The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

Abstract: In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can be served as a mini review of PMC. We emphasize that the purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization scheme and scale ambiguities. We demonstrate that the PMC predictions satisfy all of the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann--Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially-divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.