High precision tests of QCD without scale or scheme ambiguities: The 40th anniversary of the Brodsky–Lepage–Mackenzie method

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

doi:10.1016/j.ppnp.2023.104092

High precision tests of QCD without scale or scheme ambiguities: The 40th anniversary of the Brodsky–Lepage–Mackenzie method

Journal Article · Sat Nov 25 00:00:00 EST 2023 · Progress in Particle and Nuclear Physics

DOI:https://doi.org/10.1016/j.ppnp.2023.104092· OSTI ID:2405161

^[1]; Brodsky, Stanley J. ^[2]; ^[3]; ^[4]; Wang, Sheng-Quan ^[5]

University of Insubria, Como (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Milano (Italy); SLAC
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
University of Insubria, Como (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Milano (Italy)
Chongqing Univ. (China)
Guizhou Minzu University (China)

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale μ_r and thus determining the correct values of the QCD running coupling α_s (μ_r) at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process Q and vary it in the range μ_r $$\in$$ [Q/2, 2Q] in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist’s choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann–Low scheme in the N_c → 0 Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. In particular, we present a recently developed method the PMC_∞ and its applications, comparing the results with CSS. The method preserves the property of renormalizable SU(N)/U(1) gauge theories defined as Intrinsic Conformality (iCF). This property 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 pQCD. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC. A new method to identify conformal and β-terms, which can be applied either to numerical or to theoretical calculations is also shown. We present results for the thrust and C-parameter distributions in e⁺e^- annihilation showing errors and comparison with the CSS. We also show results for a recent innovative comparison between the CSS and the PMC_∞ applied to the thrust distribution investigating both the QCD conformal window and the QED N_c → 0 limit. In order to determine the thrust distribution along the entire renormalization group flow from the highest energies to zero energy, we consider the number of flavors near the upper boundary of the conformal window. In this flavor-number regime the theory develops a perturbative infrared interacting fixed point. These results show that PMC_∞ leads to higher precision and introduces new interesting features in the PMC. In fact, this method preserves with continuity the position of the peak, showing perfect agreement with the experimental data already at NNLO. We also show a detailed comparison of the PMC_∞ with the other PMC approaches: the multi-scale-setting approach (PMCm) and the single-scale-setting approach (PMCs) by comparing their predictions for three important fully integrated quantities R_e+e-, R$$_Τ$$ and Γ (H→$$b\bar{b}$$) up to the four-loop accuracy.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 2405161

Alternate ID(s):: OSTI ID: 2369120

Journal Information:: Progress in Particle and Nuclear Physics, Journal Name: Progress in Particle and Nuclear Physics Vol. 135; ISSN 0146-6410

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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