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

TL;DR

A generalization of the conventional renormalization schemes used in dimensional regularization is introduced, which illuminates the renormalized scheme and scale ambiguities of perturbative QCD predictions, exposes the general pattern of nonconformal {β(i)} terms, and reveals a special degeneracy of the terms in the perturbation coefficients.

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 {β_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.

Figures (1)

• Figure 1: The final PMC result for $R^{e^+e^- \to \textbf{h}}$ as a function of the initial renormalization scale $\mu_0$ (solid blue line), demonstrating the initial scale-invariance of the final prediction, up to strongly suppressed residual dependence. The shaded region is the experimental bounds with the central value given by the thin dashed line. For comparison we also show the pQCD prediction before PMC scale setting (dashed red line) fixed to the experimental value for $\mu_0 = Q$. This result is very sensitive to $\mu_0$, and thus it severely violates the renormalization group properties.