A Few Lessons from pQCD Analysis at Low Energies

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 $|Q|\lesssim 1.5\text{GeV},{\alpha }_s\gtrsim 0.33,$ 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.

Comments: 9 figures, 8 pages. The text of contribution to Proceedings of "Intern. Workshop on $e^{+}{e}^{-}$ Collisions from $\varphi$ to $J/\Psi$" (PHIPSI11), Novosibirsk Sept 2011; to be published in Nucl.Phys.(Proc.Suppl.)