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Title: Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling

Abstract

As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. Here in this article, we show that by using the newly suggested C -scheme coupling, one can obtain a demonstration that the principle of maximum conformality prediction is scheme-independent to all-orders for any renormalization schemes, thus satisfying all of the conditions of the renormalization group invariance. We illustrate these features for the nonsinglet Adler function and for τ decay to ν+ hadrons at the four-loop level.

Authors:
; ; ;
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE; National Natural Science Foundation of China (NNSFC)
OSTI Identifier:
1439382
Alternate Identifier(s):
OSTI ID: 1458454
Report Number(s):
SLAC-PUB-17232
Journal ID: ISSN 2470-0010; PRVDAQ; 094030
Grant/Contract Number:  
AC02-76SF00515; 11625520
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 9; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Wu, Xing-Gang, Shen, Jian-Ming, Du, Bo-Lun, and Brodsky, Stanley J. Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.094030.
Wu, Xing-Gang, Shen, Jian-Ming, Du, Bo-Lun, & Brodsky, Stanley J. Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling. United States. doi:10.1103/PhysRevD.97.094030.
Wu, Xing-Gang, Shen, Jian-Ming, Du, Bo-Lun, and Brodsky, Stanley J. Tue . "Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling". United States. doi:10.1103/PhysRevD.97.094030.
@article{osti_1439382,
title = {Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling},
author = {Wu, Xing-Gang and Shen, Jian-Ming and Du, Bo-Lun and Brodsky, Stanley J.},
abstractNote = {As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. Here in this article, we show that by using the newly suggested C -scheme coupling, one can obtain a demonstration that the principle of maximum conformality prediction is scheme-independent to all-orders for any renormalization schemes, thus satisfying all of the conditions of the renormalization group invariance. We illustrate these features for the nonsinglet Adler function and for τ decay to ν+ hadrons at the four-loop level.},
doi = {10.1103/PhysRevD.97.094030},
journal = {Physical Review D},
number = 9,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.97.094030

Citation Metrics:
Cited by: 3 works
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Works referenced in this record:

Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling
journal, October 2016

  • Jamin, Matthias; Miravitllas, Ramon
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/JHEP10(2016)059

Renormalization group and the deep structure of the proton
journal, June 1979


Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
journal, March 2005


The four-loop QCD β-function and anomalous dimensions
journal, March 2005


α s and the τ hadronic width: fixed-order, contour- improved and higher-order perturbation theory
journal, September 2008


Commensurate scale relations in quantum chromodynamics
journal, April 1995


Renormalons
journal, August 1999


Review of Particle Physics
journal, October 2016


The renormalization scale-setting problem in QCD
journal, September 2013

  • Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin
  • Progress in Particle and Nuclear Physics, Vol. 72
  • DOI: 10.1016/j.ppnp.2013.06.001

Application of the principle of maximum conformality to top-pair production
journal, July 2012


The four-loop β-function in quantum chromodynamics
journal, May 1997


Conformal expansions and renormalons
journal, September 2001


Novel all-orders single-scale approach to QCD renormalization scale-setting
journal, May 2017


Scheme Variations of the QCD Coupling and Hadronic τ Decays
journal, October 2016


Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in Perturbative QCD
journal, May 2013


Systematic scale-setting to all orders: The principle of maximum conformality and commensurate scale relations
journal, January 2014


Order α s 4 QCD Corrections to Z and τ Decays
journal, July 2008


Resolution of the renormalisation-scheme ambiguity in perturbative QCD
journal, March 1981


The three-loop QCD β-function and anomalous dimensions
journal, April 1993


Optimized perturbation theory
journal, June 1981


Setting the renormalization scale in QCD: The principle of maximum conformality
journal, October 2012


Quantum Electrodynamics at Small Distances
journal, September 1954


Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order
journal, July 1974


Ultraviolet Behavior of Non-Abelian Gauge Theories
journal, June 1973


Reliable Perturbative Results for Strong Interactions?
journal, June 1973


La normalisation des constantes dans la théorie des quanta
text, January 1953


On the LambertW function
journal, December 1996

  • Corless, R. M.; Gonnet, G. H.; Hare, D. E. G.
  • Advances in Computational Mathematics, Vol. 5, Issue 1
  • DOI: 10.1007/BF02124750

QCD corrections to the e+e− cross-section and the Z boson decay rate: concepts and results
journal, December 1996


The generalized scheme-independent Crewther relation in QCD
journal, July 2017


Five-Loop Running of the QCD Coupling Constant
journal, February 2017


Self-consistency requirements of the renormalization group for setting the renormalization scale
journal, September 2012


Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order α s 4 in a General Gauge Theory
journal, March 2010


Broken Scale Invariance in Scalar Field Theory
journal, October 1970


Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review
journal, October 2015


On the elimination of scale ambiguities in perturbative quantum chromodynamics
journal, July 1983

  • Brodsky, Stanley J.; Lepage, G. Peter; Mackenzie, Paul B.
  • Physical Review D, Vol. 28, Issue 1
  • DOI: 10.1103/PhysRevD.28.228

Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
journal, July 2012


The gell-mann-low function of QCD in the three-loop approximation
journal, June 1980


Vector correlator in massless QCD at order $ \mathcal{O}\left( {\alpha_s^4} \right) $ and the QED β-function at five loop
journal, July 2012

  • Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
  • Journal of High Energy Physics, Vol. 2012, Issue 7
  • DOI: 10.1007/JHEP07(2012)017

General properties on applying the principle of minimum sensitivity to high-order perturbative QCD predictions
journal, February 2015


Optimization and the ultimate convergence of QCD perturbation theory
journal, January 1984


Small distance behaviour in field theory and power counting
journal, September 1970

  • Symanzik, K.
  • Communications in Mathematical Physics, Vol. 18, Issue 3
  • DOI: 10.1007/BF01649434

Aspects of SU(Nc) gauge theories in the limit of small number of colors
journal, January 1998


    Works referencing / citing this record:

    Renormalization-scheme variation of a QCD perturbation expansion with tamed large-order behavior
    journal, September 2018


    Exclusive production of J / ψ + η c at the B factories Belle and BABAR using the principle of maximum conformality
    journal, November 2018


    The $$\Upsilon (1S)$$ leptonic decay using the principle of maximum conformality
    journal, August 2019