Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Extending the predictive power of perturbative QCD using the principle of maximum conformality and the Bayesian analysis

Journal Article · · European Physical Journal. C, Particles and Fields (Online)
 [1];  [1];  [2];  [3];  [3]; ORCiD logo [3];  [4]
  1. Hunan Univ., Changsha (China)
  2. Guizhou Minzu University, Guiyang (China)
  3. Chongqing Univ. (China)
  4. SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Stanford Univ., CA (United States)
+ Show Author Affiliations

In addition to the evaluation of high-order loop contributions, the precision and predictive power of perturbative QCD (pQCD) predictions depends on two important issues: (1) how to achieve a reliable, convergent fixed-order series, and (2) how to reliably estimate the contributions of unknown higher-order terms. The recursive use of renormalization group equation, together with the Principle of Maximum Conformality (PMC), eliminates the renormalization scheme-and-scale ambiguities of the conventional pQCD series. The result is a conformal, scale-invariant series of finite order which also satisfies all of the principles of the renormalization group. In this paper we propose a novel Bayesian-based approach to estimate the size of the unknown higher order contributions based on an optimized analysis of probability distributions. We show that by using the PMC conformal series, in combination with the Bayesian analysis, one can consistently achieve high degree of reliability estimates for the unknown high order terms. Thus the predictive power of pQCD can be greatly improved. We illustrate this procedure for two pQCD observables: Re+e– and Rτ, which are each known up to four loops in pQCD. Numerical analyses confirm that by using the scale-independent and more convergent PMC conformal series, one can achieve reliable Bayesian probability estimates for the unknown higher-order contributions.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); National Natural Science Foundation of China (NSFC); Graduate Research and Innovation Foundation of Chongqing, China
Grant/Contract Number:
AC02-76SF00515; 11905056; 12147102; 12175025; CYB21045; ydstd1912
OSTI ID:
2001442
Report Number(s):
SLAC-PUB-17690; TRN: US2405652
Journal Information:
European Physical Journal. C, Particles and Fields (Online), Vol. 83, Issue 4; ISSN 1434-6052
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

References (47)

Adler function, sum rules and Crewther relation of order O(αs4): The singlet case journal July 2012
Decays of a heavy lepton and an intermediate weak boson in quantum chromodynamics journal August 1977
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
Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale journal September 2015
Renormalons journal August 1999
The renormalization scale-setting problem in QCD journal September 2013
The four-loop β-function in quantum chromodynamics journal May 1997
Asymptotically Free Gauge Theories. I journal November 1973
Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders journal October 2020
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
Version 3 of RunDec and CRunDec journal March 2018
Order α s 4 QCD Corrections to Z and τ Decays journal July 2008
The three-loop QCD β-function and anomalous dimensions journal April 1993
Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD journal July 2020
Asymptotic freedom: An approach to strong interactions journal November 1974
Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy journal October 2013
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
RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses journal December 2000
Efficient Global Optimization of Expensive Black-Box Functions journal January 1998
Five-Loop Running of the QCD Coupling Constant journal February 2017
An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations journal February 2015
Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order α s 4 in a General Gauge Theory journal March 2010
A determination of the strong coupling constant ? S frome + e ? total cross-section data journal December 1989
Broken Scale Invariance in Scalar Field Theory journal October 1970
Meaningful characterisation of perturbative theoretical uncertainties journal September 2011
Scale setting in QCD and the momentum flow in Feynman diagrams journal May 1995
Basic concepts of probability theory; Grundbegriffe der Wahrscheinlichkeitsrechnung book January 1933
An analysis of Bayesian estimates for missing higher orders in perturbative calculations journal September 2021
On the elimination of scale ambiguities in perturbative quantum chromodynamics journal July 1983
Higher-order QCD corrections to hadronic τ decays from Padé approximants journal August 2018
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
Naive nonabelianization and resummation of fermion bubble chains journal April 1995
Small distance behaviour in field theory and power counting journal September 1970
Aspects of SU(Nc) gauge theories in the limit of small number of colors journal January 1998
Divergence of Perturbation Theory in Quantum Electrodynamics journal February 1952
RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses dataset January 2019

Figures / Tables (10)

Table 1(p. 7)table Table 1
Table 2(p. 7)table Table 2
Table 3(p. 7)table Table 3
Table 4(p. 7)table Table 4
Fig. 1(p. 8)figure Fig. 1
Table 5(p. 8)table Table 5
Fig. 2(p. 9)figure Fig. 2
Fig. 3(p. 9)figure Fig. 3
Fig. 4(p. 10)figure Fig. 4
Table 6(p. 10)table Table 6

Similar Records

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS