A Few Lessons from pQCD Analysis at Low Energies
arXiv:1202.3220 · doi:10.1016/j.nuclphysbps.2012.02.002
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 $|Q|\lesssim 1.5\,\GeV, α_s \gtrsim 0.33\,,$ 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.
9 figures, 8 pages. The text of contribution to Proceedings of "Intern. Workshop on Collisions from to " (PHIPSI11), Novosibirsk Sept 2011; to be published in Nucl.Phys.(Proc.Suppl.)