A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD

TL;DR

This paper presents a systematic all-orders method to eliminate renormalization-scale and scheme ambiguities in perturbative QCD, improving the precision and consistency of theoretical predictions.

Contribution

It generalizes renormalization schemes to clarify ambiguities and provides an automated, systematic way to determine the running coupling's argument at each order.

Findings

Exposes the pattern of nonconformal beta_i terms in pQCD

Reveals degeneracy in perturbative coefficients

Systematically determines the running coupling's argument

Abstract

We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal {\beta_i}-terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in pQCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error.