Extending the predictive power of perturbative QCD
Abstract
The predictive power of perturbative QCD (pQCD) depends on two important issues: (1) how to eliminate the renormalization scheme-and-scale ambiguities at fixed order, and (2) how to reliably estimate the contributions of unknown higher-order terms using information from the known pQCD series. The Principle of Maximum Conformality (PMC) satisfies all of the principles of the renormalization group and eliminates the scheme-and-scale ambiguities by the recursive use of the renormalization group equation to determine the scale of the QCD running coupling αs at each order. Moreover, the resulting PMC predictions are independent of the choice of the renormalization scheme, satisfying the key principle of renormalization group invariance. In this paper, we show that by using the conformal series derived using the PMC single-scale procedure, in combination with the Padé Approximation Approach (PAA), one can achieve quantitatively useful estimates for the unknown higher-order terms from the known perturbative series. We illustrate this procedure for three hadronic observables Re+e–, Rτ, and Γ(H → bb¯) which are each known to 4 loops in pQCD. We show that if the PMC prediction for the conformal series for an observable (of leading order αps) has been determined at order αns, then the [] = [0/n–p] Padémore »
- Authors:
-
[1];
- Chongqing Univ., Chongqing (People's Republic of China)
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1506173
- Grant/Contract Number:
- AC02-76SF00515; 11625520
- Resource Type:
- Accepted Manuscript
- Journal Name:
- European Physical Journal. C, Particles and Fields
- Additional Journal Information:
- Journal Volume: 79; Journal Issue: 3; Journal ID: ISSN 1434-6044
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Du, Bo -Lun, Wu, Xing -Gang, Shen, Jian -Ming, and Brodsky, Stanley J. Extending the predictive power of perturbative QCD. United States: N. p., 2019.
Web. doi:10.1140/epjc/s10052-019-6704-9.
Du, Bo -Lun, Wu, Xing -Gang, Shen, Jian -Ming, & Brodsky, Stanley J. Extending the predictive power of perturbative QCD. United States. https://doi.org/10.1140/epjc/s10052-019-6704-9
Du, Bo -Lun, Wu, Xing -Gang, Shen, Jian -Ming, and Brodsky, Stanley J. Thu .
"Extending the predictive power of perturbative QCD". United States. https://doi.org/10.1140/epjc/s10052-019-6704-9. https://www.osti.gov/servlets/purl/1506173.
@article{osti_1506173,
title = {Extending the predictive power of perturbative QCD},
author = {Du, Bo -Lun and Wu, Xing -Gang and Shen, Jian -Ming and Brodsky, Stanley J.},
abstractNote = {The predictive power of perturbative QCD (pQCD) depends on two important issues: (1) how to eliminate the renormalization scheme-and-scale ambiguities at fixed order, and (2) how to reliably estimate the contributions of unknown higher-order terms using information from the known pQCD series. The Principle of Maximum Conformality (PMC) satisfies all of the principles of the renormalization group and eliminates the scheme-and-scale ambiguities by the recursive use of the renormalization group equation to determine the scale of the QCD running coupling αs at each order. Moreover, the resulting PMC predictions are independent of the choice of the renormalization scheme, satisfying the key principle of renormalization group invariance. In this paper, we show that by using the conformal series derived using the PMC single-scale procedure, in combination with the Padé Approximation Approach (PAA), one can achieve quantitatively useful estimates for the unknown higher-order terms from the known perturbative series. We illustrate this procedure for three hadronic observables Re+e–, Rτ, and Γ(H → bb¯) which are each known to 4 loops in pQCD. We show that if the PMC prediction for the conformal series for an observable (of leading order αps) has been determined at order αns, then the [] = [0/n–p] Padé series provides quantitatively useful predictions for the higher-order terms. We also show that the PMC + PAA predictions agree at all orders with the fundamental, scheme-independent Generalized Crewther relations which connect observables, such as deep inelastic neutrino-nucleon scattering, to hadronic e+e– annihilation. Furthermore, by using the combination of the PMC series and the Padé method, the predictive power of pQCD theory can be greatly improved.},
doi = {10.1140/epjc/s10052-019-6704-9},
journal = {European Physical Journal. C, Particles and Fields},
number = 3,
volume = 79,
place = {United States},
year = {Thu Feb 28 00:00:00 EST 2019},
month = {Thu Feb 28 00:00:00 EST 2019}
}
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Works referenced in this record:
Estimating perturbative coefficients in quantum field theory using Padé approximants
journal, March 1994
- Samuel, Mark A.; Li, G.; Steinfelds, Eric
- Physics Letters B, Vol. 323, Issue 2
Decays of a heavy lepton and an intermediate weak boson in quantum chromodynamics
journal, August 1977
- Lam, C. S.; Yan, T. M.
- Physical Review D, Vol. 16, Issue 3
Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale
journal, September 2015
- Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang
- Physics Letters B, Vol. 748
Application of Padé approximants to determination of αs(MZ2) from hadronic event shape observables in e+e− annihilation
journal, January 1997
- Burrows, P. N.; Abraha, T.; Samuel, M.
- Physics Letters B, Vol. 392, Issue 1-2
Importance of proper renormalization scale-setting for QCD testing at colliders
journal, December 2015
- Wu, Xing-Gang; Wang, Sheng-Quan; Brodsky, Stanley J.
- Frontiers of Physics, Vol. 11, Issue 1
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
Connecting the hadron mass scale to the fundamental mass scale of quantum chromodynamics
journal, November 2015
- Deur, A.; Brodsky, S. J.; de Teramond, G. F.
- Physics Letters B, Vol. 750
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
The Padé Approximation and its Physical Applications
journal, January 1972
- Basdevant, J. L.
- Fortschritte der Physik, Vol. 20, Issue 5
Quantum spectral curve for arbitrary state/operator in AdS5/CFT4
journal, September 2015
- Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sébastien
- Journal of High Energy Physics, Vol. 2015, Issue 9
Novel all-orders single-scale approach to QCD renormalization scale-setting
journal, May 2017
- Shen, Jian-Ming; Wu, Xing-Gang; Du, Bo-Lun
- Physical Review D, Vol. 95, Issue 9
Conformal Regge theory
journal, December 2012
- Costa, Miguel S.; Goncalves, Vasco; Penedones, João
- Journal of High Energy Physics, Vol. 2012, Issue 12
Implications of the principle of maximum conformality for the QCD strong coupling
journal, October 2017
- Deur, Alexandre; Shen, Jian-Ming; Wu, Xing-Gang
- Physics Letters B, Vol. 773
Order QCD Corrections to and Decays
journal, July 2008
- Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
- Physical Review Letters, Vol. 101, Issue 1
The Higgs boson inclusive decay channels $$H \rightarrow b\bar{b}$$ H → b b ¯ and $$H \rightarrow gg$$ H → g g up to four-loop level
journal, April 2014
- Wang, Sheng-Quan; Wu, Xing-Gang; Zheng, Xu-Chang
- The European Physical Journal C, Vol. 74, Issue 4
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
Pomeron Eigenvalue at Three Loops in Supersymmetric Yang-Mills Theory
journal, December 2015
- Gromov, Nikolay; Levkovich-Maslyuk, Fedor; Sizov, Grigory
- Physical Review Letters, Vol. 115, Issue 25
Quantum Electrodynamics at Small Distances
journal, September 1954
- Gell-Mann, M.; Low, F. E.
- Physical Review, Vol. 95, Issue 5
Ultraviolet Behavior of Non-Abelian Gauge Theories
journal, June 1973
- Gross, David J.; Wilczek, Frank
- Physical Review Letters, Vol. 30, Issue 26
Comparison of the Padé Approximation Method to Perturbative QCD Calculations
journal, May 1995
- Samuel, Mark A.; Ellis, John; Karliner, Marek
- Physical Review Letters, Vol. 74, Issue 22
Reliable Perturbative Results for Strong Interactions?
journal, June 1973
- Politzer, H. David
- Physical Review Letters, Vol. 30, Issue 26
Scalar Correlator at , Higgs Boson Decay into Bottom Quarks, and Bounds on the Light-Quark Masses
journal, January 2006
- Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
- Physical Review Letters, Vol. 96, Issue 1
On the interface between perturbative and nonperturbative QCD
journal, June 2016
- Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
- Physics Letters B, Vol. 757
Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS 5 /CF T 4
journal, June 2016
- Gromov, Nikolay; Levkovich-Maslyuk, Fedor; Sizov, Grigory
- Journal of High Energy Physics, Vol. 2016, Issue 6
The generalized scheme-independent Crewther relation in QCD
journal, July 2017
- Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang
- Physics Letters B, Vol. 770
Solution to the puzzle using the principle of maximum conformality
journal, May 2018
- Wang, Sheng-Quan; Wu, Xing-Gang; Sang, Wen-Long
- Physical Review D, Vol. 97, Issue 9
Self-consistency requirements of the renormalization group for setting the renormalization scale
journal, September 2012
- Brodsky, Stanley J.; Wu, Xing-Gang
- Physical Review D, Vol. 86, Issue 5
Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order in a General Gauge Theory
journal, March 2010
- Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.
- Physical Review Letters, Vol. 104, Issue 13
A determination of the strong coupling constant ? S frome + e ? total cross-section data
journal, December 1989
- Marshall, R.
- Zeitschrift f�r Physik C Particles and Fields, Vol. 43, Issue 4
A prediction for the 4-loop β function in QCD
journal, May 1997
- Ellis, John; Karliner, Marek; Samuel, Mark A.
- Physics Letters B, Vol. 400, Issue 1-2
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
Scale setting in QCD and the momentum flow in Feynman diagrams
journal, May 1995
- Neubert, Matthias
- Physical Review D, Vol. 51, Issue 10
Why Padé approximants reduce the renormalization-scale dependence in QFT
journal, July 1997
- Gardi, Einan
- Physical Review D, Vol. 56, Issue 1
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
Quantum Spectral Curve for Planar Super-Yang-Mills Theory
journal, January 2014
- Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sébastien
- Physical Review Letters, Vol. 112, Issue 1
Higher-order QCD corrections to hadronic τ decays from Padé approximants
journal, August 2018
- Boito, Diogo; Masjuan, Pere; Oliani, Fabio
- Journal of High Energy Physics, Vol. 2018, Issue 8
Asymptotic Padé Approximants and the SQCD β-function
journal, August 1997
- Jack, I.; Jones, D. R. T.; Samuel, M. A.
- Physics Letters B, Vol. 407, Issue 2
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
Asymptotic Padé approximant predictions: Up to five loops in QCD and SQCD
journal, March 1998
- Ellis, J.; Jack, I.; Jones, D. R. T.
- Physical Review D, Vol. 57, Issue 5
Naive nonabelianization and resummation of fermion bubble chains
journal, April 1995
- Beneke, M.; Braun, V. M.
- Physics Letters B, Vol. 348, Issue 3-4
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
A prediction for the 4-loop β function in QCD
conference, January 1997
- Ellis, John; Karliner, Marek; Samuel, Mark A.
- Beyond the standard model, AIP Conference Proceedings
Quantum Electrodynamics at Small Distances
journal, July 1969
- Baker, M.; Johnson, K.
- Physical Review, Vol. 183, Issue 5
Naive nonabelianization and resummation of fermion bubble chains
text, January 1995
- Beneke, M.; Braun, Vladimir M.
- Universität Regensburg
Estimating perturbative coefficients in quantum field theory using Padé approximants
journal, July 1993
- Samuel, Mark A.; Li, G.; Steinfelds, Eric
- Physical Review D, Vol. 48, Issue 2
Review of Particle Physics
text, January 2018
- Tanabashi, M.; Hagiwara, K.; Hikasa, K.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Review of Particle Physics
text, January 2012
- Beringer, J.; Arguin, J.; Barnett, R.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
text, January 2012
- Brodsky, Stanley J.; Wu, Xing-Gang
- arXiv
Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
text, January 2012
- Brodsky, Stanley J.; Wu, Xing-Gang
- arXiv
The Renormalization Scale-Setting Problem in QCD
text, January 2013
- Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin
- arXiv
Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
text, January 2013
- Brodsky, Stanley J.; Mojaza, Matin; Wu, Xing-Gang
- arXiv
Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$
text, January 2014
- Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sebastien
- arXiv
Connecting the Hadron Mass Scale to the Fundamental Mass Scale of Quantum Chromodynamics
text, January 2014
- Deur, Alexandre; Brodsky, Stanley J.; de Teramond, Guy F.
- arXiv
Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
text, January 2015
- Gromov, Nikolay; Levkovich-Maslyuk, Fedor; Sizov, Grigory
- arXiv
Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
text, January 2015
- Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang
- arXiv
On the Interface between Perturbative and Nonperturbative QCD
text, January 2016
- Deur, A.; Brodsky, S. J.; de Teramond, G. F.
- arXiv
Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
text, January 1994
- Neubert, Matthias
- arXiv
Comparison of the Pade Approximation Method to Perturbative QCD Calculations
text, January 1995
- Samuel, Mark A.; Ellis, John; Karliner, Marek
- arXiv
Application of Pade Approximants to Determination of alpha_s(M_Z^2) from Hadronic Event Shape Observables in e+e- Annihilation
text, January 1996
- Burrows, P. N.; Abraha, T.; Samuel, M.
- arXiv
Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD
text, January 1997
- Ellis, J.; Jack, I.; Jones, D. R. T.
- arXiv