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

Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

doi:10.1016/j.physletb.2015.06.056

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

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Abstract

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 special degeneracy relations, whichmore »« less

Authors:

Bi, Huan-Yu;

; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

Publication Date:: Tue Sep 01 00:00:00 EDT 2015

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1209158

Alternate Identifier(s):: OSTI ID: 1182436

Report Number(s):: SLAC-PUB-16287
Journal ID: ISSN 0370-2693; S0370269315004785; PII: S0370269315004785

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Published Article

Journal Name:: Physics Letters B

Additional Journal Information:: Journal Name: Physics Letters B Journal Volume: 748 Journal Issue: C; Journal ID: ISSN 0370-2693

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Phenomenology-HEP; Theory-HEP; HEPPH

Citation Formats


                    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.  Netherlands: N. p., 2015. 
Web.  doi:10.1016/j.physletb.2015.06.056.

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                    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.  Netherlands.  https://doi.org/10.1016/j.physletb.2015.06.056

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                    Bi, Huan-Yu, Wu, Xing-Gang, Ma, Yang, Ma, Hong-Hao, Brodsky, Stanley J., and Mojaza, Matin. Tue .  
"Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale".  Netherlands.  https://doi.org/10.1016/j.physletb.2015.06.056.

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@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 B},

  number       = C,

  volume       = 748,

  place        = {Netherlands},

  year         = {Tue Sep 01 00:00:00 EDT 2015},

  month        = {Tue Sep 01 00:00:00 EDT 2015}

}

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