Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality

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A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 2}): The purpose of the running coupling in any gauge theory is to sum all terms involving the {beta} function; in fact, when the renormalization scale is set properly, all non-conformal {beta} {ne} 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with {beta} = 0. The resulting scale-fixed predictions ... continued below

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12 pages

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Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Di Giustino, Leonardo & /SLAC August 19, 2011.

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A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 2}): The purpose of the running coupling in any gauge theory is to sum all terms involving the {beta} function; in fact, when the renormalization scale is set properly, all non-conformal {beta} {ne} 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with {beta} = 0. The resulting scale-fixed predictions using the 'principle of maximum conformality' (PMC) are independent of the choice of renormalization scheme - a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD {beta} function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

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12 pages

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  • Journal Name: Submitted to Physics Letters B

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  • Report No.: SLAC-PUB-14479
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 1022463
  • Archival Resource Key: ark:/67531/metadc836522

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • August 19, 2011

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

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  • Dec. 8, 2016, 11 p.m.

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Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Di Giustino, Leonardo & /SLAC. Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality, article, August 19, 2011; United States. (digital.library.unt.edu/ark:/67531/metadc836522/: accessed July 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.