A Few Lessons from pQCD Analysis at Low Energies

TL;DR

This paper investigates the divergence issues in perturbative QCD series at low energies, analyzing the origin of divergence and the accuracy of finite sums through simple examples, motivated by recent experimental data on the Bjorken Sum Rule.

Contribution

It provides a detailed analysis of the divergence phenomena in perturbative QCD series at low energies and discusses the implications for data analysis, based on simple series examples.

Findings

Perturbative QCD series diverge at low energies.

Finite sums can approximate divergent series with limited accuracy.

Divergence originates from the nature of the perturbation expansion in QFT.

Abstract

Motivated by the recent 4-loop analysis of the JLab data on Bjorken Sum Rule, where the pQCD series seems to blow up at $|Q|\lesssim 1.5\,\GeV, \alpha_s \gtrsim 0.33\,,$ we overview the general origin of the divergency of common perturbation expansion over powers of a small coupling parameter in QFT and consider in detail the {\it blowing-up phenomenon} and accuracy of finite sums for simple alternating and non-alternating examples of divergent series.