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Title: Novel all-orders single-scale approach to QCD renormalization scale-setting

Authors:
; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1356735
Grant/Contract Number:
AC02-76SF00515
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 9; Related Information: CHORUS Timestamp: 2017-05-11 22:09:55; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Shen, Jian-Ming, Wu, Xing-Gang, Du, Bo-Lun, and Brodsky, Stanley J. Novel all-orders single-scale approach to QCD renormalization scale-setting. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.95.094006.
Shen, Jian-Ming, Wu, Xing-Gang, Du, Bo-Lun, & Brodsky, Stanley J. Novel all-orders single-scale approach to QCD renormalization scale-setting. United States. doi:10.1103/PhysRevD.95.094006.
Shen, Jian-Ming, Wu, Xing-Gang, Du, Bo-Lun, and Brodsky, Stanley J. Thu . "Novel all-orders single-scale approach to QCD renormalization scale-setting". United States. doi:10.1103/PhysRevD.95.094006.
@article{osti_1356735,
title = {Novel all-orders single-scale approach to QCD renormalization scale-setting},
author = {Shen, Jian-Ming and Wu, Xing-Gang and Du, Bo-Lun and Brodsky, Stanley J.},
abstractNote = {},
doi = {10.1103/PhysRevD.95.094006},
journal = {Physical Review D},
number = 9,
volume = 95,
place = {United States},
year = {Thu May 11 00:00:00 EDT 2017},
month = {Thu May 11 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevD.95.094006

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  • The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the R δ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfymore » all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio R e+e and the Higgs partial width I'(H→bb¯). Both methods lead to the same resummed (‘conformal’) series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {β i}-terms in the pQCD expansion are taken into account. In addition, we show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.« less
  • The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the R δ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfymore » all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio R e+e and the Higgs partial width I'(H→bb¯). Both methods lead to the same resummed (‘conformal’) series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {β i}-terms in the pQCD expansion are taken into account. In addition, we show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.« less