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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 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, whichmore » 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
 [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:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0370-2693; arXiv:1505.04958
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics Letters. Section B; Journal Volume: 748; Journal Issue: C
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
Phenomenology-HEP; Theory-HEP; HEPPH