in which there is a single undetermined nonperturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behavior of the Minkowskian R{sub e{sup +}}{sub e{sup -}} ratio.},

  doi          = {10.1103/PHYSREVD.74.065012},

  url          = {https://www.osti.gov/biblio/20871245},
  journal      = {Physical Review. D, Particles Fields},

  issn         = {0556-2821},

  number       = 6,

  volume       = 74,

  place        = {United States},

  year         = {Fri Sep 15 00:00:00 EDT 2006},

  month        = {Fri Sep 15 00:00:00 EDT 2006}

}

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