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Title: Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

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 satisfy 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 specialmore » 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
Authors:
 [1] ;  [1] ;  [1] ;  [1] ;  [2] ;  [3]
  1. Chongqing Univ., Chongqing (People's Republic of China)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. KTH Royal Inst. of Technology, Stockholm (Sweden); Stockholm Univ., Stockholm (Sweden)
Publication Date:
Report Number(s):
SLAC-PUB-16287
Journal ID: ISSN 0370-2693; arXiv:1505.04958
Grant/Contract Number:
AC02-76SF00515
Type:
Published Article
Journal Name:
Physics Letters. Section B
Additional Journal Information:
Journal Volume: 748; Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Phenomenology-HEP; Theory-HEP; HEPPH
OSTI Identifier:
1209158
Alternate Identifier(s):
OSTI ID: 1182436

Bi, Huan -Yu, Wu, Xing -Gang, Ma, Yang, Ma, Hong -Hao, Brodsky, Stanley J., and Mojaza, Matin. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale. United States: N. p., Web. doi:10.1016/j.physletb.2015.06.056.
Bi, Huan -Yu, Wu, Xing -Gang, Ma, Yang, Ma, Hong -Hao, Brodsky, Stanley J., & Mojaza, Matin. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale. United States. doi:10.1016/j.physletb.2015.06.056.
Bi, Huan -Yu, Wu, Xing -Gang, Ma, Yang, Ma, Hong -Hao, Brodsky, Stanley J., and Mojaza, Matin. 2015. "Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale". United States. doi:10.1016/j.physletb.2015.06.056.
@article{osti_1209158,
title = {Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale},
author = {Bi, Huan -Yu and Wu, Xing -Gang and Ma, Yang and Ma, Hong -Hao and Brodsky, Stanley J. and Mojaza, Matin},
abstractNote = {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 Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy 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 Re+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 {βi}-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.},
doi = {10.1016/j.physletb.2015.06.056},
journal = {Physics Letters. Section B},
number = C,
volume = 748,
place = {United States},
year = {2015},
month = {6}
}