Renormalization-Scale-Invariant PQCD Predictions for R_e+e- and the Bjorken Sum Rule at Next-to-Leading Order

TL;DR

This paper introduces a renormalization-scale-invariant approach to perturbative QCD predictions for $R_{e^+e^-}$ and the Bjorken sum rule using the physical effective charge and BLM scale setting, achieving high experimental agreement.

Contribution

It presents a novel method combining the physical QCD effective charge with BLM scale setting to produce unambiguous, scale- and scheme-independent perturbative predictions.

Findings

Predictions for $R_{e^+e^-}$ match experimental data.

Bjorken sum rule predictions agree well with measurements.

Method improves theoretical precision in QCD calculations.

Abstract

We discuss application of the physical QCD effective charge $\alpha_V$, defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the $e^+e^-$ annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule. In both cases the improved predictions are in excellent agreement with experiment.