Elimination of QCD Renormalization Scale and Scheme Ambiguities

TL;DR

This paper discusses the principle of maximum conformality (PMC) as a method to eliminate renormalization scheme and scale ambiguities in perturbative QCD, leading to more precise and reliable predictions across various processes.

Contribution

The paper summarizes recent applications of PMC in different QCD processes, demonstrating its effectiveness in removing scale ambiguities and improving theoretical predictions.

Findings

PMC eliminates major uncertainties from scale choices.

Improved pQCD predictions show better agreement with experimental data.

PMC is applicable to diverse processes like event shapes and heavy quark production.

Abstract

The setting of the renormalization scale ($\mu_r$) in the perturbative QCD (pQCD) is one of the crucial problems for achieving precise fixed-order pQCD predictions. The conventional prescription is to take its value as the typical momentum transfer $Q$ in a given process, and theoretical uncertainties are then evaluated by varying it over an arbitrary range. The conventional scale-setting procedure introduces arbitrary scheme-and-scale ambiguities in fixed-order pQCD predictions. The principle of maximum conformality (PMC) provides a systematic way to eliminate the renormalization scheme-and-scale ambiguities. The PMC method has rigorous theoretical foundations; it satisfies the renormalization group invariance (RGI) and all of the self-consistency conditions derived from the renormalization group. The PMC has now been successfully applied to many physical processes. In this paper, we summarize recent PMC applications, including event shape observables and heavy quark pair production near the threshold region in $e^+e^-$ annihilation and top-quark decay at hadronic colliders. In addition, estimating the contributions related to the uncalculated higher-order terms is also summarized. These results show that the major theoretical uncertainties caused by different choices of $\mu_r$ are eliminated, and the improved pQCD predictions are thus obtained, demonstrating the generality and applicability of the PMC.