Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD

Di Giustino, Leonardo; Brodsky, Stanley J.; Wang, Sheng-Quan; Wu, Xing-Gang

doi:10.1103/PhysRevD.102.014015

Title: Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD

Abstract

We identify a property of renormalizable SU(N)/U(1) gauge theories, intrinsic conformality (iCF), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in perturbative QCD (pQCD): the PMC_∞ . This new method reflects the underlying conformal properties displayed by pQCD at next-to-next-to-leading order, eliminates the scheme dependence of pQCD predictions, and is consistent with the general properties of the principle of maximum conformality (PMC). We introduce a new method to identify conformal and β -terms which can be applied from either a numerical or an analytical calculations. We illustrate the PMC ∞ for the thrust and C-parameter distributions in e⁺ e^- annihilation and then show how to apply this new method to general observables in QCD. We point out how the implementation of the PMC_∞ can significantly improve the precision of pQCD predictions; its implementation in a multiloop analysis also simplifies the calculation of higher order corrections in a general renormalizable gauge theory.

Authors:

;

; Wang, Sheng-Quan; Wu, Xing-Gang

Publication Date:: Fri Jul 10 00:00:00 EDT 2020

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

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1638119

Alternate Identifier(s):: OSTI ID: 1646802

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 102 Journal Issue: 1; 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


                    Di Giustino, Leonardo, Brodsky, Stanley J., Wang, Sheng-Quan, and Wu, Xing-Gang. Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.102.014015.

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                    Di Giustino, Leonardo, Brodsky, Stanley J., Wang, Sheng-Quan, & Wu, Xing-Gang. Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD.  United States.  https://doi.org/10.1103/PhysRevD.102.014015

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                    Di Giustino, Leonardo, Brodsky, Stanley J., Wang, Sheng-Quan, and Wu, Xing-Gang. Fri .  
"Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD".  United States.  https://doi.org/10.1103/PhysRevD.102.014015.

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@article{osti_1638119,

  title        = {Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD},

  author       = {Di Giustino, Leonardo and Brodsky, Stanley J. and Wang, Sheng-Quan and Wu, Xing-Gang},

  abstractNote = {We identify a property of renormalizable SU(N)/U(1) gauge theories, intrinsic conformality (iCF), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in perturbative QCD (pQCD): the PMC∞ . This new method reflects the underlying conformal properties displayed by pQCD at next-to-next-to-leading order, eliminates the scheme dependence of pQCD predictions, and is consistent with the general properties of the principle of maximum conformality (PMC). We introduce a new method to identify conformal and β -terms which can be applied from either a numerical or an analytical calculations. We illustrate the PMC ∞ for the thrust and C-parameter distributions in e+ e- annihilation and then show how to apply this new method to general observables in QCD. We point out how the implementation of the PMC∞ can significantly improve the precision of pQCD predictions; its implementation in a multiloop analysis also simplifies the calculation of higher order corrections in a general renormalizable gauge theory.},

  doi          = {10.1103/PhysRevD.102.014015},

  journal      = {Physical Review. D.},

  number       = 1,

  volume       = 102,

  place        = {United States},

  year         = {Fri Jul 10 00:00:00 EDT 2020},

  month        = {Fri Jul 10 00:00:00 EDT 2020}

}

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Works referenced in this record:

Studies of hadronic event structure in e+e- annihilation from 30 to 209GeV with the L3 detector
journal, September 2004

Achard, P.; Adriani, O.; Aguilar-Benitez, M.
Physics Reports, Vol. 399, Issue 2-3
DOI: 10.1016/j.physrep.2004.07.002

Thrust distribution in e+e− annihilation
journal, July 1991

Catani, S.; Turnock, G.; Webber, B. R.
Physics Letters B, Vol. 263, Issue 3-4
DOI: 10.1016/0370-2693(91)90494-B

Resummed mass distribution for jets initiated by massive quarks
journal, August 2007

Aglietti, U.; Di Giustino, L.; Ferrera, G.
Physics Letters B, Vol. 651, Issue 4
DOI: 10.1016/j.physletb.2007.06.034

Renormalons
journal, August 1999

Beneke, M.
Physics Reports, Vol. 317, Issue 1-2
DOI: 10.1016/S0370-1573(98)00130-6

The resummation of soft gluons in hadronic collisions
journal, October 1996

Catani, S.
Nuclear Physics B, Vol. 478, Issue 1-2
DOI: 10.1016/0550-3213(96)00399-9

Renormalization group improved perturbative QCD
journal, September 1980

Grunberg, G.
Physics Letters B, Vol. 95, Issue 1
DOI: 10.1016/0370-2693(80)90402-5

BLM scale fixing in event-shape distributions
journal, June 2014

Gehrmann, Thomas; Häfliger, Niklaus; Monni, Pier Francesco
The European Physical Journal C, Vol. 74, Issue 6
DOI: 10.1140/epjc/s10052-014-2896-1

A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP
journal, July 2003

DELPHI Collaboration,
The European Physical Journal C, Vol. 29, Issue 3, p. 285-312
DOI: 10.1140/epjc/s2003-01198-0

Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy
journal, October 2016

Del Duca, Vittorio; Duhr, Claude; Kardos, Adam
Physical Review Letters, Vol. 117, Issue 15
DOI: 10.1103/PhysRevLett.117.152004

Second-Order QCD Corrections to the Thrust Distribution in Electron-Positron Annihilation
journal, September 2007

Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. W. N.
Physical Review Letters, Vol. 99, Issue 13
DOI: 10.1103/PhysRevLett.99.132002

Scale setting using the extended renormalization group and the principle of maximum conformality: The QCD coupling constant at four loops
journal, February 2012

Brodsky, Stanley J.; Wu, Xing-Gang
Physical Review D, Vol. 85, Issue 3
DOI: 10.1103/PhysRevD.85.034038

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

Jet production in the CoLoRFulNNLO method: Event shapes in electron-positron collisions
journal, October 2016

Del Duca, Vittorio; Duhr, Claude; Kardos, Adam
Physical Review D, Vol. 94, Issue 7
DOI: 10.1103/PhysRevD.94.074019

Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation
journal, November 2019

Wang, Sheng-Quan; Brodsky, Stanley J.; Wu, Xing-Gang
Physical Review D, Vol. 100, Issue 9
DOI: 10.1103/PhysRevD.100.094010

Form factors of the gauge-invariant three-gluon vertex
journal, September 2006

Binger, Michael; Brodsky, Stanley J.
Physical Review D, Vol. 74, Issue 5
DOI: 10.1103/PhysRevD.74.054016

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

Mojaza, Matin; Brodsky, Stanley J.; Wu, Xing-Gang
Physical Review Letters, Vol. 110, Issue 19
DOI: 10.1103/PhysRevLett.110.192001

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

Brodsky, Stanley J.; Mojaza, Matin; Wu, Xing-Gang
Physical Review D, Vol. 89, Issue 1
DOI: 10.1103/PhysRevD.89.014027

Thrust distribution in electron-positron annihilation using the principle of maximum conformality
journal, June 2019

Wang, Sheng-Quan; Brodsky, Stanley J.; Wu, Xing-Gang
Physical Review D, Vol. 99, Issue 11
DOI: 10.1103/PhysRevD.99.114020

The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality
journal, September 2019

Wu, Xing-Gang; Shen, Jian-Ming; Du, Bo-Lun
Progress in Particle and Nuclear Physics, Vol. 108
DOI: 10.1016/j.ppnp.2019.05.003

Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams
journal, December 1997

Brodsky, Stanley J.; Ellis, John; Gardi, Einan
Physical Review D, Vol. 56, Issue 11
DOI: 10.1103/PhysRevD.56.6980

Thrust at $N^{3} LL$ with power corrections and a precision global fit for $α_{s} (m_{Z})$
journal, April 2011

Abbate, Riccardo; Fickinger, Michael; Hoang, André H.
Physical Review D, Vol. 83, Issue 7
DOI: 10.1103/PhysRevD.83.074021

Optimized perturbation theory
journal, June 1981

Stevenson, P. M.
Physical Review D, Vol. 23, Issue 12
DOI: 10.1103/PhysRevD.23.2916

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

Brodsky, Stanley J.; Di Giustino, Leonardo
Physical Review D, Vol. 86, Issue 8
DOI: 10.1103/PhysRevD.86.085026

Quantum Electrodynamics at Small Distances
journal, September 1954

Gell-Mann, M.; Low, F. E.
Physical Review, Vol. 95, Issue 5
DOI: 10.1103/PhysRev.95.1300

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
journal, December 2000

Chetyrkin, K. G.; Kühn, J. H.; Steinhauser, M.
Computer Physics Communications, Vol. 133, Issue 1
DOI: 10.1016/S0010-4655(00)00155-7

NNLO corrections to event shapes in e ⁺ e ⁻ annihilation
journal, December 2007

Ridder, A. Gehrmann-De; Gehrmann, T.; Glover, E. W. N.
Journal of High Energy Physics, Vol. 2007, Issue 12
DOI: 10.1088/1126-6708/2007/12/094

Event shapes and jet rates in electron-positron annihilation at NNLO
journal, June 2009

Weinzierl, Stefan
Journal of High Energy Physics, Vol. 2009, Issue 06
DOI: 10.1088/1126-6708/2009/06/041

Resummation of large logarithms in e+e− event shape distributions
journal, October 1993

Catani, S.; Trentadue, L.; Turnock, G.
Nuclear Physics B, Vol. 407, Issue 1
DOI: 10.1016/0550-3213(93)90271-P

Light-front hadron dynamics and AdS/CFT correspondence
journal, March 2004

Brodsky, Stanley J.; de Téramond, Guy F.
Physics Letters B, Vol. 582, Issue 3-4
DOI: 10.1016/j.physletb.2003.12.050

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

Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan
Reports on Progress in Physics, Vol. 78, Issue 12
DOI: 10.1088/0034-4885/78/12/126201

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

Brodsky, Stanley J.; Wu, Xing-Gang
Physical Review Letters, Vol. 109, Issue 4
DOI: 10.1103/PhysRevLett.109.042002

Next-to-Next-to-Leading Order Corrections to Three-Jet Observables in Electron-Positron Annihilation
journal, October 2008

Weinzierl, Stefan
Physical Review Letters, Vol. 101, Issue 16
DOI: 10.1103/PhysRevLett.101.162001

Ambiguities of the principle of maximum conformality procedure for hadron collider processes
journal, October 2019

Chawdhry, Herschel A.; Mitov, Alexander
Physical Review D, Vol. 100, Issue 7
DOI: 10.1103/PhysRevD.100.074013

Jet production rates at LEP and the scale of ?s
journal, March 1991

Kramer, G.; Lampe, B.
Zeitschrift f�r Physik A Hadrons and Nuclei, Vol. 339, Issue 1
DOI: 10.1007/BF01282948

Measurement of $α_{s}$ ( $M_{Z}^{2}$ ) from hadronic event observables at the $Z^{0}$ resonance
journal, February 1995

Abe, K.; Abt, I.; Ahn, C. J.
Physical Review D, Vol. 51, Issue 3
DOI: 10.1103/PhysRevD.51.962

A general method for the resummation of event-shape distributions in e + e − annihilation
journal, May 2015

Banfi, Andrea; McAslan, Heather; Monni, Pier Francesco
Journal of High Energy Physics, Vol. 2015, Issue 5
DOI: 10.1007/JHEP05(2015)102

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

Brodsky, Stanley J.; Huet, Patrick
Physics Letters B, Vol. 417, Issue 1-2
DOI: 10.1016/S0370-2693(97)01209-4

Studies of QCD at ${\rm e}^ + {\rm e}^-$ centre-of-mass energies between 91 and 209 GeV
journal, July 2004

ALEPH Collaboration,
The European Physical Journal C, Vol. 35, Issue 4, p. 457-486
DOI: 10.1140/epjc/s2004-01891-4

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Title: Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD

Abstract

Citation Formats

Studies of hadronic event structure in e+e- annihilation from 30 to 209GeV with the L3 detector journal, September 2004

Thrust distribution in e+e− annihilation journal, July 1991

Resummed mass distribution for jets initiated by massive quarks journal, August 2007

Renormalons journal, August 1999

The resummation of soft gluons in hadronic collisions journal, October 1996

Renormalization group improved perturbative QCD journal, September 1980

BLM scale fixing in event-shape distributions journal, June 2014

A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP journal, July 2003

Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy journal, October 2016

Second-Order QCD Corrections to the Thrust Distribution in Electron-Positron Annihilation journal, September 2007

Scale setting using the extended renormalization group and the principle of maximum conformality: The QCD coupling constant at four loops journal, February 2012

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

Jet production in the CoLoRFulNNLO method: Event shapes in electron-positron collisions journal, October 2016

Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation journal, November 2019

Form factors of the gauge-invariant three-gluon vertex journal, September 2006

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

Thrust distribution in electron-positron annihilation using the principle of maximum conformality journal, June 2019

The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality journal, September 2019

Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams journal, December 1997

Thrust at N 3 LL with power corrections and a precision global fit for α s ( m Z ) journal, April 2011

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

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses journal, December 2000

NNLO corrections to event shapes in e + e − annihilation journal, December 2007

Event shapes and jet rates in electron-positron annihilation at NNLO journal, June 2009

Resummation of large logarithms in e+e− event shape distributions journal, October 1993

Light-front hadron dynamics and AdS/CFT correspondence journal, March 2004

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

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

Next-to-Next-to-Leading Order Corrections to Three-Jet Observables in Electron-Positron Annihilation journal, October 2008

Ambiguities of the principle of maximum conformality procedure for hadron collider processes journal, October 2019

Jet production rates at LEP and the scale of ?s journal, March 1991

Measurement of α s ( M Z 2 ) from hadronic event observables at the Z 0 resonance journal, February 1995

A general method for the resummation of event-shape distributions in e + e − annihilation journal, May 2015

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

Studies of QCD at ${\rm e}^ + {\rm e}^-$ centre-of-mass energies between 91 and 209 GeV journal, July 2004

Studies of hadronic event structure in e+e- annihilation from 30 to 209GeV with the L3 detector
journal, September 2004

Thrust distribution in e+e− annihilation
journal, July 1991

Resummed mass distribution for jets initiated by massive quarks
journal, August 2007

Renormalons
journal, August 1999

The resummation of soft gluons in hadronic collisions
journal, October 1996

Renormalization group improved perturbative QCD
journal, September 1980

BLM scale fixing in event-shape distributions
journal, June 2014

A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP
journal, July 2003

Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy
journal, October 2016

Second-Order QCD Corrections to the Thrust Distribution in Electron-Positron Annihilation
journal, September 2007

Scale setting using the extended renormalization group and the principle of maximum conformality: The QCD coupling constant at four loops
journal, February 2012

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

Jet production in the CoLoRFulNNLO method: Event shapes in electron-positron collisions
journal, October 2016

Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation
journal, November 2019

Form factors of the gauge-invariant three-gluon vertex
journal, September 2006

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

Thrust distribution in electron-positron annihilation using the principle of maximum conformality
journal, June 2019

The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality
journal, September 2019

Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams
journal, December 1997

Thrust at $N^{3} LL$ with power corrections and a precision global fit for $α_{s} (m_{Z})$
journal, April 2011

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

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
journal, December 2000

NNLO corrections to event shapes in e ⁺ e ⁻ annihilation
journal, December 2007

Event shapes and jet rates in electron-positron annihilation at NNLO
journal, June 2009

Resummation of large logarithms in e+e− event shape distributions
journal, October 1993

Light-front hadron dynamics and AdS/CFT correspondence
journal, March 2004

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

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

Next-to-Next-to-Leading Order Corrections to Three-Jet Observables in Electron-Positron Annihilation
journal, October 2008

Ambiguities of the principle of maximum conformality procedure for hadron collider processes
journal, October 2019

Jet production rates at LEP and the scale of ?s
journal, March 1991

Measurement of $α_{s}$ ( $M_{Z}^{2}$ ) from hadronic event observables at the $Z^{0}$ resonance
journal, February 1995

A general method for the resummation of event-shape distributions in e + e − annihilation
journal, May 2015

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

Studies of QCD at ${\rm e}^ + {\rm e}^-$ centre-of-mass energies between 91 and 209 GeV
journal, July 2004